Simple Analytical Solution of Čerenkov-Type Terahertz Wave Generation via Difference Frequency Generation in Dielectric Waveguides

We newly analyze the Čerenkov-type terahertz wave generation via the optical difference frequency generation in nonlinear dielectric waveguides based on the coupled-mode theory. The nonlinear coupled equations are derived, and the simple analytical solution for the terahertz wave is obtained in a closed form. The validity of our solution is also checked by the nonlinear beam propagation method. The analytical solution shows that for planar waveguides, the coupling coefficient has pole singularities at the propagation constants of the leaky modes at the terahertz frequency of the waveguides, and thus, the terahertz wave generation can be significantly enhanced as the phase-matching point approaches to the propagation constant of the lowest order leaky mode, whose imaginary part is very small compared to the real part of that.