Phase-matching, nonlinear optics

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.

In a crystalline medium, the parametric gain (2) T2 is propor-tionnal to d2 Ip n-3 and the oscillation condition r2A2>aA where a is the signal residual absorption (dramatically increased by any crystalline defect), d the efficient phase-matched nonlinear susceptibility, n an average refractive index, Ip the pump intensity (limited by the optical damage threshold) and A the effective interaction length (also limited by any source of crystalline disorientation). 

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... 

The linear and nonlinear optical responses for this problem are defined by e, 2, e and respectively, as indicated in figure Bl.5.5. In order to detemiine the nonlinear radiation, we need to introduce appropriate pump radiation fields E(m ) and (co2)- If these pump beams are well-collimated, they will give rise to well-collimated radiation emitted tlirough the surface nonlmear response. Because the nonlinear response is present only in a thin layer, phase matching [37] considerations are unimportant and nonlinear emission will be present in both transmitted and reflected directions. 

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). 

Fig. 2. Optical nonlinearity and phase matching windows for commonly used NLO materials. KDP = KH2PO4 BBO = j3 — BaB2 KTP = KTiOPO. ...

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. 

I. Biaggio, P. Kerkoc, L.S. Wu, P. Gunter, and B. Zysset, Refractive-indexes of orthorhomhic KNbOs Phase-matching configurations for nonlinear-optical interactions, Journal of the Optical Society of America B 9(4), 507-517 (1992). 

Acceptor species concentrations, equations, 400-401 Acentric materials biomimetic design, 454-455 synthesis approaches, 446 Ar-(2-Acetamido-4-nitrophenyl)pyrrolidene control of crystal polymorphism with assistance of auxiliary, 480-482 packing arrangements, 480,481-482/ Acetylenes, second- and third-order optical nonlinearities, 605-606 N-Acetyltyrosine, phase-matching loci for doubling, 355,356/, t Acid dimers, orientations, 454 Active polymer waveguides, applications, 111... 

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... 

Keywords. Electro-optic chromophores, Polymers, Waveguides, Quadratic nonlinearities, Phase-matching... 

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