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Polarization-squeezed light formation in a medium with electronic Kerr nonlinearity

“…The statistical features of pulses at the output of the medium can be evaluated by using the algebra of time-dependent Bose operators [17][18][19]. In such algebra we havê…”

Self-and cross-phase modulation of ultrashort light pulses in an inertial Kerr medium: spectral control of squeezed light

“…Therefore, the momentum operator connected with the spatial evolution of the pulse field should be used instead of the interaction Hamiltonian [12] in order to obtain an equation for the annihilation Bose-operator. This approach for the case of pulse SPM in nonlinear medium with inertial electronic Kerr nonlinearity has been successfully used in [9].…”

“…The authors [6,7] have taken into account quantum and thermal noises as a fluctuating addition to the relaxation nonlinearity in the interaction Hamiltonian. In the other approach developed in [8,9,10], the interaction Hamiltonian [8] or the interaction momentum operator [9,10], which contains only a response function of the nonlinearity, have been used. In such quantum description of the SPM of ultra-short pulses (USPs), one cannot add thermal noise terms to the interaction Hamiltonian and momentum operator in order to satisfy the canonical commutation relation for the annihilation and creation Bose-operators.…”

“…In this paper, we present the quantum theory based on the interaction momentum operator [9] for the case of nonlinear propagation of two ultrashort light pulses [10]. In reality, here we will mainly analyze two combined (SPM and XPM) effects.…”

“…This combined phenomenon can be shortly called "the SPM-XPM of USPs." Since we deal with the analysis of the combined phenomena, algebra of time dependent Bose-operators developed earlier in [9,11] has to be subsequently extended.…”