High-Power Picosecond Pulse Recirculation

for Inverse Compton Scattering

Igor Jovanovic a b, Miro Shverdin b, David Gibson b, Curtis Brown b and Jeff Gronberg b

aSchool of Nuclear Engineering, Purdue University400 Central Dr, West Lafayette, IN 47907, USAbLawrence Livermore National Laboratory7000 East Ave, Livermore, CA 94550, USA

In the next generation of linear colliders, inverse Compton scattering (ICS) of intense laser pulses on relativisticelectron bunches will enable a mode of operation based on energetic γe and γγ collisions, with a significantcomplementary scientific potential. The efficiency of γ-ray generation via ICS is constrained by the Thomsonscattering cross section, resulting in typical laser photon-to-γ efficiencies of <10−9. Furthermore, repetition ratesof the state-of-art high-energy short-pulse lasers are poorly matched with those available from electron accelerators.Laser recirculation has been proposed as a method to address those limitations, but has been limited to only smallpulse energies and peak powers. We propose and experimentally demonstrate an alternative, non-interferometricmethod for laser pulse recirculation that is uniquely capable of recirculating short pulses with energies exceeding1 J [1]. ICS of recirculated Joule-level laser pulses is compatible with the proposed pulse structure for ILC andhas a potential to produce unprecedented peak and average γ-ray brightness in the next generation of sources.

1. Introduction

In the inverse Compton scattering (ICS) inter-action, the small Thomson scattering cross sec-tion limits the efficiency of conversion of incidentlaser photons to γ-rays. Typical backscatteredfraction of the incident photons is < 10−9, so thatthe ICS interaction region is essentially trans-parent to laser photons. Furthermore, a signif-icant technology gap in repetition rate exists be-tween linear accelerators and high-energy short-pulse lasers. While the linear accelerators arecapable of producing electron bunches in burstswith repetition rates of ∼GHz, typical joule-levelshort-pulse lasers are limited to ∼10-Hz repeti-tion rates.

Recirculation of the laser pulse has been pre-viously proposed as a method to bridge someof this technology gap. For the future Interna-tional Linear Collider (ILC), 2820 micropulses ina macropulse are proposed, generated by resonantcavity build-up and recirculation [2,3]. Recircula-tion of high-energy short pulses by resonant cav-ity coupling requires interferometric alignment

accuracies and requires high-energy laser sourceswith high repetition rates, or the use of multiplesuch sources.

We propose and experimentally demonstrate anovel method for high-energy laser pulse recir-culation based on the injection and trapping ofa single incident laser pulse in a passive opti-cal cavity, akin to “burst-mode” operation. Thismethod circumvents the B-integral limitations ofconventional optical switching by the use of a thinnonlinear switch based on frequency conversionin a nonlinear crystal. Following the nonlinearpulse injection, subsequent recirculation is shownto be capable of increasing the average power andbrightness of ICS-based γ-ray sources by a fac-tor of ∼100. Further, this recirculation method,termed recirculation injection by nonlinear gating(RING), is scalable to >100-J picosecond pulses,well beyond the capability of alternative recircu-lation methods. The use of RING is compati-ble with the current paradigm of ICS-based γ-ray sources, offering a significant improvement inaverage power and possible reduction in laser en-ergy and electron accelerator energy. The concept

Nuclear Physics B (Proc. Suppl.) 184 (2008) 289–294

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is complementary to the much costlier develop-ment of higher repetition rate lasers, and it couldalso be used in conjunction with higher repetitionlasers when they become available.

2. Laser recirculation methods and limita-tions

The two chief methods for achieving pulse recir-culation to date were the use of linear intra-cavityswitching components and resonant cavity cou-pling. When intra-cavity components are used,the nonlinear phase accumulation (B-integral)due to self-phase modulation of the medium froman intense optical pulse can be written as

φ(2)(x, y) =2π

λ

∫ L

0

n2I(x, y, z)dz, (1)

where φ(2) is the accumulated B-integral, λ is thelaser center wavelength, n2 is the nonlinear refrac-tive index of the material, I(x, y, z) is the pulseintensity, and L is the length of the medium alongpulse propagation direction z. For even modestpulse energies, the required apertures of linearswitching components that result in acceptablenonlinear phase accumulation are prohibitivelylarge.

In resonant coupling, a stringent phase require-ment exists for the light incident into the cavityfor the constructive interference to occur. Forcw light, this corresponds to the incident lightspectral overlap with existing cavity modes. Forpulsed light, the phase of the incident pulse needsto match the phase of the recirculating pulse andthe repetition rate of the incident pulses needsto be identical or a subharmonic of the recircu-lating pulse. These interferometric requirementscorrespond to sub-100 nm positioning of opticalcomponents for optical frequencies.

3. Recirculation injection by nonlineargating (RING)

Since the principal limitation that prevents theinjection and the recirculation of an intense laserpulse in the cavity is the nonlinear phase accumu-lation with each passage of the pulse through therelatively thick switching components, one can

consider alternative methods for pulse injectionthat reduce the nonlinear phase. Here we proposea novel method of optical switching into the cav-ity that requires significantly shorter interactionlengths than the previously used methods and isthus compatible with recirculation of an intenselaser pulse. We refer to this concept as recircula-tion injection by nonlinear gating (RING).

Figure 1. The principle of the RING technique.A frequency converter (FC) is used as a thinoptical switch.

The principle of the RING technique is pre-sented in Figure 1. In the RING technique,optical switching is achieved by placing a thinfrequency converter, such as a nonlinear opticalcrystal, into the cavity so that it is in the pathof the incident laser pulse. The frequency con-verter represents an ideal optical switch - it altersboth the frequency and the polarization state ofthe incident pulse, allowing simple selection andcontainment of the generated pulse for recircu-lation by means of dichroic mirrors and polariz-ers. The thickness of the nonlinear crystal opti-cal switch is determined by the requirement forhigh conversion efficiency in frequency mixing. Ifwe assume a typical incident pulse intensity of 5GW/cm2, the required length of the crystal forefficient conversion (switching) is only ∼3 mm,

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which is an order of magnitude shorter than lin-ear optical switches. The RING technique offersa unique advantage of the short interaction lengthof the pulse in a material, and is thus highly ap-propriate for short (picosecond and femtosecond)pulses. The mode of operation of a RING res-onator can be termed a “burst-mode”, character-ized by both high peak and average power. Theintra-cavity pulse structure consists of a train ofintense short pulses spaced by the cavity round-trip time and exhibiting a decay with characteris-tic decay time determined by total cavity losses.

The RING cavity can be realized in a unidi-rectional ring or a Fabry-Perot configuration. Inboth cases the frequency conversion of the inputpulse provides optical isolation from the pumplaser. In a simple Fabry-Perot configuration, bidi-rectional propagation of the recirculated pulse of-fers the possibility of two interactions with theelectron bunch per one cavity round-trip; how-ever, one pass through the nonlinear crystal isstill required per ICS interaction.

It is useful to consider the energy and inter-action point intensity scaling of the RING cav-ity. With the selected thickness of the nonlinearcrystal switch, the required pulse intensity andfluence on the nonlinear crystal are fixed by therequirement for high conversion efficiency (2). Ina simple RING configuration shown in Figure 1,the f-number (f/#) of intra-cavity focusing is de-termined by the focal length of the focusing lens(reflective mirror or parabola) and by the size ofthe beam. A smaller beam on the focusing opticis undesirable due to relatively high intensity ofthe pulse undergoing frequency conversion in thenonlinear crystal. The peak power P incident onthe nonlinear crystal is proportional to the squareof the beam (crystal) diameter D: P ∝ D2, whilef/# ∝ 1/D. The resulting focal spot intensity atthe interaction point is thus proportional to thefourth power of the beam diameter:

I ∝ P

w2∝ D4. (2)

In this simple cavity configuration, the twostrategies for obtaining the desired focal spotintensity are thus (1) modification of the focal

length of the focusing lens (leading to the modi-fication of cavity length), and (2) ICS operationat a variable distance from focus.

4. Experimental demonstration of theRING technique

We have performed initial experiments to es-tablish the feasibility of the RING technique andgain confidence in its scaling to high pulse ener-gies and peak powers by aperture increase. Forthe demonstration experiment we utilized a sim-ple triangular plane ring resonator configurationwithout intra-cavity focus, avoiding the need fora vacuum system. The resonator consisted ofthree high-quality plane mirrors. The mirrorswere coated on the side internal to the cavitywith a multilayer dielectric coating reflective forthe 527 nm wavelength and transmissive for the1053 nm wavelength. The multilayer dielectriccoating on the mirror sides external to the cav-ity is anti-reflective for both the 1053 nm and the527 nm wavelength. This coating selection en-ables the following functionality: (1) low loss atthe resonator wavelength of 527 nm, (2) efficientcoupling of 1053 nm light into the cavity, (3) ef-ficient removal of the fundamental 1053-nm lightand parametric fluorescence from the cavity, and(4) improved diagnostics of 527 nm recirculatedpulse by mirror leakage.

The resonator length was approximately 107cm, yielding a roundtrip time of 3.6 ns. The use ofplane-mirror resonator leads to diffraction losses,but it is estimated that they would negligible overthe maximum expected number of ∼100 cavityroundtrips with the selected beam diameter of ∼7mm and a smooth beam profile.

We used a 1-cm aperture, 1-mm thick nonlin-ear crystal of BBO for nonlinear switching. Theselection of the BBO crystal for this task is moti-vated by its numerous favorable properties in non-linear optics applications. They include excellentthermomechanical properties, low hygroscopicity,and broad spectral and thermal acceptance. Thecrystal was cut for type I SHG of 1064 nm pulsesand antireflection coated on both sides. The in-jected 10-Hz, 1053-nm pulse energy was ∼2 mJ,and the pulse duration was 1 ps, longer than the

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Fourier transform of the pulse spectrum of 200fs. The first-pass frequency doubled pulse energywas measured to be 0.5 mJ.

Figure 2. Experimentally measured pulse trainfrom the RING cavity

The recirculated pulse burst was measured us-ing a 1-ns rise time photodiode combined with a7-GHz digital oscilloscope by observing the leak-age of the 527-nm pulse through one of the cav-ity mirrors and by measuring the 527-nm scat-ter from cavity mirrors and the nonlinear crys-tal surface. The experimentally measured cavityringdown is shown in Figure 2. The measuredcavity enhancement factor was A ∼28.5, whichcorresponds to approximately 3.5% loss per cav-ity pass, likely limited by hard-edge diffraction byimperfectly collimated beam and the crystal an-tireflection coating. Our first proof-of-principleexperiment provides the first demonstration ofthe validity of the technique and increases confi-dence in the success of its scaling to high energiesat similar pulse intensities.

5. Scaling prospects of the RING tech-nique

One of the most attractive capabilities of theRING technique is its scalability to high-energyand high-peak-power pulse recirculation. In com-

parison, resonant coupling schemes exhibit lim-itations when scaled to higher energies both be-cause of the absence of practical high-energy lasersources with repetition rates comparable to thetypical cavity round-trip time on the order of∼100 ns and because of the thermal effects associ-ated with such pulses that complicate the interfer-ometric alignment. In active switching schemesthat rely on a linear switch such as an electro-optic (Pockels) cell, scaling to high energies en-tails the significant increase of the aperture tominimize accumulated nonlinear effects over thelong (several cm) interaction length. This aper-ture increase is usually accompanied by a signif-icant penalty in switching speed, which can be-come incompatible with cavity round-trip time.

The energy and peak power limitations of theRING technique are primarily driven by the non-linear phase accumulation of the nonlinear crys-tal switch, and can be addressed by increasingthe crystal aperture and length, as suggested inSection 4. Common nonlinear crystals availablein large aperture and with optical quality to dateinclude potassium dihydrogen phosphate (KDP)and its deuterated isomorph (KD*P), and can beobtained in sizes of up to 40 cm. If we assumethe nonlinear drive of 10 GW/cm2 with 10-pspulses, this implies that a single crystal of thistype could enable injection and recirculation of>100-J pulses. Furthermore, multiple nonlinearcrystals could be tiled in an array to supportmuch higher pulse energies. If required, coher-ence among beam components traversing differ-ent nonlinear crystals could be maintained by en-suring negligible thickness variation among crys-tals.

6. RING applications

The RING technique is attractive for use in ap-plications that exhibit low loss for the laser pulse.A necessary but insufficient condition for this re-quirement is the low cross section (efficiency) forthe interaction of interest. ICS of a laser pulseon a relativistic electron bunch is a prominentexample of the process that exhibits both a lowcross section for the useful interaction and simul-taneously low loss for the laser pulse. Here we

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list some of the important applications that couldbenefit from the application of the RING tech-nique.

For production of high (100 GeV-TeV) photonenergies envisioned in the γ − γ arm of the ILC[3] or for future intense positron sources [4], thestrategies for producing the correct pulse struc-ture have been presented. Production of a circu-larly polarized beam is one of the requirements forthis application. The use of two intra-cavity bire-fringent phase retarders (wave plates) can satisfythis requirement.

In the intermediate to lower energy range,RING can be used in production of monochro-matic, directed x-rays for medical imaging andradiological treatment [5], and for isotopic imag-ing via nuclear resonance fluorescence [6]. Onecan also envision applications of RING for pro-duction of ultrashort x-rays in synchrotron-basedsources [7] for materials science and productionof x-rays for lithography. Other interesting appli-cations that could benefit from the use of RINGtechnique include plasma diagnostics by Thom-son scattering, where efforts have been made torecirculate the pulse to obtain higher signal-to-noise ratio and possibly dynamical information[8], laser wire beam profile monitoring for elec-tron beam diagnostics [9], Compton polarimetry[10], and the sensitive detection and measurementof the properties of gases and optical materials bypulsed cavity ring-down spectroscopy [11].

7. Conclusion

In conclusion, we proposed and experimen-tally demonstrated a novel high-peak-power laserpulse recirculation method highly suitable for ap-plications involving ICS for high-energy, high-brightness x-ray or γ-ray beam generation. Ourmethod, termed recirculation injection by nonlin-ear gating (RING), is uniquely capable of high-efficiency injection and trapping of a short, in-tense laser pulse required in those applications.The use of a nonlinear switch for pulse injec-tion exhibits several important favorable charac-teristics, including the absence of interferometricalignment and timing requirements, compatibil-ity with both the linear and ring cavity configura-

tions, and the ability to generate and recirculatemultiple laser pulses at the same or different cen-ter frequencies and repetition rates, thus open-ing up the possibility for tunable, shaped-pulsex-ray/γ-ray source.

The principal limitation of the RING techniquein the simple implementation utilizing χ(2) non-linearities for pulse injection is due to the ac-companying χ(3) nonlinearities, resulting in thechange in focusing conditions and pulse spectralcontent [1]. It has been shown that both limita-tions can be addressed by the favorable scalingof the technique to greater apertures and longernonlinear switch interaction lengths.

We believe the RING technique to be a strongalternative to resonant coupling techniques pro-posed and implemented to date for applicationsbased on ICS, and foresee additional attractiveapplications in the area of ultrashort x-ray pulsegeneration, cavity ring-down spectroscopy andplasma diagnostics.

8. Acknowledgments

The authors wish to thank the U.S. Depart-ment of Energy Office of Nonproliferation Detec-tion (NA-22) for financial support and technicalguidance. We acknowledge valuable discussionswith F. Hartemann, S. Bisson, and C. Haefner.This work was performed under the auspices ofthe U. S. Department of Energy by the Univer-sity of California, Lawrence Livermore NationalLaboratory under Contract No. W-7405-Eng-48.

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