SURFACE-ENHANCED 2ND-HARMONIC GENERATION IN NONLINEAR CORRUGATED DIELECTRICS - NEW THEORETICAL APPROACHES

A new rigorous electromagnetic theory is developed for studying the se cond-harmonic generation process that occurs when a high-power laser b eam falls on a periodically corrugated waveguide. The waveguide can co nsist of several layers with corrugated or plane boundaries, with at l east one of the layers being filled with a nonlinear lossless or lossy dielectric. The theory uses a nonorthogonal coordinate transformation , which maps the corrugated interfaces onto planes. The Maxwell equati ons written in covariant form lead to a set of first-order partial dif ferential equations with nonconstant coefficients. Taking into account the periodicity of the system, this set of equations could be transfo rmed into a set of ordinary differential equations with constant coeff icients, which can be resolved by an eigenvalue-eigenvector technique, avoiding numerical integration. The theory is developed for both TE a nd TM polarizations and for any groove geometry and incidence; it can be used, in particular, when surface waves (guided modes or surface pl asmon-polaritons) are excited. It is a powerful tool for studying the enhancement of the second-harmonic generation resulting from local fie ld enhancement by electromagnetic resonances. In addition an approach based on the Rayleigh hypothesis is developed. Both theoretical approa ches are compared with previously developed differential theory for gr atings in nonlinear optics. A spectacular agreement is obtained betwee n the three theories for both TE and TM polarization. The new method i s free of limitations concerning the waveguide thickness, the groove d epth, and the conductivity of the grating material. It is demonstrated that the limitations of the Rayleigh hypothesis are stronger at the s econd-harmonic frequency.