Analytical solution of non-homogeneous anisotropic wave equations based on differential transfer matrices

We present a new analytical method for solution of non-homogeneous anisotropic optical systems, based on the extension of transfer matrices into differential form. This approach can be used for exact calculation of various functions including reflection and transmission coefficients, band structures and bound states. We discuss improvements of the method for infinite periodic structures and bounded modes. Then simplifications of the approach are considered for the TE and TM polarized isotropic structures, pseudo-isotropic and uniaxial non-magnetic media. Moreover a general variational representation of bound states is introduced. As application examples, we consider the reflection from inhomogeneous structures, the band structure of infinite periodic media and bounded modes in inhomogeneous anisotropic waveguides. Excellent agreement between the results from our differential transfer matrix method and other methods is observed where comparison is possible.