Computation of optical modes inside axisymmetric open cavity resonators (original) (raw)
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Computation of optical modes in axisymmetric open cavity resonators
Future Generation Computer Systems, 2005
The computation of optical modes inside axisymmetric cavity resonators with a general spatial permittivity profile is a formidable computational task. In order to avoid spurious modes the vector Helmholtz equations are discretised by a mixed finite element approach. We formulate the method for first and second order Nédélec edge and Lagrange nodal elements. We discuss how to accurately compute the element matrices and solve the resulting large sparse complex symmetric eigenvalue problems. We validate our approach by three numerical examples that contain varying material parameters and absorbing boundary conditions (ABC).
IEEE Transcations on Microwave Theory and Techniques, 2020
This article mainly investigates the classic resonant cavity problem with anisotropic and nonconductive media, which is a linear vector Maxwell's eigenvalue problem. The finite-element method based on edge element of the lowest order and standard linear element is used to solve this type of 3-D closed cavity problem. In order to eliminate spurious zero modes in the numerical simulation, the divergence-free condition supported by Gauss' law is enforced in a weak sense. After the finite-element discretization, the generalized eigenvalue problem with a linear constraint condition needs to be solved. The penalty method, augmented method, and projection method are applied to solve this difficult problem in numerical linear algebra. The advantages and disadvantages of these three computational methods are also given in this article. Furthermore, we prove that the augmented method is free of spurious modes as long as the anisotropic material is not magnetic lossy. The projection method based on singular value decomposition technique can be used to solve the resonant cavity problem. Moreover, the projection method cannot introduce any spurious modes. At last, several numerical experiments are carried out to verify our theoretical results.
Journal of Nonlinear Optical Physics & Materials, 2004
A Galerkin finite element scheme furnished with 1st-order Bayliss–Gunzburger–Turkel-like boundary conditions is formulated to compute both the guided and leaky modes of anisotropic channel waveguides of non-magnetic materials with diagonal permittivity tensor. The scheme is formulated using transverse components of magnetic fields for nodal-based quadratic triangular elements. Results for some structures will be presented. The effectiveness of the boundary conditions will be illustrated using a step-index optical fiber with computational boundaries positioned near to the core, and the leaky modes computation of a leaky rib structure. In addition, a leaky mode solving of a six-hole "photonic crystal fiber" will be demonstrated. The computed results agree with their exact values (for optical fibers) and published results (for other structures).
Analysis of light propagation in slotted resonator based systems via coupled-mode theory
Optics Express, 2011
Optical devices with a slot configuration offer the distinct feature of strong electric field confinement in a low refractive index region and are, therefore, of considerable interest in many applications. In this work we investigate light propagation in a waveguide-resonator system where the resonators consist of slotted ring cavities. Owing to the presence of curved material interfaces and the vastly different length scales associated with the sub-wavelength sized slots and the waveguide-resonator coupling regions on the one hand, and the spatial extent of the ring on the other hand, this prototypical system provides significant challenges to both direct numerical solvers and semi-analytical approaches. We address these difficulties by modeling the slot resonators via a frequency-domain spatial Coupled-Mode Theory (CMT) approach, and compare its results with a Discontinuous Galerkin Time-Domain (DGTD) solver that is equipped with curvilinear finite elements. In particular, the CMT model is built on the underlying physical properties of the slotted resonators, and turns out to be quite efficient for analyzing the device characteristics. We also discuss the advantages and limitations of the CMT approach by comparing the results with the numerically exact solutions obtained by the DGTD solver. Besides providing considerable physical insight, the CMT model thus forms a convenient basis for the efficient analysis of more complex systems with slotted resonators such as entire arrays of waveguide-coupled resonators and systems with strongly nonlinear optical properties.
Finite-element analysis of arbitrarily shaped cavity resonators using H/sup 1/(curl) elements
IEEE Transactions on Magnetics, 1997
In this paper, we propose a finite element method together with a constraint Lanczos algorithm for analysing arbitrarily-shaped microwave cavities. The proposed methodology is based on the use of (curl) tangential vector finite elements. Moreover, in order to solve for the generalized eigenmatrix equation efficiently, we have also developed a constrained Lanczos algorithm. Specifically, in the constrained Lanczos algorithm, we orthogonalize each new Krylov vector with respect to the spurious DC modes. Consequently, the iterative process can be used to solve for the physical resonant modes, including physical static fields, without the occurrences of any spurious DC modes.
Three-dimensional computation of laser cavity eigenmodes by the use of finite element analysis (FEA)
SPIE Proceedings, 2004
A new method for computing eigenmodes of a laser resonator by the use of finite element analysis (FEA) is presented. For this purpose, the scalar wave equation ∆ + k 2 Ẽ (x, y, z) = 0 is transformed into a solvable 3D eigenvalue problem by separating out the propagation factor exp(−ikz) from the phasor amplitudeẼ(x, y, z) of the time-harmonic electrical field. For standing wave resonators, the beam inside the cavity is represented by a two-wave ansatz. For cavities with parabolic optical elements the new approach has successfully been verified by the use of the gaussian mode algorithm. For a DPSSL with a thermally lensing crystal inside the cavity the expected deviation between gaussian approximation and numerical solution could be demonstrated clearly.
Higher Order Finite Element Method for Inhomogeneous Axisymmetric Resonators
Progress In Electromagnetics Research B, 2010
To analyze resonances in an axisymmetric inhomogeneous cavity, a higher-order finite element method (FEM) is developed. Mixed higher-order node-based and edge-based elements are applied to eigenvalue analysis for the azimuthal component and meridian components of the field, respectively. Compared with the lower-order FEM, the higher-order FEM can improve accuracy with the same number of unknowns and can reduce the CPU time and memory requirement for specified accuracy. Numerical results are given to demonstrate the validity and efficiency of the proposed method.
Third-Dimensional Finite Element Computation of Laser Cavity Eigenmodes
Applied Optics, 2004
A new method for computing eigenmodes of a laser resonator by the use of finite element analysis is presented. For this purpose, the scalar wave equation (Delta + k2)E~(x, y, z) = 0 is transformed into a solvable three-dimensional eigenvalue problem by the separation of the propagation factor exp(-ikz) from the phasor amplitude E~(x, y, z) of the time-harmonic electrical