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Applied Sciences

Time-Dependent, Two-Photon Rabi Frequency Shift Observed in Multi-Frequency Raman Spectra

Zujun Xu, Zhiyu Jin, Donna T. Strickland

Published Sep 20, 2023• 0 citations
Publisher

Abstract

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.

DOI
10.3390/app131810488

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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.
Quantum Langevin formalism with noise operators is used to provide quantum descriptions of photon pairs (the Stokes and anti-Stokes fields) emitted by a mesoscopic spherical particle composed of quantum particles in a double Raman configuration. The spectra of the fields obtained are sensitive to the dimension of the microsphere and can be controlled by pump and control laser fields. Spectral peaks due to quantum coherence are Stark shifted by the laser fields experiencing autofocusing inside the spherical particle, causing broadening of peaks as the size of the microsphere increases. The antinormal-order spectrum is found to be identical to the normal-order spectrum. The anti-Stokes spectrum is identical to the Stokes spectrum when the linear dispersion is neglected. Frequency-dependent dielectric functions of the Stokes and anti-Stokes spectra corresponding to the linear dispersions of the particle yield narrow morphology-dependent resonance gain peaks at certain frequencies of the Stokes and anti-Stokes spectra that depend not only on the particle size but also on the angle of observation.
We present a semi-analytical theory to describe the nonlinear scattering of Raman photon pairs from a cylindrical microparticle comprising of quantum particles in double Raman configuration. The normally ordered Stokes and anti-Stokes spectra are computed to gain insights into the quantum optical properties of the system and the variation of the spectra with microparticle’s size, orientation as well as observation angles are also analyzed and compared with the results obtained in our previous work involving mesoscopic spherical particle. Our results show several features in the spectra that are unique to the case of cylindrical microparticle and not found in the spherical particle case, such as the shifting of the side peaks originally formed due to ac Stark shifts towards the center at certain range of particle radius values, occurrence of side peaks with magnitudes comparable to that of the central peak, formation of additional peaks at certain observation angles and strong dependence of the spectra on the microparticle’s cylinder axis orientation. Most of these effects are either caused by the inhomogeneity of the incident pump and control laser fields within the volume of the cylindrical microparticle or simply due to the lack of three-dimensional symmetry of cylindrical geometry.
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.