We propose the method of effective parameters retrieval based on the Bloch mode analysis of periodic metamaterials.
We perform the surface and volume averaging of the electromagnetic field of the dominating (fundamental) Bloch mode
to determine the Bloch and wave impedances, respectively. We show that our method is able to retrieve both material
and wave EPs for a wide range of materials, which can be lossy or lossless, dispersive, possess negative permittivity,
permeability and refractive index values. It is simple and unambiguous, free of the "branch" problem, which is an issue
for the reflection/transmission based method and has no limitations on a metamaterial slab thickness. The method does
not require averaging different fields' components at various surfaces or contours. The retrieval of both wave and
material EPs is performed within a single computational cycle, after exporting fields on the unit cells facets or in its
volumes directly from Maxwell's equations solver.
In this work, we demonstrate that the compound mode properties of coupled photonic-crystal cavities can depend
critically on the interplay of distance between cavities and their longitudinal shifts. Thus the robust control over the
cavity modes can be imposed. The simple coupled-mode theory employed for such systems predicts a peculiar behavior
of band dispersion in the slow light regime at the photonic band-edge. In particular, it reveals an interesting effect that
the frequency detuning of the fundamental supermodes in the coupled cavities can be reduced down to zero. We
anticipate that this property will be generic for side-coupled cavity systems irrespectively of the individual cavity design,
e.g. point-defect cavities in a photonic crystal or linear cavities in one-dimensional arrays of elements (rods or holes).
We report here about the finite-difference frequency-domain method (FDFD) developed by us to analyze nanocavities
with a very high <i>Q</i>-factor. The method is utilized to confirm by simulations the coupled-mode theory predictions. As an
example we choose coupled cavities in one-dimensional periodic arrays of holes in dielectric nanowires known also as
We demonstrate, theoretically and experimentally, that the modes of coupled cavities created in periodic waveguides
can depend critically on the lateral shift between the cavities. In the absence of such shift, the modes
feature symmetric or antisymmetric profiles, and their frequency splitting generally increases as the cavities are
brought closer. We show that the longitudinal shift enables flexible control over the fundamental modes, which
frequency detuning can be reduced down to zero. Our coupled-mode theory analysis reveals an intrinsic link
between the mode tuning and the transformation of slow-light dispersion at the photonic band-edge. We illustrate
our approach through direct numerical modelling of cavities created in arrays of dielectric rods, nanobeam
structures, and two-dimensional photonic-crystal waveguides. We also present experimental results for coupled
rod cavities confirming our predictions.
We reveal that the reduction of the group velocity of light in periodic waveguides is generically associated with
the presence of vortex energy flows. We show that the energy flows are gradually frozen for slow-light at the
Brillouin zone edge, whereas vortices persist for slow-light states having non-vanishing phase velocity inside the
Brillouin zone. We also demonstrate that presence of vortices can be linked to the absence of slow-light at the
zone edge, and present calculations illustrating these general results.
We propose a general approach to the design of directional couplers in photonic-crystals operating in the slowlight
regime. We predict, based on a general symmetry analysis, that robust switching of slow-light pulses is
possible between antisymmetrically coupled photonic crystal waveguides. We demonstrate, through numerical
Bloch mode frequency-domain and finite-difference time-domain (FDTD) simulations that, for all pulses with
strongly reduced group velocities at the photonic band-gap edge, complete switching occurs at a fixed coupling
length of just a few unit cells of the photonic crystal.