Cerenkov phase matching

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. 

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...

In this case the output field is a radiation wave which leaves the vicinity of the waveguide, i.e. the output field is not guided. For co-propagating fundamental beams it has been shown that the Cerenkov SHG signal grows initially quadrat-ically and then later linearly with distance. A comparison of the growth of the SHG power for different phase-matching cases is shown in Fig. 7. 

Fig. 7. The evolution of the harmonic power with propagation distance (arbitrary units) for ADM,WBM and MD phase-matching (solid line). The Cerenkov power changes from quadratic (solid line) to linear long (dashed line) growth. For QPM for alternate sections with no X1-2 1 (short dashed line). The phase-mismatched case is also shown (dotted line)...

We start by reviewing specific results obtained with the Cerenkov technique for which phase-matching is relatively easy, making this a very popular approach. 

Fig.4a,b. PU1-C4B waveguides for the Cerenkov-type phase matching SHG (a), and phase-matched blue SHG arches (b) SHG wave of 380 nm and fundamental wave of 760 nm (fop) and far field pattern of Cerenkov SHG wave of 400 nm (bottom)... 

Cerenkov-type phase-matched blue SHG in such a produced waveguide is typical (Fig. 4b). The conversion efficiency of this waveguide exhibits at least one-order of magnitude higher than those of the nonphase-matched samples, even where conversion efficiency is not fully optimized. This activity typically lasts for more than... 

In this paper we report phase-matched second-harmonic generation in nonlinear optically active Langmuir-Blodgett (LB) film waveguides both by mode conversion and by use of the Cerenkov-type configuration. The experiments were done in 2-docosylamino-S-nitropyridine (DCANP) LB films (Hg.l). The synthesis, the optimum conditions for LB film transfer and the linear and nonlinear optical properties of this material have been described elsewhere [4-6]. 

Figure 2. Cerenkov-type phase-matching due to constructive interference of second-harmonic waves generated in the waveguide between the points A and B at the wavefront BC. The wave is polarized along the z-axis.

As was discussed above the necessary condition for Cerenkov-type phase-matched frequency-doubling is that the effective refractive index of the fundamental mode is smaller than the refractive index of the substrate at 2flX This condition can be fulfilled for DCANP deposited on pyrex. Table 1 lists the refractive indices at the fundamental and the second-harmonic wavelengths, the thicknesses t of the films used in our experiments and the calculated and measured Cerenkov angles. As can be seen from Table 1 the Cerenkov angles 0 co/c and Q meas are in agreement within the experimental errors. 

Sugihara, O., Kunioka, S., Nonaka, Y., Aizawa, R., Koike, Y., Kinoshita, T., and Sasaki, K., Second-harmonic generation by Cerenkov-type phase matching in a poled polymer waveguide, J. Appl. Phys., 70, 7249-7252 (1991). 

Chen, Y, Kamath, M., Jain, A., Kumar, J., and Tripathy, S., Cerenkov type phase-matched second harmonic generation in polymeric channel waveguides. Opt. Comm., 101, 231-234 (1993). 

Sasaki et al. [189] reported Cerenkov radiation phase-matching in a poled polymer waveguide. The waveguide was a copolymer of MMA dispersed with red-1-substituted methacrylate which was spin-coated on Pyrex glass. The maximum SH peak power was 3.38 W at a fundamental power of 196 kW and the total conversion efficiency was 1.72 X 10 %. 

The Cerenkov radiation method can significantly relax the phasematching conditions, but the generated SH wave front in Cerenkov radiation is conical. Therefore, a special lens is necessary to focus the SH light. Such lens will increase the complexity of a device s structure. Furthermore, the conversion efficiency of Cerenkov radiation phase-matching is, in principle, less effective than that by mode-to-mode phase-matching. 

---