Sequences of Exact Analytical Solutions for Plane-Waves in Graded Media
arXiv:1704.08929 · doi:10.1080/09500340.2017.1330975
Abstract
We present a new method for building sequences of solvable profiles of the electromagnetic (EM) admittance in lossless isotropic materials with 1D graded permittivity and permeability (in particular profiles of the optical refractive-index). These solvable profiles lead to analytical closed-form expressions of the EM fields, for both TE and TM modes. The Property-and-Field Darboux Transformations method, initially developed for heat diffusion modelling, is here transposed to the Maxwell equations in the optical-depth space. Several examples are provided, all stemming from a constant seed-potential, which makes them based on elementary functions only. Solvable profiles of increasingly complex shape can be obtained by iterating the process or by assembling highly flexible canonical profiles. Their implementation for modelling optical devices like matching layers, rugate filters, Bragg gratings, chirped mirrors or 1D photonic crystals, offers an exact and cost-effective alternative to the classical approaches
74 pages, 20 figures, Corrected typos in Annex D
References in corpus (6)
- SUSY-inspired one-dimensional transformation optics
- Analytical solution for wave propagation through a graded index interface between a right-handed and a left-handed material
- On integral and differential representations of Jordan chains and the confluent supersymmetry algorithm
- Supersymmetric Bragg gratings
- Theory of chirped photonic crystals in biological broadband reflectors
- Quantum mechanical analogy and supersymmetry of electromagnetic wave modes in planar waveguides
Cited by in corpus (3)
- Analytical Modeling of Acoustic Exponential Materials and Physical Mechanism of Broadband Anti-Reflection
- The Sech(Xi)-type profiles: a Swiss-Army knife for exact analytical modelling of thermal diffusion and wave propagation in graded media
- Multipurpose S-shaped solvable profiles of the refractive index: application to modeling of antireflection layers and quasi-crystals