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doi:10.1016/j.op

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Optics & Laser Technology 39 (2007) 1084–1088

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Design of a highly stable, high-conversion-efficiency pumping source foroptical parametric amplifier by extending efficient crystal length

Jun Kang�, Shao-He Chen, Jian-Qiang Zhu, Hui Wei

Shanghai Institute of Optics and Fine Mechanics, The Chinese Academy of Sciences, Shanghai 201800, PR China

Received 15 August 2005; received in revised form 11 April 2006; accepted 12 April 2006

Available online 13 June 2006

Abstract

The objective of this study is to improve the stability of pumping source of optical parametric amplifier. Analysis by simulation

leads to the conclusion that the stability of the second harmonic can be improved by using properly the intensity of fundamental

light and corresponding length of the crystal. By the method of the noncollinear two-pass second harmonic or the tandem

second harmonic, the efficient crystal length is extended to a proper value, and the stability of the second harmonic output

has been improved two times more than that for the fundamental light, and the conversion-efficiency is about 70% in experiment.

When the variation of the fundamental light is about 10%, the variation of the second harmonic intensity has been controlled

within 5%.

r 2006 Elsevier Ltd. All rights reserved.

Keywords: Optical parametric amplification; Second harmonic; Stability

1. Introduction

Recently, as a main method to generate ultra-short ultra-high power laser pulses, optical parametric chirped-pulseamplification (OPCPA) has been widely adopted in manyareas [1–3]. How to improve the stability of the output hasbeen increasingly gaining attention [1,4].

Two methods have been applied to improve the stabilityof optical parametric amplifier (OPA). One is to carefullychoose and balance system parameters such as the crystallength as well as pump intensity and signal intensity [5,6] inorder to achieve the stable output, the other is to improvethe stability of pump and signal source among which thestability of pump intensity matters more.

According to numerical simulation, when the pumpvariation is within 10%, the OPA output variation is within44.5% in unsaturated area while within 75.7% in stablearea [6]. As well known, the ideal OPA pump source is thestable flat pump source. It has been reported that the high-

e front matter r 2006 Elsevier Ltd. All rights reserved.

tlastec.2006.04.005

ing author. Tel.: +862169918287; fax: +8621 69918800.

ess: kangjun@siom.ac.cn (J. Kang).

order Gaussian shaped OPA pump source has beenadopted [7], but the temporal pulse-shaping system iscomplicated and the stability of the fundamental intensityis highly demanded.In this paper, we demonstrate the existence of an optimal

working area for stable optical second harmonic outputbased on numerical simulation. The stability of the secondharmonic light can be improved by carefully choosing andbalancing system parameters such as appropriate intensityof the fundamental light and corresponding length of thecrystal. By the method of the noncollinear two-pass secondharmonic or the tandem second harmonic, the stability ofthis system has been improved by two times more than thatfor the fundamental light, and the conversion-efficiency isabout 70%. In our lab, the variation of second harmonichigh-order Gaussian pulses energy can be controlled within5% for the fundamental Gaussian pulses energy withfluctuation of 10%. As we known, the fluctuation index ofOPA pump intensity in GXII and OMEGA EP are 74%and 75% [1,4]. Therefore, adopting this as stable OPApump source, the stability of OPA system will be greatlyimproved.

ARTICLE IN PRESSJ. Kang et al. / Optics & Laser Technology 39 (2007) 1084–1088 1085

2. Theoretical analysis

According to the early theoretical investigation [8,9],coupled wave equations in the slowly varying envelopeapproximation can be written in a concise and normalizedform by introducing the normalized amplitude of travelingwave component uiði ¼ 1; 2Þ. u1 is the normalized funda-mental light intensity and u2 is the normalized secondharmonic light intensity:

du1=dx ¼ �u1u2 sin y, (1a)

du2=dx ¼ u21 sin y, (1b)

dy=dx ¼ DS þ ðcos y= sin yÞd=dx½lnðu21u2Þ�, (1c)

where

u1 ¼ ½I1=ð2o1W Þ�1=2, (2a)

u2 ¼ ½I2 cos2 b=ðo2W Þ�1=2, (2b)

W ¼ I1ð0Þ þ I2ð0Þcos2 b, (2c)

DS ¼ Dkz=x, (2d)

Y ¼ Dkzþ F2 � 2F1, (2e)

x ¼ 4pdeff ðpW Þ1=2z=ðe0l21l2n

21n2 cos

2 bÞ, (2f)

where b is the Poynting Vector walk-off angle, I1 and I2 arethe intensities of two waves, I1(0) and I2(0) are the initialintensities of two waves at position z ¼ 0, o1 and o2 areangular frequencies.

0 5 10 15 20 25 30 35

1.2

1.0

0.8

0.6

0.4

0.2

0.0

Nor

mal

izab

le H

arm

onic

inte

nsity

(A

.U.)

Crystal length (mm)

Fundamental intensity Variation

A B

C

0%5%10%-5%-10%

(a)

Fig. 1. Dependence of second harmonic stability on fundamental fluctuation:

different fundamental intensity, (b) the variation with the crystal length in dif

All the waves propagate along the z- axis while Dk ¼

k2 � 2k1 refers to the corresponding mismatch of the twowave vectors, deff is the BBO effective nonlinear coefficientfor type I phase matching. Fiði ¼ 1; 2Þ represents the initialphase. niði ¼ 1; 2Þ represents refractive index.The Runge–Kutta procedure was employed to solve

differential Eqs. (1). For the sake of simplicity, we adopttype-I angle phase matching for BBO crystals in all thefollowing cases. A 1064 nm YAG laser is considered asfundamental light source and the initial intensity is 0.2Gw/cm2. Curves of second harmonic intensity dependenceupon crystal length are given in Fig. 1a with respect todifferent fundamental fluctuations, which are �10%,�5%, 5% and 10%, respectively.As shown in Fig. 1a, before A, the second harmonic

intensity grows from 0 until the saturated values and keepssaturation from A to B, while almost all fundamental lighttransfer into second harmonic light. The second harmonicintensity gradually decreases behind B, where energy beginsto flow back to the fundamental. Several curves tend toconverge around C, where the output intensity is lesssensitive to the fundamental changes. When the BBOcrystal length is designed in this area, the fluctuation ofsecond harmonic will be effectually controlled.The variation of the second harmonic light can be

expressed as D:

DðzÞ ¼ ðI spðzÞ � I s0ðzÞÞ=I s0, (3)

where Is0(z) is the second harmonic intensity at position z

not considering the variation of the fundamental intensity,Isp(z) is the is the second harmonic intensity at position z

considering the variation of the fundamental intensity. Thebest stability of the system can be defined as D ¼ 0.

0 5 10 15 20 25 30 35-20

-15

-10

-5

0

5

10

15

20

-10%

-5%

Crystal length (mm)

%

10%

5%

C

AB

(b)

(a) normalized second harmonic intensity curves with the crystal length in

ferent fundamental intensity.

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1.0

0.8

0.6

0.4

0.2

0.0

Nor

mal

izab

le in

tens

ity (

A.U

.)

t (ns)

Fundamental

2nd harmonic

0-7-14 7 14

Fig. 2. Simulated plots of the flat top second harmonic pulse and

normalized, Gaussian temporal fundamental pulse in appropriate condi-

tion.

0.2 0.4 0.6 0.8 1.0

14

16

18

20

22

24

26

28

30

32

Cry

stal

Len

gth

(mm

)

Ip(GW/Cm2)

Fig. 3. Dependence of the most appropriate crystal length on funda-

mental intensity.

1.0

0.8

0.6

0.4

0.2

0.0

Nor

mal

izab

le H

arm

onic

inte

nsity

(A

.U.)

Crystal length (mm)10 20 30

Δθ=0.02°

Δθ=0.01°

Δθ=0.001°

Δθ=0.0°

Fig. 4. The effect on the output by angle divergence from y.

J. Kang et al. / Optics & Laser Technology 39 (2007) 1084–10881086

Curves of the second harmonic variation dependenceupon crystal length are given in Fig. 1b. The secondharmonic variation is larger than the fundamental varia-tion before A, and the second harmonic variation is similarto the fundamental variation from A to B, and the secondharmonic variation becomes smaller than the fundamentalvariation from B to C. In the area of C, the stability of thesecond harmonic has been improved significantly. (Whenthe fundamental variation is 710%, the second harmonicvariation is only 4%; and when the fundamental variationis 75%, the second harmonic variation can be controlledwithin 1%.)

Fig. 2 shows the simulated temporal shape of the secondharmonic pulse and the Gaussian fundamental pulse. Inour simulation, the input fundamental peak intensity is of0.42GW/cm2 and the BBO crystal length is designed as23mm. The high-order Gaussian output pulse is observedcompared with Gaussian input pulse; the output pulsewidth becomes wider as shown in Fig. 2. This result is verysatisfying for an OPA pumping source.

Fig. 3 shows the relation between the initial fundamentalintensity and the most appropriate crystal length requiredwhen working in stable areas. The higher the initial inputintensity, the shorter the crystal length required as shownin Fig. 3. As we known, the damage threshold for BBOcrystal is 0.5GW/cm2 [10], (measured at 1064 nm with 10 nslaser pulses) so the minimal BBO length will be 20.6mm.

The second harmonic intensity is sensitive to the phasematching angle y and the angular acceptance is relativelynarrow for BBO. As shown in Fig. 4, if the beamdivergence is only 0.021, the maximum second harmonicintensity is only 50% compared to the condition of nodephasing. We suppose the effective BBO aperture is 6mm,and the corresponding minimum diffracted angle is about0.021. As the influence of dephasing, the efficient input

fundamental intensity is only a part of the total inputintensity, so the appropriate crystal length of working inthe area of stability will be larger than our calculationabove. On the other hand, when the crystal lengthincreases, the coupling efficiency will decrease as affectedby walk-off angle in BBO (about 3.21), and it is difficult torealize the stable second harmonic output through a singlelong BBO crystal.Two methods are used to solve the problem. One of the

method consists of two tandem BBO crystals configuredfor type-I phase matching whose extraordinary axes areoriented in opposing directions for walk-off compensation[11], and another method is to use a mirror to reflect thelight and the efficient interaction BBO crystal length islengthened by the way of two-pass second harmonic

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1064nm9.8ns70mJ

Nd:YAG laser

reflector

BBO

1064nm10ns70mJ

Nd:YAG laser BBO BBO

(a)

(b)

Fig. 5. (a) Diagram of the two pass second harmonic configuration, (b) diagram of the tandem second harmonic configuration.

0.0

0.2

0.4

0.6

0.8

1.0

φ=0

φ=3°φ=5°

403020

Nor

mal

izab

le H

arm

onic

inte

nsity

(A

.U.)

crystal length (mm)10

Fig. 6. The effect on the output by angle divergence from j.

J. Kang et al. / Optics & Laser Technology 39 (2007) 1084–1088 1087

through a single BBO crystal [12]. For the two-pass second-harmonic as shown in [12], the distance between crystal andmirror must be carefully controlled in accordance with thephase-matching requirement for the sake of air dispersion,and the way of the harmonic beam derived form system isnot simple as the reflected beam is reflected on the samepath where initial input light travels. As shown in Fig. 5(a),we adopt the method of noncollinear two-pass secondharmonic in experiment, in which the reflected beamdeviates from the direction of the incident beam withdeviated angle approximating 2–31 in the direction of j.

When the deviated angle in the direction of j is in therange of 751, the effect from the second harmonic outputcan be neglected, as shown in Fig. 6. In this situation, notonly the effect of walk-off angle can be mostly counteract,but also the phase matching can be satisfy through fineadjusting the angle around j on the base of firstly adjustingthe distance between the reflected mirror and the crystal.

The second harmonic beam also can be easily derived fromsystem.

3. Results and discussion

The experiment of the high stability second harmonic isdesigned on the base of above analysis. The diagram isshown in Fig. 5.Gaussian fundamental pulses are generated from a

1064 nm Q-switched single-mode Nd: YAG laser; A 2:1Galilean telescope is uses to reduce the beam diameter afterthe pulses have been amplified. Then the fundamentalpulses (about 70mJ, F2mm) enters the BBO crystal(8mm� 8mm� 12.5mm, y ¼ 22:81, j ¼ 01) , the decayedsecond harmonic pulses is detected by an oscilloscope.Fig. 7(a) shows the laser pulses shape of 1064 nm

fundamental light which has been recorded for 10min;Fig. 7(b) shows the second harmonic pulses shape in thecondition of one BBO crystal for 10min; Fig. 7(c) is thesecond harmonic pulses shape in the condition of twotandem BBO crystals for 10min. The intensity jitter of thesecond harmonic pulses can be controlled within 8% forthe 1064 nm fundamental Gaussian pulses intensity jitter of20%, the stability of this system has been improved by twotimes compared to the case of fundamental light, and theconversion-efficiency is about 70%. When the variation offundamental light is controlled within 10%, the intensityjitter of the second harmonic can be controlled within 5%in our lab.

4. Conclusion

Using numerical simulation techniques, the stability ofthe second harmonic has been analyzed in this paper. Bythe way of noncollinear two-pass second harmonic andtandem second harmonic, the high-stability and high-conversion-efficiency OPA pumping source has beenachieved in our lab.

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Fig. 7. (a) The pulse shape of 1064nm fundamental light, (b) the pulse

shape of 532 nm harmonic through the first BBO, (c) the pulse shape of

532 nm harmonic through two BBO.

J. Kang et al. / Optics & Laser Technology 39 (2007) 1084–10881088

Acknowledgment

This work was supported by National 863 Project inAdvanced Techniques in China (2005AA842010).

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