SlideShare uma empresa Scribd logo
1 de 59
Baixar para ler offline
Temporal 1D Kerr cavity solitons
      a new passive optical buffer technology


                         Stéphane Coen
                         Physics Department, The University of Auckland,
                         Auckland, New Zealand


         Work performed while on
       Research & Study Leave at        Special thanks to   François Leo
                                                  and to    Pascal Kockaert
  The Université Libre                                      Simon-Pierre Gorza
  de Bruxelles (ULB),                                       Philippe Emplit
    Brussels, Belgium                                       Marc Haelterman



1. What are cavity solitons?                      4. Experimental setup
2. Temporal cavity solitons                       5. Results
3. Theory & Historical background                 6. Conclusion
1. What are cavity solitons?
   Traditionally described in passive planar cavities

                             External plane wave
                             coherently driving the
                             cavity
                             (driving/holding beam)
      Planar
       cavity
filled with a
   nonlinear
     material
1. What are cavity solitons?
   Traditionally described in passive planar cavities

                             External plane wave
                             coherently driving the
                             cavity
                             (driving/holding beam)
      Planar
       cavity
filled with a                Intracavity soliton
   nonlinear                 superimposed on
     material                a low level
                             background
1. What are cavity solitons?
   Traditionally described in passive planar cavities

                                       External plane wave
                                       coherently driving the
                                       cavity
                                       (driving/holding beam)
      Planar
       cavity
filled with a                          Intracavity soliton
   nonlinear                           superimposed on
     material                          a low level
                                       background




       The cavity solitons are independent
       from each other and from the boundaries
       They can be manipulated by external beams
       They exist for a wide range of nonlinearities
                L. A. Lugiato, IEEE J. Quantum Elec. 39, 193 (2003)
                W. J. Firth and C. O. Weiss, Opt. & Phot. News 13, 54 (Feb. 2002)
1. What are cavity solitons?
   Traditionally described in passive planar cavities                           In semiconductor µ-cavities

                                       External plane wave
                                       coherently driving the
                                       cavity
                                       (driving/holding beam)
      Planar
       cavity
filled with a                          Intracavity soliton
   nonlinear                           superimposed on
     material                          a low level
                                       background




       The cavity solitons are independent
       from each other and from the boundaries
       They can be manipulated by external beams
       They exist for a wide range of nonlinearities
                L. A. Lugiato, IEEE J. Quantum Elec. 39, 193 (2003)                 S. Barland et al
                W. J. Firth and C. O. Weiss, Opt. & Phot. News 13, 54 (Feb. 2002)   Nature 419, 699 (2002)
1. What are cavity solitons?
   Traditionally described in passive planar cavities

                             External plane wave        Cavity solitons are solitons
                             coherently driving the
                             cavity
                             (driving/holding beam)
      Planar
       cavity                                            Diffraction       Nonlinearity
filled with a                Intracavity soliton
   nonlinear                 superimposed on
     material                a low level
                             background
1. What are cavity solitons?
   Traditionally described in passive planar cavities

                             External plane wave        Cavity solitons are solitons
                             coherently driving the
                             cavity
                             (driving/holding beam)             Coherent driving
      Planar
       cavity                                            Diffraction            Nonlinearity
filled with a                Intracavity soliton
   nonlinear                 superimposed on                           Losses
     material                a low level
                             background
                                                        ... but also cavity solitons
1. What are cavity solitons?
   Traditionally described in passive planar cavities

                             External plane wave        Cavity solitons are solitons
                             coherently driving the
                             cavity
                             (driving/holding beam)              Coherent driving
      Planar
       cavity                                            Diffraction            Nonlinearity
filled with a                Intracavity soliton
   nonlinear                 superimposed on                           Losses
     material                a low level
                             background
                                                        ... but also cavity solitons

                                                        They are not solitons in a box
                                                        W. J. Firth and C. O. Weiss,
                                                        Opt. & Phot. News 13, 54 (Feb. 2002)

                                                        2D Kerr cavity solitons are
                                                        stable while 2D Kerr nonlinear
                                                        Schrödinger solitons collapse
1. What are cavity solitons?
   Traditionally described in passive planar cavities

                                External plane wave      Cavity solitons are solitons
                                coherently driving the
                                cavity
                                (driving/holding beam)            Coherent driving
      Planar
       cavity                                             Diffraction            Nonlinearity
filled with a                   Intracavity soliton
   nonlinear                    superimposed on                         Losses
     material                   a low level
                                background
                                                         ... but also cavity solitons

                                                         They are not solitons in a box
                                                         W. J. Firth and C. O. Weiss,
                                                         Opt. & Phot. News 13, 54 (Feb. 2002)
                Cavity solitons form
          a subset of dissipative solitons               2D Kerr cavity solitons are
                                                         stable while 2D Kerr nonlinear
               for coherently-driven                     Schrödinger solitons collapse
                  optical cavities
2. Temporal cavity solitons
   Spatial versus Temporal cavity solitons
                                                             We extend the terminology
                               External plane wave           to the temporal case
                               coherently driving the
                               cavity
                               (driving/holding beam)                   Coherent driving
      Planar
       cavity                                                     Diffraction            Nonlinearity
filled with a                  Intracavity soliton                Dispersion
   nonlinear                   superimposed on                                  Losses
     material                  a low level
                               background
                                                     cw driving
                                                         beam                      Input coupler

                                                                    Input


         Temporal cavity solitons are naturally
         immune to longitudinal variations or
         imperfections along the cavity length



                                                                  Output
2. Temporal cavity solitons
Temporal cavity solitons applied to an optical buffer technology
   Several temporal CSs can be stored in a cavity like bits in an optical buffer

                                                              Coherent driving
                                                         Dispersion            Nonlinearity

                                                                      Losses

                                            cw driving
                                                beam

                                                          Input




                                                         Output
2. Temporal cavity solitons
Temporal cavity solitons applied to an optical buffer technology
   Several temporal CSs can be stored in a cavity like bits in an optical buffer
   No intracavity amplifier: The stored CSs do not
   accumulate noise as they circulate repeatedly              Coherent driving
                                                         Dispersion            Nonlinearity

                                                                      Losses

                                            cw driving
                                                beam

                                                          Input




                                                         Output
2. Temporal cavity solitons
Temporal cavity solitons applied to an optical buffer technology
   Several temporal CSs can be stored in a cavity like bits in an optical buffer
   No intracavity amplifier: The stored CSs do not
   accumulate noise as they circulate repeatedly               Coherent driving
   The driving power is independent of the                Dispersion            Nonlinearity
   number of bits stored
                                                                       Losses
           ALL-OPTICAL STORAGE

                                             cw driving
                                                 beam

                                                           Input




                                                          Output
2. Temporal cavity solitons
Temporal cavity solitons applied to an optical buffer technology
   Several temporal CSs can be stored in a cavity like bits in an optical buffer
   No intracavity amplifier: The stored CSs do not
   accumulate noise as they circulate repeatedly               Coherent driving
   The driving power is independent of the                Dispersion            Nonlinearity
   number of bits stored
                                                                       Losses
           ALL-OPTICAL STORAGE

   The double balance makes temporal         cw driving
   CSs unique attractive states                  beam

                                                           Input




                                                          Output
2. Temporal cavity solitons
Temporal cavity solitons applied to an optical buffer technology
   Several temporal CSs can be stored in a cavity like bits in an optical buffer
   No intracavity amplifier: The stored CSs do not
   accumulate noise as they circulate repeatedly               Coherent driving
   The driving power is independent of the                Dispersion            Nonlinearity
   number of bits stored
                                                                       Losses
           ALL-OPTICAL STORAGE

   The double balance makes temporal                               address pulses
                                             cw driving
   CSs unique attractive states                  beam
           ALL-OPTICAL RESHAPING
                                                           Input
   They can be excited incoherently with
   address pulses at a different wavelength
           WAVELENGTH CONVERTER




                                                          Output
2. Temporal cavity solitons
Temporal cavity solitons applied to an optical buffer technology
   Several temporal CSs can be stored in a cavity like bits in an optical buffer
   No intracavity amplifier: The stored CSs do not
   accumulate noise as they circulate repeatedly               Coherent driving
   The driving power is independent of the                Dispersion            Nonlinearity
   number of bits stored
                                                                       Losses
           ALL-OPTICAL STORAGE

   The double balance makes temporal                               address pulses
                                             cw driving
   CSs unique attractive states                  beam
           ALL-OPTICAL RESHAPING
                                                           Input
   They can be excited incoherently with
   address pulses at a different wavelength
           WAVELENGTH CONVERTER

   A periodic modulation of the driving beam
   can trap the CSs in specific timeslots
           ALL-OPTICAL RETIMING
                                                          Output
2. Temporal cavity solitons
Temporal cavity solitons applied to an optical buffer technology
   Several temporal CSs can be stored in a cavity like bits in an optical buffer
   No intracavity amplifier: The stored CSs do not
   accumulate noise as they circulate repeatedly An optical buffer
                                                       Coherent driving
   The driving power is independent of the               based on Nonlinearity
                                                      Dispersion
   number of bits stored                       temporal cavity solitons
                                                                Losses
                                             would seamlessly combine
           ALL-OPTICAL STORAGE
                                                   all these important
                                                               address pulses
   The double balance makes temporal         cw driving
   CSs unique attractive states
                                                  telecommunications
                                                 beam
                                                         functions
           ALL-OPTICAL RESHAPING
                                                       Input
   They can be excited incoherently with        Here we report,
   address pulses at a different wavelength with a Kerr fiber cavity,
           WAVELENGTH CONVERTER              the first experimental
   A periodic modulation of the driving beam
                                                  observation
   can trap the CSs in specific timeslots       of these objects
           ALL-OPTICAL RETIMING
                                                     Output
3. Theory & Historical background
The Kerr cavity
“Hydrogen atom” of nonlinear cavity

                  Input coupler

   Input                    Interferences



    Feedback
                      Nonlinearity
   & Dispersion




 Output

Combination of a simple
nonlinearity with feedback and
dispersion in a 1D geometry
3. Theory & Historical background
The Kerr cavity                             Linear regime: Fabry-Perot type response
“Hydrogen atom” of nonlinear cavity
                                                                 Constructive
                  Input coupler                                  interferences

   Input                    Interferences

                                             P
    Feedback
                                                               2p
                      Nonlinearity           Pin            = n0L
                                                            f
                                                            f0 =
   & Dispersion                                                 l

                                                   0
                                                       2(m–1)p    2mp      2(m +1)p
                                                                                   f
 Output                                                                Destructive
                                                                       interferences
Combination of a simple
nonlinearity with feedback and
dispersion in a 1D geometry
3. Theory & Historical background
The Kerr cavity: Nonlinear regime
Nonlinear resonances and Bistability                      Instantaneous pure Kerr
                                                                      nonlinearity
     When approaching the resonance ...
               ... the intracavity power P increases ...
                                                                        fLP
                                                                          NL =g
                         ... the nonlinear phase-shift increases ...
                                  ... the cavity round-trip phase shift increases ...




                                           P
                                           Pin


                                                 0                                f
                                                     2(m–1)p   2mp       2(m +1)p

                                                                        fg
                                                                        =
                                                                        f LP
                                                                         0+
3. Theory & Historical background
The Kerr cavity: Nonlinear regime
Nonlinear resonances and Bistability                     Instantaneous pure Kerr
                                                                     nonlinearity
    When approaching the resonance ...
              ... the intracavity power P increases ...
                                                                       fLP
                                                                         NL =g
    Positive            ... the nonlinear phase-shift increases ...
   feedback                      ... the cavity round-trip phase shift increases ...

                   Accelerated approach
                   of the resonance

                                          P
                                          Pin


                                                0                                f
                                                    2(m–1)p   2mp       2(m +1)p

                                                                       fg
                                                                       =
                                                                       f LP
                                                                        0+
3. Theory & Historical background
The Kerr cavity: Nonlinear regime
Nonlinear resonances and Bistability                         Instantaneous pure Kerr
                                                                         nonlinearity
       When approaching the resonance ...
                 ... the intracavity power P increases ...
                                                                          fLP
                                                                            NL =g
       Positive            ... the nonlinear phase-shift increases ...
      feedback                      ... the cavity round-trip phase shift increases ...

      Incident power
                        Accelerated approach
                        of the resonance

                                               P
P                                              Pin
Pin

                                                     0                              f
                                                         2(m–1)p   2mp     2(m +1)p

                                           Tilting of the cavity          fg
                                                                          =
                                                                          f LP
                                                                           0+
      0                                  f
                                         0 resonance and bistability
                        2mp
3. Theory & Historical background
The Kerr cavity: Nonlinear regime
Nonlinear resonances and Bistability

                                                        Bistability for various
          d0
             Linear cavity detuning                     constant detunings
          D parameter (normalized
          =
          a respect to the losses)
             with
                                                    P          D
                                                               =4

                          Bistability for various
      Incident power
                        constant driving powers


                                                                           D
                                                                           =0
P
Pin                                                                                   Pin
                                                    0
                                                           Onset of bistability: D
                                                                                 =3

                       dp
                       0
                         =f
                         2m -
                            0                  Tilting of the cavity
      0                                      f
                                             0 resonance and bistability
                        2mp
3. Theory & Historical background
The intracavity field can be in the lower state in one part of the cavity and
in the upper state in another part. The two parts can co-exist and be connected.

     Diffractive autosolitons
     Connecting the upper and lower bistable states with locked switching waves
     N. N. Rosanov and G. V. Khodova,
     J. Opt. Soc. Am. B 7, 1057 (1990)

                                                   P
                           P




                                                   0                        Pin
                                               t
3. Theory & Historical background
The intracavity field can be in the lower state in one part of the cavity and
in the upper state in another part. The two parts can co-exist and be connected.

     Diffractive autosolitons
     Connecting the upper and lower bistable states with locked switching waves
     N. N. Rosanov and G. V. Khodova,
     J. Opt. Soc. Am. B 7, 1057 (1990)

                                                    P
                           P
The domain of
existence is limited
as the switching waves
cannot always lock
and the upper state
may be unstable
                                                    0                       Pin
                                                t
 Not the type of localized structures we are concerned with in this work
3. Theory & Historical background
Intracavity modulation instability
Studied through a linear stability analysis                       Anomalous dispersion
                                                              5
The homogeneous                                                        D
                                                                       =
                                                                       4
                        L. A. Lugiato and R. Lefever          4
upper state is




                                                        Y?
                                 Phys. Rev. Lett. 58,                 D
                                                                      =
                                                                      2.5
unstable in favor of                                          3




                                                         P
                                        2209 (1987)
a modulated solution                                          2                 D
                                                                                =
                                                                                1
                           M. Haelterman, S. Trillo,
                                     and S. Wabnitz           1
                           Opt. Lett. 17, 745 (1992)
                                                              0
                                                                  0        4      8      12
                                                                               X?
                                                                                Pin



  P

                                                             Frequency domain
                                                        P

                                                  t
                                                                       0
3. Theory & Historical background
Intracavity modulation instability
Studied through a linear stability analysis                      Anomalous dispersion
                                                             5
The homogeneous                                                       D
                                                                      =
                                                                      4
                        L. A. Lugiato and R. Lefever         4
upper state is




                                                        Y?
                                 Phys. Rev. Lett. 58,                D
                                                                     =
                                                                     2.5
unstable in favor of                                         3




                                                         P
                                        2209 (1987)
a modulated solution                                         2               D
                                                                             =
                                                                             1
                           M. Haelterman, S. Trillo,
                                     and S. Wabnitz          1
It can coexist in          Opt. Lett. 17, 745 (1992)
different parts of                                           0
                                                                 0      4      8        12
the cavity with the                                                         X?
                                                                             Pin
homogeneous lower
state

  P          Localized dissipative structure




                                                  t
3. Theory & Historical background
Intracavity modulation instability
Studied through a linear stability analysis                      Anomalous dispersion
                                                             5
The homogeneous                                                       D
                                                                      =
                                                                      4
                        L. A. Lugiato and R. Lefever         4
upper state is




                                                        Y?
                                 Phys. Rev. Lett. 58,                D
                                                                     =
                                                                     2.5
unstable in favor of                                         3




                                                         P
                                        2209 (1987)
a modulated solution                                         2                 D
                                                                               =
                                                                               1
                           M. Haelterman, S. Trillo,
                                     and S. Wabnitz          1
It can coexist in          Opt. Lett. 17, 745 (1992)
different parts of                                           0
                                                                 0       4          8           12
the cavity with the                                                          X?
                                                                              Pin
homogeneous lower
state

  P           Cavity soliton                            G. S. McDonald and W. J. Firth,
                                                        J. Opt. Soc. Am. B 7, 1328 (1990)
                                                        S. Wabnitz,
                                                        Opt. Lett. 18, 601 (1993)
                                                         M. Tlidi, P. Mandel, and R. Lefever,
                                                         Phys. Rev. Lett. 73, 640 (1994)

                                                  tW. J. Firth and A. J. 1623 (1996)
                                                   Phys. Rev. Lett. 76,
                                                                         Scroggie,
3. Theory & Historical background
                                                                        Driving power (mW)
Cavity solitons arise through a sub-critical
                                                             0   50     100         150   200   250   300
Turing bifurcation
                                                                                                            9
                                                                                                            8
                                                                                                            7
                                                                                                            6
                                                                                                            5
                                                                                                            4
                                                                                                            3
                                                        10                                                  1.9
                           P [W]                                                                            1.8
                     1.6                                                                                    1.6
                                                        8
                                                                                                            1.4
                     1.2                                                                                    1.2
                                                        6
                                                                                                            1



                                                    Y
                     0.8                   4.4 ps       4                                                   0.8
                                                                                                            0.6
                     0.4                                              ? = 3.3                               0.4
                                                        2
                                                                                                            0.2
                                                        0                                                 0
                           20
                           -          0        20            0    2             4         6      8      10
                                   Time [ps]                                         X
3. Theory & Historical background
                                                                        Driving power (mW)
Cavity solitons arise through a sub-critical
                                                             0   50     100         150   200   250   300
Turing bifurcation
                                                                                                            9
                                                                                                            8
                                                                                                            7
                                                                                                            6
                                                                                                            5
                                                                                                            4
                                                                                                            3
                                                        10                                                  1.9
                           P [W]                                                                            1.8
                     1.6                                                                                    1.6
                                                        8
                                                                                                            1.4
                     1.2                                                                                    1.2
                                                        6
                                                                                                            1



                                                    Y
                     0.8                   4.4 ps       4                                                   0.8
                                                                                                            0.6
                     0.4                                              ? = 3.3                               0.4
                                                        2
                                                                                                            0.2
                                                        0                                                 0
                           20
                           -          0        20            0    2             4         6      8      10
                                   Time [ps]                                         X
3. Theory & Historical background
                                                                        Driving power (mW)
Cavity solitons arise through a sub-critical
                                                             0   50     100         150   200    250      300
Turing bifurcation
                                                                                                                9
                                                                                                                8
                                                                                                                7
                                                                                                                6
                                                                                                                5
                                                                                                                4
                                                                                                                3
                                                        10                                                      1.9
                           P [W]                                                                                1.8
                     1.6                                                                                        1.6
                                                        8
                                                                                                                1.4
                     1.2                                                                                        1.2
                                                        6
                                                                                                ? = 3.8         1



                                                    Y
                     0.8                   4.4 ps       4                                                       0.8
                                                                                                                0.6
                     0.4                                              ? = 3.3                                   0.4
                                                        2
                                                                                                                0.2
                                                        0                                                     0
                           20
                           -          0        20            0    2             4         6        8        10
                                   Time [ps]                                         X
3. Theory & Historical background
                                                                           Driving power (mW)
Cavity solitons arise through a sub-critical
                                                                0   50     100         150   200    250      300
Turing bifurcation
                                                                                                                   9
            2                                                                                                      8
  E é
  ¶     2   ¶ ù                                                                                                    7
   =( E
    êi
    -     D E (S
           ih t )
    1 +- 2 ú,t
          )-    +
  t ë
  ¶         ¶
            t                                                                                                      6
              û                                                                                                    5
                      L. A. Lugiato and R. Lefever                                                                 4
h(
= 2)
sign b             Phys. Rev. Lett. 58, 2209 (1987)                                                                3
                                                           10                                                      1.9
                              P [W]                                                                                1.8
                      1.6                                                                                          1.6
                                                           8
                                                                                                                   1.4
                      1.2                                                                                          1.2
                                                           6
                                                                                                   ? = 3.8         1



                                                       Y
                      0.8                     4.4 ps       4                                                       0.8
                                                                                                                   0.6
                      0.4                                                ? = 3.3                                   0.4
                                                           2
                                                                                                                   0.2
                                                           0                                                     0
                             20
                             -           0        20            0    2             4         6        8        10
                                      Time [ps]                                         X
3. Theory & Historical background
                                                                              Driving power (mW)
Cavity solitons arise through a sub-critical
                                                                   0   50     100         150   200    250      300
Turing bifurcation
                                                                                                                      9
             2                                                                                                        8
   E é
   ¶     2   ¶ ù                                                                                                      7
    =( E
     êi
     -     D E (S
            ih t )
     1 +- 2 ú,t
           )-    +
   t ë
   ¶         ¶
             t                                                                                                        6
               û                                                                                                      5
                         L. A. Lugiato and R. Lefever                                                                 4
h(
= 2)
sign b                Phys. Rev. Lett. 58, 2209 (1987)                                                                3
                                                              10                                                      1.9
Similar to reaction              P [W]                                                                                1.8
diffusion systems        1.6                                                                                          1.6
                                                              8
                                                                                                                      1.4
Cavity solitons
                         1.2                                                                                          1.2
are localized                                                 6
dissipative                                                                                           ? = 3.8         1



                                                          Y
structures               0.8                     4.4 ps                                                               0.8
                                                              4
“à la” Prigogine
                                                                                                                      0.6
                         0.4                                                ? = 3.3                                   0.4
                                                              2
                                                                                                                      0.2
                                                              0                                                     0
                                20
                                -           0        20            0    2             4         6        8        10
                                         Time [ps]                                         X
3. Theory & Historical background
                                                                              Driving power (mW)
Cavity solitons arise through a sub-critical
                                                                   0   50     100         150   200    250      300
Turing bifurcation
                                                                                                                      9
             2                                                                                                        8
   E é
   ¶     2   ¶ ù                                                                                                      7
    =( E
     êi
     -     D E (S
            ih t )
     1 +- 2 ú,t
           )-    +
   t ë
   ¶         ¶
             t                                                                                                        6
               û                                                                                                      5
                         L. A. Lugiato and R. Lefever                                                                 4
h(
= 2)
sign b                Phys. Rev. Lett. 58, 2209 (1987)                                                                3
                                                              10                                                      1.9
Similar to reaction              P [W]                                                                                1.8
diffusion systems        1.6                                                                                          1.6
                                                              8
                                                                                                                      1.4
Cavity solitons
                         1.2                                                                                          1.2
are localized                                                 6
dissipative                                                                                           ? = 3.8         1



                                                          Y
structures               0.8                     4.4 ps                                                               0.8
                                                              4
“à la” Prigogine
                                                                                                                      0.6
                         0.4                                                ? = 3.3                                   0.4
  Fundamental                                                 2
    example of                                                                                                        0.2
 self-organization
  phenomena in                                                0                                                     0
 nonlinear optics               20
                                -           0        20            0    2             4         6        8        10
                                         Time [ps]                                         X
4. Experimental setup
Experimental demonstration of temporal Kerr cavity solitons




 Input
                              Fiber Coupler      Output
                              90/10

Polarization
 Controller
               t R =s
                   1.85 m
                                    90m
               F   =
                   24
               Resonances: 22 kHz
                                          290m
                 Fiber
                Isolator


     To avoid Brillouin
            scattering
4. Experimental setup
Experimental demonstration of temporal Kerr cavity solitons




                  DRIVING BEAM                   EDFA
                                                                       1 kHz linewidth
                                                                 DFB
                                                                       1551 nm CW pump

                              Fiber Coupler             Output
                              90/10

Polarization
 Controller
               t R =s
                   1.85 m
                                    90m
               F   =
                   24
               Resonances: 22 kHz
                                          290m
                 Fiber
                Isolator


     To avoid Brillouin
            scattering
4. Experimental setup
Experimental demonstration of temporal Kerr cavity solitons




                  DRIVING BEAM                               EDFA
                                                                                       1 kHz linewidth
                                                                                 DFB
                                                                                       1551 nm CW pump

                                    Fiber Coupler                Fiber Coupler   Output
                                    90/10                            95/5

Polarization
 Controller
               t R =s
                   1.85 m
                                             90m
               F   =
                   24
               Resonances: 22 kHz
                                                   290m
                 Fiber
                Isolator    Piezoelectric
                           Fiber Stretcher

     To avoid Brillouin                             Controller
            scattering
4. Experimental setup
Experimental demonstration of temporal Kerr cavity solitons

                                              EDFA
      ADDRESSING                                                          1535 nm, 4 ps, 10 MHz
                             AOM                                 PRITEL
      BEAM                                                                modelocked fiber laser


       WDM        DRIVING BEAM                               EDFA
                                                                                           1 kHz linewidth
                                                                                     DFB
                                                                                           1551 nm CW pump

                                    Fiber Coupler                Fiber Coupler      Output
                                    90/10                            95/5

Polarization
 Controller
               t R =s
                   1.85 m
                                             90m
               F   =
                   24
               Resonances: 22 kHz
                                                   290m
                 Fiber
                Isolator    Piezoelectric
                           Fiber Stretcher

     To avoid Brillouin                             Controller
            scattering
4. Experimental setup
 Experimental demonstration of temporal Kerr cavity solitons

                                               EDFA
       ADDRESSING                                                          1535 nm, 4 ps, 10 MHz
                              AOM                                 PRITEL
       BEAM                                                                modelocked fiber laser


        WDM        DRIVING BEAM                               EDFA
                                                                                            1 kHz linewidth
                                                                                      DFB
                                                                                            1551 nm CW pump

                                     Fiber Coupler                Fiber Coupler      Output
                                     90/10                            95/5

 Polarization
  Controller
                t R =s
                    1.85 m
                                              90m
 Excited        F   =
                    24
via XPM         Resonances: 22 kHz
                                                    290m
                  Fiber
                 Isolator    Piezoelectric
                            Fiber Stretcher

      To avoid Brillouin                             Controller
             scattering
4. Experimental setup
 Experimental demonstration of temporal Kerr cavity solitons

                                               EDFA
       ADDRESSING                                                          1535 nm, 4 ps, 10 MHz
                              AOM                                 PRITEL
       BEAM                                                                modelocked fiber laser


        WDM        DRIVING BEAM                               EDFA
                                                                                            1 kHz linewidth
                                                                                      DFB
                                                                                            1551 nm CW pump

                                     Fiber Coupler                Fiber Coupler      Output
                                     90/10                            95/5

 Polarization
  Controller
                t R =s
                    1.85 m
                                              90m
 Excited        F   =
                    24                                            WDM
via XPM         Resonances: 22 kHz
                                                    290m
                  Fiber
                 Isolator    Piezoelectric                                 WDM
                            Fiber Stretcher

      To avoid Brillouin                             Controller
             scattering
4. Experimental setup
 Experimental demonstration of temporal Kerr cavity solitons

                                               EDFA
       ADDRESSING                                                          1535 nm, 4 ps, 10 MHz
                              AOM                                 PRITEL
       BEAM                                                                modelocked fiber laser


        WDM        DRIVING BEAM                               EDFA
                                                                                            1 kHz linewidth
                                                                                      DFB
                                                                                            1551 nm CW pump

                                     Fiber Coupler                Fiber Coupler      Output
                                     90/10                            95/5

 Polarization
  Controller
                t R =s
                    1.85 m
                                              90m
 Excited        F   =
                    24                                            WDM
via XPM         Resonances: 22 kHz
                                                    290m
                  Fiber
                 Isolator    Piezoelectric                                 WDM
                            Fiber Stretcher

      To avoid Brillouin                             Controller
             scattering
4. Experimental setup
 Experimental demonstration of temporal Kerr cavity solitons

                                               EDFA
       ADDRESSING                                                          1535 nm, 4 ps, 10 MHz
                              AOM                                 PRITEL
       BEAM                                                                modelocked fiber laser


        WDM        DRIVING BEAM                1 nm BPF       EDFA
                                                                                             1 kHz linewidth
                                                                                      DFB
                                                                                             1551 nm CW pump
                                          Remove ASE
                                                                                                    5 GSa/s
                                     Fiber Coupler                Fiber Coupler                     oscilloscope
                                     90/10                            95/5           BPF

 Polarization
  Controller
                t R =s
                    1.85 m                                                           Remove driving beam
                                              90m
 Excited        F   =
                    24                                            WDM
                                                                                  Fiber Coupler
                                                                                  50/50
via XPM         Resonances: 22 kHz
                                                    290m
                  Fiber
                 Isolator    Piezoelectric                                 WDM
                            Fiber Stretcher
                                                                                                  Optical
      To avoid Brillouin                             Controller                                   spectrum
             scattering                                                                           analyzer
5. Results
A single soliton in the cavity
Addressing pulse: Off - CS only sustained by the cw driving beam




  The intracavity pulse persists in the cavity
  for more than 1 s (> 550,000 round-trips)
               Coherent driving



                    Losses
5. Results
A single soliton in the cavity
Addressing pulse: Off - CS only sustained by the cw driving beam   Experiment
                                                                   Simulations




  The intracavity pulse persists in the cavity
  for more than 1 s (> 550,000 round-trips)
               Coherent driving
         Dispersion         Nonlinearity

                    Losses
  Autocorrelation reveals it is 4 ps long,   Dispersion
  matching simulations                       length: 230 m
5. Results
A single soliton in the cavity
Addressing pulse: Off - CS only sustained by the cw driving beam   Experiment
                                                                   Simulations




  The intracavity pulse persists in the cavity
  for more than 1 s (> 550,000 round-trips)
               Coherent driving
         Dispersion         Nonlinearity

                    Losses
  Autocorrelation reveals it is 4 ps long,   Dispersion
  matching simulations                       length: 230 m
5. Results
Storing data as binary patterns with cavity solitons
5. Results
Interactions of temporal cavity solitons
Sending two close addressing pulses and
observing the CSs within the next 1 s
Addressing pulses closer than 25 ps
     Only one CS present at
     the output
5. Results
Interactions of temporal cavity solitons
Sending two close addressing pulses and
observing the CSs within the next 1 s
Addressing pulses closer than 25 ps
     Only one CS present at
     the output

With a larger separation between
the addressing pulses ...
     The two excited CSs repel
5. Results
Interactions of temporal cavity solitons
Sending two close addressing pulses and
observing the CSs within the next 1 s
Addressing pulses closer than 25 ps
     Only one CS present at
     the output

With a larger separation between
the addressing pulses ...
     The two excited CSs repel
     ... but repulsion gets
     progressively weaker
5. Results
Interactions of temporal cavity solitons
Sending two close addressing pulses and
observing the CSs within the next 1 s
Addressing pulses closer than 25 ps
     Only one CS present at
     the output

With a larger separation between
the addressing pulses ...
     The two excited CSs repel
     ... but repulsion gets
     progressively weaker

The CSs could be easily
trapped by modulating the
driving power

Potential buffer capacity:
      45 kbit @ 25 Gbit/s
5. Results
Writing dynamics of temporal cavity solitons




       Experiment




       Simulation




                    Time (100 µs/div)
5. Results
Writing dynamics of temporal cavity solitons

                                                 Output with off-center filter

       Experiment                                               Inside the cavity




       Simulation

                                                        Time (100 µs/div)




                    Time (100 µs/div)
5. Results
Erasing of temporal
cavity solitons

Complete erasing of the
cavity can be obtained
by switching off the
driving beam for about
4 round-trips
5. Results
Erasing of temporal
cavity solitons

Complete erasing of the
cavity can be obtained
by switching off the
driving beam for about
4 round-trips


Driving beam switched
back on after
4 round-trips
5. Results
Erasing of temporal
cavity solitons

Complete erasing of the
cavity can be obtained
by switching off the
driving beam for about
4 round-trips


Driving beam switched
back on after
4 round-trips

From there on, new CSs
can be written without
affecting the erasure
of neighboring CSs
5. Results
Erasing of temporal
cavity solitons

Selective erasing of
one CS can be obtained
by overwriting it with
an addressing pulse
about 50% more
powerful




This realizes an
all-optical XOR
logic gate
5. Results
                                                            Driving power (mW)
Breathing temporal cavity solitons
                                                 0   50     100         150   200    250      300
Above a certain driving power,                                                                      9
the cavity solitons become breathers                                                                8
                                                                                                    7
                                                                                                    6
                                                                                                    5
                                                                                                    4
                                                                                           Hopf     3
                                            10                                             bifurcation
                                                                                                  1.9
                                                                                                    1.8
                                                                                                    1.6
                                            8
                                                                                                    1.4
                                                                                                    1.2
                                            6
                                                                                    ? = 3.8         1



                                        Y
                                            4                                                       0.8
                                                                                                    0.6
                                                          ? = 3.3                                   0.4
                                            2
                                                                                                    0.2
                                            0                                                     0
                                                 0    2             4         6        8        10
                                                                         X
5. Results
                                                                Driving power (mW)
Breathing temporal cavity solitons
                                                     0   50     100         150   200    250      300
Above a certain driving power,                                                                          9
the cavity solitons become breathers                                                                    8
                                                                                                        7
                                                                                                        6
                                                                                                        5
                                                                                                        4
                                                                                               Hopf     3
                                                10                                             bifurcation
                                                                                                      1.9
                                                                                                        1.8
                                                                                                        1.6
                                                8
                                                                                                        1.4
                                                                                                        1.2
                                                6
                                                                                        ? = 3.8         1



                                            Y
                                                4                                                       0.8
                                                                                                        0.6
                                                              ? = 3.3                                   0.4
                                                2
                                                                                                        0.2
                                                0                                                     0
                         Time (50 µs/div)            0    2             4         6        8        10
                                                                             X
6. Conclusion
   We have reported the first direct experimental observation of
   temporal cavity solitons as well as Kerr cavity solitons

   Temporal cavity solitons could be used as bits in an all-optical buffer,
   combining all-optical storage with wavelength conversion,
   all-optical reshaping, and re-timing

   Our experiments have been performed in a purely 1-dimensional system
   with an instantaneous Kerr nonlinearity
   Due to this simplicity, our experiments may constitute the
   most fundamental example of self-organization in nonlinear optics

   Kerr frequency combs generated in microresonators may be
   the spectral signature of a temporal cavity soliton




       P. Del’Haye et al,
Nature 450, 1214 (2007)

Mais conteúdo relacionado

Mais de NZIP

14.25 o14 i islah u-din
14.25 o14 i islah u-din14.25 o14 i islah u-din
14.25 o14 i islah u-dinNZIP
 
14.25 o15 b ingham
14.25 o15 b ingham14.25 o15 b ingham
14.25 o15 b inghamNZIP
 
14.05 o15 g willmott
14.05 o15 g willmott14.05 o15 g willmott
14.05 o15 g willmottNZIP
 
12.45 o15 m bartle
12.45 o15 m bartle12.45 o15 m bartle
12.45 o15 m bartleNZIP
 
16.20 o11 b mallett
16.20 o11 b mallett16.20 o11 b mallett
16.20 o11 b mallettNZIP
 
15.30 o11 m reid
15.30 o11 m reid15.30 o11 m reid
15.30 o11 m reidNZIP
 
16.40 o10 d wiltshire
16.40 o10 d wiltshire16.40 o10 d wiltshire
16.40 o10 d wiltshireNZIP
 
16.00 o10 h silverwood
16.00 o10 h silverwood16.00 o10 h silverwood
16.00 o10 h silverwoodNZIP
 
14.40 o8 s wimbush
14.40 o8 s wimbush14.40 o8 s wimbush
14.40 o8 s wimbushNZIP
 
16.20 o10 p chote
16.20 o10 p chote16.20 o10 p chote
16.20 o10 p choteNZIP
 
15.30 o10 p cottrell
15.30 o10 p cottrell15.30 o10 p cottrell
15.30 o10 p cottrellNZIP
 
14.20 o8 c gaedtke
14.20 o8 c gaedtke14.20 o8 c gaedtke
14.20 o8 c gaedtkeNZIP
 
14.00 o8 j stephen
14.00 o8 j stephen14.00 o8 j stephen
14.00 o8 j stephenNZIP
 
13.00 o8 g williams
13.00 o8 g williams13.00 o8 g williams
13.00 o8 g williamsNZIP
 
14.40 o7 d sullivan
14.40 o7 d sullivan14.40 o7 d sullivan
14.40 o7 d sullivanNZIP
 
14.20 o7 r davies
14.20 o7 r davies14.20 o7 r davies
14.20 o7 r daviesNZIP
 
13.30 o7 b trompetter
13.30 o7 b trompetter13.30 o7 b trompetter
13.30 o7 b trompetterNZIP
 
13.00 o7 j adams
13.00 o7 j adams13.00 o7 j adams
13.00 o7 j adamsNZIP
 
16.40 o4 s janssens
16.40 o4 s janssens16.40 o4 s janssens
16.40 o4 s janssensNZIP
 
16.20 04 j anthony
16.20 04 j anthony16.20 04 j anthony
16.20 04 j anthonyNZIP
 

Mais de NZIP (20)

14.25 o14 i islah u-din
14.25 o14 i islah u-din14.25 o14 i islah u-din
14.25 o14 i islah u-din
 
14.25 o15 b ingham
14.25 o15 b ingham14.25 o15 b ingham
14.25 o15 b ingham
 
14.05 o15 g willmott
14.05 o15 g willmott14.05 o15 g willmott
14.05 o15 g willmott
 
12.45 o15 m bartle
12.45 o15 m bartle12.45 o15 m bartle
12.45 o15 m bartle
 
16.20 o11 b mallett
16.20 o11 b mallett16.20 o11 b mallett
16.20 o11 b mallett
 
15.30 o11 m reid
15.30 o11 m reid15.30 o11 m reid
15.30 o11 m reid
 
16.40 o10 d wiltshire
16.40 o10 d wiltshire16.40 o10 d wiltshire
16.40 o10 d wiltshire
 
16.00 o10 h silverwood
16.00 o10 h silverwood16.00 o10 h silverwood
16.00 o10 h silverwood
 
14.40 o8 s wimbush
14.40 o8 s wimbush14.40 o8 s wimbush
14.40 o8 s wimbush
 
16.20 o10 p chote
16.20 o10 p chote16.20 o10 p chote
16.20 o10 p chote
 
15.30 o10 p cottrell
15.30 o10 p cottrell15.30 o10 p cottrell
15.30 o10 p cottrell
 
14.20 o8 c gaedtke
14.20 o8 c gaedtke14.20 o8 c gaedtke
14.20 o8 c gaedtke
 
14.00 o8 j stephen
14.00 o8 j stephen14.00 o8 j stephen
14.00 o8 j stephen
 
13.00 o8 g williams
13.00 o8 g williams13.00 o8 g williams
13.00 o8 g williams
 
14.40 o7 d sullivan
14.40 o7 d sullivan14.40 o7 d sullivan
14.40 o7 d sullivan
 
14.20 o7 r davies
14.20 o7 r davies14.20 o7 r davies
14.20 o7 r davies
 
13.30 o7 b trompetter
13.30 o7 b trompetter13.30 o7 b trompetter
13.30 o7 b trompetter
 
13.00 o7 j adams
13.00 o7 j adams13.00 o7 j adams
13.00 o7 j adams
 
16.40 o4 s janssens
16.40 o4 s janssens16.40 o4 s janssens
16.40 o4 s janssens
 
16.20 04 j anthony
16.20 04 j anthony16.20 04 j anthony
16.20 04 j anthony
 

Último

Introduction to Matsuo Laboratory (ENG).pptx
Introduction to Matsuo Laboratory (ENG).pptxIntroduction to Matsuo Laboratory (ENG).pptx
Introduction to Matsuo Laboratory (ENG).pptxMatsuo Lab
 
COMPUTER 10 Lesson 8 - Building a Website
COMPUTER 10 Lesson 8 - Building a WebsiteCOMPUTER 10 Lesson 8 - Building a Website
COMPUTER 10 Lesson 8 - Building a Websitedgelyza
 
The Data Metaverse: Unpacking the Roles, Use Cases, and Tech Trends in Data a...
The Data Metaverse: Unpacking the Roles, Use Cases, and Tech Trends in Data a...The Data Metaverse: Unpacking the Roles, Use Cases, and Tech Trends in Data a...
The Data Metaverse: Unpacking the Roles, Use Cases, and Tech Trends in Data a...Aggregage
 
ADOPTING WEB 3 FOR YOUR BUSINESS: A STEP-BY-STEP GUIDE
ADOPTING WEB 3 FOR YOUR BUSINESS: A STEP-BY-STEP GUIDEADOPTING WEB 3 FOR YOUR BUSINESS: A STEP-BY-STEP GUIDE
ADOPTING WEB 3 FOR YOUR BUSINESS: A STEP-BY-STEP GUIDELiveplex
 
Apres-Cyber - The Data Dilemma: Bridging Offensive Operations and Machine Lea...
Apres-Cyber - The Data Dilemma: Bridging Offensive Operations and Machine Lea...Apres-Cyber - The Data Dilemma: Bridging Offensive Operations and Machine Lea...
Apres-Cyber - The Data Dilemma: Bridging Offensive Operations and Machine Lea...Will Schroeder
 
AI Fame Rush Review – Virtual Influencer Creation In Just Minutes
AI Fame Rush Review – Virtual Influencer Creation In Just MinutesAI Fame Rush Review – Virtual Influencer Creation In Just Minutes
AI Fame Rush Review – Virtual Influencer Creation In Just MinutesMd Hossain Ali
 
Salesforce Miami User Group Event - 1st Quarter 2024
Salesforce Miami User Group Event - 1st Quarter 2024Salesforce Miami User Group Event - 1st Quarter 2024
Salesforce Miami User Group Event - 1st Quarter 2024SkyPlanner
 
Computer 10: Lesson 10 - Online Crimes and Hazards
Computer 10: Lesson 10 - Online Crimes and HazardsComputer 10: Lesson 10 - Online Crimes and Hazards
Computer 10: Lesson 10 - Online Crimes and HazardsSeth Reyes
 
Linked Data in Production: Moving Beyond Ontologies
Linked Data in Production: Moving Beyond OntologiesLinked Data in Production: Moving Beyond Ontologies
Linked Data in Production: Moving Beyond OntologiesDavid Newbury
 
KubeConEU24-Monitoring Kubernetes and Cloud Spend with OpenCost
KubeConEU24-Monitoring Kubernetes and Cloud Spend with OpenCostKubeConEU24-Monitoring Kubernetes and Cloud Spend with OpenCost
KubeConEU24-Monitoring Kubernetes and Cloud Spend with OpenCostMatt Ray
 
COMPUTER 10: Lesson 7 - File Storage and Online Collaboration
COMPUTER 10: Lesson 7 - File Storage and Online CollaborationCOMPUTER 10: Lesson 7 - File Storage and Online Collaboration
COMPUTER 10: Lesson 7 - File Storage and Online Collaborationbruanjhuli
 
VoIP Service and Marketing using Odoo and Asterisk PBX
VoIP Service and Marketing using Odoo and Asterisk PBXVoIP Service and Marketing using Odoo and Asterisk PBX
VoIP Service and Marketing using Odoo and Asterisk PBXTarek Kalaji
 
Empowering Africa's Next Generation: The AI Leadership Blueprint
Empowering Africa's Next Generation: The AI Leadership BlueprintEmpowering Africa's Next Generation: The AI Leadership Blueprint
Empowering Africa's Next Generation: The AI Leadership BlueprintMahmoud Rabie
 
How Accurate are Carbon Emissions Projections?
How Accurate are Carbon Emissions Projections?How Accurate are Carbon Emissions Projections?
How Accurate are Carbon Emissions Projections?IES VE
 
UiPath Studio Web workshop series - Day 8
UiPath Studio Web workshop series - Day 8UiPath Studio Web workshop series - Day 8
UiPath Studio Web workshop series - Day 8DianaGray10
 
Meet the new FSP 3000 M-Flex800™
Meet the new FSP 3000 M-Flex800™Meet the new FSP 3000 M-Flex800™
Meet the new FSP 3000 M-Flex800™Adtran
 
Crea il tuo assistente AI con lo Stregatto (open source python framework)
Crea il tuo assistente AI con lo Stregatto (open source python framework)Crea il tuo assistente AI con lo Stregatto (open source python framework)
Crea il tuo assistente AI con lo Stregatto (open source python framework)Commit University
 
Connector Corner: Extending LLM automation use cases with UiPath GenAI connec...
Connector Corner: Extending LLM automation use cases with UiPath GenAI connec...Connector Corner: Extending LLM automation use cases with UiPath GenAI connec...
Connector Corner: Extending LLM automation use cases with UiPath GenAI connec...DianaGray10
 

Último (20)

Introduction to Matsuo Laboratory (ENG).pptx
Introduction to Matsuo Laboratory (ENG).pptxIntroduction to Matsuo Laboratory (ENG).pptx
Introduction to Matsuo Laboratory (ENG).pptx
 
COMPUTER 10 Lesson 8 - Building a Website
COMPUTER 10 Lesson 8 - Building a WebsiteCOMPUTER 10 Lesson 8 - Building a Website
COMPUTER 10 Lesson 8 - Building a Website
 
The Data Metaverse: Unpacking the Roles, Use Cases, and Tech Trends in Data a...
The Data Metaverse: Unpacking the Roles, Use Cases, and Tech Trends in Data a...The Data Metaverse: Unpacking the Roles, Use Cases, and Tech Trends in Data a...
The Data Metaverse: Unpacking the Roles, Use Cases, and Tech Trends in Data a...
 
ADOPTING WEB 3 FOR YOUR BUSINESS: A STEP-BY-STEP GUIDE
ADOPTING WEB 3 FOR YOUR BUSINESS: A STEP-BY-STEP GUIDEADOPTING WEB 3 FOR YOUR BUSINESS: A STEP-BY-STEP GUIDE
ADOPTING WEB 3 FOR YOUR BUSINESS: A STEP-BY-STEP GUIDE
 
Apres-Cyber - The Data Dilemma: Bridging Offensive Operations and Machine Lea...
Apres-Cyber - The Data Dilemma: Bridging Offensive Operations and Machine Lea...Apres-Cyber - The Data Dilemma: Bridging Offensive Operations and Machine Lea...
Apres-Cyber - The Data Dilemma: Bridging Offensive Operations and Machine Lea...
 
AI Fame Rush Review – Virtual Influencer Creation In Just Minutes
AI Fame Rush Review – Virtual Influencer Creation In Just MinutesAI Fame Rush Review – Virtual Influencer Creation In Just Minutes
AI Fame Rush Review – Virtual Influencer Creation In Just Minutes
 
Salesforce Miami User Group Event - 1st Quarter 2024
Salesforce Miami User Group Event - 1st Quarter 2024Salesforce Miami User Group Event - 1st Quarter 2024
Salesforce Miami User Group Event - 1st Quarter 2024
 
20230104 - machine vision
20230104 - machine vision20230104 - machine vision
20230104 - machine vision
 
Computer 10: Lesson 10 - Online Crimes and Hazards
Computer 10: Lesson 10 - Online Crimes and HazardsComputer 10: Lesson 10 - Online Crimes and Hazards
Computer 10: Lesson 10 - Online Crimes and Hazards
 
201610817 - edge part1
201610817 - edge part1201610817 - edge part1
201610817 - edge part1
 
Linked Data in Production: Moving Beyond Ontologies
Linked Data in Production: Moving Beyond OntologiesLinked Data in Production: Moving Beyond Ontologies
Linked Data in Production: Moving Beyond Ontologies
 
KubeConEU24-Monitoring Kubernetes and Cloud Spend with OpenCost
KubeConEU24-Monitoring Kubernetes and Cloud Spend with OpenCostKubeConEU24-Monitoring Kubernetes and Cloud Spend with OpenCost
KubeConEU24-Monitoring Kubernetes and Cloud Spend with OpenCost
 
COMPUTER 10: Lesson 7 - File Storage and Online Collaboration
COMPUTER 10: Lesson 7 - File Storage and Online CollaborationCOMPUTER 10: Lesson 7 - File Storage and Online Collaboration
COMPUTER 10: Lesson 7 - File Storage and Online Collaboration
 
VoIP Service and Marketing using Odoo and Asterisk PBX
VoIP Service and Marketing using Odoo and Asterisk PBXVoIP Service and Marketing using Odoo and Asterisk PBX
VoIP Service and Marketing using Odoo and Asterisk PBX
 
Empowering Africa's Next Generation: The AI Leadership Blueprint
Empowering Africa's Next Generation: The AI Leadership BlueprintEmpowering Africa's Next Generation: The AI Leadership Blueprint
Empowering Africa's Next Generation: The AI Leadership Blueprint
 
How Accurate are Carbon Emissions Projections?
How Accurate are Carbon Emissions Projections?How Accurate are Carbon Emissions Projections?
How Accurate are Carbon Emissions Projections?
 
UiPath Studio Web workshop series - Day 8
UiPath Studio Web workshop series - Day 8UiPath Studio Web workshop series - Day 8
UiPath Studio Web workshop series - Day 8
 
Meet the new FSP 3000 M-Flex800™
Meet the new FSP 3000 M-Flex800™Meet the new FSP 3000 M-Flex800™
Meet the new FSP 3000 M-Flex800™
 
Crea il tuo assistente AI con lo Stregatto (open source python framework)
Crea il tuo assistente AI con lo Stregatto (open source python framework)Crea il tuo assistente AI con lo Stregatto (open source python framework)
Crea il tuo assistente AI con lo Stregatto (open source python framework)
 
Connector Corner: Extending LLM automation use cases with UiPath GenAI connec...
Connector Corner: Extending LLM automation use cases with UiPath GenAI connec...Connector Corner: Extending LLM automation use cases with UiPath GenAI connec...
Connector Corner: Extending LLM automation use cases with UiPath GenAI connec...
 

11.15 k6 s coen

  • 1. Temporal 1D Kerr cavity solitons a new passive optical buffer technology Stéphane Coen Physics Department, The University of Auckland, Auckland, New Zealand Work performed while on Research & Study Leave at Special thanks to François Leo and to Pascal Kockaert The Université Libre Simon-Pierre Gorza de Bruxelles (ULB), Philippe Emplit Brussels, Belgium Marc Haelterman 1. What are cavity solitons? 4. Experimental setup 2. Temporal cavity solitons 5. Results 3. Theory & Historical background 6. Conclusion
  • 2. 1. What are cavity solitons? Traditionally described in passive planar cavities External plane wave coherently driving the cavity (driving/holding beam) Planar cavity filled with a nonlinear material
  • 3. 1. What are cavity solitons? Traditionally described in passive planar cavities External plane wave coherently driving the cavity (driving/holding beam) Planar cavity filled with a Intracavity soliton nonlinear superimposed on material a low level background
  • 4. 1. What are cavity solitons? Traditionally described in passive planar cavities External plane wave coherently driving the cavity (driving/holding beam) Planar cavity filled with a Intracavity soliton nonlinear superimposed on material a low level background The cavity solitons are independent from each other and from the boundaries They can be manipulated by external beams They exist for a wide range of nonlinearities L. A. Lugiato, IEEE J. Quantum Elec. 39, 193 (2003) W. J. Firth and C. O. Weiss, Opt. & Phot. News 13, 54 (Feb. 2002)
  • 5. 1. What are cavity solitons? Traditionally described in passive planar cavities In semiconductor µ-cavities External plane wave coherently driving the cavity (driving/holding beam) Planar cavity filled with a Intracavity soliton nonlinear superimposed on material a low level background The cavity solitons are independent from each other and from the boundaries They can be manipulated by external beams They exist for a wide range of nonlinearities L. A. Lugiato, IEEE J. Quantum Elec. 39, 193 (2003) S. Barland et al W. J. Firth and C. O. Weiss, Opt. & Phot. News 13, 54 (Feb. 2002) Nature 419, 699 (2002)
  • 6. 1. What are cavity solitons? Traditionally described in passive planar cavities External plane wave Cavity solitons are solitons coherently driving the cavity (driving/holding beam) Planar cavity Diffraction Nonlinearity filled with a Intracavity soliton nonlinear superimposed on material a low level background
  • 7. 1. What are cavity solitons? Traditionally described in passive planar cavities External plane wave Cavity solitons are solitons coherently driving the cavity (driving/holding beam) Coherent driving Planar cavity Diffraction Nonlinearity filled with a Intracavity soliton nonlinear superimposed on Losses material a low level background ... but also cavity solitons
  • 8. 1. What are cavity solitons? Traditionally described in passive planar cavities External plane wave Cavity solitons are solitons coherently driving the cavity (driving/holding beam) Coherent driving Planar cavity Diffraction Nonlinearity filled with a Intracavity soliton nonlinear superimposed on Losses material a low level background ... but also cavity solitons They are not solitons in a box W. J. Firth and C. O. Weiss, Opt. & Phot. News 13, 54 (Feb. 2002) 2D Kerr cavity solitons are stable while 2D Kerr nonlinear Schrödinger solitons collapse
  • 9. 1. What are cavity solitons? Traditionally described in passive planar cavities External plane wave Cavity solitons are solitons coherently driving the cavity (driving/holding beam) Coherent driving Planar cavity Diffraction Nonlinearity filled with a Intracavity soliton nonlinear superimposed on Losses material a low level background ... but also cavity solitons They are not solitons in a box W. J. Firth and C. O. Weiss, Opt. & Phot. News 13, 54 (Feb. 2002) Cavity solitons form a subset of dissipative solitons 2D Kerr cavity solitons are stable while 2D Kerr nonlinear for coherently-driven Schrödinger solitons collapse optical cavities
  • 10. 2. Temporal cavity solitons Spatial versus Temporal cavity solitons We extend the terminology External plane wave to the temporal case coherently driving the cavity (driving/holding beam) Coherent driving Planar cavity Diffraction Nonlinearity filled with a Intracavity soliton Dispersion nonlinear superimposed on Losses material a low level background cw driving beam Input coupler Input Temporal cavity solitons are naturally immune to longitudinal variations or imperfections along the cavity length Output
  • 11. 2. Temporal cavity solitons Temporal cavity solitons applied to an optical buffer technology Several temporal CSs can be stored in a cavity like bits in an optical buffer Coherent driving Dispersion Nonlinearity Losses cw driving beam Input Output
  • 12. 2. Temporal cavity solitons Temporal cavity solitons applied to an optical buffer technology Several temporal CSs can be stored in a cavity like bits in an optical buffer No intracavity amplifier: The stored CSs do not accumulate noise as they circulate repeatedly Coherent driving Dispersion Nonlinearity Losses cw driving beam Input Output
  • 13. 2. Temporal cavity solitons Temporal cavity solitons applied to an optical buffer technology Several temporal CSs can be stored in a cavity like bits in an optical buffer No intracavity amplifier: The stored CSs do not accumulate noise as they circulate repeatedly Coherent driving The driving power is independent of the Dispersion Nonlinearity number of bits stored Losses ALL-OPTICAL STORAGE cw driving beam Input Output
  • 14. 2. Temporal cavity solitons Temporal cavity solitons applied to an optical buffer technology Several temporal CSs can be stored in a cavity like bits in an optical buffer No intracavity amplifier: The stored CSs do not accumulate noise as they circulate repeatedly Coherent driving The driving power is independent of the Dispersion Nonlinearity number of bits stored Losses ALL-OPTICAL STORAGE The double balance makes temporal cw driving CSs unique attractive states beam Input Output
  • 15. 2. Temporal cavity solitons Temporal cavity solitons applied to an optical buffer technology Several temporal CSs can be stored in a cavity like bits in an optical buffer No intracavity amplifier: The stored CSs do not accumulate noise as they circulate repeatedly Coherent driving The driving power is independent of the Dispersion Nonlinearity number of bits stored Losses ALL-OPTICAL STORAGE The double balance makes temporal address pulses cw driving CSs unique attractive states beam ALL-OPTICAL RESHAPING Input They can be excited incoherently with address pulses at a different wavelength WAVELENGTH CONVERTER Output
  • 16. 2. Temporal cavity solitons Temporal cavity solitons applied to an optical buffer technology Several temporal CSs can be stored in a cavity like bits in an optical buffer No intracavity amplifier: The stored CSs do not accumulate noise as they circulate repeatedly Coherent driving The driving power is independent of the Dispersion Nonlinearity number of bits stored Losses ALL-OPTICAL STORAGE The double balance makes temporal address pulses cw driving CSs unique attractive states beam ALL-OPTICAL RESHAPING Input They can be excited incoherently with address pulses at a different wavelength WAVELENGTH CONVERTER A periodic modulation of the driving beam can trap the CSs in specific timeslots ALL-OPTICAL RETIMING Output
  • 17. 2. Temporal cavity solitons Temporal cavity solitons applied to an optical buffer technology Several temporal CSs can be stored in a cavity like bits in an optical buffer No intracavity amplifier: The stored CSs do not accumulate noise as they circulate repeatedly An optical buffer Coherent driving The driving power is independent of the based on Nonlinearity Dispersion number of bits stored temporal cavity solitons Losses would seamlessly combine ALL-OPTICAL STORAGE all these important address pulses The double balance makes temporal cw driving CSs unique attractive states telecommunications beam functions ALL-OPTICAL RESHAPING Input They can be excited incoherently with Here we report, address pulses at a different wavelength with a Kerr fiber cavity, WAVELENGTH CONVERTER the first experimental A periodic modulation of the driving beam observation can trap the CSs in specific timeslots of these objects ALL-OPTICAL RETIMING Output
  • 18. 3. Theory & Historical background The Kerr cavity “Hydrogen atom” of nonlinear cavity Input coupler Input Interferences Feedback Nonlinearity & Dispersion Output Combination of a simple nonlinearity with feedback and dispersion in a 1D geometry
  • 19. 3. Theory & Historical background The Kerr cavity Linear regime: Fabry-Perot type response “Hydrogen atom” of nonlinear cavity Constructive Input coupler interferences Input Interferences P Feedback 2p Nonlinearity Pin = n0L f f0 = & Dispersion l 0 2(m–1)p 2mp 2(m +1)p f Output Destructive interferences Combination of a simple nonlinearity with feedback and dispersion in a 1D geometry
  • 20. 3. Theory & Historical background The Kerr cavity: Nonlinear regime Nonlinear resonances and Bistability Instantaneous pure Kerr nonlinearity When approaching the resonance ... ... the intracavity power P increases ... fLP NL =g ... the nonlinear phase-shift increases ... ... the cavity round-trip phase shift increases ... P Pin 0 f 2(m–1)p 2mp 2(m +1)p fg = f LP 0+
  • 21. 3. Theory & Historical background The Kerr cavity: Nonlinear regime Nonlinear resonances and Bistability Instantaneous pure Kerr nonlinearity When approaching the resonance ... ... the intracavity power P increases ... fLP NL =g Positive ... the nonlinear phase-shift increases ... feedback ... the cavity round-trip phase shift increases ... Accelerated approach of the resonance P Pin 0 f 2(m–1)p 2mp 2(m +1)p fg = f LP 0+
  • 22. 3. Theory & Historical background The Kerr cavity: Nonlinear regime Nonlinear resonances and Bistability Instantaneous pure Kerr nonlinearity When approaching the resonance ... ... the intracavity power P increases ... fLP NL =g Positive ... the nonlinear phase-shift increases ... feedback ... the cavity round-trip phase shift increases ... Incident power Accelerated approach of the resonance P P Pin Pin 0 f 2(m–1)p 2mp 2(m +1)p Tilting of the cavity fg = f LP 0+ 0 f 0 resonance and bistability 2mp
  • 23. 3. Theory & Historical background The Kerr cavity: Nonlinear regime Nonlinear resonances and Bistability Bistability for various d0 Linear cavity detuning constant detunings D parameter (normalized = a respect to the losses) with P D =4 Bistability for various Incident power constant driving powers D =0 P Pin Pin 0 Onset of bistability: D =3 dp 0 =f 2m - 0 Tilting of the cavity 0 f 0 resonance and bistability 2mp
  • 24. 3. Theory & Historical background The intracavity field can be in the lower state in one part of the cavity and in the upper state in another part. The two parts can co-exist and be connected. Diffractive autosolitons Connecting the upper and lower bistable states with locked switching waves N. N. Rosanov and G. V. Khodova, J. Opt. Soc. Am. B 7, 1057 (1990) P P 0 Pin t
  • 25. 3. Theory & Historical background The intracavity field can be in the lower state in one part of the cavity and in the upper state in another part. The two parts can co-exist and be connected. Diffractive autosolitons Connecting the upper and lower bistable states with locked switching waves N. N. Rosanov and G. V. Khodova, J. Opt. Soc. Am. B 7, 1057 (1990) P P The domain of existence is limited as the switching waves cannot always lock and the upper state may be unstable 0 Pin t Not the type of localized structures we are concerned with in this work
  • 26. 3. Theory & Historical background Intracavity modulation instability Studied through a linear stability analysis Anomalous dispersion 5 The homogeneous D = 4 L. A. Lugiato and R. Lefever 4 upper state is Y? Phys. Rev. Lett. 58, D = 2.5 unstable in favor of 3 P 2209 (1987) a modulated solution 2 D = 1 M. Haelterman, S. Trillo, and S. Wabnitz 1 Opt. Lett. 17, 745 (1992) 0 0 4 8 12 X? Pin P Frequency domain P t 0
  • 27. 3. Theory & Historical background Intracavity modulation instability Studied through a linear stability analysis Anomalous dispersion 5 The homogeneous D = 4 L. A. Lugiato and R. Lefever 4 upper state is Y? Phys. Rev. Lett. 58, D = 2.5 unstable in favor of 3 P 2209 (1987) a modulated solution 2 D = 1 M. Haelterman, S. Trillo, and S. Wabnitz 1 It can coexist in Opt. Lett. 17, 745 (1992) different parts of 0 0 4 8 12 the cavity with the X? Pin homogeneous lower state P Localized dissipative structure t
  • 28. 3. Theory & Historical background Intracavity modulation instability Studied through a linear stability analysis Anomalous dispersion 5 The homogeneous D = 4 L. A. Lugiato and R. Lefever 4 upper state is Y? Phys. Rev. Lett. 58, D = 2.5 unstable in favor of 3 P 2209 (1987) a modulated solution 2 D = 1 M. Haelterman, S. Trillo, and S. Wabnitz 1 It can coexist in Opt. Lett. 17, 745 (1992) different parts of 0 0 4 8 12 the cavity with the X? Pin homogeneous lower state P Cavity soliton G. S. McDonald and W. J. Firth, J. Opt. Soc. Am. B 7, 1328 (1990) S. Wabnitz, Opt. Lett. 18, 601 (1993) M. Tlidi, P. Mandel, and R. Lefever, Phys. Rev. Lett. 73, 640 (1994) tW. J. Firth and A. J. 1623 (1996) Phys. Rev. Lett. 76, Scroggie,
  • 29. 3. Theory & Historical background Driving power (mW) Cavity solitons arise through a sub-critical 0 50 100 150 200 250 300 Turing bifurcation 9 8 7 6 5 4 3 10 1.9 P [W] 1.8 1.6 1.6 8 1.4 1.2 1.2 6 1 Y 0.8 4.4 ps 4 0.8 0.6 0.4 ? = 3.3 0.4 2 0.2 0 0 20 - 0 20 0 2 4 6 8 10 Time [ps] X
  • 30. 3. Theory & Historical background Driving power (mW) Cavity solitons arise through a sub-critical 0 50 100 150 200 250 300 Turing bifurcation 9 8 7 6 5 4 3 10 1.9 P [W] 1.8 1.6 1.6 8 1.4 1.2 1.2 6 1 Y 0.8 4.4 ps 4 0.8 0.6 0.4 ? = 3.3 0.4 2 0.2 0 0 20 - 0 20 0 2 4 6 8 10 Time [ps] X
  • 31. 3. Theory & Historical background Driving power (mW) Cavity solitons arise through a sub-critical 0 50 100 150 200 250 300 Turing bifurcation 9 8 7 6 5 4 3 10 1.9 P [W] 1.8 1.6 1.6 8 1.4 1.2 1.2 6 ? = 3.8 1 Y 0.8 4.4 ps 4 0.8 0.6 0.4 ? = 3.3 0.4 2 0.2 0 0 20 - 0 20 0 2 4 6 8 10 Time [ps] X
  • 32. 3. Theory & Historical background Driving power (mW) Cavity solitons arise through a sub-critical 0 50 100 150 200 250 300 Turing bifurcation 9 2 8 E é ¶ 2 ¶ ù 7 =( E êi - D E (S ih t ) 1 +- 2 ú,t )- + t ë ¶ ¶ t 6 û 5 L. A. Lugiato and R. Lefever 4 h( = 2) sign b Phys. Rev. Lett. 58, 2209 (1987) 3 10 1.9 P [W] 1.8 1.6 1.6 8 1.4 1.2 1.2 6 ? = 3.8 1 Y 0.8 4.4 ps 4 0.8 0.6 0.4 ? = 3.3 0.4 2 0.2 0 0 20 - 0 20 0 2 4 6 8 10 Time [ps] X
  • 33. 3. Theory & Historical background Driving power (mW) Cavity solitons arise through a sub-critical 0 50 100 150 200 250 300 Turing bifurcation 9 2 8 E é ¶ 2 ¶ ù 7 =( E êi - D E (S ih t ) 1 +- 2 ú,t )- + t ë ¶ ¶ t 6 û 5 L. A. Lugiato and R. Lefever 4 h( = 2) sign b Phys. Rev. Lett. 58, 2209 (1987) 3 10 1.9 Similar to reaction P [W] 1.8 diffusion systems 1.6 1.6 8 1.4 Cavity solitons 1.2 1.2 are localized 6 dissipative ? = 3.8 1 Y structures 0.8 4.4 ps 0.8 4 “à la” Prigogine 0.6 0.4 ? = 3.3 0.4 2 0.2 0 0 20 - 0 20 0 2 4 6 8 10 Time [ps] X
  • 34. 3. Theory & Historical background Driving power (mW) Cavity solitons arise through a sub-critical 0 50 100 150 200 250 300 Turing bifurcation 9 2 8 E é ¶ 2 ¶ ù 7 =( E êi - D E (S ih t ) 1 +- 2 ú,t )- + t ë ¶ ¶ t 6 û 5 L. A. Lugiato and R. Lefever 4 h( = 2) sign b Phys. Rev. Lett. 58, 2209 (1987) 3 10 1.9 Similar to reaction P [W] 1.8 diffusion systems 1.6 1.6 8 1.4 Cavity solitons 1.2 1.2 are localized 6 dissipative ? = 3.8 1 Y structures 0.8 4.4 ps 0.8 4 “à la” Prigogine 0.6 0.4 ? = 3.3 0.4 Fundamental 2 example of 0.2 self-organization phenomena in 0 0 nonlinear optics 20 - 0 20 0 2 4 6 8 10 Time [ps] X
  • 35. 4. Experimental setup Experimental demonstration of temporal Kerr cavity solitons Input Fiber Coupler Output 90/10 Polarization Controller t R =s 1.85 m 90m F = 24 Resonances: 22 kHz 290m Fiber Isolator To avoid Brillouin scattering
  • 36. 4. Experimental setup Experimental demonstration of temporal Kerr cavity solitons DRIVING BEAM EDFA 1 kHz linewidth DFB 1551 nm CW pump Fiber Coupler Output 90/10 Polarization Controller t R =s 1.85 m 90m F = 24 Resonances: 22 kHz 290m Fiber Isolator To avoid Brillouin scattering
  • 37. 4. Experimental setup Experimental demonstration of temporal Kerr cavity solitons DRIVING BEAM EDFA 1 kHz linewidth DFB 1551 nm CW pump Fiber Coupler Fiber Coupler Output 90/10 95/5 Polarization Controller t R =s 1.85 m 90m F = 24 Resonances: 22 kHz 290m Fiber Isolator Piezoelectric Fiber Stretcher To avoid Brillouin Controller scattering
  • 38. 4. Experimental setup Experimental demonstration of temporal Kerr cavity solitons EDFA ADDRESSING 1535 nm, 4 ps, 10 MHz AOM PRITEL BEAM modelocked fiber laser WDM DRIVING BEAM EDFA 1 kHz linewidth DFB 1551 nm CW pump Fiber Coupler Fiber Coupler Output 90/10 95/5 Polarization Controller t R =s 1.85 m 90m F = 24 Resonances: 22 kHz 290m Fiber Isolator Piezoelectric Fiber Stretcher To avoid Brillouin Controller scattering
  • 39. 4. Experimental setup Experimental demonstration of temporal Kerr cavity solitons EDFA ADDRESSING 1535 nm, 4 ps, 10 MHz AOM PRITEL BEAM modelocked fiber laser WDM DRIVING BEAM EDFA 1 kHz linewidth DFB 1551 nm CW pump Fiber Coupler Fiber Coupler Output 90/10 95/5 Polarization Controller t R =s 1.85 m 90m Excited F = 24 via XPM Resonances: 22 kHz 290m Fiber Isolator Piezoelectric Fiber Stretcher To avoid Brillouin Controller scattering
  • 40. 4. Experimental setup Experimental demonstration of temporal Kerr cavity solitons EDFA ADDRESSING 1535 nm, 4 ps, 10 MHz AOM PRITEL BEAM modelocked fiber laser WDM DRIVING BEAM EDFA 1 kHz linewidth DFB 1551 nm CW pump Fiber Coupler Fiber Coupler Output 90/10 95/5 Polarization Controller t R =s 1.85 m 90m Excited F = 24 WDM via XPM Resonances: 22 kHz 290m Fiber Isolator Piezoelectric WDM Fiber Stretcher To avoid Brillouin Controller scattering
  • 41. 4. Experimental setup Experimental demonstration of temporal Kerr cavity solitons EDFA ADDRESSING 1535 nm, 4 ps, 10 MHz AOM PRITEL BEAM modelocked fiber laser WDM DRIVING BEAM EDFA 1 kHz linewidth DFB 1551 nm CW pump Fiber Coupler Fiber Coupler Output 90/10 95/5 Polarization Controller t R =s 1.85 m 90m Excited F = 24 WDM via XPM Resonances: 22 kHz 290m Fiber Isolator Piezoelectric WDM Fiber Stretcher To avoid Brillouin Controller scattering
  • 42. 4. Experimental setup Experimental demonstration of temporal Kerr cavity solitons EDFA ADDRESSING 1535 nm, 4 ps, 10 MHz AOM PRITEL BEAM modelocked fiber laser WDM DRIVING BEAM 1 nm BPF EDFA 1 kHz linewidth DFB 1551 nm CW pump Remove ASE 5 GSa/s Fiber Coupler Fiber Coupler oscilloscope 90/10 95/5 BPF Polarization Controller t R =s 1.85 m Remove driving beam 90m Excited F = 24 WDM Fiber Coupler 50/50 via XPM Resonances: 22 kHz 290m Fiber Isolator Piezoelectric WDM Fiber Stretcher Optical To avoid Brillouin Controller spectrum scattering analyzer
  • 43. 5. Results A single soliton in the cavity Addressing pulse: Off - CS only sustained by the cw driving beam The intracavity pulse persists in the cavity for more than 1 s (> 550,000 round-trips) Coherent driving Losses
  • 44. 5. Results A single soliton in the cavity Addressing pulse: Off - CS only sustained by the cw driving beam Experiment Simulations The intracavity pulse persists in the cavity for more than 1 s (> 550,000 round-trips) Coherent driving Dispersion Nonlinearity Losses Autocorrelation reveals it is 4 ps long, Dispersion matching simulations length: 230 m
  • 45. 5. Results A single soliton in the cavity Addressing pulse: Off - CS only sustained by the cw driving beam Experiment Simulations The intracavity pulse persists in the cavity for more than 1 s (> 550,000 round-trips) Coherent driving Dispersion Nonlinearity Losses Autocorrelation reveals it is 4 ps long, Dispersion matching simulations length: 230 m
  • 46. 5. Results Storing data as binary patterns with cavity solitons
  • 47. 5. Results Interactions of temporal cavity solitons Sending two close addressing pulses and observing the CSs within the next 1 s Addressing pulses closer than 25 ps Only one CS present at the output
  • 48. 5. Results Interactions of temporal cavity solitons Sending two close addressing pulses and observing the CSs within the next 1 s Addressing pulses closer than 25 ps Only one CS present at the output With a larger separation between the addressing pulses ... The two excited CSs repel
  • 49. 5. Results Interactions of temporal cavity solitons Sending two close addressing pulses and observing the CSs within the next 1 s Addressing pulses closer than 25 ps Only one CS present at the output With a larger separation between the addressing pulses ... The two excited CSs repel ... but repulsion gets progressively weaker
  • 50. 5. Results Interactions of temporal cavity solitons Sending two close addressing pulses and observing the CSs within the next 1 s Addressing pulses closer than 25 ps Only one CS present at the output With a larger separation between the addressing pulses ... The two excited CSs repel ... but repulsion gets progressively weaker The CSs could be easily trapped by modulating the driving power Potential buffer capacity: 45 kbit @ 25 Gbit/s
  • 51. 5. Results Writing dynamics of temporal cavity solitons Experiment Simulation Time (100 µs/div)
  • 52. 5. Results Writing dynamics of temporal cavity solitons Output with off-center filter Experiment Inside the cavity Simulation Time (100 µs/div) Time (100 µs/div)
  • 53. 5. Results Erasing of temporal cavity solitons Complete erasing of the cavity can be obtained by switching off the driving beam for about 4 round-trips
  • 54. 5. Results Erasing of temporal cavity solitons Complete erasing of the cavity can be obtained by switching off the driving beam for about 4 round-trips Driving beam switched back on after 4 round-trips
  • 55. 5. Results Erasing of temporal cavity solitons Complete erasing of the cavity can be obtained by switching off the driving beam for about 4 round-trips Driving beam switched back on after 4 round-trips From there on, new CSs can be written without affecting the erasure of neighboring CSs
  • 56. 5. Results Erasing of temporal cavity solitons Selective erasing of one CS can be obtained by overwriting it with an addressing pulse about 50% more powerful This realizes an all-optical XOR logic gate
  • 57. 5. Results Driving power (mW) Breathing temporal cavity solitons 0 50 100 150 200 250 300 Above a certain driving power, 9 the cavity solitons become breathers 8 7 6 5 4 Hopf 3 10 bifurcation 1.9 1.8 1.6 8 1.4 1.2 6 ? = 3.8 1 Y 4 0.8 0.6 ? = 3.3 0.4 2 0.2 0 0 0 2 4 6 8 10 X
  • 58. 5. Results Driving power (mW) Breathing temporal cavity solitons 0 50 100 150 200 250 300 Above a certain driving power, 9 the cavity solitons become breathers 8 7 6 5 4 Hopf 3 10 bifurcation 1.9 1.8 1.6 8 1.4 1.2 6 ? = 3.8 1 Y 4 0.8 0.6 ? = 3.3 0.4 2 0.2 0 0 Time (50 µs/div) 0 2 4 6 8 10 X
  • 59. 6. Conclusion We have reported the first direct experimental observation of temporal cavity solitons as well as Kerr cavity solitons Temporal cavity solitons could be used as bits in an all-optical buffer, combining all-optical storage with wavelength conversion, all-optical reshaping, and re-timing Our experiments have been performed in a purely 1-dimensional system with an instantaneous Kerr nonlinearity Due to this simplicity, our experiments may constitute the most fundamental example of self-organization in nonlinear optics Kerr frequency combs generated in microresonators may be the spectral signature of a temporal cavity soliton P. Del’Haye et al, Nature 450, 1214 (2007)