The propagation of electromagnetic fields through inhomogeneous media is an essential requirement in the modeling and design of optoelectronic devices. In the most general case, this requires the application of finite-difference techniques in frequency or time domain, or other rigorous solutions of Maxwell’s equations, which often results in too high a numerical effort for practical applications. However, if the inhomogeneity is represented by a smoothly varying refractive index, e.g. in a GRIN lens, fiber, or acousto-optic modulator, the propagation of the electromagnetic fields can be modeled by fast algorithms. They are based on recent major achievements in fast physical optics and make use of the identification of the diffractive and geometric zones of electromagnetic fields. Dependent on the situation, this can enable vectorial propagation through graded-index media in seconds, including even the crosstalk between polarization directions. The theory and the resulting algorithms include established beam propagation techniques as special cases, e.g. the popular paraxial split-step technique.
Frank Wyrowski, Huiying Zhong, Site Zhang, Rui Shi, and Christian Hellmann, "Fast propagation of electromagnetic fields through graded-index media (Conference Presentation)," Proc. SPIE 10526, Physics and Simulation of Optoelectronic Devices XXVI, 105260T (Presented at SPIE OPTO: January 30, 2018; Published: 14 March 2018); https://doi.org/10.1117/12.2290779.5751406848001.
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