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Photonics North (PN)

Double-pulse Model for the Study of Red-shifted Spectrum in Multi-frequency Raman Generation

Zujun Xu, Zhiyu Jin, Donna T. Strickland

Published May 24, 2022• 0 citations
Publisher

Abstract

Pumped by two frequency chirped pulses in the transient regime, the anti-Stokes orders from multi-frequency Raman Generation are spectrally broadened on the lower frequency side, causing each of the orders to have a broader spectrum with double-peak pattern. In this letter, a double-pulse model is introduced to analyze the measured spectrograms. We think the red-shifted spectrum comes from the linear Raman scattering between manifolds in the two-photon dressed states.

DOI
10.1109/pn56061.2022.9908379

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Pumped by two frequency chirped pulses in the transient regime, the anti-Stokes orders from multi-frequency Raman Generation are spectrally broadened on the lower frequency side, causing each of the orders to have a broader spectrum with double-peak pattern. In this letter, a double-pulse model is introduced to analyze the measured spectrograms. We think the red-shifted spectrum comes from the linear Raman scattering between manifolds in the two-photon dressed states.
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.
When multifrequency Raman scattering is driven in the transient regime by two chirped pump pulses, the resulting anti-Stokes orders exhibit asymmetric spectral broadening toward lower frequencies, leading to a characteristic double-peaked structure in each order. In this Letter, frequency-resolved optical gating (FROG) is used to investigate the spectral evolution of the first anti-Stokes Raman component. To interpret the observed features, we introduce a double-pulse interference model and employ an adaptive learning-based reconstruction algorithm using the Adam optimizer to retrieve the temporal field evolution. The simulation results show good agreement with the experimental measurements. Our analysis indicates that the observed red-shifted spectral component originates from linear Raman processes within the two-photon dressed-state framework.
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.
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.
Recently Swanson et al.1 have shown that, even in the transient regime of a Raman generator, when the Stokes pulses are nominally transform-limited, the mean frequency of the pulses fluctuates from pulse to pulse. The coherent modes model2 provides a simple, intuitive and computationally efficient method for determining the statistics of the Stokes light from a Raman generator. We use this model to calculate the probability density of the mean frequency of the Stokes pulse energy spectrum and show that it gives reasonable agreement with Swanson et al.'s experimental results. The spectral fluctuations in the transient regime arise because the excitation of high-order temporally coherent modes produces a time-dependent phase structure in the Stokes pulse. The phase of the Stokes field is more sensitive to the excitation of these high-order modes than is its amplitude, so that the pulse energy spectrum exhibits measurable fluctuations in the transient regime, even though the pulse temporal shape does not.3
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.