Higher-Order Correlations of Supercontinuum Light

Abstract

Intensity correlations and coherence properties of supercontinuum light are studied in spectral and temporal domains by simulating laser pulse propagation in optical fibers by numerically solving the generalized nonlinear Schrödinger equation for various initial conditions. Different input peak powers and pulse durations are used in order to explore correlations and coherence in various regimes of supercontinuum dynamics. An ensemble of a thousand simulations with varying random input noise is generated for each set of input parameters to ensure reliability of the results and conclusions. An emphasis is laid on the interpretation of the correlations and coherence properties in terms of well known nonlinear optical effects and previous research regarding electric field coherence of supercontinua. The intensity correlations are studied by calculating and analyzing the correlation coefficients. A cross-domain correlation function is introduced to examine correlations between temporal and spectral features. Coherence properties are explored and discussed with the help of mutual coherence functions and cross-spectral densities for both electric fields and intensities. Detailed explanations for the structure and patterns of the correlation and coherence functions are given in terms of nonlinear optical processes. The optical phenomena responsible for the observed correlations and coherence properties are identified and shown to be different depending on input pulse duration. Certain mechanisms responsible for the spectral broadening of short pulses are shown to lead to more coherent supercontinua than other phenomena that characterize supercontinuum generation in the long-pulse regime. Applications of both coherent and incoherent supercontinua are briefly mentioned with relevant citations. The results presented here lay the cornerstone for future work in intensity correlations and higher-order coherence of supercontinua. With the ultimate goal of complete control over supercontinuum properties in mind, possibilities for future research are presented in the concluding chapter.