Optical Waveguide Theory by the Finite Element Method

Abstract

SUMMARY Recent progress in research on the finite element method (FEM) for optical waveguide design and analysis is reviewed, focusing on the author's works. After briefly reviewing fundamentals of FEM such as a theoretical framework, a conventional nodal element, a newly developed edge element to eliminate nonphysical, spurious solutions, and a perfectly matched layer to avoid undesirable reflections from computational window edges, various FEM techniques for a guided-mode analysis, a beam propagation analysis, and a waveguide discontinuity analysis are described. Some design examples are introduced, including current research activities on multi-core fibers. key words: finite element method, beam propagation method, spurious solutions, fiber optics, nanophotonics

First shear horizontal mode plate wave in LiNbO<inf>3</inf> showing 20 km/s phase velocity

“…One of the two stopband frequencies at the open-circuit grating electrode is equal to one of the two stopband frequencies at the short-circuit grating. The lower and higher frequencies except for the above-mentioned two frequencies correspond to the resonant ifr) and anti-resonant frequencies ifa), respectively [6] [13]. The relative bandwidth (BW) is defined as BW=lOOxCfa-fr)lfr (%).…”

“…Al-IDT thickness of O.OlA, the metallization ratio (MR) of 0.3, and a LiNb03 plate thickness of O.lA were used in the FEM calculation. Four frequencies at the upper and lower stopband edges at open-and shorted-circuit grating electrodes are calculated by the FEM, respectively[6][13]…”

Galerkin Finite-Element Method for the Analysis of the Second Harmonic Generation in Wagon Wheel Fibers

“…The values of the linear relative permittivity tensor elements could be found from references [11,12]. …”

“…The ordinary and the extraordinary refractive indices [11] for LiTaO 3 at  0 and  0 /2 are n o ( 0 )=2.148, n e ( 0 )=2.152, n e ( 0 /2)=2.253, and n o ( 0 /2)=2.258. The non-zero nonlinear elements of optical tensor [21,22] In Table 2, we list the values of  β 2 -2β 1 for the first four modes.…”

3D pseudospectral time domain for modeling second-harmonic generation in periodically poled lithium niobate ridge-type waveguides

“…Many numerical methods are available for wave propagation modeling. The Finite-Difference Time-Domain method [8] (FDTD), the Split-Step Method [7] (SSM) and the Finite Element Method [6] (FEM) belongs to the time-domain methods while the Beam Propagation Method [9] (BPM), the Transfer Matrix Method (TMM) and the Eigen Mode Expansion method (EME) work in the frequency-domain. Among these numerical techniques, the FDTD (implemented in a large number of both free and commercially available sofware) is the most general and rigorous time-domain method.…”