Noncritical phase matching

Certainly for real samples where the distribution function is intermediate between the isotropic and Ising limits the susceptibilities also lie between. Two interesting points can be made. 1) Disregarding variation of F, the macroscopic nonlinearity can be enhanced by up to a factor of five over the maximum achievable in isotropic media by use of liquid crystal host and 2) The nonlinearity which might be used for noncritical phase-matched SHG via the birefringence (which must depend on the magnitude of... 

Consequently only second-order processes employing one e- and two o-waves may occur and the second conclusion of the last paragraph applies beyond the noncritical phase-matched case. 

Two types of phase-matching exist for SHG Type I, where the two fundamental photons are of the same polarization, and Type II, where they are orthogonally polarized. The phase- matching direction and one of the principal vibration directions of the crystal may be coincident in biaxial and uniaxial (birefringent) crystals. This situation, called noncritical phase-matching, is quite... 

In many cases the contribution from the first derivative dominates and the second term can be neglected. This case is referred to as critical phase matching. However, using a careful waveguide design, it is sometimes possible to cancel the first term by requiring that that the first derivative vanishes [Aj8 (/ o) 0]. This noncritical phase matching is very desirable, because it eases the acceptable tolerances. 

The acceptable tolerances for critical and noncritical phase matching are therefore 0.88677... 

FIGURE 11 Acceptable thickness tolerances for phase-matched SHG in a 1-cm-long planar DANS polymer waveguide for various conversions. TTie peaks represent the noncritical phase matching points, where the first derivative of the phase mismatch vanishes [Aj8 (/i) = 01. 

Urn, E. J., Matsumoto, S., and Fejer, M. M., Noncritical phase matching for guided-wave frequency conversion, Appl. Phys. Lett., 57, 2294-2296 (1990). 

One may wish to pursue the bulk phase-matched behavior beyond the noncritical (8=w/2, 8 defined below) case. In bulk samples birefringence is the usual means to overcome the natural dispersion... 

Dolinchuk SG, Kornienko NE, Zadorozhnii VI (1994) Noncritical vectorial phase matchings in nonlinear optics of crystals and infrared up-conversion. Infrared Phys Techn 35 881-895... 

Bortz, M. L., Field, S. J., Fejer, M. M., Nam, D. W., Waarts, R. G., and Welch, D. F., Noncritical quasi-phase-matched second harmonic generation in an annealed proton-exchanged LiNbOj waveguide, IEEE J. Quantum Electron., 30, 2953-2960 (1994). 

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