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Quantum Electronics

Statistical study of the spectrum of a partially coherent subpicosecond pulse undergoing self-modulation in a gas

Valeriy P. Kandidov, O.G. Kosareva, Svyatoslav A. Shlenov

Published Oct 31, 1993• 1 citation
Publisher

Abstract

We investigate the changes in the frequency spectrum of a partially coherent pulse brought on by a Kerr nonlinearity and by multiphoton ionization in a gas. We find that fluctuations in the parameters of the laser light cause the average spectrum of a pulse in a medium with a Kerr nonlinearity to be symmetric, with a single maximum at the center frequency. In the case of free-carrier generation, a long wing forms in the average spectrum that extends into the anti-Stokes region. We show that the ionization-induced nonlinearity gives rise to two time scales in the correlation function of the light.

DOI
10.1070/qe1993v023n10abeh003185

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We investigate the changes in the frequency spectrum of a partially coherent pulse brought on by a Kerr nonlinearity and by multiphoton ionization in a gas. We find that fluctuations in the parameters of the laser light cause the average spectrum of a pulse in a medium with a Kerr nonlinearity to be symmetric, with a single maximum at the center frequency. In the case of free-carrier generation, a long wing forms in the average spectrum that extends into the anti-Stokes region. We show that the ionization-induced nonlinearity gives rise to two time scales in the correlation function of the light.
A systematic theory of the formation of squeezed states during the propagation of coherent light pulses in a medium with an inertial Kerr nonlinearity is developed. It is established that the region of the spectrum where the quadrature fluctuations are weaker than the shot noise depends on both the relaxation time of the nonlinearity and the magnitude of the nonlinear phase shift. It is also shown that the frequency at which suppression of the fluctuations is greatest can be controlled by adjusting the phase of the pulse.
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.
Optical experiments reveal the fact that real laser pulses have random fluctuations in their amplitude and phase that crucially affect pulse evolution. Statistical optics considers the random nature of light to give a more realistic description of laser pulses behavior. Generation of ultrashort pulses, operating at frequencies close to internal transition frequencies of medium atoms, motivated the growing interest in studying on-resonance light-matter interactions. Moreover, there exist optical phenomena that only occur at optical resonance. Thus, near resonance light-matter interactions are of great importance. In this dissertation, statistical properties of ultrashort pulses propagating in different linear and nonlinear media near optical resonance is studied. Various partially coherent pulses are simulated and effects of initial statistical properties of pulses on their propagation in resonant absorbing and amplifying media are explored. The research performed throughout this thesis leads to following results. 1- Various classes of ultrashort self-similar partially coherent pulses are explored along with closed form expressions for their correlation functions. Also, the evolution of coherence properties of pulses upon their short-distance and long-distance propagation is investigated. 2- Generic partially coherent pulses are simulated and their global and local correlation properties upon propagation in resonant linear absorber media are studied. The evolution of the coherence functions of pulses shows that partially coherent pulses are strongly affected by the medium regarding to their coherence levels. A correlation area theorem is also derived to describe global correlation properties of stochastic pulses propagating in such media. 3- Evolution of small-area pulse coherence properties, propagating in linear amplifiers near optical resonance, is studied. Our simulation results reveal that more coherent pulses are amplified more effectively by the medium than are their less coherent counterparts. 4- Propagation of partially coherent pulses in resonant, inhomogenously broadened nonlinear media is simulated. Stochastic pulses of different coherence levels are generated to investigate effects of initial properties of pulses on their long-term evolution. We also provide evidence of self-induced transparency phenomena and soliton formation for relatively coherent pulses. Also, evolution of the coherence functions reveal that low-coherence pulses lose their coherence level upon propagation faster than do highly coherent pulses.
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.
The systematic theory of the formation of the short light pulses in the squeezed state during the propagation in a medium with inertial Kerr nonlinearity is developed. The algebra of time-dependent Bose-operators is elaborated and the normal-ordering theorem for them is formulated. It is established that the spectral region where the quadrature fluctuations are weaker than the shot-noise, depends on both the relaxation time of the nonlinearity and the magnitude of the nonlinear phase shift. It is also shown that the frequency at which suppression of the fluctuation is greatest can be controlled by adjusting the phase of the initial coherent light pulse. The spectral correlation function of photons is introduced and photon antibunching is found.
We have observed self-modulation and self-compression of a femtosecond laser pulse after passing the beam through a Raman-active medium of hydrogen. Femtosecond pulses produce Stokes emissions of ortho-hydrogen and para-hydrogen, depending on the input beam conditions. The shape of the output pulses drastically changed as a function of the intensity of the Stokes emissions and the total width of the spectrum. This is attributed to nonlinear modulation of the wave form induced by coherent rotational motions of hydrogen molecules in the time domain.