Backward Stimulated Raman Scattering Research Articles

Inflation threshold: A nonlinear trapping-induced threshold for the rapid onset of stimulated Raman scattering from a single laser speckle

The rapid onset, with increasing laser intensity, of levels of backward stimulated Raman scattering (BSRS) exceeding linear convective predictions, from single laser hot spots was predicted by simulations [Vu et al., Phys. Plasmas 9, 1745 (2002)], and has been observed [Montgomery et al., Phys. Plasmas 9, 2311 (2002)] in nonlinear regimes dominated by electron trapping. A theory for this inflation threshold is given here. The threshold is the result of competition between velocity diffusion and trapping, and is exceeded when the convectively amplified SRS Langmuir wave (LW) achieves an amplitude for which the coherent trapping velocity increment of electrons in the LW (the half-width of the trapping separatrix) exceeds the rms diffusion velocity (resulting from background plasma fluctuations), accumulated in one bounce time, for electrons with mean velocities near the phase velocity of the LW. The results of this theory, when the kinetic theory of the one-dimensional (1D) reduced-description particle-in-cell (RPIC) simulation is used, are in good agreement with a series of 1D RPIC simulations. The theory is naturally generalized to three dimensions, and is compatible with macroscopic laser interaction codes such as pF3d [Berger et al., Phys. Plasmas 5, 4337 (1998)]. Comparison of the LW trapping-induced inflation threshold to the LW threshold for the Langmuir decay instability provides an estimate for the transition between nonlinear saturation regimes. In an independent hot spot model of many hot spots, statistics suggests that the inflation threshold intensity will control the rapid onset of strong BSRS in laser beams smoothed by random phase plates.

Spontaneous and backward stimulated Raman scattering of light in methane

The initial phase of development of stimulated Raman scattering (SRS) in the backward direction in compressed methane (the excess of the SRS intensity over the signal of spontaneous scattering in the experiment is ∼100) has been studied theoretically and experimentally. The theory, developed on the basis of simple assumptions about the mechanism of SRS formation from spontaneous scattering, shows good agreement with experiment. The implicit consideration of backward SRS is shown to be significant for the conditions of depletion of the pump energy due to its continuous loss in the medium and conversion into SRS.

Transient Development of Backward Stimulated Raman and Brillouin Scattering on a Picosecond Time Scale Measured by Subpicosecond Thomson Diagnostic

The excitation and the relaxation of the plasma waves and ion acoustic waves (IAW), respectively, driven by stimulated Raman (SRS) and Brillouin (SBS) backscatterings have been experimentally investigated with short-pulse lasers. The spectra have been obtained with a 0.3 ps time resolution. It is shown that SRS develops before SBS and suddenly decays around the peak of the pump, as the IAW reaches saturation. On this short time scale, electron kinetic effects play a major role for SRS saturation, contrary to ion dynamics. These results are supported by particle-in-cell simulations.

Nonlinear backward stimulated Raman scattering from electron beam acoustic modes in the kinetic regime

The backward stimulated Raman scattering (BSRS) of a laser from electron beam acoustic modes (BAM) in the presence of self-consistent non-Maxwellian velocity distributions is examined by linear theory and particle-in-cell (PIC) simulations in one and two dimensions (1D and 2D). The BAM evolve from Langmuir waves (LW) as electron trapping modifies the distribution to a non-Maxwellian form that exhibits a beam component. Linear dispersion relations using the nonlinearly modified distribution from simulations are solved for the electrostatic modes involved in the parametric coupling. Results from linear analysis agree well with electrostatic spectra from simulations. It is shown that the intersection of the Stokes root with BAM (instead of LW) determines the matching conditions for BSRS at a nonlinear stage. As the frequency of the unstable Stokes mode decreases with increasing wave number, the damping rate and the phase velocity of BAM decreases with the phase velocity of the Stokes mode, providing a self-consistently evolving plasma linear response that favors continuation of the nonlinear frequency shift. Coincident with the emergence of BAM is a rapid increase in BSRS reflectivity. The details of the wave-particle interaction region in the electron velocity distribution determine the growth/damping rate of these electrostatic modes and the nonlinear frequency shift; in modeling this behavior, the use of sufficiently large numbers of particles in the simulations is crucial. Both the reflectivity scaling with laser intensity and the spectral features from simulations are discussed and are consistent with recent Trident experiments.

Effect of Thermal Defocusing on Backward Stimulated Raman Scattering in CH4

The conversion efficiency of stimulated Raman scattering (SRS) in CH4 is studied by using a single longitudinal mode second-harmonic Nd:YAG laser (532 nm, linewidth 0.003 cm1, pulse-width (FWHM) 6.5 ns). Due to the heat release from vibrationally excited particles, SRS processes often suffer from the thermal defocusing effect (TDE). In view of 6.5 ns laser pulse width is much shorter than the vibrational relaxation time of CH4 molecules, TDE can only affect the SRS processes afterwards. In the cases of low laser repetition, TDE will be not serious, because it will be removed by the thermal diffusion in Raman medium before the next pulse arrives. At the laser repetition rate 2 Hz, CH4 pressure 1.1 MPa and pump laser energy 95 mJ, the quantum conversion efficiency of backward first-Stokes (BS1) has attained 73%. This represents the highest first-stokes conversion efficiency in CH4. Furthermore, due to the relaxation oscillation, the BS1 pulses are narrowed to about 1.2 ns. As a result, the BS1 peak power turns out to be 2.7 times that of the pump. Its beam quality is also much better and is only slightly affected by TDE. This reason is that BS1 represents a wave-front-reversed replica of the pump beam, which can compensate the thermal distortions in Raman amplify process. Under the same conditions, but pump laser repetition rate as 10 Hz, the conversion efficiency of BS1 goes down to 36% due to TDE. From this study, we expect that a well-behaved 630 nm Raman laser may be designed by using a closed CH4/He circulating-cooling system, which may have some important applications.

Nonlinear development of stimulated Raman scattering from electrostatic modes excited by self-consistent non-Maxwellian velocity distributions

The parametric coupling involving backward stimulated scattering of a laser and electron beam acoustic modes (BAM) is described as observed in particle-in-cell (PIC) simulations. The BAM modes evolve from Langmuir waves (LW) as the electron velocity distribution is nonlinearly modified to be non-Maxwellian by backward stimulated Raman scattering (BSRS). With a marginal damping rate, BAM can be easily excited and allow an extended chirping in frequency to occur as later SRS pulses encounter modified distributions. Coincident with the emergence of this non-Maxwellian distribution is a rapid increase in BSRS reflectivities with laser intensities. Both the reflectivity scaling with laser intensity and the observed spectral features from PIC simulations are consistent with recent Trident experiments.

Study of the competition between forward and backward stimulated Raman scattering in methane

Simultaneous forward and backward stimulated Raman scattering (SRS) in methane pumped by a single longitudinal mode Nd:YAG laser at 355 nm has been investigated both experimentally and numerically. For forward SRS, a maximum energy-conversion efficiency of 55% was obtained under 24 atm, while for backward SRS the corresponding figure was 58% under 4.7 atm. Under low pressures or at low pump energies, the conversion efficiency for backward SRS was found to be much higher than that for forward SRS, while the situation is quite the contrary under high pressures and at high pump energies. A quasi-two-dimensional numerical model is introduced to elucidate the competition between forward and backward SRS; we conclude that the high-pressure and high-pump-energy experimental results should be caused by the thermal defocusing effect in the SRS process. This is confirmed by the experimental fact that a decrease of the pulse-repetition rate increases the conversion efficiency for backward SRS but decreases that for forward SRS under high pressures. Our calculated results are in good agreement with the experimental results at a pulse-repetition rate of 2 Hz.

Nonlinear Spectral Signatures and Spatiotemporal Behavior of Stimulated Raman Scattering from Single Laser Speckles

Simulations are reported of the Thomson scatter spectrum of electrostatic waves (ESWs) excited in single laser hot spots by backward stimulated Raman scattering (BSRS). Under conditions similar those in the recent experiments of Kline et al. [Phys. Rev. Lett. 94, 175003 (2005)], a spectral streak, resulting from the trapping-induced frequency shift of the ESW, is found for high wave-number ESWs, similar to the observations. This shift and parametric frequency matching lead to isolated BSRS pulses. Modes with acoustic dispersion, resulting from the trapping-modified electron velocity distribution, can enhance the frequency range of the streak.

Stimulated Raman back-scattering from a mm-scale inhomogeneous plasma irradiated with ultra-intense laser pulse

Stimulated Raman scattering (SRS) from a mm-scale inhomogeneous plasma irradiated with an ultra-intense laser pulse was studied. Experimental results show that backward SRS spectral intensities increase with scattered light wavelength up to 1.3 λ0 and saturate at longer wavelength, where λ0 is the wavelength of the ultra-intense laser. Nonlinear phase mismatch was found to cause the saturation from a fully relativistic nonlinear 1D fluid simulation due to the relativistic mass increase of electron. The total amount of SRS was measured to be less than 3% of the incident laser energy.

Kinetic inflation of stimulated Raman backscatter in regimes of high linear Landau damping

Kinetic simulations and analysis show that backward stimulated Raman scattering (BSRS), in regimes of large linear Landau damping of the primary Langmuir wave, attains levels greatly exceeding the predictions of models based on fixed damping. These regimes are encountered in plasma conditions expected for target designs to be fielded at the National Ignition Facility [J. D. Lindl, Inertial Confinement Fusion (Springer-Verlag, New York, 1998)]. Trapped electrons in the Langmuir wave have the dual effect of reducing its damping, thereby enhancing the BSRS response, and saturating this response by phase detuning, a consequence of the trapping-induced, time-dependent, frequency shift. BSRS, then, occurs as a train of sub-picosecond pulses, arising from the competition between phase detuning and parametric regeneration. A simple three wave parametric model, including the effect of the nonlinear frequency shift and residual nonlinear damping, reproduces these essential features. A similar scenario applies to backward stimulated Brillouin scattering (BSBS). BSRS activity many orders of magnitude above noise level is found for intense laser speckles even when the primary Langmuir wave number times the Debye length is as high as 0.55. The simulation model consistently accounts for the competition of other instabilities, including BSBS, forward stimulated Raman scattering, and the Langmuir decay instability with cavitation.

Transient enhancement and detuning of laser-driven parametric instabilities by particle trapping.

Kinetic simulations of backward stimulated Raman scattering (BSRS), where the Langmuir wave coherence time is greater than the bounce time for trapped electrons, yield transient reflectivity levels far above those predicted by fluidlike models. Electron trapping reduces the Langmuir wave damping and lowers the Langmuir wave frequency, and leads to a secular phase shift between the Langmuir wave and the BSRS beat ponderomotive force. This phase shift detunes and saturates BSRS and a similar effect, due to ion trapping, is the saturation mechanism for backward stimulated Brillouin scattering. Competition with forward SRS is discussed.

Asymmetry of the forward and backward Raman gain coefficient at 154 µm in methane

The threshold pump energies at 1.06 mum and Raman gain coefficients of stimulated Raman scattering (SRS) at 1.54 mum have been measured in both single-pass and half-resonator configurations at various methane pressures. In the single-pass configuration, the Raman gain coefficients of the backward and forward SRS are 0.32 and 0.23 cm/GW at 95 atm, respectively. The backward Raman gain coefficient is higher than the forward Raman gain coefficient. This gain reduction is caused by the depletion of local pump intensity, the phase-matching conditions, and the transient effect of the high amplification rate in the forward SRS process. In the half-resonator configuration, the Raman gain coefficient was 0.46 cm/GW at 75 atm of methane.

Backward stimulated Raman scattering in water

The backward Stimulated Raman scattering (BSRS) is studied in liquid water. We show that BSRS can be produced by small volumes of active materials. Our experimental results and calculations with different geometries and intensities of excitation allow us to choose the best experimental set-up for BSRS efficiencies. The competition with librational scattering is also observed.

Wave-front reconstruction by backward-stimulated Raman scattering in a multimode graded-index optical fiber

We have experimentally observed, for the first time to our knowledge, wave-front reconstruction by backward-stimulated Raman scattering (BSRS) in a multimode graded-index fiber. The wave-front reconstruction was quantitatively verified by experiments on beam collimation, intensity distribution, and aberration correction of the BSRS after the beam passed through an aberrator. Polarization experiments also showed that, for a BSRS beam, the sense of circular polarization is nearly identical to that of the incident beam. An interesting aspect of this observation is that, even though the pump excited a large number of modes, the BSRS process appeared to be single-mode-like, and wave-front reconstruction was accomplished.

Backward stimulated Raman scattering of a modulated laser pulse in plasmas

The specific features of backward stimulated Raman scattering (BSRS) of a short modulated (multi-frequency) laser pulse in underdense plasmas are studied. The effect of resonant suppression of the BSRS of higher frequency pulse components is explored. For an arbitrary pair of pulse components, in the conditions of weak coupling, it is demonstrated that the backscattering of a higher frequency laser pulse component is a five-wave resonant process at a frequency difference between the components close to the double plasma frequency. In the conditions of strong coupling the backscattering of neither pulse component is suppressed and the spectrum of the instability is not connected immediately with the details of a spectrum of a laser pulse. Numerical modelling of the BSRS of a multi-frequency laser pulse is in complete agreement with the analytical predictions.

Effects of density scale length on backward and forward stimulated Raman scattering in 0.53 μm laser–plasma interaction

Forward and backward stimulated Raman scattering (SRS) have been investigated in three different plasma geometries: in exponential density profile, in Gaussian density profile, and in quasihomogeneous preformed plasmas. The experiments were performed with the same irradiation setup at 0.53 μm wavelength and at a laser intensity ∼1015 W/cm2. Time-resolved spectra and energy rates of this instability have been measured in the three experiments. A strong increase of the backward SRS energy rate—up to 1%—with the increasing length of the plasma was observed. From data analysis, backward SRS is explained in terms of absolute instability. On the other hand, forward SRS can be interpreted by considering linear scattering of the incident laser light on the plasma wave driven by backward SRS. This assumption is adequately supported both by the spectral characteristics and by the energy rates of the forward emission light.

Statistical characteristics of the energies of pulses of forward and backward stimulated Raman scattering under linear, intermediate, and nonlinear scattering conditions

An experimental investigation was made of the distribution of the energies of pulses of forward (concurrent) and backward first Stokes components of stimulated Raman scattering (STRS), and of pump (exciting) radiation pulses, transmitted by a scattering medium. The study was carried out under linear, intermediate, and nonlinear scattering conditions. The dependences of the coefficients of variation and of the asymmetry of the distributions on the energy of the pump pulses were determined. The statistical properties of the energy of the backward STRS pulses differed in a number of respects from the forward STRS pulses, including a relatively high coefficient of variation in the former case. An interpretation of these differences was developed. It was found that STRS gave rise to fluctuations of the energy of the transmitted pump pulses and the statistical characteristics of these pulses were determined. The results obtained for forward STRS were in satisfactory agreement with the conclusions reached on the basis of a quantum theory.

Continuous-wave stimulated Raman scattering

We report what is to our knowledge the first observation of continuous-wave stimulated Raman scattering (SRS). Both forward and enhanced backward SRS were observed in liquids, and the large spectral frequency shift between pump and probe makes signal detection easy. No separate collection optics are necessary for the backscattered SRS, whose signal-to-noise ratio is much improved compared with that measured by forward or side scatter. This is attributed to the existence of a phase-conjugate beam. Higher orders of Stokes scattering are also observed in return. Contrary to theoretical expectation, both forward-scattered and backscattered signals have identical gains owing to saturation effects in a number of the high-gain liquids studied.

In-line bsrs optical signal amplification using fibre nonlinear coupler

Here a scheme which uses a nonlinear fibre coupler with in-line backward stimulated Raman scattering (BSRS) optical signal amplification for long-span optical fibre communications is presented. The introduction of a nonlinear optical fibre coupler to the in-line fibre Raman amplification promises to circumvent a considerable power penalty which amounts to more than 6dB when conventional (linear) coupling devices are used.

Vlasov simulation of stimulated Raman scattering in one dimension

Vlasov simulations of stimulated Raman scattering (SRS) are presented, both for low laser irradiance when the plasma waves remain linear and for high laser irradiance when particle trapping occurs. At low irradiance the energy in scattered radiation and in plasma kinetic energy approach values given by the Manley–Rowe relations. At high irradiance the effective damping rate of the plasma waves is greatly increased over the Landau damping rate while electron trapping is occurring. A relativistic model for electron trapping has been developed. It yields expressions for the number and maximum energy of the trapped electrons and the threshold for their production. Forward SRS dominates at high plasma temperatures and produces faster trapped electrons compared to backward SRS.