The effects of self-phase modulation on an incoherent field are calculated. I show that the field’s coherence time is shortened, i.e., an incoherent light spectral distribution is broadened, if this field propagates in a nonlinear Kerr medium.
A theory describing propagation of partially coherent pulse trains in Kerr media is proposed. It is shown that changes in the statistical properties of chaotic modulated pulses propagating under self-phase modulation (SPM) are easily obtained within the framework of cyclostationary processes. Specific applications for laser light and thermal light are considered showing that in contrast with laser light, the thermal light spectrum on propagation suffers a significant change which smears out the characteristic peaks of the SPM spectrum.
Quantum theory of self-phase and cross-phase modulation of ultrashort light pulses in the Kerr medium is developed, taking into account the response time of an electronic nonlinearity. The corresponding algebra of time-dependent Bose operators is elaborated. It is established that the spectral region of the pulse where the quadrature fluctuation level is lower than the shot-noise one depends on the value of the nonlinear phase shift, the intensity of another pulse and the relaxation time of the nonlinearity. It is shown that the frequency of the pulse spectrum at which the suppression of fluctuations is maximum can be controlled by adjusting the other pulse intensity.
We develop a travelling-wave formulation of the theory of quantum optics and apply it to the description of the self-phase modulation of a short coherent pulse of light. The infinite nonlinear phase shift that is produced by the vacuum fluctuations is treated, within our approach, through a renormalization procedure. The renormalized theory successfully describes the nonlinear chirp that the pulse undergoes in the course of its propagation and permits the calculation of the squeezing characteristics of self-phase modulation.