We show by experiment and mathematical model that angular and frequency acceptance bandwidths for frequency mixing in a nonlinear crystal can often be improved by segmenting the crystal and reversing the spatial or temporal walk-off in alternating segments. We analyze nonlinear mixing primarily in real space, (x, t), rather than Fourier space, (k, ω), and show that acceptance bands for sum- and difference-frequency mixing can be increased by up to a factor equal to the number of crystal segments. We consider both high- and low-efficiency mixing as well as parametric gain, and show that in many cases of practical interest the increased bandwidth substantially improves conversion efficiency. We also attempt to clarify the role of acceptance bandwidths in frequency mixing.

Increased acceptance bandwidths in optical frequency conversion by use of multiple walk-off-compensating nonlinear crystals

We present a quantitative theory of nonlinear frequency conversion in stacks of crystals where the phase mismatch due to dispersion is compensated by changing the sign of the nonlinear coupling coefficient in successive crystals-a method first proposed by Armstrong et al. We include pump depletion in our calculations of the second harmonic generation and sum and difference frequency generation. We start with ideal stacks in which the crystal lengths are tailored to achieve perfect phase compensation. When the conversion in each coherence length is small, all crystal lengths tend to equal the coherence length \pi/\Deltak . Frequency conversion in such stacks is well approximated by that in an equivalent phase-matched crystal with the nonlinear coupling coefficient reduced by a factor of 2/\pi . The effect of systematic as well as random departures in crystal lengths are studied with special attention to the evolution of the relative phase. We show that with appropriate choice of the signs of the nonlinear coupling coefficient in various crystals, high efficiency frequency conversion should be possible using practically any sufficiently large set of nonlinear crystals. The theory of second harmonic generation in periodic stacks and in rotationally twinned crystals of zinc-blend structure is described in detail.

Optical frequency conversion in quasi-phase-matched stacks of nonlinear crystals

The effects of focusing in type-I and type-II difference-frequency generations

Nonlinear effects in optics offer the possibility of generating or manipulating light in almost any manner. The laser itself, producing light not available in nature, is the most obvious example. Therefore nonlinear interactions are the basis of photonics.

Nonlinear Interactions of Light and Matter Without Absorption

Frequency-doubled telecom fiber laser for a cold atom interferometer using optical lattices

We analyze second-harmonic generation (SHG) with focused pump beams in the high-conversion regime where pump depletion is significant. Numerical solutions of the coupled equations for pump and harmonic fields are obtained for the cylindrically symmetric case of collinear phase matching. The optimum values of phase mismatch and confocal parameters σ and b found by Boyd and Kleinman are very nearly independent of pump power to above 95 percent conversion. When phase mismatch is not optimized, the best confocal parameter depends upon the input power. The conversion efficiency versus input power is determined numerically for optimum \sigma, b , and approximate analytical formulas are given for this relation.

D. White

Papers

Theory of second-harmonic generation with high-conversion efficiency