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Sun et al. Vol. 26, No. 3 /March 2009/J. Opt. Soc. Am. B 549

Femtosecond spontaneous parametricupconversion and downconversion in a quadratic

nonlinear medium

Jinyu Sun, Shian Zhang, Tianqing Jia, Zugeng Wang, and Zhenrong Sun*

Department of Physics, State Key Laboratory of Precision Spectroscopy, East China Normal University,Shanghai 200062, China

*Corresponding author: zrsun@phy.ecnu.edu.cn

Received September 9, 2008; revised December 21, 2008; accepted January 8, 2009;posted January 12, 2009 (Doc. ID 101287); published February 26, 2009

Spontaneous parametric upconversion (SPUC) and spontaneous parametric downconversion (SPDC) have beenobserved in the �-barium borate (BBO) crystal, and their mechanisms are experimentally and theoreticallyinvestigated. SPUC, tuned from 530 to 600 nm with a FWHM of about 25 nm, can be attributed to the sumfrequency between the quantum noise and the fundamental laser pulse in the type II phase matching condition�e+o→e�. SPDC, tuned from 480 to 520 nm with a FWHM of about 15 nm, can be attributed to the differencefrequency between the quantum noise and the fundamental laser pulse in the type I phase matching condition�e→o+o�. © 2009 Optical Society of America

OCIS codes: 190.4410, 190.7220, 190.4380, 190.7110, 320.0320, 320.7110.

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. INTRODUCTIONarametric upconversion (PUC) and parametric downcon-ersion have been well-known since the earliest days ofonlinear optics [1,2]. As a pumping laser pulse �p pumpsquadratic nonlinear medium, the modulation instability

MI) [3,4] and the exponential growth of perturbation ashe quantum noise in time or space [5] can lead to spon-aneous parametric emission [6–8]. Spontaneous para-etric upconversion (SPUC) emission can provide the

igher frequency component than that of the pumping la-er beam, and spontaneous parametric downconversionSPDC) emission can provide the lower frequency compo-ent than that of the pumping laser beam.SPDC [9] has been widely used as a source of the cor-

elated and the entangled photon pairs, including theests of basic quantum mechanics [10,11], precise opticaleasurements [12,13], quantum imaging [14–17], and

uantum information [18–20]. Due to the broad band-idth of SPDC, it has attracted considerable attention asbroadly tunable laser source covering the entire visible,ear IR, and near UV regions, which has been widely in-estigated in theory and experiment [21–23].

SPUC can be applied in the generation of very shortavelength radiation, up to the range of hard x rays.PUC has been investigated in plasma [24] and experi-entally demonstrated via free electron laser mechanism

25]. PUC of an electromagnetic wave was investigated inhe presence of a gyrating electron beam [26,27], and Hir-hfield [28] pointed out that the unstable Bernsteinodes could be coupled to the electromagnetic waves to

enerate the higher frequency radiation. Under the fem-osecond laser pulse pumping of 6 mm thick �-BBO crys-al, a tunable emission has been observed from80 to 800 nm [6], and a tunable line emission over aarge wavelength of 340–980 nm is obtained by pumping

0740-3224/09/030549-5/$15.00 © 2

ith the picosecond pulses of 532 nm [29]. Here, thehase matching condition has the advantages of secondarmonic generation (SHG) and two-photon excitation,hich will exert positive impacts on the tunable emission.owever, although SPUC has been theoretically dis-

ussed in the early nonlinear optics [30–32], true SPUCas not been experimentally confirmed in a quadraticonlinear medium. In this paper, a 4 mm thick �-BBOrystal is pumped by 50 fs laser pulses and rotatedround the optical Z axis, and the SPUC from80 to 520 nm and the SPDC from 530 to 600 nm haveeen alternately observed. The experimental and theoret-cal results indicate that SPUC is directly generated byhe sum frequency of the quantum noise and the funda-ental laser pulses. Two or multiphoton excitation of the

undamental laser pulses has no effect on the SPUC gen-ration in our experiments, which is different from the ex-erimental results [6,29].

. EXPERIMENThe experimental setup is sketched in Fig. 1. A regenera-ive amplified Ti:sapphire femtosecond laser (Spitfire,pectra-Physics) is used as the excited source with a rep-tition rate of 1 KHz, a pulse-width of about 50 fs, and aenter wavelength of 800 nm. The output laser pulsesith the energy of about 400 �J is focused by a lens �f40 cm� into a 4 mm thick �-BBO crystal ��=29.2° � at

he laser incident angle � of about 9°, and a variable at-enuator is placed before the lens to adjust the laser in-ensity. When the �-BBO crystal is rotated around the zxis, the bright cyan and Kelly spontaneous parametriconical emission (CE) are alternately observed. Their im-ges on a white screen are recorded by a digital camera,nd their wavelengths are measured by a spectrographOOIBase32, S2000).

009 Optical Society of America

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550 J. Opt. Soc. Am. B/Vol. 26, No. 3 /March 2009 Sun et al.

. RESULTS AND DISCUSSIONhen the �-BBO crystal is rotated around the z axis toinimize SHG, a bright Kelly CE, with a center wave-

ength of about 550 nm and a FWHM of 25 nm [as shownn Fig. 2(c)], can be generated. Its conical angle is 3.2°,nd its angular width is about 0.5° [as shown in Fig. 2(a)].n the output laser pulses through the BBO crystal, onlyhe fundamental frequency component of around 800 nman be observed, but its second harmonics have not beeneasured [as shown in Fig. 2(b)]. The wavelength of theE is shorter than the fundamental laser pulses, there-

ore the bright Kelly CE can be attributed to the SPUC ofhe fundamental laser pulses.

If the BBO crystal is rotated around the z axis to gethe maximal SHG, a bright cyan CE can be observed at a

VND LENS �-BBO SCREEND

Pump-beamZ axis

Optical axis

� ��

Pump-beam

Signal-beam

Fig. 1. Schematic of the experimental setup for SPUC.

ig. 2. (Color online) (a) SPUC emission and (c) spectra pumpedy the 800 nm fundamental pulses and the corresponding trans-itted pumping laser pulse spectrum after (b) BBO crystal, (d)PDC emission, and (f) spectra pumped by the 800 and 400 nmumping laser pulses and the corresponding transmitted pump-ng laser pulse spectrum after (e) BBO crystal, (g) SPDC emis-ion, and (i) spectra pumped by only the 400 nm pumping laserulses and the corresponding transmitted pumping laser pulsepectrum after (h) BBO crystal.

arger conical angle of 5.1° and an angular width of about.3° [as shown in Fig. 2(d)]. The center wavelength of theright cyan emission is measured to be 480 nm in the in-er and 540 nm in the outer, and its FWHM is about5 nm [as shown in Fig. 2(f)]. Both the fundamental fre-uency component of around 800 nm and its second har-onics can be measured in the output pumping laser

ulses through the BBO crystal [as shown in Fig. 2(e)]. Toxplore the provenance of the cyan CE, the CE, pumpedy the second harmonics of the fundamental laser pulses,as been investigated. A 1 mm thick BBO crystal (type I,=28.9°) is placed before the lens to obtain the secondarmonics of the fundamental laser pulses, and a dichro-

sm plate is used to reflect the 800 nm fundamental laserulses and transmit their second harmonics. When themm thick BBO crystal is pumped by the second har-onics (no fundamental frequency component) [as shown

n Fig. 2(h)], a rainbow CE can be observed at a conicalngle similar to the cyan CE [as shown in Fig. 2(g)]. Itsavelength is observed to be 480 nm in the inner and10 nm in the outer, and its FWHM is about 30 nm [ashown in Fig. 2(i)]. Its wavelength range is much widerhan the cyan CE. Accordingly, the cyan and the rainbowE at the same conical angle can be reasonably attributed

o the SPDC of the second harmonics of the 800 nm fun-amental laser pulses. Because of the group velocity dis-ersions, the phase matching condition for SHG of around00 nm in the 1 mm BBO crystal (type I, �=28.9°) is bet-er than that in the 4 mm �-BBO crystal (type I, �29.2°), and thus the SHG in the 1 mm BBO crystal isore intense than that in the 4 mm �-BBO crystal (type

, �=29.2°) at the same 800 nm fundamental laser pulses.ore intense second harmonics will produce a larger andider SPDC. Consequently, the rainbow CE wavelength

s much wider than the cyan CE one.As an intense femtosecond laser pulse pumps a qua-

ratic nonlinear crystal at the frequency �0, the quantumoise around the pumping laser beam from the spontane-us emission [33] as �0 /2±� will get exponential growth7] for the spatiotemporal MI (� is the frequency shiftway from the spontaneous emission). In our experi-ents, SPUC can be attributed to the type II phaseatching condition �e+o→e�, and the SPUC can be

chieved by the sum frequency of the quantum noise andhe fundamental laser pulses. According to the phaseatching condition �k�=ks

�−kp���0�−ki

�=0 [23] and the en-rgy conservation �s=�i+�p, the CE angle �spuc of thePUC will be calculated as cos �spdc= �kp

2−ks2−ki

2� / �2kpks�34] [as shown in Fig. 3(a)]. Here, the type II phaseatching condition �e+o→e� makes for SPUC generation,hich is the sum frequency of the quantum noise and the

undamental laser pulses. Two–photon or multiphoton ex-itation of the fundamental laser pulses has no observableffect on the SPUC generation, which is different from thexperimental results [6,29].

As the BBO crystal is rotated to maximize the SHG�0, the SPDC can be achieved by the difference fre-uency of the second harmonics 2�0 and the quantumoise �0±� in the type I phase matching condition �e→oo�. When the phase matching condition �k�=kp�2�0�� −ks

�

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Sun et al. Vol. 26, No. 3 /March 2009/J. Opt. Soc. Am. B 551

ed, the CE angle �SPDC of the SPDC will be calculated asos �spdc= �kp

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2� / �2kpks� [as shown in Fig. 3(b)]. It isistinct that the CE angle of the SPDC is larger than thatf the SPUC, and the tunable wavelength range of thePDC is much wider than that of the SPUC. If two-hoton or multiphoton excitation of the fundamental la-er pulses has contributions to the SPUC, the CE angle ofhe SPUC should be the same as that of the SPDC. There-ore, it is further validated that there are no two-photonr multiphoton excitation effects of the fundamental laserulses on the SPUC.In our experiment, SPUC and SPDC can be achieved by

otating the BBO crystal around the Z axis. The depen-ences of SPUC and SPDC generation on the femtosecondulse intensity and the width are investigated, and thexperimental results are presented in Figs. 4(a)–4(c). Ashown in Fig. 4(a), the SPDC intensity shows a decreases the fundamental laser pulse-width increases. However,PUC can be generated only at the fundamental laserulse-width of 90–130 fs, where it will approach theaximal value at the fundamental laser pulse-width of

00 fs. Because the SPDC depends on SHG, the shorterundamental laser pulse-width will produce a more in-ense SHG and generate a more intense SPDC. Becausehe SPUC depends on the fundamental laser pulses, aroper chirp of fundamental laser pulses will make forhe phase matching condition for SPUC (type II, e+o→e)n the 4 mm �-BBO crystal, and the maximal SPUC wille at the fundamental laser pulse-width of 100 fs. Whenhe fundamental laser pulse-width is too wide, the peakntensity of the fundamental laser pulses will be too lowo generate SPUC and SPDC. As shown in Fig. 4(b),PUC evidently requires higher intense fundamental la-er pulses than SPDC, and the SPDC generation is more

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ig. 3. Experimental (square) and calculated (curve) results forhe CE angle of (a) SPUC and (b) SPDC.

fficient than the SPUC generation. Moreover, the quan-um noise generation needs high intense fundamental la-er pulses up to a certain energy threshold, and theumping energy lies on its frequency components. In ourxperiment, the fundamental laser frequency componentsre much lower than its second harmonics, therefore thePUC generation needs a higher fundamental laserower than the SPDC generation.To explore the phase matching conditions of SPUC and

PDC, the intensity dependences of SPUC and SPDC onhe angle �� between the incident polarized orientationnd the principal section are measured and shown in Fig.(c). When the BBO crystal is rotated to maximize SHG,he SPDC will approach the maximum, and contrarily thePUC will reduce to the minimum. The angle �� of the

ncident polarized orientation and the principal sectionnd the angle ���� of the incident beam and the opticalxis are calculated and shown in Fig. 4(c); determines

60 90 120 150 180 2100

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60

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CEpulseenergy(arb.unit)

Pump beam pulse width (fs)

0 4 8 12 160

20

40

60

80SPDCSPUC

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0 45 90 135 180 225 270 315 3600

20

40

60

80

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ig. 4. Dependences of the SPUC and the SPDC intensity onhe fundamental (a) pulse-width and (b) intensity, and the rota-ion angle of the �-BBO crystal around the z axis. Here, �� (deg.)orresponds to the angle between the incident ray and the opticalxis, and (deg.) gives the angle between the pulse polarized ori-ntation and the principal section.

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552 J. Opt. Soc. Am. B/Vol. 26, No. 3 /March 2009 Sun et al.

hat the incident ray is an ordinary or an extraordinaryight. When the phase matching condition of ��=29° and=90° is satisfied, the second harmonics of the fundamen-

al laser beam get the maximum and SPDC will generate.n contrast, when the phase matching condition of ��20° and =0° is satisfied, the second harmonics will note generated, and the SPUC will be given birth to. Ac-ordingly, it is clearly suggested that the phase matchingngle of SPDC is ��=29° and =90° and that of SPUC is�=20° and =0°.

. CONCLUSIONn summary, spontaneous parametric upconversionSPUC) and spontaneous parametric downconversionSPDC) have been successfully observed in the �-bariumorate (BBO) crystal. The central wavelength of SPUCrom 530 to 600 nm and that of SPDC from80 to 520 nm are generated in turn by rotating the BBOrystal around the Z axis. The tunable range of SPUC isuch wider than SPDC, and the conical angle of SPUC isuch smaller than SPDC. It is demonstrated that the

hase matching condition of SPUC is about ��=20° and=0° (type II, e+o→e) and that of SPDC is about ��29° and =90° (type I, e→o+o�. No matter, SPUC orPDC can be supported as a novel technique for ultra-roadband parametric amplification to generate the in-ense tunable ultrashort pulses.

CKNOWLEDGMENTShis research was supported by National Natural Scienceoundation of China (NNSFC) (10574046), Ministry ofcience and Technology of China (2006CB806006 and006CB921105), Ministry of Education of China (PCSIRT,CET-04-0420, and 30800), and Shanghai Science andechnology Committee (07dz22025 and 06QH14003).

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