For an inhomogeneous dielectric in which the dielectric constant ε depends on

only, it has been shown that it is possible to consider modes propagating in the

direction having

or

such that other field components can be expressed in terms of E
xand H
x. The usual TE and TM modes are obtained in the special case of no

dependence of the fields. Explicit field patterns and the propagation constants have been obtained for a square-law medium.