Phase-matching in isotropic and homogeneous materials via Talbot effect

Abstract

Figure 1 THG in homogeneous silica sample. (a) Scheme for self-induced QPM. (b) Intensity of the pump at θ=12.4 0 .(c) Power of the TH beam at the output vs. the angle, θ, normalized to the power in the "standard" case; L=lc, and d=0. (d) power spectra of TH beams at angles that give rise to phase-matching. Note that each line-type corresponds to different angle, marked in (c). Intensity (e) and scheme for the phase-matching (f) for THG at θ=16 0 . Intensity patterns of the TH beams at θ=19.7 0 (g) and θ=12.4 0 (h). Abstract:We suggest a method for obtaining phase-matching of harmonic generation processes in homogeneous isotropic materials. The intensity of the pump beam is modulated along the direction of propagation giving rise to QPM-like signal generation.Phase matching is critical for the efficient implementation of any nonlinear parametric process, e.g. harmonics generation. The most common approach for obtaining phase matching is through birefringence. However, this technique is limited to anisotropic materials. In isotropic materials, on the other hand, efficient harmonics generation is possible in inhomogeneous structures, e.g., waveguides [1] and quasi-phase matching (QPM) samples [2]. QPM makes use of modulation of the generation process (e.g. by modulating the sign of the relevant nonlinear coefficient or the intensity of the pump beam [3]), enabling to compensate for the intrinsic phase-mismatch by a QPM wave vector.Here, we suggest a technique for obtaining phase-matched frequency conversion in homogeneous and isotropic materials (e.g., glass). The distinguishing feature in this method is that the intensity of the pump beam is modulated through the spatial or temporal Talbot effect. In this case, harmonics are generated predominantly at within confined regions where intensity is largest, giving rise to QPM-like effects. We specifically discuss phasematched processes in two different regimes. First, we consider third harmonic generation (THG) in fused silica (SiO 2 ), employing the spatial Talbot effect. Then, we discuss phase matching of high harmonic generation (HHG) in plasmas, making use of the temporal Talbot effect.For the THG example, we assume a non-depleted pump beam at λ 1 =1.5µm in the form of ( ) ( ) ( ) ( ) .