The couple between modes of planar wave guides and the evanescent fields produced in the total internal reflection.

The coupling between the modes of planar wave guides and the evanescent fields produced in the total internal reflection (TIR) system is studied theoretically. The planar guides are assumed as a semi-infinite inhomogeneous periodic medium (IM) with modulation only in the $y$-direction and period $a$, which is perpendicular to the propagation ($z$-axis) of the modes. This medium is separated by a vacuum (VA) gap, of uniform thickness $d_{2}$, from a semi-infinite homogeneous dielectric medium (HM). Then, two interfaces are found, one at z = 0 between HM/VA and other at $z=d_{2}$ between VA/IM. A transverse magnetic electromagnetic plane wave with wavelength \textit{$\lambda $}$_{0}$, is impinging the VA/IM interface and its wave vector, in the $z-y$ plane, is doing an angle \textit{$\theta $}$_{i}$ with the $z$-axes. The solution of the electromagnetic diffracted field in the IM is a multimodal expansion as proposed by Burckhardt [J. Opt. Soc. Am. \textbf{56 }(1966) pp. 1502]. Following the approach used by Glass and Maradudin [Phys. Rev. B \textbf{29} (1984) pp. 321] a matrix equation for the amplitudes of the diffracted field is found. Numerical results of the near field intensity are presented.