An optical Fibonacci superlattice has been proposed to produce the second-harmonic generation and the third-harmonic generation, which is the sum frequency of the second-harmonic and the fundamental frequency in the same material. Because of the quasiperiodicity of the optical Fibonacci superlattice, the phase mismatches of the optical parametric processes caused by the frequency dispersion of the refractive index can be compensated with the reciprocal vectors which the optical Fibonacci superlattice provides. A theory which analyzes the second-harmonic generation and the third-harmonic generation processes in the material and the calculations applied to the optical Fibonacci superlattice made from a single ${\mathrm{LiNbO}}_3$ crystal is presented in detail. The calculations show that the efficiencies of the second-harmonic generation and the third-harmonic generation are comparable to, or even larger than, those obtained with commonly used phase-matching methods.

• Received 28 November 1989

DOI:https://doi.org/10.1103/PhysRevB.41.5578