88 research outputs found
JCMmode: An Adaptive Finite Element Solver for the Computation of Leaky Modes
We present our simulation tool JCMmode for calculating propagating modes of
an optical waveguide. As ansatz functions we use higher order, vectorial
elements (Nedelec elements, edge elements). Further we construct transparent
boundary conditions to deal with leaky modes even for problems with
inhomogeneous exterior domains as for integrated hollow core Arrow waveguides.
We have implemented an error estimator which steers the adaptive mesh
refinement. This allows the precise computation of singularities near the
metal's corner of a Plasmon-Polariton waveguide even for irregular shaped metal
films on a standard personal computer.Comment: 11 page
Efficient resonance computations for Helmholtz problems based on a Dirichlet-to-Neumann map
We present an efficient procedure for computing resonances and resonant modes
of Helmholtz problems posed in exterior domains. The problem is formulated as a
nonlinear eigenvalue problem (NEP), where the nonlinearity arises from the use
of a Dirichlet-to-Neumann map, which accounts for modeling unbounded domains.
We consider a variational formulation and show that the spectrum consists of
isolated eigenvalues of finite multiplicity that only can accumulate at
infinity. The proposed method is based on a high order finite element
discretization combined with a specialization of the Tensor Infinite Arnoldi
method. Using Toeplitz matrices, we show how to specialize this method to our
specific structure. In particular we introduce a pole cancellation technique in
order to increase the radius of convergence for computation of eigenvalues that
lie close to the poles of the matrix-valued function. The solution scheme can
be applied to multiple resonators with a varying refractive index that is not
necessarily piecewise constant. We present two test cases to show stability,
performance and numerical accuracy of the method. In particular the use of a
high order finite element discretization together with TIAR results in an
efficient and reliable method to compute resonances
Elastic Wave Eigenmode Solver for Acoustic Waveguides
A numerical solver for the elastic wave eigenmodes in acoustic waveguides of
inhomogeneous cross-section is presented. Operating under the assumptions of
linear, isotropic materials, it utilizes a finite-difference method on a
staggered grid to solve for the acoustic eigenmodes of the vector-field elastic
wave equation. Free, fixed, symmetry, and anti-symmetry boundary conditions are
implemented, enabling efficient simulation of acoustic structures with
geometrical symmetries and terminations. Perfectly matched layers are also
implemented, allowing for the simulation of radiative (leaky) modes. The method
is analogous to eigenmode solvers ubiquitously employed in electromagnetics to
find waveguide modes, and enables design of acoustic waveguides as well as
seamless integration with electromagnetic solvers for optomechanical device
design. The accuracy of the solver is demonstrated by calculating
eigenfrequencies and mode shapes for common acoustic modes in several simple
geometries and comparing the results to analytical solutions where available or
to numerical solvers based on more computationally expensive methods
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