Two mechanisms of optical coupling between spherical cavities, tight-binding between their whispering gallery modes and focusing produced by periodically coupled microlenses, are directly observed using spatially resolved scattering spectroscopy and imaging. The results can be used for developing device concepts of lasers, optical filters, microspectrometers and sensors based on mesoscopic systems of coupled microspheres.

1. PIERS ONLINE, VOL. 3, NO. 3, 2007 278
Optical Properties of Mesoscopic Systems of Coupled
Microspheres
V. N. Astratov1
, S. P. Ashili1
, and A. M. Kapitonov2
1
Department of Physics and Optical Science, Center for Optoelectronics and Optical Communications
University of North Carolina at Charlotte
9201 University City Blvd., Charlotte, NC 28223, USA
2
Center for Optoelectronics and Optical Communications, University of North Carolina at Charlotte
9201 University City Blvd., Charlotte, NC 28223, USA
Abstract— Two mechanisms of optical coupling between spherical cavities, tight-binding be-
tween their whispering gallery modes and focusing produced by periodically coupled microlenses,
are directly observed using spatially resolved scattering spectroscopy and imaging. The results
can be used for developing device concepts of lasers, optical filters, microspectrometers and sen-
sors based on mesoscopic systems of coupled microspheres.
DOI: 10.2529/PIERS060908001922
In this paper we consider structures formed by coupled spherical cavities which can be regarded
as mesoscopic systems due to the fact that the size of their building blocks (spheres) is comparable
to the characteristic wavelength. In contrast to metamaterials or photonic crystals conceptualized
through the process of homogenization, the optical phenomena in such mesoscopic systems are
essentially based on the properties of the constituting cavities. These include their ultra high
quality whispering gallery mode (WGM) resonances [1] and their ability to focus plane waves into
“nanoscale photonic jets” [2] at the shadow-side. These properties lead to two different mechanisms
of optical transport between the cavities: (i) tight-binding between WGMs, (ii) propagation in a
series of periodically coupled microlenses. These mechanisms are directly studied in the present
work.
1. TIGHT-BINDING BETWEEN WGMS
Previously we observed WGM-related propagation effects [3] in one-dimensional (1D) chains of
slightly disordered spheres using evanescently coupled dye-doped spherical cavities pumped above
the lasing threshold for WGMs. In the present work we integrated spherical cavities into 3D closed
packed structures with the thickness varying from one monolayer up to ∼ 50 monolayers. The
samples were obtained by self-assembly of spheres (with sizes in 2-10 micron range with standard 3%
size dispersion) directed by hydro-dynamic flow in a specially designed cuvette placed in ultrasonic
bath. The spheres were dye-doped and locally excited to create a built-in source of whispering
gallery modes (WGMs). In the scattering spectra of such samples we observed fringes due to
light propagation via coupled WGMs, as illustrated in Fig. 1. The study of pump dependence of
scattering spectra indicated that above WGM lasing threshold the emission is provided in localized
modes formed by multiple spheres. This is confirmed by observation of double peak structures,
the spectral signature of strong coupling regime between multiple cavities. Although size disorder
plays a negative role in the efficiency of such transport, we show that due to existence of multiple
paths for photons the optical transport can be very efficient. The study of thickness dependence of
scattering spectra indicates that attenuation length of light in such 3D samples exceeds 50 µm. The
results show that the optical transport in such systems is provided along particular configurations
of cavities according to a principle of minimization of the total WGM detuning.
2. PROPAGATION IN A SERIES OF PERIODICALLY COUPLED MICROLENSES
We report on the light transport phenomena in linear chains composed of several tens of touching
spherical microcavities. A new optical mode type, namely nanojet-induced modes (NIMs) is directly
observed [4]. Theoretically, formation of periodic nanojets has been predicted [5] as a result of
the optical coupling of microspheres acting as a series of micro-lenses, which periodically focus
propagating wave into photonic nanojets.

2. PIERS ONLINE, VOL. 3, NO. 3, 2007 279
520 540 560 580 600
13nm
17nm
28nm
Intensity(a.u)
Wavelength (nm)
5 m
2.9 m
2.2 m
A
B
C
fcc
520 540 560 580 600
13nm
17nm
28nm
Intensity(a.u)
Wavelength (nm)
5
2.9
2.2
520 540 560 580 600
13nm
17nm
28nm
Intensity(a.u)
Wavelength (nm)
5
2.9
2.2
A
B
C
fcc
A
B
C
A
B
C
fcc
µ
µ
µ
Figure 1: Scattering spectra of 3D systems of microspheres obtained using evanescently coupled sources
of light (dye-doped spheres) with WGM peaks. The spectra exhibit fringes due to light propagation via
coupled WGMs. Different sizes of microspheres result in different free spectral ranges. The sketch in the
inset illustrates propagation between ABC layers along (111) direction of fcc lattice.
The chains were formed by means of the self-assembly directed by micro-flows of water suspen-
sion of polystyrene microspheres. The standard size dispersion of spheres in each particular chain
was below 3%, while mean size of spheres was varied in the 2–10 micron range. To couple light to
NIMs we used built-in emission sources formed by several locally excited dye-doped microcavities
from the same 1-D chain.
Figure 2: Visualization of NIMs in a locally excited chain of 2.9 µm spheres. (a) Image obtained with the
background illumination, (b) same chain imaged due to propagation and scattering of light originating from
the local fluorescence source.
The formation of NIMs as illustrated in Fig. 2. Conversion of modes emitted by the light source
into the NIMs results in losses of several dB per sphere in the vicinity (first few tens of spheres) of
such sources. At longer distances we found an attenuation rate as small as 0.5 dB per sphere, that
reveals low intrinsic propagation loss for NIMs. The NIMs have potential applications for coupling
of light in and out of spherical cavities characterized by extremely high quality (Q) whispering
gallery modes and for guiding of emission in compact arrays of such microcavities.
ACKNOWLEDGMENT
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. A.M.K. was partly supported by DARPA Grant No. W911NF-05-2-0053. The authors
are thankful to Duke Scientific Corp. for donating microspheres for the research presented in this
work.
REFERENCES
1. Ilchenko, V. S. and A. B. Matsko, “Optical resonators with whispering-gallery mode—Part II:
Applications,” IEEE J. Sel. Topics Quantum Electron, Vol. 12, No. 1, 15–32, January/February
2006.

3. PIERS ONLINE, VOL. 3, NO. 3, 2007 280
2. Chen, Z., A. Taflove, and V. Backman, “Photonic nanojet enhancement of backscattering of
light by nanoparticles: A potential novel visible-light ultramicroscopy technique,” Opt. Express,
Vol. 12, No. 7, 1214–1220, April 2004.
3. Astratov, V. N., J. P. Franchak, and S. P. Ashili, “Optical coupling and transport phenomena
in chains of spherical dielectric microresonators with size disorder,” Appl. Phys. Lett., Vol. 85,
No. 23, 5508–5510, December 2004.
4. Kapitonov, A. M. and V. N. Astratov, “Observation of nanojet-induced modes with small
propagation losses in chains of coupled spherical cavities,” Opt. Lett., Vol. 32, No. 4, 409–411,
February 2007.
5. Chen, Z., A. Taflove, and V. Backman, “Highly efficient optical coupling and transport phe-
nomena in chains of dielectric microspheres,” Opt. Lett., Vol. 31, No. 3, 389–391, February
2006.