Birefringence phase matching

H3uasi-phase matching (QPM), modal dispersion phase matching (MDPM), anomalous dispersion phase matching (ADP), and birefringent phase matching (BPM). 

The poled polymer has a mm symmetry [59,60,80] only three of the tensor elements are nonzero d y and Kleinman symmetry, there are only two independent nonzero tensor elements for the poled polymeric system. It was believed that birefringence phase-matching in poled polymers is not possible owing to [141]. This is because... 

In the single-domain state, many ferroelectric crystals also exhibit high optical nonlinearity and this, coupled with the large standing optical anisotropies (birefringences) that are often available, makes the ferroelectrics interesting candidates for phase-matched optical second harmonic generation (SHG). 

The first and third order terms in odd powers of the applied electric field are present for all materials. In the second order term, a polarization is induced proportional to the square of the applied electric field, and the. nonlinear second order optical susceptibility must, therefore, vanish in crystals that possess a center of symmetry. In addition to the noncentrosymmetric structure, efficient second harmonic generation requires crystals to possess propagation directions where the crystal birefringence cancels the natural dispersion leading to 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... 

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... 

Comparison of these two polarizations shows that P2 Pi- Hence, in an isotropic medium such as a gas or a liquid x " = 0 and second order phenomena are not observable. Thus, only anisotropic media such as certain crystals are suitable for three-wave mixing processes. A consequence of a crystal being anisotropic is that it exhibits birefringence. However, the crystal birefringence enables phase matching to be achieved resulting in efficient generation of the new wave. 

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... 

Figure 6. The guided mode dispersion curves for a birefringent film and an optically isotropic substrate. Both the fundamental and harmonic curves are shown. The TE mode utilizes the ordinary refractive index and TM primarily the extraordinary index. Note the change in horizontal axis needed to plot both the fundamental and harmonic dispersion curves. Phase-matching of the TEq(co) to the TMo(2o>) is obtained at the intersection of the appropriate fundamental and harmonic curves.

Recently, a second-order nonlinear photonic crystal has been realized.38 In this nonlinear optical bandgap material, there is a periodicity in the nonlinear optical properties of the engineered material. With this definition, a periodically poled second-order nonlinear optical material could be called a nonlinear photonic crystal. However, its linear optical properties do not show a periodicity, except for the (small and useless for bireffingent phase-matching) poling-induced birefringence. Here, the material is the same in the complete structure. It is only periodically made into a non-centrosymmetric structure for second-order nonlinear and phase-matching... 

Fig.4. Schematic representation of the different common phase-matching techniques in the k space representation. (ADM) anomalous dispersion (WBM) waveguide birefringence (MD) modal dispersion (QPM) quasi-phase-matching (C) Cerenkov and (CP) counter propagating Cerenkov...

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