Eikonal groups of photon and phonon propagators in one-dimensional structures

Abstract

A general tensor eikonal method is proposed for solving wave equations of the optics and acoustics of stratified anisotropic media in the case of non-commutation of the tensor eikonals. Such an approach allows one to operate with electromagnetic and acoustic fields in inhomogeneous anisotropic media without any division of them into partial waves and not referring to a particular coordinate systems. The tensor eikonals which are determined by the polarization of waves are involved in the evolution operators (propagators) and are expressed in terms of the normal refraction tensors. These tensors are non-commutative in the general case and disentangling the evolution operators is necessary, including ones for waves in isotropic media. Such disentangling is performed with the use of known standard operator procedures. An example of the calculation of the photon propagator is given for a stratified medium with the inhomogeneity profile e(z) = a + b/z2.