Spatial coherence effects in second-harmonic generation of scalar light fields

Abstract

We consider the spectral spatial coherence characteristics of scalar light fields in second-harmonic generation in an optically non-linear medium. Specifically, we take the fundamental-frequency (incident) field to be a Gaussian Schell-model (GSM) beam with variable peak spectral density and different coherence properties. We show that with increasing intensity the overall degree of coherence of both the fundamental and the second-harmonic field in general decreases on passage through the non-linear medium. In addition, the spectral density distributions and the two-point degree of coherence may, for both beams, deviate significantly from those of the GSM, especially at high intensities. Propagation in the non-linear medium is numerically analyzed with the Runge–Kutta and the beam-propagation methods, of which the latter is found to be considerably faster. The results of this work provide means to synthesize, via non-linear material interaction, random optical beams with desired coherence characteristics.

Partial spectral and temporal coherence of plane-wave pulse trains in second-harmonic generation

“…We checked that this number ensures the convergence of the results. The procedure for generating the ensemble is analogous to that described in [22] in the spatial domain. In short, a realization is expressed in terms of the HG modes in equation ( 21) with random coefficients and they are required to lead to the coherent-mode representation of equation (20).…”

“…We analyzed this feature and found that the various ensembles effectively imply the same results if the number of realizations N is large and the value N = 500 that we use is sufficient. The analogous property but with spatial domain fields was assessed in [22].…”

“…We also point out that the commonly used slowly-varying envelope approximation (SVEA) [16], which we also tried in analogy with the spatial-domain analysis in [22], failed to predict the transfer of power back to the F wave after certain pump power levels ( √ S 0 above 15 GV m −1 , see figure 2). We therefore resorted to rigorous solutions of Maxwell's equations by the RK algorithm.…”

“…Previous studies concerning coherence and SHG relate to the SHG efficiency [17][18][19] and the influence of incoherence on the produced spectrum [20,21]. Recently, the spatial coherence properties of the involved fundamental (F) and second-harmonic (SH) waves were considered in the context of stationary fields whose spectral components are necessarily uncorrelated [22].…”