The new analytical representation of the Green’s function of the pulse propagating in the medium with a single process of resonant relaxation is presented. The different possible types of pulse dynamics are studied.
In this book, we focus on the stochastic nature of pulses to achieve a more realistic description of ultra-short optical pulses affected by noise. In order to simulate ultra-short pulses, various stochastic pulse models were applied. The effects of pulse amplitude and phase fluctuations on its propagation in various linear and non-linear media were studied based on optical coherence theory. The response of the medium atoms to the applied stochastic pulses was investigated for the particular resonant case in which the pulse frequency nearly coincides with the atom resonance frequency. Analytical and numerical propagation methods were applied to explore evolutions of ultra-short stochastic pulses in the vicinity of optical resonance.
The propagation of two short different-wavelength optical pulses in three-level absorbers is studied. Combined numerical and analytic techniques are used to solve the three-level Maxwell-Bloch equations that provide the semiclassical description of the problem. The electric field in the model studied consists of two copropagating plane waves, each of which is in near resonance with a transition in the absorber. A new conservation law, holding in the absence of relaxation mechanisms, and independent of particular values of fields and detunings, is given. It is an analog of the law expressing conservation of the Bloch vector length known for two-level atoms. The possibility of simultaneous lossless propagation of the two optical pulses is established. New analytic solutions having the form of simultaneous different-wavelength optical solitons have been found. These pairs of solitons are called simultons. In order for simulton propagation to occur, both the pulses and the medium have to be prepared in a manner determined by the medium's physical parameters. The conditions for such preparation are given. Simultons are predicted to be distinct from the single-wavelength multiple-pulse solutions resulting from large-area-pulse breakup known in two-level absorbers, as well as from two-photon self-induced transparency. Results of numerical experiments on different-wavelength simultaneous propagation are also presented and indicate that simultaneous propagation may also be obtained under less stringent conditions than those predicted by the analytic solutions. Evidence of pulse evolution and breakup is seen.
We study the features of spatial and temporal evolution of two powerful short different-wavelength laser pulses interacting with optical dense three-level Lambda-type medium under condition of coherent population trapping for the general case of unequal transition oscillator strengths. The pulses are simultaneously sent into an atom. The durations of probe and coupling pulses T1,2 (T2>T1) are supposed to be shorter than all relaxation times in the medium. We present analytical and numerical solutions of the self-consistent set of coupled Schr\\"{o}dinger equations and reduced wave equations in adiabatic limit with taking into account the first non-adiabatic correction. The adiabaticity criterion with account of pulse propagation is studied. We find that propagation dynamics depends on the relationship between the transition oscillator strengths. It is shown that at the initial stage of propagation the envelopes of the pulses slightly change along the length of the medium. This distance can be large compared to one-photon resonant absorption length of the medium. Also it is possible a regime of complete reemitting of the probe pulse into the coupling one during propagation. A spatial evolution of the atomic Raman coherence is investigated in detail too.