Efficient upconversion by a frequency factor between two and three using an optical parametric oscillator

We present the theory of a scheme for frequency up-conversion from pump frequency ω_p to a desired frequency ω_d between 2ω_p and 3ω_p. The proposed device consists of three nonlinear crystals in series inside a cavity resonating light at a signal frequency ωs. Sum-frequency generation (SFG) in the first crystal produces the desired radiation, ω_s+ω_p=ω_d. Second-harmonic generation (SHG) in the second crystal doubles the frequency of the residual pump, 2ω_p=ω_h, while the signal passes through unaffected. Optical parametric oscillation (OPO) in the third crystal generates the signal and idler frequencies, ω_h=ω_s+ω. A plane-wave analysis predicts a quantum efficiency close to 30% over an extended range of pump intensity. Iteration of the plane-wave solutions over many passes yields dynamics very similar to that recently calculated for the SFG-OPO device. As in that device, a small detuning of the SFG interaction enlarges the dynamic range yielding stable operation. Highest efficiency occurs when ω_i is at the low-frequency end of the OPO crystal transmission window. As an example, we consider a device using a noncritically phase-matched KTP SFG crystal, a quartz crystal polarization rotator, an angle-tuned KTP SHG crystal, and a noncritically phase-matched LiNbO₃ OPO crystal. This device is designed to convert λ_p=1.064 μm to λ_d=0.455 μm. We calculate a power conversion efficiency as great as 73%