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Bragg solitons

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Bragg solitons

  1. 1. Bragg Solitons Research Scholar Center for Nanoscience and Engineering Indian Institute of Science, Bangalore Course presentation: Nonlinear Photonics Ajay Singh
  2. 2. Solitons Bragg Grating Bragg Solitons Mathematical Analysis Experimental Applications Fiber Brag Grating Optical solitons: From fibers to photonic crystals,“Yuri S. Kivshar and Govind P. Agrawal” cademic PressElsevier Science, USA (2003)
  3. 3. Solitons Bragg Grating Bragg Solitons Mathematical Analysis Experimental Applications Fiber Brag Grating How to write: Irradiation from UV Irradiate germanium doped fiber with argon laser Holographic technique kg= 2π/Λ Λ =~o.5 µm for λ=1.55 µm region Optical solitons: From fibers to photonic crystals,“Yuri S. Kivshar and Govind P. Agrawal” cademic PressElsevier Science, USA (2003)
  4. 4. Solitons Bragg Grating Bragg Solitons Mathematical Analysis Experimental Applications Fiber Brag Grating Coupled-Mode Equations How to write: Irradiation from UV Irradiate germanium doped fiber with argon laser Holographic technique kg= 2π/Λ Λ =~o.5 µm for λ=1.55 µm region Optical solitons: From fibers to photonic crystals,“Yuri S. Kivshar and Govind P. Agrawal” cademic PressElsevier Science, USA (2003)
  5. 5. Solitons Bragg Grating Bragg Solitons Mathematical Analysis Experimental Applications Fiber Brag Grating Coupled-Mode Equations How to write: Irradiation from UV Irradiate germanium doped fiber with argon laser Holographic technique kg= 2π/Λ Λ =~o.5 µm for λ=1.55 µm region Optical solitons: From fibers to photonic crystals,“Yuri S. Kivshar and Govind P. Agrawal” cademic PressElsevier Science, USA (2003)
  6. 6. Coupled-Mode Equations and Nonlinear Propagation Equations Solitons Bragg Grating Bragg Solitons Mathematical Analysis Experimental Applications Optical solitons: From fibers to photonic crystals,“Yuri S. Kivshar and Govind P. Agrawal” cademic PressElsevier Science, USA (2003)
  7. 7. Coupled-Mode Equations and Nonlinear Propagation Equations Solitons Bragg Grating Bragg Solitons Mathematical Analysis Experimental Applications Optical solitons: From fibers to photonic crystals,“Yuri S. Kivshar and Govind P. Agrawal” cademic PressElsevier Science, USA (2003)
  8. 8. Coupled-Mode Equations and Nonlinear Propagation Equations Anomalous GVD Normal GVD Solitons Bragg Grating Bragg Solitons Mathematical Analysis Experimental Applications Optical solitons: From fibers to photonic crystals,“Yuri S. Kivshar and Govind P. Agrawal” cademic PressElsevier Science, USA (2003) Link
  9. 9. Solitons Bragg Grating Bragg Solitons Mathematical Analysis Experimental Applications Introduction Nonlinearity (SPM) Dispersion (Material) Soliton Nonlinearity (SPM) Dispersion (Grating) Soliton Like Pulses https://en.wikipedia.org/wiki/Soliton_(optics) Instantaneous Frequencychirp
  10. 10. Solitons Bragg Grating Bragg Solitons Mathematical Analysis Experimental Applications Effective NLS Equation Optical solitons: From fibers to photonic crystals,“Yuri S. Kivshar and Govind P. Agrawal” cademic PressElsevier Science, USA (2003) Now introduce the speed reduction factor f:
  11. 11. Solitons Bragg Grating Bragg Solitons Mathematical Analysis Experimental Applications Effective NLS Equation Fig.. Intensity (solid line) and normalized spatial width (dot- dashed line) of fundamental soliton pulses, [6]. Optical solitons: From fibers to photonic crystals,“Yuri S. Kivshar and Govind P. Agrawal” cademic PressElsevier Science, USA (2003) Now introduce the speed reduction factor f:
  12. 12. Solitons Bragg Grating Bragg Solitons Mathematical Analysis Experimental Applications Effective NLS Equation Fig.. Intensity (solid line) and normalized spatial width (dot- dashed line) of fundamental soliton pulses, [6]. Fig. Evoluation of (a) |Af|2 and (b) |Ab|2 [6]. Optical solitons: From fibers to photonic crystals,“Yuri S. Kivshar and Govind P. Agrawal” cademic PressElsevier Science, USA (2003) Now introduce the speed reduction factor f:
  13. 13. Solitons Bragg Grating Bragg Solitons Mathematical Analysis Experimental Applications Let us consider different cases of Bragg solitons 1-<v<1 Ψ=π/2: Center of the stop band: Combination of two counter-propogating waves VG = v.νg If equal amplitude: νg= 0  Stationary gap soliton |v|=1 Bragg soliton ceases to exist since the grating becomes ineffactive General solution (coupled mode eqn) of shape preserving solitons: Solition exist in normal Dispersion region also: Dark solitions Video: Propagation of a single bragg soliton in a uniform grating [17]
  14. 14. Solitons Bragg Grating Bragg Solitons Mathematical Analysis Experimental Applications B. J. Eggleton, R. E. Slusher (Bell Laboratories, Lucent Technologies, New Jersey 07974) and C. Martijn de Sterke (University of Sydney): Vol. 16, No. 4/ April 1999/J.Opt. Soc. Am. B [7] Fig. Schematic of our experimental setup.
  15. 15. Solitons Bragg Grating Bragg Solitons Mathematical Analysis Experimental Applications B. J. Eggleton, R. E. Slusher (Bell Laboratories, Lucent Technologies, New Jersey 07974) and C. Martijn de Sterke (University of Sydney): Vol. 16, No. 4/ April 1999/J.Opt. Soc. Am. B [7] Fig. Schematic of our experimental setup. Link
  16. 16. Solitons Bragg Grating Bragg Solitons Mathematical Analysis Experimental Applications Fig. Schematic of our experimental setup. B. J. Eggleton, R. E. Slusher (Bell Laboratories, Lucent Technologies, New Jersey 07974) and C. Martijn de Sterke (University of Sydney): Vol. 16, No. 4/ April 1999/J.Opt. Soc. Am. B [7] Link 818 m-1 3612 m-1
  17. 17. Solitons Bragg Grating Bragg Solitons Mathematical Analysis Experimental Applications B. J. Eggleton, R. E. Slusher (Bell Laboratories, Lucent Technologies, New Jersey 07974) and C. Martijn de Sterke (University of Sydney): Vol. 16, No. 4/ April 1999/J.Opt. Soc. Am. B [7]
  18. 18. Link Solitons Bragg Grating Bragg Solitons Mathematical Analysis Experimental Applications B. J. Eggleton, R. E. Slusher (Bell Laboratories, Lucent Technologies, New Jersey 07974) and C. Martijn de Sterke (University of Sydney): Vol. 16, No. 4/ April 1999/J.Opt. Soc. Am. B [7]
  19. 19. Fig. 16. transmitted pulse for incoming pulse energies of 0.66 µJ Left experimental results; right follow numerical calculation.(solid curves) The values of the detuning are 876 m- 1 [traces (a) and (b)], 994 m-1 [traces (c) and (d)], 1318 m-1 [traces (e) and (f )], and 1847 m-1 [traces (g) and (h)]. Intensity(a.u.) Link Link Solitons Bragg Grating Bragg Solitons Mathematical Analysis Experimental Applications B. J. Eggleton, R. E. Slusher (Bell Laboratories, Lucent Technologies, New Jersey 07974) and C. Martijn de Sterke (University of Sydney): Vol. 16, No. 4/ April 1999/J.Opt. Soc. Am. B [7] Link
  20. 20. Mathematical Analysis….. • All-optical switching [5,8,9], • Pulse compression [10,11,25], • Pulse Limiting [12], • Logic operations [13], • Promising for the fiber-sensing technology [14], • Optical communication systems [15,16], • All optical buffers and storing devices can be based on such fibers [18], • Pulse source for the soliton transmission system [19,20 ], • All-optical modulation and demultiplexing systems [23], • Tunable optical pulse source [24, 26], • A possible way to trap a zero-velocity soliton is to use an attractive finite-size or Local defect in BG [22] , • THz pulse generation !!! • Suppercontinuum generation !!! Solitons Bragg Grating Bragg Solitons Mathematical Analysis Experimental Applications Applications of Bragg Solitons…..
  21. 21. Solitons Bragg Grating Bragg Solitons Mathematical Analysis Applications References: [1] K. O. Hill, Y. Fujii, D. C. Johnson, and B. S. Kawasaki, Appl. Phys. Lett.,Vol. 32, pp. 647, 1978. [2] E. Yablonovitchand T. J. Gmitter,Phys. Rev. Lett.,Vol. 63, pp. 1950, 1989. [3] A. A. Sukhorukov, Y. S. Kivshar, H. S. Eisenberg and Y. Silberberg, IEEE J. QuantumElectron, Vol. 39, pp. 31, 2003. [4] W. Chen and D. L. Mills, Phys. Rev. Lett., Vol. 58, pp. 160, 1987. [5] S. Larochelle, V. Mizrahi, and G. Stegeman, Electron. Lett., Vol. 26, pp. 1459, 1990. [6] A. B. Aceves and S. Wabnitz, Phys. Lett. A, Vol. 141, pp. 37, 1989. [7] B. J. Eggleton,C. M. de, Sterke, and R. E. Slusher, J. Opt. Soc. Am. B, Vol. 16, pp. 587, 1999. [8] N. G. R. Broderick, D. Taverner, and D. J. Richardson, Opt. Express,Vol. 3, pp. 447, 1998. [9] Amer Kotb and Kyriakos, Optical Engineering (SPIE),Optical Engineering , Vol. 55(8), pp. 087109 (1-7), 2016. [10] N. G. R. Broderick, D. Taverner, D. J. Richardson, M. Ibsen and R. I. Laming, Opt. Lett. Vol. 22, pp. 1837, 1997. [11] N. G. R. Broderick, D. Taverner, D. J. Richardson, M. Ibsen and R. I. Laming, Phys. Rev. Lett.,Vol.79,pp. 4566, 1997. [12] D. E. Pelinovsky, L. Brzozowski, and E. H. Sargent. Phys. Rev. E, Vol. 62, pp. 4536, 2000. [13]. L. Brzozowski and E. H. Sargent, IEEE J. QuantumElectron, Vol. 36, pp. 550, 2000. [14] W. C. K. Mak, B. A. Malomed, and P. L. Chu, J. Opt. Soc. Am. B, Vol. 20, pp. 725, 2003. [15] R. H. Goodman, R. E. Slusher, and M. I. Weinstein,J. Opt. Soc. Am. B, Vol. 19, pp. 1635, 2002. [16] G. P. Agrawal, Nonlinear Fiber Optics. (New York: Academic), 1989. [17]. https://www.youtube.com/watch?v=GxmjYNuaoSE [18]. Xiaolu Li, Yuesong Jiang, and Lijun Xu, Communicationand Network, Vol. 2, pp. 44, 2010 [19] N. Dogru and M. S. Ozyazici, LFNM. September 2004, pp. 115. [20]. N. Dogru, 2005, IEEE NUSOD’05, September 2005, pp.89. [21] C. M. de Sterke, B. J. Eggleton,and P. A. Krug, J. Lightwave Technol,Vol. 15, pp. 1494, 1997. [22] K. T. Mc-Donald, Am. J. Phys., Vol. 68, pp. 293, 2000. [23]. J. H. Lee, L. Katsuo, K. S. Berg, A. T. Clausen, D. J. Richardson, and P. Jeppesen, J. Lightwave Technol,Vol. 21, pp. 2518, 2003. [24]. J. H. Lee, Y. M. Chang, Y. G. Han, S. H. Kim, H. Chung,and S. B. Lee, IEEEPhoton. Technol.Lett., Vol. 17, pp. 34, 2005. [25]. G. Lenz and B. J. Eggleton,J. Opt. Soc. Am. B, Vol. 15, pp. 2980, 1998. [26] Norihiko Nishizawa,Yoshimichi Andou, Emiko Omoda, Hiromichi Kataura, and Youichi Sakakibara, Opt. Exp. 23403, Vol. 24, 2016.
  22. 22. !
  23. 23. 1553.2 nm Q-switching of the laser at a repetition rate of 500 Hz. train of pulses, each with a duration of approximately 80 ps. To avoid thermal effects, an electro-optic pulse selector was used to select one pulse in each train. fast photodiode with a response time of 9 ps The net time resolution, including trigger jitter and oscilloscope resolution, was approximately 20 ps. 75-mm-long unchirped, apodized fiber grating Back
  24. 24. Schematic illustration of a fiber grating. Dark and light shaded regions withi n the fiber core show periodic variations of the refractive index. Solitons Bragg Grating Bragg Solitons Mathematical Analysis Experimental Applications First photo-induced optical fiber Bragg gratings by Hill and coworkers in 1978 [1] Photonic band structure” concept: Yablonovitch in the late 1980’s [2] Light interaction with nonlinear periodic media yields a diversity of fascinating phenomenan: discrete (or lattice) solitons and gap (or Bragg) solitons [11-12] Larochelle, Hihino, Mizrahi and Stegeman (in 1990): experimental investigation of the optical response of nonlinear periodic structures. investigation of nonlinear pulse propagation in uniform fiber gratings: the Bragg solitons easily generated in the laboratory travel at 60–80% of veocity of light in fiber absence of grating [5] Fiber Brag Grating How to write: Irradiation from UV Irradiate germanium doped fiber with argon laser Holographic technique kg= 2π/Λ Λ =~o.5 µm for λ=1.55 µm region Optical solitons: From fibers to photonic crystals,“Yuri S. Kivshar and Govind P. Agrawal” cademic PressElsevier Science, USA (2003)
  25. 25. Optical solitons: From fibers to photonic crystals,“Yuri S. Kivshar and Govind P. Agrawal” cademic PressElsevier Science, USA (2003) Coupled-Mode Equations And here dispersion comes into play….. Figure : Dispersion curves showing variation of 6 with q and the existence of the photonic bandgap for a fiber grating. Anomalous GVD Normal GVD o β2 changes its sign on the two sides of the stop band centered at the Bragg wavelength, whose location is easily controlled and can be in any region of the optical spectrum. o β2 is anomalous on the shorter-wavelength side of the stop band, unlike for wavelengths longer than the zero dispersion wave-length in the fibers o The magnitude of β2 > 100ps2/cm Solitons Bragg Grating Bragg Solitons Mathematical Analysis Experimental Applications o the negative sign appearing in front of the ∂Ab/∂Z term: because of backward propagation of Ab and o the presence of linear coupling between the counter propagating waves governed by the parameter k Back
  26. 26. Fig. 13. Comparison between the estimated pulse energy in the fiber and the deduced value of the peak intensity. The result, which is consistent with the expected proportionality between the two quantities, leads to a proportionality constant of 47 GW/cm2 µJ-1. Fig. 8. Intensity versus time after propagation through the grating at a pulse energy of approximately 0.66 µJ, for a detuning close to the edge of the gap (solid curve) and far from the edge of the gap (dashed curve). The pulse tuned close to the edge of the gap is delayed by approximately 310 ps, corresponding to an average velocity of approximately 0.50V. Fig. 7. Intensity versus time after propagation through the grating at a peak input intensity of 11 GW/cm2, for seven different values of the detuning (solid curve, 729 m-1; dotted curve, 788 m-1; short-dashed curve, 847 m-1; long- dashed curve, 935 m-1; short-dashed–dotted curve, 1053 m-1; long- dashed–dotted curve, 1406 m-1; long–short- dashed curve, 3612 m-1) Fig. 6. Delay of the transmitted pulses versus detuning at low intensity. Experimental results are indicated by dots, numerical results by the solid curve. Solitons Bragg Grating Bragg Solitons Mathematical Analysis Experimental Applications B. J. Eggleton, R. E. Slusher (Bell Laboratories, Lucent Technologies, New Jersey 07974) and C. Martijn de Sterke (University of Sydney): Vol. 16, No. 4/ April 1999/J.Opt. Soc. Am. B Back
  27. 27. Fig. 16. transmitted pulse for incoming pulse energies of 0.66 µJ at 4 different detunings. Left figures are experimental results; right follow from solving Eq. (1) numerically and convolving the result with the estimated response of the detection system (solid curves) and from the NLSE followed by a convolution (dashed curves). The values of the detuning are 876 m-1 [traces (a) and (b)], 994 m-1 [traces (c) and (d)], 1318 m-1 [traces (e) and (f )], and 1847 m-1 [traces (g) and (h)]. Fig. 9. FWHM of the transmitted pulses versus detuning at an estimated pulse energy of 0.06 µJ. Experimental results are indicated by dots, numerical results obtained by solving Eq. (1) are indicated by the solid curve, and numerical obtained by solving q. (10) are indicated by the dashed curve; in both sets of numerical results the peak intensity of the incoming pulse is taken to be 3 GW/cm2. Fig. 15. Solid curve: Estimated peak power of the fundamental soliton versus detuning with the parameters from the text. Dots: Similar results, but deduced from the experiments, with the criterion that the width does not change upon propagation. Solitons Bragg Grating Bragg Solitons Mathematical Analysis Experimental Applications B. J. Eggleton, R. E. Slusher (Bell Laboratories, Lucent Technologies, New Jersey 07974) and C. Martijn de Sterke (University of Sydney): Vol. 16, No. 4/ April 1999/J.Opt. Soc. Am. B Back
  28. 28. Fig. 5. Full-width at half-maximum (FWHM) of the transmitted pulses versus detuning at low intensity. Experimental results are indicated by dots, numerical results by the solid curve. Solitons Bragg Grating Bragg Solitons Mathematical Analysis Experimental Applications Fig. Schematic of our experimental setup. B. J. Eggleton, R. E. Slusher (Bell Laboratories, Lucent Technologies, New Jersey 07974) and C. Martijn de Sterke (University of Sydney): Vol. 16, No. 4/ April 1999/J.Opt. Soc. Am. B [7] Fig. Intensity versus time after propagation through the grating at low intensity, for seven different values of the detuning (solid curve, 818 m-1; dotted curve, 847 m-1; short-dashed curve, 906 m-1; long- dashed curve, 965 m-1; short-dashed– dotted curve, 1023 m-1; long- dashed–dotted curve, 1171 m-1; long–short- dashed curve, 3612 m- 1). Back
  29. 29. Back

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