May 1, 2010 / Vol. 35, No. 9 / OPTICS LETTERS 1361

Terawatt femtosecond laser storage cavitywith cholesteric liquid crystals for an x-ray source

based on Compton scattering

Xin Hao, Qi-hua Zhu,* Ying Zhang, Wan-qing Huang, Yuan-chao Geng, Xiao Wang, and Xiao-dong WangResearch Center of Laser Fusion, Chinese Academy of Engineering Physics, P.O. Box 919-988,

Mianyang, Sichuan 621900, China*Corresponding author: xinh19@126.com

Received December 1, 2009; revised March 6, 2010; accepted March 15, 2010;posted March 22, 2010 (Doc. ID 120054); published April 23, 2010

In laser Compton scattering systems, the limitation to higher average brightness is the low repetition rateof high-power lasers. We propose and demonstrate for the first time, as far as we know, a simple method bywhich x-ray yield could be enhanced nearly 2 orders of magnitude per second. The method, utilizing choles-teric liquid crystals as the entrance mirror of the laser storage cavity, can be used not only for storing fem-tosecond laser pulses with a peak power of several terawatts, but also to make high coupling efficiency andenergy utilization efficiency accessible. © 2010 Optical Society of America

OCIS codes: 320.0320, 340.7480.

High-flux x-rays have many applications in variousfields, such as medical diagnosis, biological science,and material science. However, synchrotron x-raysrequire huge facilities and high expense. Thanks tothe great development in ultrashort laser and accel-erator technology, the compact x-ray source based onCompton scattering has been studied in more andmore laboratories. In a laser Compton scattering sys-tem, the primary obstacle to higher average bright-ness is the low repetition rate of high-power lasers.As proposed by Huang and Ruth in 1997 [1], thislimitation can be overcome by the use of a laser pulsestorage cavity; therefore electrons and photons couldcontinuously interact and generate a high-flux x-raythrough the laser Compton process [2]. Researchersin the KEK (High Energy Accelerator Research Orga-nization) developed a Fabry–Perot cavity, called asuper-cavity [3,4], that injected a low-energy pulsetrain and required interferometeric alignment accu-racy. Jovanovic and co-workers [5] of Lawrence Liv-ermore Laboratory proposed a method based on non-linear frequency conversion, which used dichroicmirrors as resonator mirrors, traversed the funda-mental pulse, and trapped the second-harmonicpulse inside the cavity. As to this method, the 2��400 nm� femtosecond (fs) laser would be stretched tothe picosecond scale after several round trips acrossthe BBO crystal, in addition to the low conversion ef-ficiency. The optical crystals in the electro-optic (oraccousto-optic) pulse switch, with a typical thicknessof 1 cm, even lead to beam breakup as a result of non-linear phase accumulation. Therefore, there shouldbe as few transparent materials as possible insidethe fs laser storage cavity.

In this Letter, we present a design for the Comptonscattering fs laser storage cavity. The design usescholesteric liquid crystal (Ch-LC) as the entrancemirror without any optical materials inside the cav-ity. It can, on the one hand, significantly increase thecoupling energy and, on the other hand, avoid dura-

tion stretch and beam breakup. We have validated

0146-9592/10/091361-3/$15.00 ©

the feasibility of utilizing Ch-LC in the terawatt(TW) laser cavity and proposed a future improvementscheme.

Ch-LC [6,7], owing to its helical structure, pos-sesses selective reflection and transmission spectra.For example, right-handed Ch-LC can highly trans-mit left-handed circularly polarized light and reflect(nearly 99.9%) right-handed circularly polarized lightof a certain waveband. The reflected light at a wave-length peak can be given by the Bragg formula �0= n̄P0, where n̄ is the average refractive index and P0is the pitch. The spectral width of the reflection peakis given by ��=P0�n, where �n is the birefringence.Furthermore, 50% of the linearly polarized light cantraverse, with the passed light being left-handed cir-cularly polarized. Here, we use the Jones matrixmethod [8] to numerically calculate the reflectivityand transmittance of Ch-LC. The reflection andtransmission spectra of a Ch-LC with a uniformright-handed twist are shown in Fig 1. The Ch-LChas the following parameters: pitch P0=0.49 �m, no=1.52, and ne=1.77. The thickness of the Ch-LC is 10pitches. The incident light is parallel to the helicalaxis.

The reflection will rotate the left-handed circularlypolarized light to the right-handed polarization.Thus, the incident left-handed circularly polarizedpulse, after an odd numbers of reflections inside thecavity, becomes right-handed. It will be highly re-flected by the entrance mirror of right-handed Ch-LC, and the fs laser pulse becomes trapped inside thestorage cavity.

An experiment was done to validate the design[Fig. 2(a)]. The experiment was conducted onSILEX-I [9,10] (Super Intense Laser for Experimentson the Extremes) at the Research Center of Laser Fu-sion in China. The incident pulse was linearly polar-ized at 800 nm, 1 Hz, 100 fs, with a pulse energy of5 mJ. The spatial profile of the incident beam wasnearly Gaussian, with a spot size of 20 mm and

nearly a flat top in the time domain. Nearly 2.43 mJ

2010 Optical Society of America

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1362 OPTICS LETTERS / Vol. 35, No. 9 / May 1, 2010

of incident beam was trapped. The right-handedCh-LC was inside two bare fused silica plates [Fig.2(b)]. The thickness of the fused silica plate is0.5 mm. A plane mirror, with reflectivity of 99.5%,was spaced 31 cm from the Ch-LC. A fast photodiodemonitored the recirculating pulse by measuring theleakage through the plane mirror.

The cavity ring-down signal is shown in Fig. 3. Thetemporal pulse separation is about 2 ns. In this ex-periment, the total signal enhancement is 12.6, cal-culated as the ratio of the integrated energy of all theround trips divided by the initial energy. Further-more, we measured the damage threshold of experi-mental Ch-LC at 800 nm, 30 fs. Without electricity,the Ch-LC possesses a high damage threshold, about1 TW/cm2. The Ch-LC layer was so thin, like a high-reflecting coating, that the pulse dispersion can beneglected. The pulse dispersion in the experimentwas caused mainly by the fused silica plate outsidethe Ch-LC with a thickness of 0.5 mm. Since theGVD of fused silica is 361 fs2/cm at 800 nm, thepulse duration will be stretched to 1 ps after nearly200 round trips.

The laser pulse decays primarily because of theleakage at Ch-LC mirror. The transmittance of theincident beam and trapped beam are 48.5% and 7%,respectively (Fig. 4). The reflectivity of the Ch-LC

Fig. 1. (Color online) Reflection and transmission spectralarized incident light, (b) left-handed circularly polarized in

Fig. 2. (Color online) (a) Experimental setup of a fs l

Fig. 3. Energy of leaked signal versus time. The temporalpulse separation of about 2 ns corresponds to the round-

trip time of the cavity.

mirror for the trapped beam is not too high, becausethe fused silica plates outside the Ch-LC are un-coated, and the Ch-LC layer is just 5 �m, a bit thin.We estimated that the reflectivity would be improvedto 99% (as [11] has mentioned), if the glass wereantireflection coated and the Ch-LC layer were thick-ened.

Figures 5(a) and 5(b) show the expected perfor-mance of the two-mirror cavity after antireflectioncoating with the improved Ch-LC, with a reflectivityof 99% at the Ch-LC and 99.9% at the other mirror.We estimate the nonlinear refractive index of fusedsilica as 2.36�10−16 cm2/W and an intensity of16 GW/cm2 in the incident pulse, and we neglect thediffraction losses. Assuming a total loss of 1.1% perround trip, we predicted a cavity enhancement of84.3 by integrating the energy versus round tripscurve in Fig. 5(a). The nonlinear phase accumulationin the fused silica approaches 2.5 rad after 250 cavityround trips.

In the future, we plan to improve the performanceof the Ch-LC and design a robust, reliable storagecavity that is simple to align and operate.

The storage cavity should meet specifications in-cluding a focal spot of 20 �m, laser pulse duration of30 fs, and total pulse energy of 100 mJ at 800 nm.Our storage cavity design is shown in Fig. 6. A thin-film polarizer (TFP) and a quarter-wave plate areused to make the incident beam circular polarized.The Z-form storage cavity consists of two concave

e right-handed Ch-LC with (a) right-handed circularly po-nt light, (c) linearly polarized incident light.

storage cavity; (b) Schematic of experimental Ch-LC.

Fig. 4. Transmission spectra of the experimental Ch-LCwith (a) linearly polarized incident beam and (b) right-

of th

aser

handed circularly polarized light.

May 1, 2010 / Vol. 35, No. 9 / OPTICS LETTERS 1363

mirrors with identical radii of curvature, a right- (orleft-) handed Ch-LC, and a plane mirror. The de-signed cavity is self-imaging, meaning that theABCD matrix for one round trip is

�− 1 0

0 − 1� .

It is equivalent to a confocal resonator. Assuming aloss of 1.5% per round trip, the Z-form storage cavity

Fig. 5. (Color online) Numerical calculation of storage cav-ity performance, assuming a total loss of 1.1% per roundtrip, (a) pulse energy in the cavity versus number of roundtrips. The total predicted cavity enhancement is 84.3. (b)Nonlinear phase accumulation versus the number ofroundtrips.

Fig. 6. (Color online) “Z” form storage cavity design forCompton scattering. With reflectivity of 99% at the Ch-LCand 99.9% at other mirrors, assuming a loss of 1.5% perroundtrip, the “Z” form storage cavity enhancementreaches 64.4.

enhancement reaches 64.4. The repetition rate of the

laser pulses in the cavity will be set to an integermultiple of the repetition rate of electron bunches,i.e., 20 MHz. The electron beam is steered with exter-nal magnets and focused at the laser focus. X-raygeneration occurs at the focus of the storage cavity inthe propagation direction of the e− beam.

In this Letter, we propose a design of fs laser pulsestorage cavity for a Compton scattering x-ray sourceand experimentally demonstrate the feasibility ofutilizing Ch-LC as the entrance mirror in the TW-scale peak power laser cavity. The design is suitablefor trapping ultrashort high-energy laser pulses andminimizes pulse dispersion and nonlinear phase ac-cumulation. The storage cavity can provide an im-provement of nearly 2 orders of magnitude in averagebrightness of a Compton scattering ultrashort x-raylight source.

We thank Prof. Da-yong Zhang and Associate Prof.Yong-quan Luo for useful discussions. We also thankJian-zhong Peng of Nanjing Huari Liquid CrystalDisplay Ltd. for providing the Ch-LC. This work wassupported by the Chinese National Foundation ofNatural Sciences under contract 10735050.

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