1. Suppression of a Parasitic Pump Side-Scattering in Backward Raman Amplifiers of Laser Pulses in Plasmas A.A. Solodov, V. M. Malkin, N. J. Fisch

2. In backward Raman amplifiers (BRA), the pump laser pulse can be prematurely depleted through Raman scattering, seeded by the plasma noise, as the pump encounters plasma before reaching the counter-propagating seed pulse. It was shown previously that detuning of the Raman resonance, either by a plasma density gradient or a pump frequency chirp, can prevent the premature pump backscattering, even while the desired amplification of the seed pulse persists with a high efficiency. However, parasitic pump side-scattering is not automatically suppressed together with the parasitic backscattering, and might be even more dangerous for BRA. What we show here is that by combining the above two detuning mechanisms one can suppress parasitic pump side-scattering as well. Apart from the simplest counterpropagating geometry, we examine BRA for arbitrary angles between the directions of pump and seed propagation. We show that, by selecting an appropriate direction of the plasma density gradient, one can favorably minimize the detuning in the direction of the seed pulse propagation, while strongly suppressing the parasitic pump side-scattering in all the other directions. This work was supported in part by DOE and DARPA. Abstract

3. Conceptual Scheme of Backward Raman Amplifiers (BRA) pump beamseed beam ω 2, k 2 ω 1, k 1 kpkp plasma wave pump beam seed pulse depleted pump amplified pulse k p =k 1 -k 2, ω p =ω 1 -ω 2 The plasma wave forms a 3D Bragg cell grating that scatters power from the pump into the seed At the nonlinear amplification stage the amplified seed can completely deplete the pump

4. seed pulse plasma target pump pulse Conceptual Scheme of BRA (Continued) Resent studies showed that short pumped pulses of nearly relativistic non-focused intensities are expected: I~10 17 W/cm 2 for λ=1 μm [1]. This is 5 orders of magnitude higher than currently available through chirped pulse amplification [2]. Additional intensity gain is provided by focusing. [1] V. M. Malkin, G. Shvets, and N. J. Fisch, Phys. Rev. Lett. 82, 4448 (1999). [2] G. A. Mourou, C. P. J Barty, and M. D. Perry, Phys. Today 51, 22 (1998).

5. Problem: Pump Can be Prematurely Depleted by Raman Scattering Seeded by Thermal Langmuir Noise, before it Reaches the Seed Pulse pump SRS It is the same efficiency of stimulated Raman scattering, that makes possible the fast compression, which can complicate the pump transporting to the seed. The problem is aggravated by the fact that the linear Raman scattering (responsible for the noise amplification) has a larger growth rate than its nonlinear counterpart (responsible for the useful amplification of the seed).

6. The Premature Pump Backscattering Can be Suppressed by an External Detuning of the Raman Resonance [3] 0 z pump front δω pump δω δω detuning δω plasma -z pulse location δω= δω plasma -δω pump It appears to be possible to suppress the unwanted Raman backscattering of the pump by noise, while not suppressing the desirable seed pulse amplification. The filtering effect occurs because in the nonlinear regime the pumped pulse duration decreases inversely proportional to the pulse amplitude. The increased frequency bandwidth allows to tolerate larger and larger external frequency detuning. [3] V. M. Malkin, G. Shvets, and N. J. Fisch, Phys. Rev. Lett. 84, 1208 (2000).

7. The Goal of the Present Paper is to Analyze How a Parasitic Pump Side-Scattering in BRA Can be Suppressed pump SRS z y x θ The Raman growth rate maximizes for backscattering: (linearly polarized pump with normalized amplitude a 0 =eA/mc 2, scattering in the plane perpendicular to the pump polarization). However, the side-scattered radiation has more time and a longer distance to be amplified by the pump, before it leaves the plasma. These two effects practically compensate each other making suppression of pump side-scattering an important task.

8. Main Equations The linear stage of SRS is described by where the vector-potential envelopes of the pump and scattered Stokes waves and Langmuir wave electric field are defined: The pump wave frequency, wavenumber, and the unit polarization vector are

9. pump SRS z y x θ φ z1z1 Main Equations (Continued)

11. Green’s Function z 1 =ct/2 b0b0 c/2γ 0

12. Green’s Function (Continued) z1z1 |b 0 | c 0

13. Premature Pump Backscattering and Side-Scattering in Absence of Detuning z z1z1 θ l 0

14. Suppression of a Parasitic Pump Side-Scattering in a Backward Raman Amplifier δω pump δω plasma z 0 δω

15. Suppression of a Parasitic Pump Side-Scattering in a Backward Raman Amplifier (Continued) 0 z pump front δω pump δω δω detuning δω plasma -z Stokes pulse front location

16. Suppression of a Parasitic Pump Side-Scattering in a Backward Raman Amplifier (Continued) linear polarization, φ=π/2 linear polarization, φ=π/6 circular polarization; also linear polarization, φ=π/4

17. Scattering Cross-Section of the Pump Beam in BRA with Frequency Detuning

18. Scattering Cross-Section of the Pump Beam in BRA with Frequency Detuning (Continued)

19. Suppression of a Parasitic Pump Scattering in a Raman Amplifier with Arbitrary Angles between Pump and Seed Pulses seed pulse density gradient z θsθs θdθd y

20. Suppression of a Parasitic Pump Scattering in a Raman Amplifier with Arbitrary Angles between Pump and Seed Pulses (Continued)

21. Suppression of a Parasitic Pump Scattering in a Raman Amplifier with Arbitrary Angles between Pump and Seed Pulses (Continued)

22. Suppression of a Parasitic Pump Scattering in a Raman Amplifier with Arbitrary Angles between Pump and Seed Pulses (Continued)

23. Conclusions Detuning of the Raman resonance by a plasma density gradient and a pump chirp can suppress parasitic pump side-scattering in Backward Raman Amplifiers By selecting appropriate values of the pump chirp and plasma density gradient as well as direction of the density gradient, one can favorably minimize the detuning in the direction of the seed pulse propagation, while strongly suppressing the parasitic pump side-scattering in all the other directions