Journal
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
Volume 124, Issue 5, Pages 1035-1054Publisher
WILEY
DOI: 10.1002/nme.7144
Keywords
discrete differential forms; discrete exterior calculus; finite difference time domain method; photonic band gap; photonic crystal waveguide
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Discrete exterior calculus is a promising discretization method for photonic crystal waveguides, offering efficient handling of nonhomogeneous computational domains and curved surfaces. In this study, we present a two-dimensional discretization method for photonic crystal waveguides using discrete exterior calculus and demonstrate its advantages through numerical experiments.
The discrete exterior calculus (DEC) is very promising, though not yet widely used, discretization method for photonic crystal (PC) waveguides. It can be seen as a generalization of the finite difference time domain (FDTD) method. The DEC enables efficient time evolution by construction and fits well for nonhomogeneous computational domains and obstacles of curved surfaces. These properties are typically present in applications of PC waveguides that are constructed as periodic structures of inhomogeneities in a computational domain. We present a two-dimensional DEC discretization for PC waveguides and demonstrate it with a selection of numerical experiments typical in the application area. We also make a numerical comparison of the method with the FDTD method that is a mainstream method for simulating PC structures. Numerical results demonstrate the advantages of the DEC method.
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