Mode dispersion phase matching

MDPM mode dispersion phase matching MIM mirror image method... 

Mode dispersion phase-matching (MDPM) has been applied to many materials [170-174], including crystalline materials and poled polymers. It is based on the fact that waveguides generally support several modes, each with a different propagation constant (i.e., a different effective refractive index iV n = tif sin 6). This index is lower for the higher-order modes therefore, PM can occur if the fundamental wave propagates in... 

Using the refractive index value of the pyrazine LB film, we calculated the mode dispersion curves of the TM fundamental and the TM second-harmonic waves in the waveguide device composed of a waveguiding pyrazine layer and a fused quartz substrate when Nd YAG laser is used as a fundamental light (Fig. 18). These curves show that the Cerenkov type phase matching is possible in the range of the thickness from 410 nm to 510 nm. 

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.

The example shows the typical dispersion in Neff with both frequency and film thickness for a few pertinent TMm modes. Note that TM0(co) and TM0(2co) never intersect, and can therefore not be phase-matched to each other. This is a consequence of the dispersion in the refractive index and due to waveguiding. Note however that TM0(co) and TMj(2co) do intersect indicating that phasematching can take place between these two modes (which have different symmetries in the field distribution) and this is the MD case. However, for WBM it is possible to have an intersection between TM0(co) and TE0(2co) in a birefrin-gent film. For QPM, there is a vertical effective index shift of q[K/2ko(co)] which... 

In integrated optics devices, phase matching must occur in a waveguide structure. The quantized effective indices of refraction vary for different modes of propagation in the waveguide, and the dispersion in the effective mode... 

The relation of effective refractive indices of different modes with the thickness of film is called mode dispersion, as shown in Fig. 7. The cross points of the fundamental and the second-harmonic waves indicate the phase-matching points. Therefore, such type of phase-matching is obtained by adjusting the thickness of the waveguide and is very difficult to achieve. 

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