45 research outputs found
Open geometry Fourier modal method: Modeling nanophotonic structures in infinite domains
We present an open geometry Fourier modal method based on a new combination
of open boundary conditions and an efficient -space discretization. The open
boundary of the computational domain is obtained using basis functions that
expand the whole space, and the integrals subsequently appearing due to the
continuous nature of the radiation modes are handled using a discretization
based on non-uniform sampling of the -space. We apply the method to a
variety of photonic structures and demonstrate that our method leads to
significantly improved convergence with respect to the number of degrees of
freedom, which may pave the way for more accurate and efficient modeling of
open nanophotonic structures
Calculation, normalization and perturbation of quasinormal modes in coupled cavity-waveguide systems
We show how one can use a non-local boundary condition, which is compatible
with standard frequency domain methods, for numerical calculation of
quasinormal modes in optical cavities coupled to waveguides. In addition, we
extend the definition of the quasinormal mode norm by use of the theory of
divergent series to provide a framework for modeling of optical phenomena in
such coupled cavity-waveguide systems. As an example, we apply the framework to
study perturbative changes in the resonance frequency and Q value of a photonic
crystal cavity coupled to a defect waveguide.Comment: 4 pages, 3 figure
Impact of slow-light enhancement on optical propagation in active semiconductor photonic crystal waveguides
We derive and validate a set of coupled Bloch wave equations for analyzing
the reflection and transmission properties of active semiconductor photonic
crystal waveguides. In such devices, slow-light propagation can be used to
enhance the material gain per unit length, enabling, for example, the
realization of short optical amplifiers compatible with photonic integration.
The coupled wave analysis is compared to numerical approaches based on the
Fourier modal method and a frequency domain finite element technique. The
presence of material gain leads to the build-up of a backscattered field, which
is interpreted as distributed feedback effects or reflection at passive-active
interfaces, depending on the approach taken. For very large material gain
values, the band structure of the waveguide is perturbed, and deviations from
the simple coupled Bloch wave model are found.Comment: 8 pages, 5 figure
Modeling open nanophotonic systems using the Fourier modal method: Generalization to 3D Cartesian coordinates
Recently, an open geometry Fourier modal method based on a new combination of
an open boundary condition and a non-uniform -space discretization was
introduced for rotationally symmetric structures providing a more efficient
approach for modeling nanowires and micropillar cavities [J. Opt. Soc. Am. A
33, 1298 (2016)]. Here, we generalize the approach to three-dimensional (3D)
Cartesian coordinates allowing for the modeling of rectangular geometries in
open space. The open boundary condition is a consequence of having an infinite
computational domain described using basis functions that expand the whole
space. The strength of the method lies in discretizing the Fourier integrals
using a non-uniform circular "dartboard" sampling of the Fourier space. We
show that our sampling technique leads to a more accurate description of the
continuum of the radiation modes that leak out from the structure. We also
compare our approach to conventional discretization with direct and inverse
factorization rules commonly used in established Fourier modal methods. We
apply our method to a variety of optical waveguide structures and demonstrate
that the method leads to a significantly improved convergence enabling more
accurate and efficient modeling of open 3D nanophotonic structures
Three-dimensional integral equation approach to light scattering, extinction cross sections, local density of states, and quasi-normal modes
We present a numerical formalism for solving the Lippmann-Schwinger equation
for the electric field in three dimensions. The formalism may be applied to
scatterers of different shapes and embedded in different background media, and
we develop it in detail for the specific case of spherical scatterers in a
homogeneous background medium. In addition, we show how several physically
important quantities may readily be calculated with the formalism. These
quantities include the extinction cross section, the total Green's tensor, the
projected local density of states and the Purcell factor as well as the
quasinormal modes of leaky resonators with the associated resonance frequencies
and quality factors. We demonstrate the calculations for the well-known
plasmonic dimer consisting of two silver nanoparticles and thus illustrate the
versatility of the formalism for use in modeling of advanced nanophotonic
devices.Comment: 14 pages, 10 figures. Accepted for JOSA
On the theory of coupled modes in optical cavity-waveguide structures
Light propagation in systems of optical cavities coupled to waveguides can be
conveniently described by a general rate equation model known as (temporal)
coupled mode theory (CMT). We present an alternative derivation of the CMT for
optical cavity-waveguide structures, which explicitly relies on the treatment
of the cavity modes as quasinormal modes with properties that are distinctly
different from those of the modes in the waveguides. The two families of modes
are coupled via the field equivalence principle to provide a physically
appealing yet surprisingly accurate description of light propagation in the
coupled systems. Practical application of the theory is illustrated using
example calculations in one and two dimensions.Comment: 14 pages, 9 figure
Modeling open nanophotonic systems using the Fourier modal method: Generalization to 3D Cartesian coordinates
Recently, an open geometry Fourier modal method based on a new combination of
an open boundary condition and a non-uniform -space discretization was
introduced for rotationally symmetric structures providing a more efficient
approach for modeling nanowires and micropillar cavities [J. Opt. Soc. Am. A
33, 1298 (2016)]. Here, we generalize the approach to three-dimensional (3D)
Cartesian coordinates allowing for the modeling of rectangular geometries in
open space. The open boundary condition is a consequence of having an infinite
computational domain described using basis functions that expand the whole
space. The strength of the method lies in discretizing the Fourier integrals
using a non-uniform circular "dartboard" sampling of the Fourier space. We
show that our sampling technique leads to a more accurate description of the
continuum of the radiation modes that leak out from the structure. We also
compare our approach to conventional discretization with direct and inverse
factorization rules commonly used in established Fourier modal methods. We
apply our method to a variety of optical waveguide structures and demonstrate
that the method leads to a significantly improved convergence enabling more
accurate and efficient modeling of open 3D nanophotonic structures