Propagation of waves in a medium varying transverse to the direction of propagation

For an inhomogeneous dielectric in which the dielectric constant ε depends onxonly, it has been shown that it is possible to consider modes propagating in thezdirection havingHₓ = 0orEₓ = 0such that other field components can be expressed in terms of Exand Hx. The usual TE and TM modes are obtained in the special case of noydependence of the fields. Explicit field patterns and the propagation constants have been obtained for a square-law medium.