| The interaction of an ultrashort pulse laser with atoms and molecules is currently one of the hottest study subjects of nonlinear optics and the propagation of an ultrashort pulse laser in atom or molecular media is an import part of the study. During the past two decades, supershort and superfast laser technology has made substantial progress and this provides a powerful tool for quantum coherent control under extreme non-linear optical condition. Based on high-power ultrashort pulse laser source generation and various pulse shaping technology appearing one after another, the study of the quantum coherent control has become a frontier area in recent years.Based on the semiclassical theory, the Maxwell and Bloch equations are used to describe the laser fields and media. In this paper, the full Maxwell–Bloch equations without the rotating wave and slowly varying envelope approximations are solved by using a predictor-corrector finite-difference time-domain method. Under extreme nonlinear optics condition, the propagation characteristics and spectral properties of a few-cycle chirped Gaussian pulse in aΛ-type three-level atomic medium are theoretically investigated. The main innovative results are as follows:1. We investigate effect of atomic densities on propagation and spectral property of femtosecond Gaussian pulse in a three-levelΛ-type atomic medium. It is shown that, variation of value of the atomic density has considerable effect on propagation and spectral property and the effect is closely relative to size of the pulse area. When the pulse with smaller area, 2π, propagates in the dilute medium with smaller and larger atomic density and dense medium with large atomic density, pulse splitting doesn't occur and new high frequency component doesn't basically appear; but different from the case in the dilute medium, in the dense medium the strength of the spectral component near the central frequency decreases considerably. The spectral strength distribution has obvious blue and red shifts, the spectral strength near the center frequency decreases remarkably, the strength of the blue shift and red shift components increases significantly and oscillation appears. For the pulse with area 4π, when the pulse propagates in the dilute medium with smaller atomic density, clear pulse splitting doesn't occur, slight pulse spectrum broadening apears, the strength of the spectral component with higher frequency increases with the distance increasing; when the pulse propagates in the dilute medium with larger atomic density an in the dense medium, the main pulse splits into two sub-pulses, and the spectrum broadening in the dilute medium with larger atomic density is much larger than that in the dense medium. For the pulse with larger area 8π, the case of the pulse propagates in the dilute medium with smaller atomic density is similar to that of the 4πpulse; but when the pulse propagates in the dilute medium with larger atomic density and in the dense medium, the case is considerably different from that for 4πpulse, the main pulse splits into three sub-pulses, and the spectrum broadening in the dilute medium with larger atomic density is much smaller than that in the dense medium. Our numerical calculation result shows that, when the pulse area is larger than 2πbut smaller than 5π, the propagation and spectral properties of the pulse are similar to those for 4πpulse; when the pulse area is equal to or larger than 5π, the propagation and spectral properties of the pulse are similar to those for 8πpulse.2. Based on the work of chapter 4, we investigate propagation of femtosecond chirped Gaussian laser pulse in a dense three-levelΛ-type atomic medium. It is shown that, variation of the sign and size of the chirp coefficient has considerable effect on pulse propagation property, and the effect is closely relative to size of the pulse area. When area of the chirped pulse is smaller than 4π, splitting doesn't occur and the chirped pulse evolves gradually to an approximate normal Gaussian pulse (C=0), and this characteristic doesn't vary with the chirp coefficient varying; however, variation of the chirp coefficient will change amplitude and group velocity of the pulse. For the positive chirp(C>0)case, amplitude and group velocity of the pulse decrease with chirp coefficient increasing; For the negative chirp(C<0)case, amplitude and group velocity of the pulse don't monotonously increase or decrease with absolute value of C increasing. Both the chirped pulses with area equaling to 4πand larger than 4πwill split into sub-pulses with different numbers and shapes, the time and number of the pulse splitting will be determined by the sign and size of the chirp coefficient. But in the two cases, the pulse splitting patterns are much different, and the effects of the coefficient are also different. When the pulse area equals to 4π, larger chirp coefficient will lead to sub-pulse number increase, but when the pulse area is larger than 4π, larger chirp coefficient will lead to sub-pulse number decrease. In addition, regardless of pulse area being larger or smaller, changing sign and size of the chirp coefficient always produces obvious effect on the atomic population.3. We investigate spectral properties of femtosecond chirped Gaussian laser pulse propagating in a dense three-levelΛ-type atomic medium. It is shown that, variation of the sign and size of the chirp coefficient (C) of the pulse has considerable effect on spectral properties of the pulse and the effect is closely relative to size of the pulse area. When the pulse with smaller area, 2πpulse, propagates in the medium, pulse splitting doesn't occur and the pulse evolves gradually to an approximate normal Gaussian pulse (C=0);new high frequency component doesn't basically appear; with increasing value of C, oscillation amplitude of blue shift and red shift components increases and blue shift component oscillates more severely; moreover, the strength of the spectral component near the central frequency decreases considerably but the strength of blue shift component increases obviously. When the 4πpulse propagates in the medium, the pulse will split into sub-pulses with different numbers and shapes,new high frequency component can be produced, but the strength of the high frequency component is smaller; Similar to the case of 2πpulse, blue shift component oscillates more severely; in addition, the strength of the spectral component with higher frequency decreases evidently with increasing value of C. When the pulse with larger area, 8πpulse, propagates in the medium, the pulse splitting is similar to that in the 4πpulse case, but super-continuum spectrum with larger strength, higher frequency and wider frequency range than that in the 4πpulse case can be obtained; varying the sign and size of C can not produce new high frequency component, but can change strength of different frequency components in the spectrum, thus can get high frequency components with higher strength.4. By the numerical analyzing and simulation, we investigate effect of carrier envelope phase on propagation of femtosecond chirped Gaussian laser pulse in a dense three-levelΛ-type atomic medium. It is shown that, when the small area 2πnegative chirped pulses (or the 2πpositive chirped pulses) with different value of initial carrier envelope phaseφ0, splitting don't occur and the chirped pulses evolve gradually to approximate normal Gaussian pulses (C=0) with equal amplitude and group velocity, and the phase differences between them remain the same as the case of initial input pulses. When the 4πnegative chirped pulses with differentφ0 propagate in the medium, the pulses will split into at least two sub-pulses and the amplitude of the first sub-pulse is far more than the second sub-pulse; Thereinto, these first sub-pulses have equal amplitudes and propagating with equal group velocity in the medium, and the phase differences between these first sub-pulses remain the same as the case of initial input pulses; The amplitudes of these second sub-pulses are not equal and don't change monotonously with linearly increasing ofφ0 but take on a invert S-shaped pattern, and the phase differences between these second sub-pulses are different. The case of 4πpositive chirped pulses is similar to the case of 4πnegative chirped pulses, but the amplitudes of these second sub-pulses split off from the 4πpositive chirped pulses have no obvious changes compared with the case of 4πnegative chirped pulses. For the large area pulse, the 6πnegative chirped pulses with differentφ0 propagate in the medium will split into at least three sub-pulses with different shapes, and the amplitude of the first sub-pulse or the second sub-pulse is far more than the third sub-pulse; similar to that in the 4πpulse case that these first sub-pulses (or these second sub-pulses) have equal amplitudes and propagating with equal group velocity in the medium, and the phase differences between these first sub-pulses (or these second sub-pulses) remain the same as the case of initial input pulses; The amplitudes of these third sub-pulses are not equal but take on a S-shaped pattern with linearly increasing ofφ0, and the phase differences between these third sub-pulses are different. The case of 6πpositive chirped pulses is similar to the case of 6πnegative chirped pulses, but the amplitudes of these third sub-pulses split off from the 6πpositive chirped pulses have an invert S-shaped pattern with linearly increasing ofφ0.5. We studied the method for achieving efficient and stable coherent population transfer by ultrashort double pulses. It is shown that, when two femtosecond chirped Gaussian pulses with equal areas, same size but opposite sign of the chirp coefficient, which will be simply called as double pulses, overlap and propagate in the three-levelΛ-type atomic medium, coherence between the double pulses arises, adjusting size of the chirped coefficient can change shape, i.e. field distribution, of the composite pulse of the double pulses, at the same time affect the interaction between the composite pulse electric field and atoms, and thereby control oscillation process and value of the populations of the medium. By selecting suitable size of the chirp coefficient, we can make the atoms at the lowest level exciting completely to the higher level; moreover the population distribution is stationary. It is also shown that, for the double pulses with any area, efficient and stable population transfer always can be realized by adjusting size of the chirp coefficient. And this conclusion doesn't vary with width of the double pulses or density of the medium varying.This paper consists of night chapters, and in the first three chapters, we introduce simply the current research state, the main contents and the calculation method of this research subject. Chapter 1 gives a brief introduction of the development and applications of ultrashort laser pulses, the interaction of ultrashort laser pulses with matter. In Chapter 2, we introduce the basic theories on the propagation of the ultrashort laser pulses. The complex function form of the pulse eclectic field and the function form of chirped Gaussian pulse are presented first. Then we introduce simply the physical meaning of the pulse chirp and carrier phase, the main nonlinear optical phenomena on the ultrashort pulse propagation. In Chapter 3, we derive Maxwell-Bloch equations beyond slowly varying envelope approximation (SVEA) and rotation-wave approximation (RWA), and detailed elucidate the predictor-corrector finite-difference time-domain method. From Chapter 4 to Chapter 8, my own study works are showed and the main results are alluded above. At last, the conclusions and prospect are given in Charpter 9.
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