Study on the eight-pass single grating stretcher

Jianjun Yang Shuangchen Ruan Xun Hou

Xi'an Institute ofOptics and Precision Mechanics, Academia Sinica, Xi'an , China. 710068

ABSTRACT

In chirped pulse amplification system pulse stretching is an important part. To investigate the behavior ofaneight-pass single grating pulse stretcher, we examine in two steps: firstly a unchirped ultrashort pulse goes firstfour-pass through the stretcher, it will be broadened in pulsewidth and provided with amount of positive chirps.

Secondly this chirped pulse will has another four-pass experience through the stretcher. Followed by our closecalculations, it is clear that stretching factor in the second part is almost 2, and the total stretching factor of thissystem is equal to the multiplication ofthe two factors.

1. INTRODUCTION

The chirped pulse amplification (CPA) technique applied to solid-state lasers has made possible development of

table-top laser systems providing terawatt-level peak power. Recently this technique was extended to generatedmultiterawatt pulses of approximately l5fs in time duration' and pulse energy as high as 1 .1J was obtained 2 Such

laser systems can promise as convenient tools for investigation of high-field (>10'W/cm2) phenomena and forgeneration of ultrafast coherent and incoherent x-ray radiation. The basic idea of chirped pulse amplification is to

amplify efficiently a short pulse while avoiding nonlinear effects in the amplifier rod. With this technique, a shortpulse is imtially stretched in time to keep the amplified peak intensities below the level where catastrophic nonlinear

effects would occur. Then the amplified chirped pulse is recompressed to near its Fourier transform limit to getultrashort, high energy output. Evidently the operation of stretching an compressing is critical for a successfulamplification.

In principle, femtosecond lasers can achieve extraction efficiencies that approach 55%,most CPA lasers,however, achieve only 5%-20% efficiency. To achieve very high efficiencies, one must operate the amplifier at veryhigh flunces. Barty' have calculated that to achieve efficiencies near the theoretical limit of Ti:sapphire, one needs to

reach a flunce of 2J/cm2. This indicates that the pulse duration in the amplifier must be at least 400ps. in most

practical systems, traditional four-pass pulse stretcher is used. But recently W.E.White and M.D.Perrey haveadopted a eight-pass grating stretcher to expend the seed pulse from lOOfs to 400ps and 3ns respectively. in addition,

some commercial amplifier products in the market adopted such optical design.

In this paper we concentrate on the eight-pass single grating stretcher. Through detailed analysis we calculate thestretching factors in the first and second four-pass through stretcher. The results show that the stretching factor in the

second part is approximately 2, and total stretching factor of this system is almost twice the first one..

2. STRETCHING PRINCIPLE AND OPTICAL DESIGN

Pulse stretching can be achieved with the use of diffraction gratings. In a pulse stretcher, the input beam is

746 SPIE Vol. 3516 • 0277-786X199/$1O.lJO

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L2Grating Li

_________________ Grating

Mirror

Grating

Reoflecter

I z2

f2 f2

Fig.2. A four-pass single-grating stretcher

3.CALCULATION OF STRETCHING FACTOR

3.1 First fourpass stretchingFor a incident non-chirped Gaussian ultra-short pulse, it can be described by foilowing term:

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incident on a diffraction grating, causing the different frequencies present to disperse. The grating can beconfigure in such a way so the bluer frequency components have to travel further through the stretcher than redder

components. The result is that the redder frequency components exit the stretcher first, the pulse has beenstretched. Figi .shows a typical pulse stretcher which was developed by Martinez .

I I1

Fig. 1. A typical double-grating stretcher

In most practical pulse stretchers, single grating is often used, and is multipassed to reduce complexity.Furthermore it is necessary to four-pass the grating to ensure that the stretched laser beam is spatiallyreconstructed. This keeps the design simple and compact as shown in Fig.2. The detail analysis can be seen in

Ref.6.

Lens

Mirror

4

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( 21n(2) 2'E0—exp— 2 I (1)

\\ T0 ,1

where v0 is time duration of incident laser pulse.

Since the positive group velocity dispersion introduced by stretcher only depends on its structural parameters and hasnothing to do with the seed pulse. Now we suppose the stretcher provide amount ofpositive dispersion cJ the time

intensity of stretched chirped pulse from the pulse expender can be written as:

21n(2)z-02 2 8(ln(2))2 2E1 (t) exp —

2 exp —i 2 (2)r04+16(ln(2)) 2 04+16Qn(2)) 2 )

Thus the time duration of output chirped pulse is:

16(ln(2))2152'2

z-1=To 1+ (3)To

The stretching factor M1, the ratio oftime duration of output pulse to the time duration of incident pulse can be

obtained by:

V ( l6(1n(2))2 224

S

(4)V0 )

3.2 The second four-pass stretchingAfter the first four-pass through the stretcher, pulse is broadened in time width and provided with amount of

positive chirps, then it will go for another four-pass stretching through this pulse expender. Substituting equation (3)

into equation (2), one obtains the following equation:

t2]

.t2 I6(1n(2))2cI•exp —I---• 2 2

V1 V0

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1 t2 t2 4(1n(2))= exp — 2 / exp —i —. 2 /2 2T1 /,/41n(2) //41fl(2)

ii 4ln(2) _______=exp—-1l±i 2 2 /

To )T1//'4 ln(2)

(5)

41n(2)(1 ______Nowwe defme C =2

Sas a chirp parameter of laser pulse, and suppose T = , then equation (5)21i

will become the following term:

E1(t) exp_!(1+iC)J (6)

For the output stretched pulse through eight passes in the stretcher, its intensity can be obtained as:

(I +iC)t2E2(t)—exp -— (7)2[T2 —17?5(1+ic)J

So that for the second four-pass stretching, the stretching factor M2 can be described by following term:

M2 ==[(i+)2 j2JY

=

2

+ ln(2)2]

(8)

Substituting equation (4) into equation (8), we can get

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(

r02(r12_r02)]22

To

[ (= +

12 )

1//2+ —

T2 V14

750

2=(43

I(\ M12

Since in most practical systems , there is M1>>l, equation (9) an be simplified as

M2 = 2

(9)

(10)

This suggests that the stretching factor in the second four-pass is no more than 2. According to equation (9),

when the first factor M1 is becoming larger, the second factor M2 will get more close to 2. Finally we can get the

whole stretching factor M for a seed pulse going through eight passes in the single grating stretcher.

M = = 2 M1V0 V1 T1

4.CONCLUTION

(11)

Based on the principle of a pulse stretcher, stretching properties for a ultrashort pulse experiencing eight passesthrough a single grating stretcher have been investigated. Finally we found that the stretching factor in the second

four-pass is approximately 2, and the total stretching factor ofthis system was multiplication of these two stretching

factors.

5. REFERENCES

[1]C.P.J.Barty,C.L.Gordon III , et al , " Methods for generation of 10Hz , l00-TW optical pulses" , Proc. SPIE,

2377,311-322,1995[2]A.Sullivian,J.Bonhie,D.F.Price, and W.E.White,Opt.Letter.2 1 ,603 (1996)

[3] J.D.Bonlie , W.E.White , et al , " Chirped-pulse Amplification with Flashlamp-pumpedTi:sapphire

V2

TI V14

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Amplifiers" , Proc. SPIE, 2116, 3 l2322, 1994

[4] B.C.StUart , M.D.Perry, Ct al , "125-TW Ti:sapphirefNd:glass laser system" , Opt.Lett. 22(4): 242244(l997)[5]O.E.Martinez, 3000 Times Grating Compressor with positive Group Velocity Dispersion Apilication to Fiber

Compensation in I 3l .6 i m Region, IEEE.J.Quatum.Electron. , 23(10): 5964 ,1987[6] JianjunYang, Yanlmg Sun, Shuangchen Ruan, et al, "Study on the single-grating siretcher in chirped pulse

amplification" , Acta Optic Sinica Vol.18(4), 1998.

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