Optimization of the Čerenkov sum-frequency generation in proton-exchanged Mg:LiNbO3 channel waveguides

Optical sum-frequency generation has been investigated in channel waveguides produced by proton exchange in Mg-doped as well as standard LiNbO3. Pyrophosphoric acid was used as an exchange media and Ta mask were patterned on z-cut plates by reactive-ion etching to form diffusion apertures ranging in width from 1 to 3 μm running parallel to the y axis. Samples were made by direct immersion in acid held at a temperature of 240 °C for times ranging from 10 to 28 min. End-fire coupling at 1.06 μm revealed that the Čerenkov radiation output at the second harmonic was optimized for the narrowest channel with a diffusion time of 24 min. A coupled throughput of 0.57 mW would produce a Čerenkov second-harmonic radiation mode due to the TM00 fundamental of 0.031 μW for a sample 4 mm in length. Diffusion times differing by 1 min around the optimum time would result in a reduction in harmonic generation efficiency by approximately a factor of 5. Samples pumped at 0.833 μm showed peak efficiency for a correspondingly shorter diffusion time. Severe drift in both fundamental throughput as well as harmonic generation is observed if pump throughput exceeds 2 mW in specimens formed in either Mg-doped or undoped LiNbO3. In addition, diffusion times for optimized nonlinear generation varied from batch to batch. The Čerenkov generation efficiency has been modeled using a step-index approximation for channel waveguides generalized to the z-cut y-propagating orientation used. The nonlinear source polarization at the sum frequency is considered to be due to only d33. Using values for the increase in extraordinary index estimated from fitting mode indices to the step-index approximation, we find optimum second-harmonic generation due to the TM00 takes place for the mode close to cutoff at either 1.06 or or 0.833 μm. The magnitude of the peak SHG efficiency is found to agree reasonably well with experiment. The variation in guide depth over which the optimum SHG is observed is roughly 0.05 μm. The model predicts this should be larger by a factor of 3. We attribute the discrepancy to the inability of the channel waveguide model to accurately calculate the propagation and decay constants of the pump mode near cutoff. Our effective index measurements further indicate the dispersion in the increase of the extraordinary index (Δne) under the ion-exchange process is essentially equivalent to results published for guides made using benzoic acid when the exchange is performed at 249 °C.