Study of chirped pulse amplification based onRaman backscattering

X. Yang, G. Vieux, A. Lyachev∗, J. Farmer, G. Raj, B. Ersfeld, E. Brunetti,M. Wiggins, R. Issac, D.A. Jaroszynski

Department of Physics, University of Strathclyde107 Rottenrow, Glasgow, G4 0NG, UK

ABSTRACT

Raman backscattering (RBS) in plasma is an attractive source of intense, ultrashort laser pulses, which has thepotential asa basic for a new generation of laser amplifiers.1 Taking advantage of plasma, which can withstandextremely high power densities and can offer high efficiencies over short distances, Raman amplification inplasma could lead to significant reductions in both size and cost of high power laser systems. Chirped laser pulseamplification through RBS could be an effective way to transfer energy from a long pump pulse to a resonantcounter propagating short probe pulse. The probe pulse is spectrally broadened in a controlled manner throughself-phase modulation. Mechanism of chirped pulse Raman amplification has been studied, and features ofsupperradiant growth associated with the nonlinear stage are observed in the linear regime. Gain measurementsare briefly summarized. The experimental measurements are in qualitative agreement with simulations andtheoretical predictions.

Keywords: Raman backscattering, chirped pulse, superradiant amplification, plasma density measurement,capillary, white light

1. INTRODUCTION

Laser intensities inside conventional amplifiers are limited to 1010 W/cm2 by nonlinear modification of the mate-rial refractive index which result in damaging distortions of the laser pulses. The advent of laser systems basedon chirped pulse amplification (CPA) technique has allowed the production of femtosecond pulses with intensi-ties up to 1021 W/cm2. However, these ultrahigh laser intensities are achieved using very large and expensivecompressor gratings. The development of future laser systems may need to use a different technology. Amplifiersbased on stimulated Raman backscattering in plasma could represent the next generation of amplifiers.1–3 RBSis a very promising means of transferring energy from a long pump pulse to a short probe pulse. Moreover,plasma can withstand extremely high power densities and therefore is a very robust gain medium.

This paper starts with a brief review of the theory of Raman backscattering in plasma, which is followed bya description of the experimental setup and a discussion of results obtained.

2. THEORY

Raman backscattering in plasma can be simply characterized as the resonant decay of an incident photon into afrequency down-shifted scattered photon and an electron plasma wave (a Langmuir wave). The frequency andwave number matching conditions are given by:

ω0 = ω1 + ωp, k1 = k2 + kp (1)

where ω0,1,p and k0,1,p are the frequencies and wave numbers of the incident wave, back scattered wave and theLangmuir wave, respectively.4

Raman scattering is a parametric instability that can occur spontaneously or be stimulated by a probe pulse atthe Stokes frequency, which is then amplified in this process. Amplification offers a potential means of producinglaser pulses with powers exceeding the breakdown threshold of current state-of-the-art solid state amplifiers.

∗Dr. Andrey Lyachev is now working at Rutherford Appleton Laboratory, STFC, Chilton, UK

Invited Paper

Harnessing Relativistic Plasma Waves as Novel Radiation Sources from Terahertz to X-Rays and Beyond, edited by Dino A. Jaroszynski, Antoine Rousse, Proc. of SPIE Vol. 7359, 73590Q · © 2009 SPIE

CCC code: 0277-786X/09/$18 · doi: 10.1117/12.821106

Proc. of SPIE Vol. 7359 73590Q-1

For simplicity, the amplification process can be described using two counter propagating monochromaticpulses as example. First, the interaction of the two beams generates a beatwave. The ponderomotive forceassociated with the beatwave pushes electrons away from the region where the electromagnetic field is strongestand excites a plasma wave if the beatwave frequency is resonant with the plasma frequency. The periodic densityoscillations of the electrons have a spatial frequency ≈ 2k0. The pump wave then backscatters from the densityfluctuations into the probe. The growth of the probe wave reinforces the beatwave and therefore induces afeedback loop resulting in exponential amplification.

RBS amplification can be divided into linear and nonlinear regimes. In the linear regime, pump deple-tion is negligible and the amplitude of the probe pulse increases exponentially in time for each frequency asa1(t) = a1(0)eγt (where γ is the linear growth rate and a1 is the reduced vector potential of the probe).For interaction between two linearly polarized laser pulses, when the resonant condition is perfectly satisfiedγ = γ0 = |a0|

√ω0ωp/4 5 (where a0 = eE0/mω0c is the reduced vector potential of the pump, with E0 the

electric field amplitude). When there is a small detuning δ = |ω0−ω1−ωp| between the three waves, the relationbetween the growth rate and detuning is γ(δ) =

√γ20 − δ2/4. Although the gain can be high, for a monochro-

matic pump, the narrow gain frequency bandwidth ∼ πγ0 of linear amplification leads to lengthening of theprobe pulse in time. Since pump depletion is negligible, the energy of the pump will always be backscatteredfrom the plasma wave and to the rear of the probe. Therefore, the peak of the probe pulse travels at the speedc/2, while the leading edge of the pulse travels at c, the speed of light.

In the nonlinear regime there are two stages: pump depletion regime and Compton regime. With sufficientlyhigh amplitude of the probe pulse, i.e. a ∼ (ωp/4ω0)3/2, the pump will be depleted by the front of the probepulse, and therefore the growth at the rear is suppressed. Due to Burnham-Chiao ringing,6 energy can trans-fer both ways between the pump and probe and the probe evolves into a series of short pulses.3 When theponderomotive potential is suffiently strong for the oscillation frequency of the electrons to exceed the plasmafrequency, unharmonic electron motion leads to an increase as the bandwidth of the effective interaction. Inthis Compton regime the intensity of the pump and probe pulses are so strong that their ponderomotive forcedominates the collective oscillations of the plasma wave. Hence, the frequency matching condition (1) does notneed to be perfectly satisfied anymore, as electrons perform forced oscillations at the frequency dictated by theponderomotive potential. In both non-linear regimes, the probe amplitude grows linearly with the interactiontime, while the pulse duration, with self-similar contraction, is inversely proportional to the interaction time.

This discussion suggests that a short probe pulse can only be amplified in the non-linear regime. However,theoretical investigations of Raman amplification using a broad bandwidth chirped pump pulse show that in thelinear regime the probe pulse amplitude can grow linearly with the propagation distance while the duration isself-similarly contracted.7 By using a chirped pump pulse, distributed gain along the plasma is obtained. Eachfrequency of the probe pulse is amplified at a different position where the resonant condition is satisfied. In thelinear regime, with a pump pulse with chirp rate α, the Raman gain for each frequency component becomesG = eπγ2

0/2α − 1, which is independent of time and is a function of γ20 and therefore a function of the intensity

of the pump laser pulse. By integrating the gain for every probe frequency, the probe amplitude grows linearlywith the interaction time.7 The use of a chirped pump pulse can also efficiently reduce early pump depletionfrom noise and avoid plasma wave breaking.

Before describing our experiment, we briefly introduce the concept of laser filamentation in gas. A laserfilament is a dynamic structure with an intense core which is able to propagate over extended distances muchlarger than the typical diffraction length of a laser beam while keeping a small spot size without the help ofany external guiding mechanism. This phenomenon can be ascribed mainly to two nonlinear physical effects:the optical Kerr effect, which counteracts diffraction and tends to focus the beam on itself, and multiphotonabsorption and plasma creation which has the opposite effect, defocusing the beam and preventing its collapse.The formation of optical filaments is accompanied by a strong spectral broadening which is also called ‘whitelight generation’. The conversion rate into white light varies from a few tenths of percent up to an appreciablefraction of the initial energy. New frequencies are preferentially added to the high energy side of the spectrum.

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3. EXPERIMENT

3.1 Experiment setupThe experimental setup, shown in Fig. 1, is designed to investigate chirped pulse amplification through RBS.This experiment is performed using the laser beam from the Strathclyde CPA laser chain, which offers 200 pslong laser pulses with energy up to 350 mJ centered at λ0 = 800 nm before the final amplifier and compressor. Alarge fraction (≈ 90%) of the beam energy is extracted and used as a chirped pump beam, while the probe beamconsists of the remaining energy. In order to maximize the energy transfer from the pump to the probe, the twobeams are required to satisfy the resonant condition (Eq. 1). To meet this requirement, a white light generatoris currently added to the setup. After splitting out a fraction of the main beam, the probe is compressed andspectrally broadened in a controlled manner through self-phase modulation.8

Laserchain

Pump

Probe

Flip mirror

Periscope

SPIDER

CCD

Whitelight generator

Wave plate & Polariser

Diagnostics for pump

Delay stage

Compressor

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System

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System

Figure 1: Schematic of the experimental setup

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Figure 2: Spectra of frequency downshifted probe pulse

The high frequency components of the spectrally broadened probe beam are ejected by a cut-off filter. The

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ioopm

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combination of white light generator (a 1 m long argon filled tube) and the cut-off filter offers a completelydetuned probe pulse of wavelength adjustable over a large range up to 850 nm. The probe wavelength is shownin Fig. 2.

The two beams are then focused on each side of a 40mm long preformed plasma channel, inside a 300μmdiameter capillary filled with H2. The focused spot sizes of both pump and probe beams are adjusted to obtaina matched spot size for the plasma channel.9 The role of the plasma is two-fold: it acts as a gain medium andsimultaneously as a waveguide to obtain interaction with constant intensity over many Rayleigh lengths.10, 11 4%of the probe is split off and sent to a diagnostic system with a CCD camera to image the beam and a SPIDER(spectral phase interferometry for direct electric-field reconstruction) to monitor the spectra, pulse duration andphase change before and after amplification.

After interaction in the capillary, both beams follow exactly the same, opposite colinear optical paths, andthen are ejected by pairs of wave plates and polarizers to protect the laser chain from damage. The wave platesand polarizers are also used to change the initial polarization of the laser beam from linear to circular, whichwill raise the growth rate by

√2.

The capillary waveguide is on a 5-axis stage. A power supply which delivers 10 to 15 kV is used to ionizethe hydrogen inside the capillary. The high voltage discharge is struck across the capillary through two copperelectrodes placed at each extremity of the waveguide block which is machined by femtosecond laser with properspot diameter.9 The pre-formed plasma channel has a transverse electron density profile that increases withradial distance from the axis, corresponding to a radially-decreasing refractive index. A matching spot size,which is proportional to square root of the capillary diameter and inverse proportional to the fourth root ofthe ambient plasma density, is required at the entrance of the capillary. The guided pump and probe withperfectly matched spot sizes are shown in Fig. 3 and Fig. 4 providing images of the focus at the input side andthe exit guided laser pulse at the output of the capillary. The spot size for both pump and probe is ≈ 45 μm.In comparison with a plasma channel formed in a gas jet, which is only several millimeters long,12 the use ofcapillary wave guides extend the duration of the amplification process dramatically.

(a) Focus of the probe (b) Output of the guided probe

Figure 3

(a) Focus of the pump (b) Output of the guided pump

Figure 4

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BT C

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40 60 80 100 120 140 160 180 200

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3.2 Experimental results

3.2.1 Chirped pulse Raman amplification

We start with the study of the gain versus the relative delay between the chirped pump and a short probepulse. In this experiment, there is no shifting of the probe beam frequency as white light generation is not usedyet. A 18.5 nm bandwidth, 800 nm wavelength, 3 mJ, 610 fs probe pulse, with normalised vector potentialsa0 =2.44 × 10−3 collides in a plasma channel with a 170 ps, 220 mJ pump pulse, with a1 =3.23 × 10−3 · The gainG(λ) is determined from the normalized difference between the two spectra: G(λ) = (I ′(λ) − I(λ))/I(λ), whereI ′ and I are normalized spectral intensities with and without the pump beam respectively. Assuming that ω0 isthe central frequency for both beams, since RBS transfers energy from the two waves between the frequenciesmatching the resonant condition (Eq. 1), we will see an energy gain peak at the Stokes frequency ω0 −ωp, whilean energy loss peak will appear at the anti-Stokes frequency ω0 + ωp.

Figure 5: Maximum gain for the Stokes (square) and anti-Stokes (circle) peakswith respect to relative delay

Figure 6: Wavelength for the Stokes (square) and anti-Stokes (circle) peakswith respect to relative delay

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(2C

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(3

10 800 20 840WaeIenglh (nmj

(C) 0eIer17Or,m(b) Dey120mm 0.2

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(e) 01710mm

780 600 820

WvIen0th [nr0]840 640760 600 620

Wavelength tnml

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0.100 5.OxlO'2 1.0x103 1.5x10 2.0x103

Pump power density [Wcm]

To improve the signal to noise ratio, averages of 40 spectra were recorded. Measurements of the values andwavelengths of Raman gain as function of the relative delay are shown in Fig. 5 and 6. Three distinct regionsof interaction A, B, C were observed. Region B gives constant maximum gain at 30% and loss at 20% whichcorresponds to the short probe pulse interacting with the full length of the pump in the plasma channel. Ideally,region B should last 80 mm for a 40 mm capillary, however, due to a plasma density gradient between the endof the capillary and the vacuum chamber, it drops to a length of 55 mm. Region A corresponds to the centralfrequency of the pump appering earlier than the probe. Therefore, the probe pulse interacts only with the rear(high frequency part) of the pump and only gain is observed. In this region the gain becomes smaller (Fig. 5)and the Stokes wavelength increases in frequency (Fig. 6) as the interaction with the pump approaches its tail.In the probe reference frame, the gain wavelength has the same gradient as the chirp rate (shown on Fig. 5),since the rate of the frequencies introduced into the waveguide is given by the chirp rate of the pump beam.Identically, in region C, the probe pulse interacts only with front (low frequency part) of the pump and onlyenergy loss is observed. Gain curves as function of wavelength of different regions are shown on Fig. 7.

Figure 7: Gain measurements of region A, B, C

The separation between the Stokes and anti-Stokes frequencies in region B corresponds to twice the Bohm-Gross frequency which is the plasma frequency corrected for thermal effects ω2 = ωp

2 + 3k2vth2 where vth is the

thermal velocity and k is the longitudinal wavenumber.13 This enables us to deduce the plasma frequency ωp

and then the on-axis density ne. In this experiment, in order to find the optimal probe frequency, we shoulddetermine the plasma frequency beforehand. By utilizing RBS, we can easily measure the plasma frequencywithout any assistance of other techniques. RBS provides a new non invasive method to determine the localplasma density, which is not only important for this experiment, but also a crucial parameter for many plasmarelated topics, such as the wake field plasma accelerator.14

Figure 8: Intensity dependence of the gain

According to the parameters we used in this experiment, the product of |a0a1| is a factor 12 below the

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threshold for enter the Compton regime, thus we conclude that we are investigating the linear regime. Asmentioned in section 2, the theoretical prediction for the Raman gain of chirped pulse amplification in the linearregime is a function of the pump intensity (G = eπγ2

0/2α − 1 where γ0 is propotional to pump amplitude) andnot the amplitude (G = eγt − 1). Measurements of the spectral gain values as function of the pump intensity arereproduced in Fig. 8. A good agreement is obtained between the linear fit curve (solid line) and the experimentaldata in spite of the large error bars. For comparison, a fit curve (dashed line) with the usual dependence inpump amplitude has been added.

3.2.2 Gain and efficiency measurements

Here we report results of experiments where just optical cut-off filters are used to provide a slightly detunedprobe and pump beams. The pulse duration and energy of the probe and pump are 80 fs, 5mJ and 137ps,220mJ respectively, and the measured plasma density is ∼ 1.3 × 1018 cm−3. Under these conditions, the peakgain reaches 900% at λ = 818nm. Moreover, as a promising sign, the total probe energy increases by 32% andthe energy transfer efficiency has a peak of about 3.5% at a wavelength around 805 nm (Fig. 9).

Figure 9: Energy transfer efficiency

Figure 10: Gain measurement

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Experiment using the new setup (Fig 1) with the white light generator is currently carried on. Laser pulsebandwidth is 35 nm after the laser system upgrade. To find the ’0’ delay between the pump and probe, whitelight generator is not used. A initial gain measurement result is shown on Fig. 10. With energy of 185 mJand 1 mJ in the pump and probe, 450% gain is observed at λ = 818nm and probe energy gain (including theenergy loss at anti-Stokes frequencies) is 27.6%. 1.3 × 1018 cm−3 plasma density is measured from the Stokes andanti-Stokes frequency. Higher gain is expected with completely detuned probe pulse and higher plasma density.

4. CONCLUSION

We have carried out experiments on chirped pulse amplification based on Raman backscattering in plasma at theTOPS lab at the university of Strathclyde. We demonstrated the feasibility of chirped pulse Raman amplifier(CPRA). The analysis of the experimental results shows a qualitative agreement with the theoretical predictions.The supperradiant growth of the probe pulse is observed in the linear regime. A new method to determine theplasma density is proposed. The gain measurement shows a total energy increases of 32% for a frequency detunedshort probe pulse with an energy transfer efficiency up to 3.5% from a chirped pump pulse. In the next stageof the experiment, we will optimize the resonant conditions for RBS by broadening the spectrum of the probepulse using self phase modulation. With such further improvements, we expect to increase the energy transferefficiency and reach the non-linear regime.

ACKNOWLEDGMENTS

We acknowledge the EPSRC for the support of this project. Many thanks to Mr David Clark and Mr TomMcCanny for their great help on experimental design and manufacture of all home made equipments for theexperiment.

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