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Physical Review A

Stimulated Raman Emission in Diamond: Spectrum, Gain, and Angular Distribution of Intensity

A. K. McQuillan, Wallace R. L. Clements, Boris Peter Stoicheff

Published Mar 1, 1970• 88 citations
Publisher

Abstract

An experimental study of normal and stimulated Raman emission in diamond is presented, including measurements of linewidth, intensity, and angular distribution of radiation having a frequency shift of 1332.0 ${\mathrm{cm}}^{\ensuremath{-}1}$. The diamond crystal formed a Raman resonator; excitation was by a giant-pulse ruby laser. The dependence of normal Stokes emission on laser intensity and the threshold for oscillation were investigated. A value for the Raman gain ($g=6.9\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ ${\mathrm{cm}}^{\ensuremath{-}1}$ per MW/${\mathrm{cm}}^{2}$) was calculated from the measured linewidth ($\ensuremath{\Delta}\ensuremath{\nu}=2.04$ ${\mathrm{cm}}^{\ensuremath{-}1}$) and cross section for scattering, and found to be in good agreement with a value determined from the threshold for oscillation. The angular distributions of anti-Stokes and Stokes emission and absorption for parallel and convergent laser light are also in good agreement with theory: The emission cone angles are strongly dependent on the angle of convergence of the incident light, and it is established that the preferred directions for emission are those making use of the most intense first-order Stokes radiation which is peaked in the forward direction within the Raman resonator.

DOI
10.1103/physreva.1.628

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The correlated Stokes-anti-Stokes Raman scattering: a study of the influence of temporal width of the excitation pulse

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In this work, we study the correlated Stokes-anti-Stokes (SaS) Raman scattering in a diamond sample and the influence that the excitation pulse width has in the intensity of generation of the correlated pairs in the process. For this investigation, we used two excitation systems with different temporal pulse width, one with femtosecond temporal width and one with picosecond temporal width. We did two distinct experiments with this excitation systems with difference in the way of filtering the signal: In the first experiment, the signal filtering is made with band-pass filters, this configuration has a greater efficiency that allow us compare better the correlated pair formation efficiency between the different excitation systems. In the second experiment, we used a monochromator to filtering the signal, this configuration allow us to change the wavelength of the detection so we can measure the formation spectrum of the correlated pairs. The results obtained from these experiments show us that the correlated pairs generation efficiency is larger with the use of the system with femtosecond temporal width, what is expected for a non-linear process. In the resonant Raman frequency region, we observed a intensity 1.5 times larger with the use of femtosecond system, and in the out-of-ressonance Raman region, we observed a intensity 5 times larger in the region with lowest Raman shift and 9 times larger in the region with largest Raman shift. We also measure the formation pairs spectrum around the first order Raman peak of the diamond, confirming the existence of a asymmetry in the formation of this pairs with respect to the positive versus negative detuning from phonon resonance. This asymmetry still remains without a satisfactory theoretical explanation.

•Oct 21, 2022•0 citations
An experimental study of normal and stimulated Raman emission in diamond is presented, including measurements of linewidth, intensity, and angular distribution of radiation having a frequency shift of 1332.0 cm\ensuremath−1{\mathrm{cm}}^{\ensuremath{-}1}cm\ensuremath−1. The diamond crystal formed a Raman resonator; excitation was by a giant-pulse ruby laser. The dependence of normal Stokes emission on laser intensity and the threshold for oscillation were investigated. A value for the Raman gain (g=6.9\ifmmode×\else\texttimes\fi10\ensuremath−3g=6.9\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}g=6.9\ifmmode×\else\texttimes\fi10\ensuremath−3 cm\ensuremath−1{\mathrm{cm}}^{\ensuremath{-}1}cm\ensuremath−1 per MW/cm2{\mathrm{cm}}^{2}cm2) was calculated from the measured linewidth (\ensuremathΔ\ensuremathν=2.04\ensuremath{\Delta}\ensuremath{\nu}=2.04\ensuremathΔ\ensuremathν=2.04 cm\ensuremath−1{\mathrm{cm}}^{\ensuremath{-}1}cm\ensuremath−1) and cross section for scattering, and found to be in good agreement with a value determined from the threshold for oscillation. The angular distributions of anti-Stokes and Stokes emission and absorption for parallel and convergent laser light are also in good agreement with theory: The emission cone angles are strongly dependent on the angle of convergence of the incident light, and it is established that the preferred directions for emission are those making use of the most intense first-order Stokes radiation which is peaked in the forward direction within the Raman resonator.
A simple description of the stimulated Raman emission of Stokes radiation, and of the induced absorption found by Stoicheff at the anti-Stokes frequency, is based on the semiclassical theory of radiation. This theory gives the well-known formulas for absorption and stimulated emission when carried to the first order in the time-dependent perturbation due to the interaction of the light beam with the molecules. If there are two light beams of frequencies ωL and ω, the second-order perturbation may be associated with stimulated emission at the Stokes frequency ω=ω−1=ωL—ωR and with induced absorption at the anti-Stokes frequency ω=ω1=ωL+ωR, where ωL is the laser frequency and ωR a Raman-active vibrational frequency; in both cases, there is a molecular transition to the excited vibrational state. The highly directional and very sharp anti-Stokes emission at ω1 arises from the conversion by molecules in intense beams at ωL and ω−1 of two ωL photons into an ω−1, ω1 pair. Like spontaneous emission from excited states, the production of this anti-Stokes radiation requires the full quantum theory of radiation for an adequate description. The emission of ω1 and the observed directional absorption of ω−1 due to the reverse conversion ω−1+ω1→2ωL are explained. The anti-Stokes emission is proportional to the Stokes intensity and to the square of that of the laser, and to the square of the molecular number density; its sharpness is due to the absence of a molecular transition. The generation of photon pairs ω−n+ωn, where ωn=ωL+nωR, can occur for all values of n, but it is most efficient for n=1, due to resonance in the appropriate molecular hyperpolarizability and to the intensity of the Stokes beam at ω−1.
A three-dimensional analysis of stimulated Raman emission is presented for a medium through which a cylindrical laser beam passes. The buildup of the Stokes radiation from the spontaneous fluctuations in the Raman medium is considered. A generalization of the fluctuation-dissipation theorem is derived relating the current-current fluctuations at the Stokes frequency to the laser-induced (negative) conductance at this frequency. The anti-Stokes radiation is treated as arising from the interaction of the laser field and the molecular vibrations accompanying the Stokes radiation. The anti-Stokes radiation emerges in a narrow cone around the familiar phase-matching direction given by ${\mathbf{\ensuremath{\beta}}}_{\ensuremath{-}}=2{\mathbf{k}}_{L}\ensuremath{-}{\mathbf{\ensuremath{\beta}}}_{+}$, where ${\mathbf{\ensuremath{\beta}}}_{\ensuremath{-}}$ and ${\mathbf{\ensuremath{\beta}}}_{+}$ are the (real parts of the) propagation constants of Stokes and anti-Stokes waves in the medium, and kL{\mathbf{k}}_{L}kL​ is the laser propagation vector. The angular width of the anti-Stokes radiation cone is evaluated.
Strong interference of the first Stokes Raman radiation with the stimulated Brillouin radiation has been observed in an off-axis resonator: Brillouin gain decreases appreciably by the presence of the Raman radiation in a medium such as CS2, in which the Raman and Brillouin scatterings can be stimulated simultaneously. Such a type of interference can be explained as the Raman scattering of the Brillouin photons stimulated by the first Stokes Raman photons. A classical theory has shown a quantitative agreement with the experiment. The anti-Stokes Brillouin components have not been observed even though the laser excitation was intense enough to allow the observation of the multiple Stokes components which were excited directly in the off-axis resonator without the feed-back effect of the laser as an amplifier.
Narrow-linewidth diamond Raman lasers hold significant potential for applications in special-wavelength laser generation, coherent detection, and precision measurement. Resonant pumping is an effective approach for achieving low-threshold excitation of diamond Raman lasers. In this operating regime, the output-coupler transmittance directly affects the Stokes cavity loss, but its influence on the realized Raman linewidth has not been systematically investigated. Here, a narrow-linewidth continuous-wave pump laser combined with Pound–Drever–Hall locking is used to resonantly pump a diamond Raman oscillator, and the Stokes characteristics are compared for different output-coupler transmittances. The output-coupler transmittance significantly affects the Raman lasing threshold, conversion efficiency, locking robustness, and output linewidth. Increasing the transmittance from 0.6% to 3.0% increases the Stokes output power and conversion efficiency but shortens the stable locking duration. Conversely, reducing the transmittance progressively narrows the Stokes linewidth. At a transmittance of about 0.2%, a Stokes linewidth of 5.70 kHz, slightly narrower than that of the pump laser, is achieved. This result indicates that low output-coupling loss extends the intracavity Stokes photon lifetime and enhances the suppression of pump-to-Stokes frequency-noise transfer, thereby enabling linewidth compression. This study reveals the role of output-coupling loss in controlling the linewidth evolution of resonantly pumped diamond Raman lasers and provides important experimental guidance for the design of low-threshold, highly stable, narrow-linewidth diamond Raman lasers.
In this work, we study the correlated Stokes-anti-Stokes (SaS) Raman scattering in a diamond sample and the influence that the excitation pulse width has in the intensity of generation of the correlated pairs in the process. For this investigation, we used two excitation systems with different temporal pulse width, one with femtosecond temporal width and one with picosecond temporal width. We did two distinct experiments with this excitation systems with difference in the way of filtering the signal: In the first experiment, the signal filtering is made with band-pass filters, this configuration has a greater efficiency that allow us compare better the correlated pair formation efficiency between the different excitation systems. In the second experiment, we used a monochromator to filtering the signal, this configuration allow us to change the wavelength of the detection so we can measure the formation spectrum of the correlated pairs. The results obtained from these experiments show us that the correlated pairs generation efficiency is larger with the use of the system with femtosecond temporal width, what is expected for a non-linear process. In the resonant Raman frequency region, we observed a intensity 1.5 times larger with the use of femtosecond system, and in the out-of-ressonance Raman region, we observed a intensity 5 times larger in the region with lowest Raman shift and 9 times larger in the region with largest Raman shift. We also measure the formation pairs spectrum around the first order Raman peak of the diamond, confirming the existence of a asymmetry in the formation of this pairs with respect to the positive versus negative detuning from phonon resonance. This asymmetry still remains without a satisfactory theoretical explanation.