Modal Phase Matching

The conversion efficiency is directly proportional to the overlap integral between fundamental and harmonic optical fields of given modes 

Up to now, no significant conversion efficiencies q = PiJ co where P is power at given frequency, were reported. This is mainly due to the poor overlap integral, limited propagation length caused by the nonoptimized propagation properties of polymeric waveguides, and limited values of ( (-2cu,cu,cu) susceptibility. 

We note also that PM SHG was obtained with poled polymer thin films using a planar waveguide with corrugated grating [ 187]. 

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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...

Fig. 8. An approach to increasing the overlap integral via modal dispersion phase-matching. The sign of the nonlinearity d(y) is reversed at the same point as the TM1(2co) field. The solid lines show the nonlinearity for TM0(a>)— TM ft)).

Fig. 12. SHG figure of merit r reported in poled-polymer devices using quasi-phase matching (QPM) and modal dispersion phase matching (MDPM)...

FIGURE 14 (a) Tuning curve for modal dispersion phase-matched SHG in a 3-mm-long DANS channel waveguide. The acceptance bandwidth (full width at half-maximum, FWHM) is 4.0 nm. (b) Narrowing of the FWHM acceptance bandwidth versus the sample length L (data and theoretical fit) [26]. 

Jager, M., Stegeman, G. I., Flipse, M. C., Diemeer, M., and Mohlmann, G., Modal dispersion phase matching over 7 mm length in overdamped polymeric channel waveguides, Appl. Phys. Lett., 69, 4139-4141 (1996). 

Rikken, G. L. J. A., Seppen, C. J. E., Staring, E. G. J., and Venhuizen, A. H. J., Efficient modal dispersion phase-matched frequency doubling in poled polymer waveguides, Appl. Phys. Lett., 62, 2483-2485 (1993). 

Experiments on transition for 2D attached boundary layer have revealed that the onset process is dominated by TS wave creation and its evolution, when the free stream turbulence level is low. Generally speaking, the estimated quantities like frequency of most dominant disturbances, eigenvalues and eigenvectors matched quite well with experiments. It is also noted from experiments that the later stages of transition process is dominated by nonlinear events. However, this phase spans a very small streamwise stretch and therefore one can observe that the linear stability analysis more or less determines the extent of transitional flow. This is the reason for the success of all linear stability based transition prediction methods. However, it must be emphasized that nonlinear, nonparallel and multi-modal interaction processes are equally important in some cases. 

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