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Applied Sciences

Effect of Two-Photon Stark Shift on the Multi-Frequency Raman Spectra

Hao Yan, Donna T. Strickland

Published Sep 5, 2014• 8 citations
Publisher

Abstract

High order Raman generation has received considerable attention as a possible method for generating ultrashort pulses. A large number of Raman orders can be generated when the Raman-active medium is pumped by two laser pulses that have a frequency separation equal to the Raman transition frequency. High order Raman generation has been studied in the different temporal regimes, namely: adiabatic, where the pump pulses are much longer than the coherence time of the transition; transient, where the pulse duration is comparable to the coherence time; and impulsive, where the bandwidth of the ultrashort pulse is wider than the transition frequency. To date, almost all of the work has been concerned with generating as broad a spectrum as possible, but we are interested in studying the spectra of the individual orders when pumped in the transient regime. We concentrate on looking at extra peaks that are generated when the Raman medium is pumped with linearly chirped pulses. The extra peaks are generated on the low frequency side of the Raman orders. We discuss how linear Raman scattering from two-photon dressed states can lead to the generation of these extra peaks.

DOI
10.3390/app4030390

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High order Raman generation has received considerable attention as a possible method for generating ultrashort pulses. A large number of Raman orders can be generated when the Raman-active medium is pumped by two laser pulses that have a frequency separation equal to the Raman transition frequency. High order Raman generation has been studied in the different temporal regimes, namely: adiabatic, where the pump pulses are much longer than the coherence time of the transition; transient, where the pulse duration is comparable to the coherence time; and impulsive, where the bandwidth of the ultrashort pulse is wider than the transition frequency. To date, almost all of the work has been concerned with generating as broad a spectrum as possible, but we are interested in studying the spectra of the individual orders when pumped in the transient regime. We concentrate on looking at extra peaks that are generated when the Raman medium is pumped with linearly chirped pulses. The extra peaks are generated on the low frequency side of the Raman orders. We discuss how linear Raman scattering from two-photon dressed states can lead to the generation of these extra peaks.
It has been observed that when the multi-frequency Raman scattering process is pumped by two frequency chirped pulses in the transient regime, the anti-Stokes orders are spectrally broadened on the lower-frequency side, causing each of the orders to have a broader spectrum with double-peak pattern. In this article, we employ frequency-resolved optical gating to study the spectral shift of the first anti-Stokes Raman order. A double-pulse model is introduced to determine the electric field of the anti-Stokes orders from the experimental FROG spectrogram. With the help from the double-pulse model, we demonstrate that the double-peaked spectrum comes from linear Raman scattering between manifolds in the two-photon dressed states.
We have investigated the behavior of high-order stimulated Raman scattering in a highly-transient regime. We demonstrate efficient collinear generation of vibrational sidebands in molecular hydrogen and methane using two-color pumping with pulses of duration $\ensuremath{\tau}\ensuremath{\sim}100\phantom{\rule{0.3em}{0ex}}\mathrm{fs}$ tuned to a vibrational Raman transition. A Raman spectrum with a large bandwidth was observed, ranging from the IR to the UV. Under some conditions strong pump depletion was observed and up to five anti-Stokes sidebands were observed to have energies exceeding 10% of the transmitted pump pulse energies. A numerical simulation reproduces qualitatively and quantitatively the experimental results and allows us to explain key experimental features. The simulation also confirms that the molecular coherence in the medium is substantially increased by the two-color pumping and allows us to deduce values for the degree of material excitation. The use of this technique looks promising for efficient subfemtosecond pulse generation.
The dynamics of high-intense laser fields at coherent Raman self-scattering are investigated by the use of numerical simulation. The processes under investigation take place at the Raman scattering on electronic states in atoms with transition to be forbidden in electro-dipole approximation, on vibrational or rotational states in molecules, on states connected with the spin flip and other. It is found that the threshold intensities exist provided that the pulse duration is smaller than dephasing time of the Raman transition in the medium. Under this, the following processes occur: an effective generation of the high-order harmonics comes up; the plateau forms in the harmonic spectrum. The maximum which arises on this plateau shifts to the higher-harmonic numbers in case of the higher threshold intensities of the pulse. It is shown how the transformation of the initial pulse intensity into high-order harmonics intensity can be considerably increased with the different initial parameters of the pulse and the medium.
A theory is presented to describe the propagation of a laser pulse with several frequency components ${\ensuremath{\omega}}_{j}$=${\ensuremath{\omega}}_{O}$+j${\ensuremath{\omega}}_{R}$ through a Raman medium, where ${\ensuremath{\omega}}_{0}$ is the initial laser frequency and ${\ensuremath{\omega}}_{R}$ is the frequency of the Raman transition. We consider primarily the transient regime, where the pulse width is comparable to or less than the relaxation times of the medium. We formulate the Maxwell-Bloch equations in terms of a two-photon Rabi frequency \ensuremath{\Omega} and an overall phase theta. The resulting equations are similar in form to those describing self-induced transparency, and exhibit solutions corresponding to slowly traveling, but ultimately decaying, pulses. Numerical solutions to the equations are presented that include pump depletion, the ac Stark shift, and finite relaxation times. Significant frequency conversion to high-order (j\ensuremath{\sim}8) anti-Stokes modes is observed in the numerical results.
A study is made of the problem of stimulated Raman scattering (STRS) in a resonant medium pumped by a strong pulse satisfying the adiabaticity condition. It is shown that in the absence of relaxation the maximum STRS gain is reached during the tail (trailing edge) of the pump pulse, which is the reason for the absence of the Stark shift. If the pump pulse is considerably longer than the relaxation time, the lag of the STRS pulse behind the pump pulse is short and then the Stark shift is manifested in the spectrum and a characteristic interference structure is formed. Noise and monochromatic "seeding" variants are considered.