On the efficiency of the second harmonic generation in optical waveguides: TM case

In this paper we analyse the second harmonic generation of TM polarisation in a planar waveguide with a non-linear anisotropic substrate using the coupled mode theory under the non-depleted pump approximation. It is an extention of our previous paper in which we treated TE polarisation. Moreover, both guided waves and Čerenkov radiation are now taken into account simultaneously. It is shown both analytically and numerically that the Čerenkov efficiency peak follows the L3/2 dependence on the interaction length L also for TM polarisation. In an anisotropic KTP/Si3N4/SiO2 waveguide, higher maximum attainable second harmonic generation (SHG) efficiency was calculated for the TM polarisation than for the optimum TE case.