Eigenmodes of a lamellar optical grating: Profile, propagation, reflection, transmission, and nonadiabatic mode coupling

We present the explicit analytic formulas for the electromagnetic (optical) eigenmodes propagating in a lamellar grating. Then, we analytically calculate a mutual transformation of the wave's spatial harmonics due to diffraction in the course of propagation through the grating as well as the matrices of the eigenmode reflectance and transmittance at the grating boundaries. Finally, we develop a theory of the nonadiabatic transformation of the eigenmodes in the inhomogeneous gratings. It allows one to disclose the effects which go beyond the geometrical optics of eigenmodes. We show that in a transition layer of a thick nonlamellar grating such effects occur due to mode coupling of just a few lower-band eigenmodes. This approach allows one to find the overall optical response of the nonlamellar gratings fully and efficiently. The results are given for both transverse electric and transverse magnetic polarizations, as well as for any absorptive permittivity.