The effects of inter-cavity separation on optical coupling in dielectric bispheres

The effects of inter-cavity separation on optical
coupling in dielectric bispheres
Shashanka P. Ashili and Vasily N. Astratov
Department of Physics and Optical Science, Center for Optoelectronics and Optical Communications, University of
North Carolina at Charlotte, Charlotte, NC 28211
astratov@uncc.edu
E. Charles H. Sykes
Center for Optoelectronics and Optical Communications, University of North Carolina at Charlotte, Charlotte, NC
28211
Abstract: The optical coupling between two size-mismatched spheres was
studied by using one sphere as a local source of light with whispering
gallery modes (WGMs) and detecting the intensity of the light scattered by a
second sphere playing the part of a receiver of electromagnetic energy. We
developed techniques to control inter-cavity gap sizes between microspheres
with ~30nm accuracy. We demonstrate high efficiencies (up to 0.2-0.3) of
coupling between two separated cavities with strongly detuned eigenstates.
At small separations (<1 μm) between the spheres, the mechanism of
coupling is interpreted in terms of the Fano resonance between discrete
level (true WGMs excited in a source sphere) and a continuum of “quasi”-
WGMs with distorted shape which can be induced in the receiving sphere.
At larger separations the spectra detected from the receiving sphere
originate from scattering of the radiative modes.
©2006 Optical Society of America
OCIS codes: (230.5750) Resonators; (250.5300) Photonic integrated circuits
References and links
1. B. E. Little, S. T. Chu, P. P. Absil, J. V. Hryniewicz, F. G. Johnson, F. Seiferth, D. Gill, V. Van, O. King,
and M. Trakalo, “Very high-order microring resonator filters for WDM applications,” IEEE Photon.
Technol. Lett. 16, 2263-2265 (2004).
2. A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, “Coupled-resonator optical waveguide: a proposal and
analysis,” Opt. Lett. 24, 711-713 (1999).
3. S. Deng, W. Cai, and V. N. Astratov, “Numerical study of light propagation via whispering gallery modes
in microcylinder coupled resonator optical waveguides,” Opt. Express 12, 6468-6480 (2004),
http://www.opticsexpress.org/abstract.cfm?id=83604
4. J. K. S. Poon, L. Zhu, G. A. DeRose, and A. Yariv, “Transmission and group delay of microring coupled-
resonator optical waveguides,” Opt. Lett. 31, 456-458 (2006).
5. J.E. Heebner, R. W. Boyd, and Q. H. Park, “SCISSOR solitons and other novel propagation effects in
microresonator-midified waveguides,” J. Opt. Soc. Am. B 19, 722-731 (2002).
6. M. Sumetsky and B. J. Eggleton, “Modeling and optimization of complex photonic resonant cavity
circuits,” Opt. Express 11, 381-391 (2003), http://www.opticsexpress.org/abstract.cfm?id=71298
7. D. D. Smith, H. Chang, and K. A. Fuller, “Whispering-gallery mode splitting in coupled microresonators,”
J. Opt. Soc. Am. B 20, 1967-1974 (2003).
8. J. E. Heebner, P. Chak, S. Pereira, J. E. Sipe, and R. W. Boyd, “Distributed and localized feedback in
microresonator sequences for linear and nonlinear optics,” J. Opt. Soc. Am. B 21, 1818-1832 (2004).
9. A. B. Matsko, A. A. Savchenkov, D. Strekalov, V. S. Ilchenko, and L. Maleki, “Interference effects in lossy
resonator chains,” J. Mod. Opt. 51, 2515-2522 (2004).
10. J. B. Khurgin, “Expanding the bandwidth of slow-light photonic devices based on coupled resonators,”
Opt. Lett. 30, 513-515 (2005).
11. S. V. Boriskina, T. M. Benson, P. Sewell, and A. I. Nosich, “Optical modes in 2-D Imperfect Square and
Triangular Microcavities,” IEEE J. Quantum Electron. 41, 857-862 (2005).
#71773 - $15.00 USD Received 12 June 2006; revised 16 August 2006; accepted 13 September 2006
(C) 2006 OSA 2 October 2006 / Vol. 14, No. 20 / OPTICS EXPRESS 9460

12. R.G. DeVoe and R.G. Brewer, “Observation of superradiant and subradiant spontaneous emission of two
trapped ions,” Phys. Rev. Lett. 76, 2049-2052 (1996).
13. S. Mahnkopf, M. Kamp, A. Forchel, and R. März, “Tunable distributed feedback laser with photonic crystal
mirrors,” Appl. Phys. Lett. 82, 2942-2944 (2003).
14. Y. Liu, Z. Wang, M. Han, S. Fan and R. Dutton, “Mode-locking of monolithic laser diodes incorporating
coupled-resonator optical waveguides,” Opt. Express 13, 4539-4553 (2005),
http://www.opticsexpress.org/abstract.cfm?uri=OE-13-12-4539
15. T. Mukaiyama, K. Takeda, H. Miyazaki, Y. Jimba, and M. Kuwata-Gonokami, “Tight-binding photonic
molecule modes of resonant bispheres,” Phys. Rev. Lett. 82, 4623-4626 (1999).
16. B. M. Möller, U. Woggon, M. V. Artemyev, and R. Wannemacher, “Photonic molecules doped with
semiconductor nanocrystals,” Phys. Rev. B 70, 115323 (2004).
17. Y. P. Rakovich, J. F. Donegan, M. Gerlach, A. L. Bradley, T. M. Connolly, J. J. Boland, N. Gaponik, and
A. Rogach, “Fine structure of coupled optical modes in photonic molecules,” Phys. Rev. A 70, 051801
(2004).
18. Y. Hara, T. Mukaiyama, K. Takeda, and M. Kuwata-Gonokami, “Heavy photon states in photonic chains of
resonantly coupled cavities with supermonodispersive microspheres,” Phys. Rev. Lett. 94, 203905 (2005).
19. B. M. Möller, U. Woggon, and M. V. Artemyev, “Coupled-resonator optical waveguides doped with
nanocrystals,” Opt. Lett. 30, 2116-2118 (2005).
20. V. N. Astratov, J. P. Franchak, and S. P. Ashili, “Optical coupling and transport phenomena in chains of
spherical dielectric microresonators with size disorder,” Appl. Phys. Lett. 85, 5508-5510 (2004).
21. A. V. Kanaev, V. N. Astratov, and W. Cai, “Optical coupling at a distance between detuned spherical
cavities,” Appl. Phys. Lett. 88, 111111 (2006).
22. Z. Chen, A. Taflove, and V. Backman, “Photonic nanojet enhancement of backscattering of light by
nanoparticles: a potential novel visible-light ultramicroscopy technique,” Opt. Express 12,1214-1220
(2004), http://www.opticsexpress.org/abstract.cfm?id=79442
23. Z. Chen, A. Taflove, and V. Backman, “Highly efficient optical coupling and transport phenomena in
chains of dielectric microspheres,” Opt. Lett. 31, 389-391 (2006).
1. Introduction
The mechanisms of optical coupling between microcavities supporting high quality (Q)
whispering gallery mode (WGM) resonances have attracted considerable interest in the past
few years. This interest is driven by potential applications of integrated microrings, cylinders,
or spheres for controlling dispersion relations for photons in various structures such as high
order filters [1], coupled resonator optical waveguides [2-4] (CROW), side-coupled integrated
spaced sequences of resonators [5] (SCISSOR) and more complicated [6-11] coupled cavity
structures. In most of the theoretical work on this subject the cavities are assumed to be
identical, leading to efficient resonant coupling between WGMs in adjacent cavities. Such
coupling has an analogy with a coherent interaction between atoms [12] in a quantum limit.
It should be noted however, that the studies of coupling mechanisms between nonidentical
cavities constitute an important subject for developing applications of multiple cavity systems.
Firstly, the detuning between the cavities can be introduced in a controllable fashion to
achieve vernier effect tuning [13], stabilize mode-locking [14] of lasers or to expand the
transmission band of such filters and delay lines. Secondly, continuous improvement of Q
factors of individual cavities due to technological breakthroughs makes it inevitable that even
systems with highly uniform resonators begin to display the properties of a disordered system
if the random detuning between the cavity resonances exceeds their individual linewidths.
Dielectric microspheres can be considered as very attractive building blocks of more
complicated coupled cavity structures due to ultra-high Q factors of their WGM resonances,
and due to the possibility of sorting cavities on the basis of their spectral characterization.
Some effects determined by the interplay of order and disorder in such systems have already
been observed. These include normal mode splitting [15-17] and band structure effects
[18,19] in uniform chains, as well as optical transport effects [20] in systems with disorder.
The coupling between detuned cavities is, however, not well studied at present.
Recently it has been argued that coupling between cylindrical or spherical cavities can be
achieved by two mechanisms distinctly different from the resonant optical tunneling. In one of
these mechanisms [21] the coupling occurs due to a Fano resonance between a discrete energy
state (true WGM) in a sphere containing a source of light and a continuum of “quasi”-WGMs

with irregular shape which can be induced in the second sphere. Such evanescent coupling can
be achieved between the cavities with strongly detuned eigenstates in a regime of weak
coupling. Another mechanism is based on the phenomenon of formation of photonic nanojets
[22] emerging from the shadow-side surface of a dielectric microcylinder or a microsphere
under plane wave illumination. In a chain of nanojet-inducing microspheres, the constituent
spheres are coupled [23] due to the periodical nature of nanojets.
In the present work by employing scattering spectroscopy with spatial resolution we
demonstrate high efficiencies (up to 0.2-0.3) of coupling between two separated, size-
mismatched cavities with strongly detuned WGM eigenstates. We developed techniques for
controlling interresonator gap sizes between optically coupled microspheres with nanometric
(~30 nm) accuracy. At small inter-cavity separations d <1 μm, the coupling is shown to have
an evanescent nature, and is explained by the recently suggested mechanism [21] of Fano
resonance between true WGMs excited in the cavity containing a source of light, and a
continuum of quasi-WGM states which can be induced in the cavity receiving electromagnetic
energy. At larger separations the spectral peaks detected from the receiving sphere are
explained by the illumination effect provided by the scattering of WGMs in the source sphere.
2. Structures and method of controlling the inter-cavity gap sizes
We study optical coupling phenomena in dielectric bispheres by using one of the spheres as a
local light source (S) and the second sphere as a passive radiation receiver (R). The sizes of
the spheres were different in most of the experiments. The source of light was created by dye-
doped fluorescent (FL) polystyrene microspheres with sizes Ds = 10 or 5 μm and size
dispersion ~3% obtained from Duke Scientific Corp. As the receivers of radiation we used
undoped spheres with various sizes in a 3 μm ≤ Dr ≤ 20 μm range and size dispersion ~1%.
We developed a technique for controlling the separations between the cavities based on
placing the spheres at the top of the stretchable substrate, as illustrated in Figs. 1(a) and 1(b).
If the spheres are attached to the substrate and not to each other, one can control the
separation (d) between the spheres by creating a tensile strain in the substrate. The substrate
material was selected on the basis of its ability to withstand a significant strain up to ~0.2, and
to provide strong surface adhesion with the spheres. Such substrates were synthesized using a
robust and inert material, namely polydimethylsiloxane (PDMS). To increase its elasticity and
Fig. 1. (a) Optical image of a bisphere formed by 5 μm dye-doped source (S) sphere and 8 μm
undoped receiving (R) sphere. (b) Schematic sketch illustrating use of a stretchable substrate
for controlling gaps d between the spheres. Additional markers (spheres) for calibrating strain
are indicated. (c) Experimental setup for spatially resolved spectroscopic measurements.
Objective
x100
NA=0.5
Filter
λ >500nm
Spatial
Filter
Fiber-to-
spectrometer
OPO, λ=467nm
d
SR
Uniform Strain
Stage
(a) (b)
(c)
PDMS
d
L+ΔL
Objective
x100
NA=0.5
Filter
λ >500nm
Spatial
Filter
Fiber-to-
spectrometer
OPO, λ=467nm
d
SR
Uniform Strain
Stage
(a) (b)
(c)
PDMS
d
L+ΔL

the adhesion of the spheres to its surface a smaller than normal concentration (~0.1) of cross-
linker was used during the curing step of the manufacture of the PDMS substrate.
The polystyrene spheres were deposited at the top of stretchable substrate according to the
following steps. Firstly, a droplet of a mixture of spheres with different sizes was dried on a
microscope slide. After that the slide with the spheres was pressed into the PDMS substrate to
deposit the spheres at its surface. Next, the PDMS substrate was detached and stretched until
it reached its maximum strain ~0.2. The spheres were then micromanipulated at top of the
substrate under microscope control to form a bisphere with d~2-3 μm. After that the strain
was released step by step using a translational stage to control d.
Since the distribution of strain in a centimeter sized substrate can be nonuniform, it is
important to characterize the strain in the same area where the bisphere under study is
assembled. For this purpose we used two additional microspheres as markers spanning the
area of interest, see Fig. 1(b). The distance between the markers (L) was sufficiently small to
ensure the uniformity of the strain, but it was large enough (~0.5 mm) to enable very simple
and accurate optical calibration of the strain using imaging. As follows from the geometrical
sketch in Fig. 1(b), the distance between the spheres is related to the strain by the formula:
d = (ΔL/L)(DS+DR)/2, (1)
where L – distance between two markers corresponding to the bisphere touching case, ΔL –
increment of L due to stretching, DS(R) – diameters of two spheres (S and R) under study.
It is important to note that this simple technique provides a measurement of the separation
d with nanometric accuracy, far beyond the limitations (~1 μm) of direct microscopic
visualization of the gap sizes. This accuracy is determined by the possibility of precisely
calibrating the strain (ΔL/L) by using distant markers with better than ~1% accuracy. This
translates into ~30 nm accuracy in determining changes of intersphere separations d.
3. Experimental results
As illustrated in Fig. 1(c) the doped spheres were pumped at the center of the absorption band
of the dye (467 nm) by a linearly polarized tunable OPO system with a repetition frequency of
20 Hz, and pulse duration of 20 ns. The illumination was provided by a slightly focused beam.
Due to the fact that the incident light waves are not effectively coupled to WGMs the
absorption was not influenced by the resonances in spheres. The excitation power was
selected to be slightly above the lasing threshold for the WGMs peaks. The emission spectra
display multiple TE- and TM-like WGMs peaks in 500-560 nm range. The individual cavities
were imaged in the plane of spatial filter by using additional white light illumination through
the transparent substrate using a Mitutoyo ×100 objective with a numerical aperture NA=0.5.
The typical example of results of characterization of such bispheres with controllable
separation are presented in Fig. 2 for Ds = 5 μm and Dr = 8 μm. The spectra contain two well
separated peaks around 518 nm and 526 nm associated with two different WGMs excited in
the S sphere. The width of the resonances ~0.2 nm is limited by the resolution of the
spectrometer. The weak coupling regime is evident from the fact that split components [15-
17] do not appear in these spectra even for smallest separations between the cavities. In the
touching sphere case this can be seen by comparing spectra in Fig. 2(a) and 2(b).
As the cavities become closer one can see a slight shift of spectral peaks to shorter
wavelengths indicated as γ in Fig. 2. This shift is present in spectra of both cavities, and it has
a similar magnitude for all peaks. The relative shift reaches its maximum value γ/λ ~ 7×10-4
in
the d = 0 case. This shift is not related to strong coupling phenomena since it does not depend
on the individual characteristics of the resonances involved such as detuning between WGM
eigenstates in S and R sphere. The most likely explanation of this shift is connected with the
changes of the average index experienced by the optical modes confined in spheres. The SEM
images of the structure indicate that the spheres are slightly embedded (~0.5 μm) into
elastomeric PDMS slab, as illustrated in the inset in Fig. 2. As a result, the modes confined in
the polystyrene spheres with index n = 1.59 are influenced by the closely located PDMS

region with index nPDMS = 1.45. The effective index experienced by these modes is slightly
increased for this reason. In the course of releasing the tensile strain the spheres are pushed up
by the shrinking material of the substrate that result in a short wavelength shift of peaks due to
slightly smaller effective index experienced by the modes in spheres.
As a measure of the coupling efficiency (η) between S and R spheres we used the ratio of
the amplitudes of scattering peaks induced in R sphere (IR), see Fig. 2(b), to the amplitudes of
the corresponding peaks in the spectrum of isolated S sphere (IS), as shown in Fig. 2(i) (the
distance d = 3.2 μm is sufficiently long to consider the S sphere isolated). Since all spectra in
Fig. 2 were obtained at practically identical conditions of collection of light, the changes in
the intensity of scattering peaks can be attributed to variations of the coupling efficiency
between S and R spheres. We additionally corrected coupling efficiency by a geometrical
factor (A) related to a finite size of the hole in the spatial filter. In our experiments it
corresponded to a size ~6 μm at the sample plane that means that FL from 5 μm S sphere was
totally transmitted through the hole, whereas only a part (1/A=(6/8)2
=0.56) of the image of the
8 μm R sphere was coupled to the spectrometer. Finally, a rough estimate of the coupling
efficiency was obtained using the following formula: η = A× (IR / IS).
Fig. 2. Spectra of 5 μm dye-doped source (S) sphere (red), and spectra of 8 μm undoped
receiving (R) sphere (black) for different distances d between cavities: (a) and (b) touching
case, (c) 0.17 μm, (d) 0.29 μm, (e) 0.46 μm, (f) 0.69 μm, (g) 1.32 μm, (h) 2.18 μm, and (i)
3.2 μm. The shift of peaks (γ) associated with change of the average index experienced by
WGMs is indicated. The amplitudes of peaks in scattering spectra of R sphere (IR) and in
FL spectra of S sphere (IS) are indicated. In the inset the SEM image demonstrates a slight
embedding (~0.5 μm) of spheres into elastomeric PDMS slab.
2.18
1.32
0.69
0.46
0.29
0.17
0
d=0μm
518 520 522 524 526
IR
IS (i)
(h)
(g)
(f)
(e)
(d)
(b)
(c)
(a)
x40
x30
x20
x10
x5
x5
γ
x5Intensity(a.u.)
Wavelength (nm)
S
S R
3.2
R
R S
2.18
1.32
0.69
0.46
0.29
0.17
0
d=0μm
518 520 522 524 526
IR
IS (i)
(h)
(g)
(f)
(e)
(d)
(b)
(c)
(a)
x40
x30
x20
x10
x5
x5
γ
x5Intensity(a.u.)
Wavelength (nm)
S
S R
3.2
R
R S

4. Discussion and summary
As illustrated in Fig. 3 the experimental dependence of η as a function of d demonstrates the
following properties: (i) maximum efficiencies η=0.2-0.3 in touching case, (ii) somewhat
reduced, but still remarkably high (η>0.1) efficiencies for inter-sphere separations up to d~0.3
μm, (iii) nearly exponential decay with ~0.2-0.3 μm attenuation length for longer separations
0.3 μm < d < 1.0 μm, and (iv) small, almost constant level η~0.02 at 1.0 μm > d > 2.3 μm.
In analogy to the case of atoms where the typical length of coherent interaction [12]
corresponds to d ~ λ one can assume the possibility of coherent coupling between two cavities
at small separations. The behavior of η at d<1 μm is found to be in a good qualitative
agreement with the results of theoretical modeling [21] performed for smaller S (3 μm) and R
(2.4 μm) spheres. It is important to stress that this modeling considers coupling between size-
mismatched cavities in the situation where the WGM eigenstates in S and R cavities are
strongly detuned. This is similar to the bispheres studied in the present work. In such cases the
evanescent coupling has been shown to result from the Fano resonance between a discrete
energy state (true WGM) in S sphere and a continuum of “quasi”-WGMs with noncircular
shape and reduced Q factors which can be induced in R sphere. It should be noted however,
that the exact amount of detuning is unknown in our experiments, since the R sphere was
undoped making it difficult to observe its WGM eigenstates.
An interesting alternative mechanism [23] of coupling between spherical or cylindrical
cavities is theoretically predicted in the case of their plane wave illumination due to the
formation of localized “nanoscale photonic jet” at the shadow-side of spheres. In our
experiments however, the excitation is provided by spherically symmetric WGM in the S
sphere as evident from the spectroscopic data that shows that the photonic jet mechanism is
not directly applicable in this situation.
A small and nearly constant level (η~0.02) of scattering detected from R sphere at larger
separations between the cavities (1 μm > d > 2.3 μm) cannot be explained by the model [21]
of evanescent coupling described above. A likely explanation of this result is related to an
illumination effect produced by the S sphere at the WGM frequencies due to scattering modes.
A small fraction of such modes is reflected at the surface of R sphere into the objective, thus
determining the level of background scattering peaks in our experiments. Due to its
Fig. 3. The efficiency of coupling between 5 μm dye-doped source (S) sphere and 8 μm
undoped receiving (R) sphere as a function of distance d. The coupling efficiency was
estimated as: η = A×(IR/IS), where A – geometrical factor related to finite size of the
hole in the spatial filter, IR – amplitude of the peak in scattering spectrum of R sphere, IS
– amplitude of the corresponding peak in the lasing spectrum of isolated S sphere. Red
and blue curves represent peaks around 518 nm and 526 nm in Fig. 3, correspondingly.
0.0 0.5 1.0 1.5 2.0 2.5
0.01
0.1
1
Couplingefficiencyη(a.u.)
Inter-resonator gap d (μm)

nonevanescent nature, this illumination effect depends on d weakly. However, as expected,
the level of background scattering can be reduced with further increase of d (>2.5 μm).
In conclusion, we experimentally demonstrate high efficiencies (up to 0.2-0.3) of coupling
between separated and size-mismatched cavities with strongly detuned WGM eigenstates. At
small inter-cavity separations d <1 μm the coupling is explained by the mechanism [21] based
on the Fano resonance between a discrete energy state (true WGM excited in the S cavity) and
a continuum of quasi-WGM states which can be induced in the R cavity. The level of coupling
efficiencies presented in this work leaves a room for further improvement which can be
achieved by selecting more uniform cavities assembled as a long chain. However, the
mechanisms of coupling between detuned cavities studied in this work should still play an
important role in a variety of real physical systems with a degree of disorder.
Acknowledgments
The authors thank A. M. Kapitonov, M. S. Skolnick, A. M. Fox, D. M. Whittaker, and M. A.
Fiddy for stimulating discussions. This work was supported by ARO under Grant No.
W911NF-05-1-0529 and by NSF under Grant No. CCF-0513179 as well as, in part, by funds
provided by The University of North Carolina at Charlotte. Shashanka Ashili and Charles
Sykes were supported by DARPA Grant No. DAAD 19-03-1-0092. The authors are thankful
to Duke Scientific Corp. for donating microspheres for the research presented in this work.

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