Resonant light transport through Mie modes in photonic glasses
P. D. García,
1,
*
R. Sapienza,
1
J. Bertolotti,
2
M. D. Martín,
3
Á Blanco,
1
A. Altube,
1
L. Viña,
3
D. S. Wiersma,
2
and C. López
1
1
Instituto de Ciencia de Materiales de Madrid (CSIC) and Unidad Asociada CSIC-UVigo, Cantoblanco 28049 Madrid, Spain
2
European Laboratory for Nonlinear Spectroscopy & INFM-BEC, 50019 Sesto Fiorentino (Florence), Italy
3
Departamento de Fisica de Materiales, Universidad Autonoma de Madrid, Cantoblanco 28049 Madrid, Spain
Received 8 April 2008; published 13 August 2008
We present an optical characterization of photonic glasses, composed of randomly arranged, monodisperse
dielectric spheres packed at high filling fractions. We provide a detailed optical study of the resonant behavior
of diffuse light transport through such systems. By means of independent static and dynamic measurements, we
show resonances in the transport mean free path, diffusion constant, and also energy velocity of light. We also
show that the main transport parameters can be controlled by varying the sphere diameter.
DOI: 10.1103/PhysRevA.78.023823 PACS numbers: 42.25.Dd, 42.25.Bs
I. INTRODUCTION
The control of light transport is crucial to design and tai-
lor new photonic devices with increased optical performance
in the same manner as controlling electron transport is at the
basis of semiconductor and electronic technology. In recent
years, a new frontier has emerged, with the goal of control-
ling light propagation through interference in artificially en-
gineered optical materials and metamaterials. Extraordinary
progress has been made in the fabrication of nanophotonic
structures, with many novel optical properties 1. While or-
dered periodic photonic media, i.e., photonic crystals, take
advantage of the periodicity in the dielectric constant and the
consequent long-range correlation to mold the flow of light
2,3, disordered ones, with no positional order, can still
strongly affect light transport 1,4 –6 and, for example, in
the presence of short-range correlation, exhibit band-gap-like
effects 7. Conventional nonabsorbing materials are homo-
geneous and nondispersive, i.e., they are clear and transpar-
ent, and phase and energy travel with the same velocity. Op-
tical propagation is then determined by the shape of the
interfaces between various such materials e.g., a curve sur-
face boundary acts as a lens. If the material is absorptive,
dispersion is introduced brought about by the Kramers-
Kronig relations whereby the phase velocity loses most of
its usefulness, and group velocity at which pulses travel
takes over to describe the transport of energy. In contrast,
nonabsorbing but nanostructured materials can create a new
class of systems in which the dispersion is controlled via
light interference. Photonic band-gap materials, for instance,
are systems where extinction is built up from multiple inter-
ference Bragg reflection creating a region of extinction and
anomalous dispersion. In this way, the relevant velocities can
be engineered, for instance, to create devices for dispersion
compensation. An entirely new scenario is presented when
disorder is added to the mixture.
Usually, disordered media are opaque and white, i.e., non-
dispersive. In such a disordered medium, the group velocity
can only be associated with the ballistic or unscattered
component, and therefore cannot be applied to describe the
transport of energy, which, for large enough optical thick-
nesses, is governed by the scattered light.
When this regime of diffusive propagation is set up, not
only phase but also group velocity fail to give an account of
light transport, and a new quantity describing the transport of
energy in the new diffusive regime is required. The velocity
of the scattered light propagation inside disordered media
needs to be defined by the velocity of the transported energy
and is given by the ratio of the energy flux to the energy
density in any point of the sample. This, in general, is very
complex and given neither by the group velocity nor the
phase velocity 8,9. The energy velocity can be drastically
altered reduced in the presence of scattering resonances: in
an extreme case of light diffusion in a cold atomic cloud, the
atomic energy spectrum can be so resonant to the incident
light that the energy velocity can be as low as a few thousand
meters per second v
e
/ c 10
-5
10.
Disordered materials are composed basically by oxides or
semiconductor powders 11,12, random solid distributions
of polydisperse spheres 13,14, nanostructured semiconduc-
tors such as porous GaP 15, or by colloidal suspensions of
polymer spheres 7. In ordinary disordered materials, like a
semiconductor powder, the individual modes of each build-
ing block are usually neglected and a homogeneous distribu-
tion of light, in wave vector and frequency, is assumed 1. In
contrast, a single dielectric sphere with size comparable to
the wavelength of light can sustain electromagnetic reso-
nances, called Mie modes 16. Figure 1 shows two different
modes in a dielectric sphere at two different energies 17.
These resonant electromagnetic modes in dielectric spheres
are analogous to electronic orbitals in atoms 18. In this
work, we present a detailed characterization of the resonant
behavior of light transport through a resonant random mate-
rial we recently proposed and dubbed “photonic glass” PG
19,20. The main property of this new system compared
with other commonly used disordered materials is the mono-
dispersity of its constituents Fig. 2. We discuss the proper-
ties of light diffusion through such a system and present the
optical characterization by means of static and dynamic mea-
surements. With an optical characterization of the system, we
also point out that light transport can be controlled by chang-
*
Author to whom correspondence should be addressed.
dgarcia@icmm.csic.es
PHYSICAL REVIEW A 78, 023823 2008
1050-2947/2008/782/02382311 ©2008 The American Physical Society 023823-1