Nonlinear frequency conversion in waveguide directional couplers

Nonlinear optical effects for frequency conversion require a phase-matching condition to efficiently generate a coherent field at the new wavelength. We find that the phase-matching condition can be replaced by a resonance condition when the nonlinear effect takes place in a waveguide directional coupler. We apply this theory to second-harmonic generation and find a theoretical conversion efficiency of 100%, equivalent to the perfect phase-matching condition. An example of the design of such waveguide directional coupler is presented.