Author:
Saif M. Hassan Ali,S.A. Hasan Waleed,A. Shukri Mohamed
Abstract
Quantum theory of generalized X waves with orbital angular momentum in dispersive media, and the interaction of quantized X waves in quadratic nonlinear media were studied in (J. opt,20,065201 (2018)). We present a kind of phase matching, which is called velocity phase matching, and this phase matching can be used for determining the length of the nonlinear crystal or the interaction time in the experiment setup, to produce X waves with particular velocity v. Moreover, we introduce more analysis for the dependence of squeezing of X waves on its spectral order, and for spectral orders j>0, we predict the existence of a characteristic axicon aperture for maximal squeezing. Then, we find the quantum squeezed state of the down-converted state generated by the χ2-nonlinear process. Finally, we detect their entanglement using a criterion of separability.