Here we compare the Raman signal characteristics of both seeded Raman scattering (S-RS) and amplified noise Raman scattering (N-RS) as a function of pump intensity. To determine the extent of N-RS we compare the energy scattered in the oblique (175°) direction with that backscattered in the direct counter-propagating direction. The focused pump and seed beams define a solid angle of 1.8 × 10−3 sr and 5 × 10−4 sr, respectively, while the detection solid angles are 7.8 × 10−3 sr on-axis and 5 × 10−3 sr off-axis.

Energy measurements

To determine the energy gain and efficiency in the oblique direction, the energy of the Raman signal has been measured as a function of pump energy both with and without the presence of the external seed, as shown in Fig. 1, where we identify the two respective measurements by the labels (S-RS + N-RS) and (N-RS). The Raman signal energy is observed to increase from 4 nJ(N-RS)/1 μJ(S-RS + N-RS) to 70 mJ/170 mJ, respectively, as the nominal pump energy is increased from 1 to 70 J. At the highest pump energies the seed is amplified by nearly nine orders of magnitude. Because the seed interaction length is 1.1 mm at 175°, the observed maximum gain in 5 × 10−3 sr sets a lower limit to the gain coefficient of 180 cm−1, which is two orders of magnitude larger than conventional high power solid state amplifying media.

Figure 1 Measured and numerically calculated Raman signal energies. Experimental (numerical) results are shown by filled (empty, gray) symbols. (Blue) square: N-RS; (orange) circle: S-RS + N-RS; (green) up-pointing triangle: S-RS with the (green) dashed line showing an exponential fit with respect to the square root of the pump energy. For comparison, results from simulations are shown. Cross: results from Leap. down-pointing triangle: OSIRIS simulations; Diamond: cplPIC simulations. The effective pump intensity is an estimated value used to enable comparison between experimental and simulation results. See Methods for details. Measured Raman signal energies backscattered along the pump axis are presented (right-pointing, purple triangle) in addition to results from OSIRIS simulations for a 2.6 mm long plasma (up-pointing triangle). (Purple) dash-dot line: power law fit to on-axis scattering data with exponent 2.2. Note that the horizontal lines across the symbols are error bars. Full size image

For pump energies of ~1 J, the amplified seed pulse is a factor of 250 larger than the noise signal, which is sufficient for pJ seed signals to be amplified above the noise. At higher pump energies, this ratio drops to 2.5 (at 70 J), which shows that N-RS can reach significant levels, comparable with S-RS. Because N-RS depends on both the particle density and temperature at any time, and is integrated in time convectively, the seed sees a spatio-temporal evolving gain medium, as we show later, which accounts for the variation of the gain. Above 70 J the Raman signal appears to drop, but this should be interpreted cautiously because the laser beam quality degrades rapidly at higher energies. Furthermore, significant N-RS energy is scattered directly backwards with an energy angular density of up to 50 times that of obliquely scattered radiation, as is discussed later.

To distinguish between the energy gained by the seed, S-RS, and that resulting from N-RS, the two sets of measurements are subtracted. We find that in the range of 600 nJ to 100 mJ the amplified seed energy, ε 1 , approximately fits an exponential dependence, \({\varepsilon }_{1}({\varepsilon }_{0})\propto \exp ({c}_{1}\sqrt{{\varepsilon }_{0}})\), on the pump energy, ε 0 , up to a pump energy of 70 J, where c 1 is a fitting parameter. However, the growth rate is much lower than predicted theoretically for the linear regime. We observe that the total efficiency measured in the oblique (175°) direction, within 5 × 10−3 sr, is less than 0.5%, when only considering the energy of the amplified seed, and around 1% for the total signal. As we show below, the total fraction of the pump that is directly backscattered can be significantly larger, which suggests that much higher efficiencies, in excess of 10% should be possible for properly angular matched collinear Raman amplification geometries.

Transverse profile of the Raman signal

Measurement of the transverse profiles of the obliquely backscattered Raman radiation provides information on the beam quality and peak fluence. A selection of six typical shots for three different nominal pump energies, 3, 20 and 70 J, are presented in Fig. 2. Figures 2a–c illustrate N-RS shots, while Fig. 2d–f represent S-RS + N-RS shots. At comparable pump energies, S-RS + N-RS and N-RS profiles are similar. The transverse energy distribution is inhomogeneous and the scattered radiation profile seems mainly to be determined by the (poor) optical characteristics of the pump beam. Increasing the pump energy results in larger volumes of ionized gas, i.e., larger scattering volumes, which is accentuated by the non-uniformity of the pump transverse profile. As the pump energy is varied between 1 and 70 J, the cross-section area of the backscattered light grows by an order of magnitude. The largest fluence measured from the radiation profiles is 12.8 J cm−2 for injection of the external seed. This is still two orders of magnitude less than predicted theoretically for an efficient Raman amplifier33. However, it demonstrates the potential of the medium for amplifying seed pulses with initial energies as low as a few 100s of pJ for non-optimal pump beams.

Figure 2 Transverse profile of the Raman signal. Recorded beam profiles for three different nominal pump energies: 3 J (a,d), 20 J (b,e) and 70 J (c,f). (a–c) are obtained from amplification from noise, while (d–f) are recorded with external seed injection. Note the very different fluence scales. Full size image

Spectral analysis

The measured signal spectra, shown in Fig. 3, are typical spectra obtained for a pump energy of ~35 J, which reveal several interesting features. The N-RS spectra are broad and roughly Gaussian in profile, while for S-RS a narrow peak is superposed on the N-RS feature (Fig. 3b). The central wavelengths and the spectral widths are shown in Fig. 3a, where it is observed that the spectral width of the amplified seed varies between 10 and 20 nm, which is close to the original KGW spectral width. However, an increase in the N-RS signal is accompanied by a rapid broadening of the spectral bandwidth, from 10 nm at low pump energies to 60 nm at 20 J and above. This is consistent with noise amplification45, where the bandwidth of the N-RS spectra is determined by the linear gain bandwidth. For joule-level (1–2 J) pump energies, the central wavelength of the spectra remains around 1.15 μm for both sets of measurements. This value is very close to the seed central wavelength, which confirms that the plasma is resonant. Above several joules, the central wavelength of the N-RS spectra is strongly blue-shifted by up to 50 nm, which is consistent with trapping of electrons in the plasma wave, which leads to an effective local reduction in the plasma density14, 46. This is confirmed by a less pronounced blue shift in S-RS spectra of approximately 20 nm, which is within the initial bandwidth of the seed and shows that the lower intensity blue parts of the spectrum are preferentially amplified when the pump energy is low and Raman gain bandwidth is narrow. The increase in the gain bandwidth at very high pump intensities also reduces these bandwidth effects, as is evident in Fig. 3a. Measurement of seed spectra show that it maintains its initial spectral characteristics, particularly at low pump energies, which demonstrates the fidelity of the amplifier, with some evidence of nonlinearities at higher intensities. However, it should be noted that spectral features at wavelengths beyond ~1.165 μm, the CCD’s sensitivity range limit, cannot be observed, if present.

Figure 3 Spectra analysis. (a) Comparison between the central wavelengths of (blue circle) N-RS spectra and (orange square) S-RS + N-RS spectra. The error bars in the vertical axis represent the measured bandwidth at FWHM. The grey area illustrates the initial seed features. (b) Examples of spectra for a nominal pump energy of 35 J: N-RS spectrum shown in dashed (blue) line, S-RS + N-RS spectrum presented in solid (orange) line. (c) and (d) spectral images of Raman amplification without and with seed, respectively. The spectra correspond to the ones presented in (b). (e) example of a spectrum showing strong modulations, obtained for a 6 J pump beam only. Full size image

Stimulated Raman backscattering from noise

Our studies show that N-RS becomes significant, and even dominant, as the pump intensity is increased, even at large angles. At pump intensities of around 1014 W cm−2 (a 0 ≈ 0.01), the level of amplified noise is more than two orders of magnitude below that of the amplified seed. However, the ratio of S-RS to N-RS decreases rapidly as the pump intensity increases because the initial noise signal is proportional to the pump intensity.

The total N-RS energy in the direct-backscattered direction can become significant because the interaction length and gain are maximised in this direction, for a Fresnel number (of the central spot) F ≈ 1. To investigate N-RS, light transmitted through the final pump mirror (before the gas jet) is measured using a calorimeter, for energy measurements, and an imaging spectrometer, for spectral measurements. The on-axis collection solid angle is 7.8 × 10−3 sr, which is 1.6 times larger than for off-axis measurements. Figure 4 shows the ratio of the Stokes-shifted (Raman) energy compared with (near-)unshifted (elastic/Brillouin) scattering, for pump energies ranging from 1 to 50 J. At 50 J approximately 5 J (10%) of the pump energy is converted to backscattered radiation, giving an angular energy density of 640 J sr−1, calculated by assuming the scattered radiation fills the collection solid angle. This underestimates the efficiency as some pump energy is scattered outside the measurement solid angle. The backscattered energy is almost fifty times larger for 50 J than what is collected off-axis for 70 J, where the maximum angular energy density is 14 J sr−1 (70 mJ). These measurements are consistent with N-RS strongly dominating for our interaction geometry, F ≈ 1, even at low pump intensities. At higher energies noise backscattering is dominant and can exceed 10%. Elastic scattering is at least one order of magnitude lower. To compare the energy measurements of N-RS in the direct-backscattered direction with off-axis scattering we have also included this data in Fig. 1, notwithstanding the different collection angles. The scaling law follows a dependence on the pump energy of \({\varepsilon }_{0}^{2.2}\), which may indicate amplification in the superradiant regime with the noise source being proportional to the pump laser power, giving an overall scaling of \({\varepsilon }_{0}^{2.5}\).