Quasi phase matching

A nonlinear crystal with a length L shows the output power P(2(o) of the second-harmonic wave as a function of the propagation length z depicted by curve a in Fig. 6.13c. After one coherence length the power decreases again because of destructive interference between the second-harmonic and the out-of-phase fundamental wave. 

however, the crystal has length L = followed by a second crystal with L = 2Lc but opposite orientation of its optical axis, then the phase mismatch is reversed and the phase difference decreases from jt to —n. Now the next layer follows with the orientation of the first one and the phase difference again increases from —7T to +71, and so on. This yields the output power of the second harmonic as shown in Fig. 6.13c, curve b. 

For these reasons many modem nonlinear liequency-doubling or mixing devices, in particular, optical parametric oscillators, use quasi phase matching [562, 563]. Gallium arsenide has a very high nonlinear coefficient and a wide transparency range of 0.7-17 pm. It is therefore very attractive for widely tunable optical parametric oscillators in the mid-infrared. It is now possible to fabricate orientation-patterned GaAs which can be used as quasi-phase-matched material. 

The advantages of quasi-phase-matching can be summarized as follows  

For comparison, the curve c of a perfectly phase-matched long crystal is shown in Fig. 5.107c. This demonstrates that the quasi-phase-matching device gives a lower output power than the perfectly matched crystal, but a much larger power than for a single crystal in the case of slight phase mismatches. 

For frequency doubling of tunable lasers, it is difficult to maintain perfect phase matching for all wavelengths therefore phase mismatches cannot be 

For these reasons many modern nonlinear frequency-doubling or mixing devices, in particular, optical parametric oscillators, use quasi phase matching [5.244,5.245]. 

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Organic polymeric flocculating agents, mechanisms of, 77 632-633 Organic polymeric thin films, quasi phase matching in, 7 7 451 Organic polymers... 

Following the previously described method we obtain an expression for the SH amplitude, S L, p), at the output of a nonlinear media with linearly chirped (aperiodically-poled) quasi-phase-matched (QPM) grating ... 

M. M. Fejer, G.A. Magel, D.H. Jundt, and R.L. Byer, Quasi-phase-matched second harmonic generation - tuning and tolerances, IEEE Journal of Quantum Electronics 28, 2631-2654 (1992). 

M.A. Arbore, O. Marco, and M.M. Fejer, Pulse compression during second-harmonic generation in aperiodic quasi-phase-matching gratings. Optics Letters 22(12), 865-867 (1997). 

M. Yamada, N. Nada, M. Saitoh, and K. Watanabe, First-order quasi-phase matched LiNbOs wave-guide periodically poled by applying an external-field for efficient blue second-harmonic generation. Applied Physics Letters 62(5), 435-436 (1993). 

H. Karlsson, F. Laurell, and L.K. Cheng, Periodic poling of RbTiOPQ for quasi-phase matched blue light generation. Applied Physics Letters 74(11), 1519-1521 (1999). 

K. Fradkin-Kashi and A. Arie, "Multiple-wavelength quasi-phase-matched nonlinear interactions, IEEE Journal of Quantum Electronics 35 1649 (1999). 

L.E. Myers, R.C. Eckardt, M.M. Fejer, R.L. Byer, and W.R. Bosenberg, "Multigrating quasi-phase-matched optical parametric oscillator in periodically poled LiNb03, Optics Letters 21, 591 (1996). 

Nanometer scale domain configurations in fe bulk crystals pave the way for a new class of photonic devices. As an example, preliminary calculations show that a uv laser (A = 300 nm) based on second harmonic generation in LiTaC>3 crystal requires a periodic nanodomain superlattice with domain widths of around 700 nm. In addition, the current domain gratings in ferroelectric crystals are suitable only for quasi-phase-matched nonlinear interactions in the forward direction, where the pump and generated beams propagate in the same direction. Sub-micron ferroelectric domain gratings are the basis for a new family of devices based on backward nonlinear quasi-phase-matched optical interactions in which the generated beam travels in a reverse or another non-collinear direction to the incident beam. Non-collinear... 

Figure 10.4 Nanodomain grating (domain period is 410 nm) tailored for integrated optical device in LiNbC>3 crystal by application of dc voltage (U = 2.0kV). (b) Domain grating (domain period is 1180nm) fabricated in the RbTiOPCU crystal for non-collinear quasi-phase-matched nonlinear optical converter.

The analysis of organic polymer waveguides with quasi-phase matched structures has also been theoretically addressed, taken into account pump depletion and attenuation [11]. 

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

Table 1. Comparison of selected quasi-phase-matched SHG devices reported in organic and some inorganic materials d -coefficient fundamental wavelength Xy efficiency t, device length Ly figure of merit T, waveguide losses aja2m and waveguide structure. Note that not all of the relevant parameters were reported in die publications quoted...

FIG. 11.27 Potential application of the induced quasi-phase matched structure as a polymer waveguide for frequency conversion. ... 

Saco, M., Yaguchi, H., Shoji, I., Onabe, K., Ito, R., Shiraki, Y., Nakagawa, S., and Yamada, N. (2000). Second-harmonic generation from GaP/AlP multilayers on GaP (111) substrates based on quasi-phase matching for the fundamental standing wave. Jpn. J. Appl. Phys. 39, 334-336. 

Quasi-Phase Matching in Periodically Poled Polymer Films... 

Fig. 45. Schematic representation of alternate quasi-phase-matched structure. Arrows shows orientation of dipolar moments (and consequently the orientation of the diagonal com-...

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