Theory of the propagation of coupled waves in arbitrarily-inhomogeneous stratified media

Abstract

We generalize the invariant imbedding theory of the wave propagation and derive new invariant imbedding equations for the propagation of arbitrary number of coupled waves of any kind in arbitrarily-inhomogeneous stratified media, where the wave equations are effectively one-dimensional. By doing this, we transform the original boundary value problem of coupled second-order differential equations to an initial value problem of coupled first-order differential equations, which makes the numerical solution of the coupled wave equations much easier. Using the invariant imbedding equations, we are able to calculate the matrix reflection and transmission coefficients and the wave amplitudes inside the inhomogeneous media exactly and efficiently. We establish the validity and the usefulness of our results by applying them to the propagation of circularly-polarized electromagnetic waves in one-dimensional photonic crystals made of isotropic chiral media. We find that there are three kinds of bandgaps in these structures and clarify the nature of these bandgaps by exact calculations.

arXiv comment7 pages, 1 figure, to appear in Europhys. Lett

References in corpus (4)

• Twist Defect in Chiral Photonic Structures
• Reflection coefficient and localization length of waves in one-dimensional random media
• Relation between Anderson- and Invariant Imbedding Models for Transport in Finite Chains and Study of Phase- and Delay Time Distributions for Strong Disorder
• Localization in a random phase-conjugating medium

Cited by in corpus (15)

• Invariant imbedding theory of mode conversion in inhomogeneous plasmas: I. Exact calculation of the mode conversion coefficient in cold, unmagnetized plasmas
• Invariant imbedding theory of mode conversion in inhomogeneous plasmas. II. Mode conversion in cold, magnetized plasmas with perpendicular inhomogeneity
• Anderson localization of two-dimensional massless pseudospin-1 Dirac particles in a correlated random one-dimensional scalar potential
• Invariant imbedding theory of wave propagation in arbitrarily inhomogeneous stratified bi-isotropic media
• Resonant absorption and amplification of circularly-polarized waves in inhomogeneous chiral media
• Spectral and polarization effects in deterministically nonperiodic multilayers containing optically anisotropic and gyrotropic materials
• Omnidirectional excitation of surface waves and super-Klein tunneling at the interface between two different bi-isotropic media
• Giant enhancement of reflectance due to the interplay between surface confined wave modes and nonlinear gain in dielectric media
• Transmission, reflection and localization in a random medium with absorption or gain
• Exact localization length for s-polarized electromagnetic waves incident at the critical angle on a randomly-stratified dielectric medium
• Broadband wide-angle absorption enhancement due to mode conversion in cold unmagnetized plasmas with periodic density variations
• Mode conversion and resonant absorption in inhomogeneous materials with flat bands
• Resonant absorption of electromagnetic waves in transition anisotropic media
• Scaling behavior of the localization length for TE waves at critical incidence on short-range correlated stratified random media
• Direct calculation of the strong Goos-Hänchen effect of a Gaussian light beam due to the excitation of surface plasmon polaritons in the Otto configuration