On- and off-resonance second-harmonic generation in GaAs microdisks

We present a theoretical description of on- and off-resonance, 4¯-quasi-phasematched, second-harmonic generation (SHG) in microdisks made of GaAs or other materials possessing 4¯ symmetry, such as GaP or ZnSe. The theory describes the interplay between quasi-phasematching (QPM) and the cavity-resonance conditions. For optimal conversion, all waves should be resonant with the microdisk and should satisfy the 4¯-QPM condition. We explore χ(2) nonlinear mixing if one of the waves is not resonant with the microdisk cavity and calculate the second-harmonic conversion spectrum. We also describe perfectly destructive 4¯-QPM where both the fundamental and second-harmonic are on-resonance with the cavity but SHG is suppressed.