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Back-reflector design in thin-film silicon solar cells by rigorous 3D light propagation modeling
(2014)
Hp-finite-elements for simulating electromagnetic fields in optical devices with rough textures
(2015)
Finite-element simulations of light propagation through subwavelength apertures in metal films
(2009)
Advanced finite-element methods for design and analysis of nano-optical structures: Applications
(2013)
Finite-element based electromagnetic field simulations: Benchmark results for isolated structures
(2013)
3D Finite-Element Simulations of Enhanced Light Transmission Through Arrays of Holes in Metal Films
(2009)
The paper is motivated by the need for a fast robust adaptive multigrid method to solve complex Helmholtz eigenvalue problems arising from the design of optical chips. A nonlinear multigrid method is developed, which can be regarded as an extension of a previous adaptive Rayleigh quotient minimization method for selfadjoint Helmholtz eigenproblems. Since the complex Helmholtz operator is just a compact nonselfadjoint perturbation of a selfadjoint operator, linear algebra techniques like Schur decomposition can be extended from the finite dimensional case. The efficiency of the derived adaptive nonlinear multigrid method is illustrated by computations for a technologically relevant integrated optics component containing Multi Quantum Well Layers.
{\bf Efficient eigenmode computation for the design of integrated optical chips.}The paper deals with adaptive multigrid methods for 2D Helmholtz eigenvalue problems arising in the design of integrated optical chips. Typical features of the technological problem are its geometric complexity, its multiscale structure, the possible occurrence of eigenvalue clusters, and the necessity of quite stringent required relative error tolerances. For reasons of sheer computational complexity, multigrid methods must be used to solve the discretized eigenvalue problems and adaptive grids must be automatically constructed to avoid an undesirable blow-up of the required number of nodes for these accuracies. In view of the problem specifications, an adaptive multigrid method based on Rayleigh quotient minimization, simultaneous eigenspace iteration, and conjugate gradient method as smoother is carefully selected. Its performance in the numerical simulation of a component of a rather recent optical chip (heterodyne receiver of HHI) is documented.
The paper presents a construction scheme of deriving transparent , i. e. reflection-free, boundary conditions for the numerical solution of Fresnel's equation (being formally equivalent to Schrödinger's equation). These boundary conditions appear to be of a nonlocal Cauchy type. As it turns out, each kind of linear implicit discretization induces its own discrete transparent boundary conditions.
Transparent boundary conditions for a wide-angle approximation of the one-way Helmholtz equation
(2000)
Transparent Boundary Conditions for a Wide-Angle Approximation of the One-Way Helmholtz Equation
(1999)
We present nonlocal discrete transparent boundary conditions for a fourth-order wide-angle approximation of the two-dimensional Helmholtz equation. The boundary conditions are exact in the sense that they supply the same discrete solution on a bounded interior domain as would be obtained by considering the problem on the entire unbounded domain with zero boundary conditions at infinity. The proposed algorithm results in an unconditionally stable propagation method. Numerical examples from optics illustrate the efficiency of our approach.