General analysis of type I second-harmonic generation with elliptical Gaussian beams

On the design of enhancement cavities for second harmonic generation

“…Further, as we have shown elsewhere [6], the optimal beam for harmonic generation is often itself elliptical (and tolerant of a degree of ellipticity), in which case the larger of the corresponding confocal parameters may approach cavity dimensions.…”

“…The e ciency depends upon the nonlinearity and Poynting vector walk-o together with the crystal dimensions, which are usually constrained by availability and cost. Calculation of the theoretical conversion e ciency has been thoroughly described elsewhere [6,8] and will not be repeated here; for its absolute calculation, it will be necessary to assume the intensity enhancement due to the cavity, which depends upon the mirror re¯ec-tivity and cavity losses and will typically be a factor of between 20 and 100. Whether or not a Brewster's angled crystal cut is chosen will probably depend upon the availability of anti-re¯ection coatings for the normal incidence case.…”

“…Having chosen the crystal, we calculate the optimal fundamental beam [6,8]. 1 Generally elliptical, this is characterized in the tangential and sagittal planes by the complex Gaussian beam parameters q x;y z , de®ned at the foci by…”

“…We allow for inclination of the frequency-doubling crystal either within or perpendicular to the resonator plane, and consider explicitly the speci®c cases of normal and Brewster's angle incidence. Starting from the ellipticity of the fundamental laser beam, an arbitrary choice of mirror curvature and the desired beam pro®le in the crystal, whose determination we have addressed in a previous paper [6], we provide a recipe by which dimensions of a suitable resonator may be calculated.…”

High power 404 nm source based on second harmonic generation in PPKTP of a tapered external feedback diode laser

“…Hence a trade off has to be made between having a circular focus inside the PPKTP crystal and having a circular harmonic output beam. For crystals with no birefringence the use of a circular beam optimizes the conversion efficiency, whereas elliptical focusing can advantageously be used with birefringent crystals like BiBO [10].…”