Changes in the modulus and phase of a slowly varying envelope of an ultrashort pulse are calculated for the case of propagation across a saturable absorber. Vibronic relaxation of the optical transition in the absorber is allowed for. A study is made of the dependences of the duration of a pulse transmitted by a nonlinear absorber on the vibrational relaxation time of dye molecules and on the detuning of the carrier frequency of a pulse relative to the maximum of the equilibrium absorption spectrum. It is shown that a chirp appears even in the absence of such detuning provided the energy of lf quanta of optically active vibrations is comparable with the thermal excitation energy. This chirp originates from partial completion of the vibrational relaxation process during a pulse, so that absorption and refraction occur in a system which is not in a vibrational equilibrium.
Changes in the modulus and phase of a slowly varying envelope of an ultrashort pulse are calculated for the case of propagation across a saturable absorber. Vibronic relaxation of the optical transition in the absorber is allowed for. A study is made of the dependences of the duration of a pulse transmitted by a nonlinear absorber on the vibrational relaxation time of dye molecules and on the detuning of the carrier frequency of a pulse relative to the maximum of the equilibrium absorption spectrum. It is shown that a chirp appears even in the absence of such detuning provided the energy of lf quanta of optically active vibrations is comparable with the thermal excitation energy. This chirp originates from partial completion of the vibrational relaxation process during a pulse, so that absorption and refraction occur in a system which is not in a vibrational equilibrium.
Equations are proposed for the nonlinear interaction between optical pulses and dye solutions allowing for the contribution of the stimulated emission band to the nonlinear dispersion of the solution. A numerical solution of the equations showed that, for pulses having a carrier frequency near the absorption band of the solution, phase modulation of the pulses transmitted by the solution took the form of a deviation of the instantaneous frequency toward the red, and the "chirp" was positive.
We model the response of a molecular medium to an intense pulse of light. We begin by reducing the Maxwell-Bloch equations for a multilevel molecular model system to a set of simplified propagation equations. We thereby obtain expressions for the frequency, temperature, and field intensity dependence of the ground and excited electronic state absorption cross sections, and the emission cross section, as well as the temperature dependence of the decay rate of the excited state. The phenomena of saturation, excited-state absorption, optically induced dichroism and birefringence, vibronic energy transfer, induced molecular alignment, decay of the matter-field interaction energy, and rotational diffusion are considered within the general formalism for describing the propagation of an intense pulse of light in the molecular medium. We find that the cross section for absorption (emission) of a photon is not identical to the cross section for molecular excitation (deexcitation) via the matter-field interaction. This is explained in terms of an energy balance between the matter, radiation, the matter-radiation interaction, and the bath responsible for the broadening of the molecular transitions. The inequality of these cross sections determines whether the system supplies or draws energy from the thermal bath. The rise in the vibrational temperature of molecules subjected to an intense short pulse is shown to significantly affect propagation of the pulse. The alignment of the molecular system resulting from saturation of the ground-state transition by a polarized laser pulse and the effects of the orientational dependence of the matter-field interaction including effects of rotational diffusion are determined. As an example of the formalism we consider pulse propagation in a Rhodamine 6G solution. We fit the parameters of the model to determine the frequency dependence of the ground- and excited-state absorption cross sections and the emission cross section and compare with experimentally determined cross sections. We describe the propagation of a pulse whose temporal width is comparable to the rotational diffusion time of the molecules in the dye solution and calculate polarization pulse probe signals.
The time dependence of the frequency shift (δω) due to colliding-pulse phase modulation (CPPM) is computed, for collision of femtosecond optical pulses, both in nonresonant and in saturable media. In particular, thin material slabs (up to several pulse widths τ) are considered, and although the results are more generally applicable, special attention is given to a typical saturable-absorber jet in a colliding-pulse mode-locked laser. Results show that CPPM in nonresonant media causes noticeable effects on the chirp, both for thin slabs with L ≈ laser wavelength, where the coherence of the pulses leads to interference effects, and for thicker slabs with L ≈ cτ. Complications to CPPM by saturable media are discussed, and it is shown that the consequences of dispersion by the ground-state population, and finite phase-relaxation time, may be important for short, low-energy pulses. The results show, for parameters typical of contemporary colliding-pulse mode-locked lasers, what conditions are favorable for short, stable pulse formation in solitonlike pulse shaping. It is also shown that there are conditions for which the pulses produced would be spread by any sign of group-velocity dispersion.
We experimentally measure the propagation delays for chirped optical pulses with asymmetric temporal envelope functions, through a resonantly absorbing dye solution. The transmitted pulses suffer a strong deformation and the arrival times are dramatically modified by the interaction between the chirp and the absorption effect of the sample. It is shown that the arrival time, represented by the centroid of energy of the transmitted pulse, can be well described by the reshaping delay and has a greater significance than the peak of the pulse.
We analyze the phase modulation, or chirping, of coherent lossless light pulses propagating without distortion through resonant absorbers. In order to do this, we generalize the pioneering work of McCall and Hahn in two different directions. In the first place, of course, we abandon their assumption that the phase of the pulses has no temporal dependence. We prove that for slowly varying single pulses, chirping is not possible. However, we describe many multiple-pulse trains which are necessarily chirped, even under the slowly varying envelope restriction, and also describe the envelope modulations which produce large chirps. We show that certain zero-$\ensuremath{\pi}$ chirped pulse trains are contained as special cases of our general results. Our second generalization of the McCall-Hahn work concerns the background material in which the two-level resonant atoms are suspended. We allow the host medium to possess significant nonresonant nonlinearities. We find that undistorted lossless single pulses are possible in such a medium and that they are necessarily chirped.
Pulse shaping is the technique which controls the ultra-short pulse shape, and it became of great technological interest because of its potential applications in laser pulse compression, digital communications, microscopy etc. We demonstrate the idea of pulse-shaping technique and pulse propagation with low energy losses in a resonant linear absorbing medium. This thesis presents the results of a study of the propagation of Gaussian and hyperbolic secant ultrashort chirped and chirp-free pulses in homogeneously and inhomogeneously broadened resonant linear absorbers. Changes to the pulse shape and energy loss factor are presented as the pulse propagates in the absorber. The Fast Fourier method is used to numerically determine both the normalized intensity profile and the pulse spectrum. Our results show that, for pulse durations shorter than the relaxation time, chirped pulses in absorbing media obey the area theorem, with their shape changing with the propagation distance. Simulation results of the spectra of chirped pulses clearly show the burning of a spectral ’hole’ as the pulse propagates, with the pulse energy pushed away towards the wings. When compared to chirp-free pulses, chirped pulses reshape faster and develop wings in their tail due to initial phase modulation. Simulation results of the energy loss factor show that chirped pulses propagating in resonant linear absorbers sustain less energy losses than do chirp-free pulses. A comparison of chirped secant and Gaussian pulses shows that secant pulses propagate with lower energy losses. Analytic solutions are presented for long-distance asymptotic expressions of initial rms spectral bandwidth as well as for the attenuation factor of chirped Gaussian pulses. These analytical results are in agreement with numerical simulations. The comparison of energy losses of short chirped Gaussian pulses and long pulses of any profile in linear absorbers is also discussed in the thesis.