Dynamical Properties Of Ultrashort Laser Pulses In A Three-level Molecular Medium

The propagation of ultraintense and ultrashort laser pulses in nonlinear mediaexhibits abundant novel optical phenomena which are different from those innanosecond and picosecond time domains, leading the study of the interaction betweenlaser and matter to a completely new field. The dynamical studies of these nonlinearprocesses enable us to understand the physical mechanism of all kinds of nonlineareffects from the microscopic point of view, provide theoretical basis for the designationand utilization of laser and predict nonlinear properties of the media. Organic molecularmaterials have many advantages, such as large nonlinear optical coefficient, wideresponse wave band, good flexibility, high optical damage threshold, low cost, and easycombination and modification. They have gained wide range attention due to theseexcellent properties. This dissertation performs a systematic research on the dynamicalproperties of the propagation of ultrashort (femtosecond) laser pulses in the symmetricalorganic molecular medium, and a series of innovative results are achieved.Based on the semiclassical theory, the Maxwell and Bloch equations are used todescribe laser fields and media, respectively. The medium that we choose is theone-dimensional symmetrical π-conjugated molecule 4, 4′-bis(dimethylamino) stilbenewith strong two-photon absorption (TPA) property. Optimization of the moleculargeometric structure and calculation of the electronic configuration are completed inGAUSSIAN-98 package using the time-dependent DFT/B3LYP method with 6-31G*basis set. The ab initio results show that this molecule only has one charge transfer statein lower energy region, here it is the first excited state. The transition electric dipolemoment between the first and the fourth excited states is also very large. It is found thatthe transition electric dipole moments among other states are very small. And for suchone-dimensional symmetrical molecule, the permanent dipole moment of each state isapproximately equal to zero. So the three-level model can be used to simplify theelectronic configuration of this molecule. The three levels are marked as 1, 2 and 3. TheBloch equations for three-level system are derived from density matrix equationcontaining relaxation effects. Then iterative predictor-corrector finite-differencetime-domain method is used to numerically solve the Maxwell-Bloch equations tosimulate the propagation of femtosecond laser pulses in the strong two-photonabsorption organic molecular medium. The main results are as follows:1. When the incident ultrashort laser pulse induces single-photon resonanttransition between energy level 1 and 2, the slowly varying envelope approximation(SVEA) and the rotating wave approximation (RWA) cannot accurately describe thepropagation of the ultra-short pulse in the molecular medium. With the pulse widthunchanged, the two-level model can well describe the interaction between the small areapulse and the molecular system. While for large area pulse, due to the occurrence ofstrong secondary excitation to higher-lying levels, the three-level model must then beadopted. When the amplitude of the incident electric field is kept constantly, the thirdlevel's population increases with the increase of the pulse area, that is to say thesecondary excitation is strengthened. So when the interaction between ultrashort laserpulse and one-dimensional symmetrical π conjugated molecule is considered, themulti-level model should be used to simplify the energy level structure of the molecule.2. For the initially in-phase two-color ultrashort laser pulses, if each of the twolaser pulses is resonant with the permitted single-photon transition as ω p1 = ω21andω p2 = ω32, the two-step cascade stimulation, namely two-step TPA, plays a main role inthe interaction process. So the two pulses will be gradually separated decreasing theinteraction opportunities between the pulse with the ω3 2 carrier frequency and themedium while the pulse with the ω 21carrier frequency evolving like a same pulse in atwo-level system.If the two-color laser pulses are two-photon resonant but single-photon off-resonantwith the medium, the one-step TPA occurs as two photons with respectivefrequency ω p1and ω p2 are simultaneously absorbed. The delay between these two pulsesis very small. The electric field strengths are gradually decreased and the TPA intensityis weakened along the propagation of the pulses illustrated by the decrease of the thirdlevel's population. Higher and lower spectra components are generated due tofour-wave mixing effect indicating the invalidity of RWA.3. When the frequency of the input pulse is tuned to satisfy the two-photonresonant absorption condition, 4,4′-bis(dimethylamino) stilbene molecule demonstratesa good optical power limiting ability. The breakdown of the optical power limitingbehavior is also observed. The underlying mechanism of TPA based optical powerlimiting and its breakdown is analyzed from the population distribution of the strongtwo-photon absorption state. When the population inversion is reached at appropriateintensities of the pump laser, a two-photon pumped upconversion lasing pulse can beproduced. The optical power limiting ability is facilitated when the pulse widthdecreases as a result of the remarkable enhancement of the optical power limitingbreakdown threshold, but the output saturation value ascends simultaneously. Theoutput saturation value and optical power limiting breakdown threshold can bedetermined through our numerical simulation which has instructive meanings to theexperimental work.4. In the one-step resonant TPA case, the population of the TPA state is determinedby the single pulse energy fluence for a given molecular system, the effect of energyfluence on one-step resonant TPA process is similar to that of pulse area on one-photonresonant absorption process.5. The results of dynamic TPA cross section show that in femtosecond timedomain maily one-step resonant TPA occurs if the intensity of the two-photon resonantpulse is not very high, and the two-step off-resonant TPA is suppressed. Dynamic TPAcross section increases linearly with the broadening of the input pulse. Propagationdistance also has an obvious influence on TPA cross section, but it is not as expected tobe a monotonic increasing function. Various steady-state theoretical methods aredeveloped to calculate the one-step resonant TPA cross section, whereas experimentsmeasure both the one-step resonant and two-step off-resonant TPA cross sectionsbecause they are indistinguishable, so the theoretical and the experimental results aresignificantly different from each other. The method for calculating the dynamic TPAcross section makes it possible to compare the theoretical and the experimental resultsdirectly.