Abstract

The theory of three wave mixing was formulated in a classic paper by Armstrong, Bloembergen, Ducuing, and Pershan over 25 years ago.¹ A theoretical description of three wave mixing for multimode time-dependent input fields (as opposed to cw single frequency time independent input fields) has recently been presented.² Analytic solutions were developed for die time-dependent intensities of the output fields. These solutions differ dramatically from those for single-mode fields. New frequencies in the sum-frequency output spectrum and in the input-field output spectrum are created and grow in magnitude as the input intensities are increased. The output spectrum broadens under conditions of strong nonlinear coupling, ultimately reaching the phasematched bandwidth limit. Here, we review the results presented in Ref. 2 for sum frequency generation (SFG) and explicidy compare these results with those for second harmonic generation (SHG). We show that SHG cannot be described as a limit of the SFG formalism for multimode fields. The SFG formulation for the interaction of photons close to frequency ω₁ with photons close to frequency ω₂ producing photons close to frequency ω ₃= ω ₁+ ω ₂ does not allow ω₁(ω₂) photons to interact with each other to produce photons close to frequency 2ω₁(2ω₂). This self interaction is crucial for SHG and must be incorporated. Therefore, a separate formulation is used to describe SHG with multimode input fields.

© 1991 Optical Society of America