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Physica Scripta

Lineshape dependence of ultrafast saturation of absorption and fluorescence

Anil K. Patnaik, Sukesh Roy, James R. Gord

Published Oct 1, 2015• 7 citations
Publisher

Abstract

Ultrafast saturation of signals from an optical process occurs when intense laser pulses, with the duration of the driving laser pulse shorter than the effective decay timescales, interact with the target system. Recently, it has been shown that such saturation is marked by transition from transient-absorption to the transient-gain regime, unlike in continuous-wave or long-duration excitations where saturation occurs once the underdamping regime is achieved. The threshold intensities of the drive pulse that drives the optical signal to saturate can be estimated by calculating the area of the pulse. We demonstrate that depending on the shape of the pulse, the saturation behavior differs. The lineshape dependence of ultrafast saturation of absorption and fluorescence is studied for a variety of pulse shapes. We demonstrate that the saturation threshold is lower for super-Gaussian pulses and almost an order of magnitude lower for sech pulses compared to a Gaussian pulse.

DOI
10.1088/0031-8949/2015/t165/014031

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Ultrafast saturation of signals from an optical process occurs when intense laser pulses, with the duration of the driving laser pulse shorter than the effective decay timescales, interact with the target system. Recently, it has been shown that such saturation is marked by transition from transient-absorption to the transient-gain regime, unlike in continuous-wave or long-duration excitations where saturation occurs once the underdamping regime is achieved. The threshold intensities of the drive pulse that drives the optical signal to saturate can be estimated by calculating the area of the pulse. We demonstrate that depending on the shape of the pulse, the saturation behavior differs. The lineshape dependence of ultrafast saturation of absorption and fluorescence is studied for a variety of pulse shapes. We demonstrate that the saturation threshold is lower for super-Gaussian pulses and almost an order of magnitude lower for sech pulses compared to a Gaussian pulse.
A generalized formulation is presented for determining the saturation thresholds for optical processes excited by ultrafast pulses based on the pulse area of the excitation pulse. It is demonstrated that the threshold of driving-pulse intensity for absorption and fluorescence saturation in a two-level system is inversely proportional to the square of the duration of the excitation pulse. These results are obtained from both a simplified analytical solution assuming a Gaussian excitation pulse shape and a detailed numerical calculation based on density-matrix equations. The calculation is generalized further to obtain the saturation condition for a two-photon Raman process by defining a two-photon pulse area both analytically and numerically. These results not only provide predictive capabilities for determining thresholds of signal saturation using ultrashort durations with arbitrary pulse shapes and durations but also open up possibilities for predetermining the threshold intensities of various resonant nonlinear processes.
Ultrafast laser pulses with broad bandwidth can simultaneously excite multiple quantum states, forming coherent superpositions. The phases of the associated optical transitions evolve in time, giving rise to spectral line profiles that range from symmetric Lorentzian to asymmetric Fano-like forms. Yet, the line shape relations between different transitions within such superpositions remain largely unexplored. Here, we use transient absorption spectroscopy to probe transitions from coherent superpositions. While each transition’s line profile evolves over time, the relative line shape relations between different transitions remain fixed. We identify 4 fundamental types of line shape relations, each producing distinct spectral signatures. These relations naturally arise from second-order perturbation processes and can be actively tuned via the laser–matter interaction strength. Our findings establish a pathway for line shape-engineered control across atomic and molecular systems.
The saturation threshold of a probe pulse in an ultrafast electronic-resonance-enhanced (ERE) coherent anti-Stokes Raman spectroscopy (CARS) configuration is calculated. We demonstrate that while the underdamping condition is a sufficient condition for saturation of ERE-CARS with the long-pulse excitations, a transient gain must be achieved to saturate the ERE-CARS signal for the ultrafast probe regime. We identify that the area under the probe pulse can be used as a definitive parameter to determine the criterion for a saturation threshold for ultrafast ERE-CARS. From a simplified analytical solution and a detailed numerical calculation based on density-matrix equations, the saturation threshold of ERE-CARS is compared for a wide range of probe-pulse durations from the 10-ns to the 10-fs regime. The theory explains both qualitatively and quantitatively the saturation thresholds of resonant transitions and also gives a predictive capability for other pulse duration regimes. The presented criterion for the saturation threshold will be useful in establishing the design parameters for ultrafast ERE-CARS.
We investigate the effects of the input laser beam’s temporal pulse shape on a forward degenerate four-wave mixing (FDFWM) signal, assuming two-level saturable absorbers. Under conditions in which the coherence time is far shorter than the pulse-duration, we can calculate the signal easily in the time and frequency domains. From this result it is shown that, when the pulse duration is longer than ten times the population relaxation time, the calculated signal intensity is almost the same as that obtained by assuming a steady state throughout duration of the laser pulse. With this assumption, we obtain the signal by summing all the steady-state signals at each time-domain grid point during the pulse. The calculation is performed with three input beam temporal pulse shapes: square, Gaussian, and typical Q-switched pulses. After reaching a maximum, the signal intensity decreases. The rates of the signal increase and decrease depend strongly on the temporal shape of the input beam. For the same average power, the square-pulse input saturates the absorber faster than the other pulses. These results indicate that the weak part of the pulse input plays an important role in generating the signal, yielding differences in saturation behavior of the signal intensity and the spectral line shape. We compare the calculations with experiments by fitting the saturation curve of the FDFWM signal of argon atoms in a radio frequency inductively coupled plasma. Also, the spectral line shape of the DFWM signal is fitted with the calculation by use of published experimental data.
The theory of transient stimulated Raman scattering has been extended to include an arbitrary shape of the laser pump pulse. It is shown that the maximum Stokes gain depends on the total energy content per unit area of the pump pulse, and not on the instanteous intensity for an exciting pulse of short duration. The Stokes pulse has a leading edge which rises sharply to a maximum, where the maximum occurs with some delay with respect to the maximum of the pump pulse. The trailing edge follows the decay of the pump. In a nondispersive medium, the gain is not reduced by frequency broadening of the laser output, while in a dispersive medium, considerable gain reduction is expected. Numerical results for various laser-pulse shapes and spectral distributions are presented.
We consider the nonlinear propagation of an intense short pulse of polarized light through a molecular medium with ground- and excited-state absorption, excited-state emission, and fluorescence from the excited state to the ground state and possibly to a lower-lying excited state. We incorporate the effects of saturation, field-induced alignment, and rotational diffusion of the molecules in the medium. Our approach uses a slowly varying envelope approximation for the light propagation and rate equations for the effective parallel and perpendicular (and higher-multipole) population components of the molecular states. The time dependence of the anisotropy of the fluorescence occurring after preparation of the medium by the intense short pulse is determined. We can treat propagation through an optically nonthin medium wherein the intensity of the pulse decreases while propagating through the medium. An example of a 100-ps pulse propagating through a sample of Rhodamine-6G is presented. We compare our method with others used to describe intense-short-pulse propagation in molecular media.