Polarization-dependent nonlinear refractive index of BiB3O6

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Optical Materials 30 (2008) 1469–1472 www.elsevier.com/locate/optmat

Polarization-dependent nonlinear refractive index of BiB3O6 S. Miller a, F. Rotermund b, G. Xu c, F. Noack a, V. Panyutin a, V. Petrov a,* a

Max-Born-Institute for Nonlinear Optics and Ultrafast Spectroscopy, 2A Max-Born-Strasse 12489 Berlin, Germany b Division of Energy Systems Research, Ajou University, 443-749 Suwon, Republic of Korea c Department of Electrical and Computer Engineering, Lehigh University, Bethlehem, PA 18015, USA Received 18 October 2007; received in revised form 16 November 2007; accepted 16 November 2007 Available online 31 December 2007

Abstract The nonlinear refractive index of the monoclinic biaxial nonlinear crystal BiB3O6 (BIBO) was measured at 1064 nm for light polarization along the three principal optical axes using the single-beam z-scan technique. Strong anisotropy was observed with n2 values about two-times larger for polarization parallel to the Z-axis in comparison to the X-axis. BIBO exhibits lower nonlinear refractive index than KTP although its effective nonlinearity is larger. Ó 2007 Elsevier B.V. All rights reserved. PACS: 42.65.An; 42.70.Mp

1. Introduction Bismuth triborate (BiB3O6 or shortly BIBO) is a relatively new nonlinear optical crystal belonging to the borate family which is suitable for frequency conversion from the UV to the near-IR. BIBO is nonhygroscopic and possesses relatively high damage threshold but its unique features originate mainly from the exceptionally high, having in mind the band-gap, second-order nonlinear susceptibility [1] which is associated with the contribution of the BiO4 anionic group [2]. Thus, being transparent down to 270 nm (cut-off wavelength) [3,4], BIBO exhibits effective nonlinearity which can be larger (e.g. for frequency doubling of 1064 nm radiation) than that of KTiOPO4 (KTP) at almost equal band-gap (4.6 eV). High effective nonlinearity relaxes the requirements to the crystal length and the light intensity, i.e. allows one to operate far below the damage threshold and makes this material interesting for high power (high intensity) applications. Numerous frequency conversion schemes including up- and down-conversion have already been demonstrated with BIBO, a *

Corresponding author. E-mail address: [email protected] (V. Petrov).

0925-3467/$ - see front matter Ó 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.optmat.2007.11.015

full list of these achievements can be found in the recent review [5]. The nonlinear index of refraction, or the third-order susceptibility, is an important parameter in the applications of any nonlinear optical crystal at high powers, especially when short (ns to fs) pulses are employed, because it can lead to favourable but also to unwanted effects related to the modification of the spatial (e.g. self-focusing) or temporal (e.g. self-phase modulation) phase profile. In the present work, we investigated the third-order nonlinear properties of BIBO using samples cut along the three principal optical axes of this monoclinic biaxial crystal, employing the zscan technique at a wavelength of 1064 nm (the pump wavelength mostly used in the applications demonstrated so far with BIBO [3,4,6–12]). The analysis of closed-aperture (CA), i.e. aperture transmission <1, z-scan signals yielded information on the anisotropy of the nonlinear refractive index of BIBO. 2. Experimental The z-scan technique, introduced by Sheik-Bahae et al. [13], was used to determine the nonlinear refractive index (n2) of BIBO in dependence on the polarization of the

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propagating light. This method is based on self-focusing or self-defocusing of the laser beam in a thin medium and allows the simultaneous measurement of the nonlinear refraction and absorption. However, for the chosen wavelength of 1064 nm which is far from the band-gap, nonlinear losses due to two-photon absorption can be neglected in BIBO. The nonlinear refraction was measured by detecting the intensity-dependent transmission changes through a small aperture when translating the sample along the beam using the set-up shown schematically in Fig. 1. An aperture having a transmittance of 10% (S = 0.1) was used. A 10-Hz mode-locked Nd:YAG laser (B.M. Industries) delivering 56-ps long (FWHM assuming Gaussian shape from autocorrelation measurements) pulses at 1064 nm was used in the present z-scan set-up. The output was divided into two beams by using a 1:5 beam splitter. The beam with higher energy was focused on the sample using a convex lens with a focal length of 20 cm and the other beam served as the reference. The sample was then translated near the focal point. The incident pulse energy in the different measurements varied between 21 and 31 lJ but this had no effect on the results obtained because thermal contributions are negligible at such low repetition rates. The above values correspond to peak on-axis intensity from 33 to 48 GW/cm2, incident on the uncoated crystals in the focal region. These values were calculated for a beam waist of w0 = 27.0 lm which was measured by using a beam analyzer system (DataRay Inc., WinCamD TM Series), in close agreement (deviation < 2%) with the value derived from the CA z-scan measurements themselves. The pulse energy transmitted through the CA was detected by using an energy meter D1. Subsequently, the signal was corrected with the reference signal measured by D2. The window in the incident energy used in each measurement was ±10%, shots deviating from this level were discarded. BIBO belongs to the monoclinic symmetry class 2 with the crystallographic axis b coinciding with the principal optical axis X (defined by the relation nX < nY < nZ for the three linear refractive indices). The frame of the optical indicatrix rotates with wavelength and temperature around the twofold symmetry axis b  X but the effect is rather weak near 1064 nm and can be ignored [14]. Thus, having in mind the monoclinic angle of b = 105.62° between the a and c crystallographic axes, the principal optical axis Z is rotated near 1 lm at 31.5° counterclockwise from the crystallographic a-axis when the b-axis shows towards the observer [14]. The orthogonal frame of the optical indicatrix is the simplest choice for reporting the nonlinear optical properties of BIBO [15,16] and we selected it also for

measurement of the nonlinear refractive index. Thus the three samples of BIBO (CRYSTECH Inc.) with an aperture of 5  6 mm2 were cut along the three principal optical axes X, Y and Z with their edges parallel to the other two axes. All of them were 3.45-mm-thick. Our aim was to estimate the three diagonal elements of the third-order susceptibility tensor using light linearly polarized along one of the principal optical axes. 3. Results and conclusions First, the reliability of the z-scan set-up was tested by performing measurement of a 4-mm-thick fused silica plate. Defining the nonlinear refractive index n2 (cm2/W) from n = n0+n2I, where n0 is the linear part of the refractive index n and I is the light intensity we obtained n2(SiO2) = 2.14  1016 cm2/W, which agrees very well with the value of 2.1  1016 cm2/W (±20%) previously reported [17]. To determine the nonlinear refractive index, the measured zscan traces were fitted with equations described elsewhere [13]. For CA z-scan, the normalized transmittance T is given by T ðx; hDu0 iÞ ¼ 1 

½ðx2

4xhDu0 i þ 9Þðx2 þ 1Þ

ð1Þ

where hDu0i is the time averaged phase change and x = z/ z0 with z0 ¼ kw20 =2 is the translation coordinate normalized by the diffraction length of the beam. Both hDu0i and w0 can be determined from the fit using Eq. (1), which can be used to confirm independently the beam waist in the focus. In practice, we calculated directly hDu0i using the simDT vp ple relation hDu0 i ¼ 0:406ð1SÞ 0:25 valid for |Du0| 6 p where DTv–p is the difference between the valley and peak energy transmittance in the trace as determined from the fit. The average phase shift for pGaussian temporal shape is given ffiffiffi simply by hDu0 i ¼ Du0 2, where Du0 is the peak on-axis phase shift. Thus, the nonlinear refractive index n2 can be calculated for Gaussian pulses from n2 ffi

0:38kw20 sp hDu0 i Leff Ei

ð2Þ

where sp is the laser pulse FWHM and Ei is the pulse energy corrected by the Fresnel reflection at the entrance face. The effective sample length Leff is defined by Leff = (1  exp(aL))/a, where a is the linear absorption coefficient and L is the sample thickness; in our case Leff  L. For all the three samples the CA z-scan signals measured showed self-focusing indicating positive nonlinear refraction. The results are summarized in Figs. 2–4 and BIBO

ps mode -locked Nd:YAG 1064nm , 56ps @ 10Hz

D1 BS

translation

D2 Fig. 1. Schematic diagram of the z-scan measurement set-up: D1 and D2, energy meters, BS, beam splitter.

S. Miller et al. / Optical Materials 30 (2008) 1469–1472

a

a

1.20 1.15

X-cut BIBO E // Z-axis

Normalized transmittance

Normalized transmittance

1.05 1.00 0.95 0.90

Y-cut BIBO E // X-axis

1.10 1.05 1.00 0.95 0.90 0.85

0.85 0.80 -20

1.20 1.15

1.10

1471

-15

-10

-5

0

5

10

15

0.80 -20

20

-15

-10

-5

z [mm]

1.15

Normalized transmittance

b

1.20 Y-cut BIBO E // Z-axis

1.10 1.05 1.00 0.95 0.90

10

15

20

5

10

15

20

Z-cut BIBO E // X-axis

1.10 1.05 1.00 0.95 0.90 0.85

0.85 0.80 -20

5

1.20 1.15

Normalized transmittance

b

0

z [mm]

-15

-10

-5

0

5

10

15

0.80 -20

20

-15

-10

-5

z [mm]

z [mm]

Table 1. The n2 values were independent of the propagation direction for the same polarization and the deviations in this case are indicative of the accuracy. For polarization parallel to the Y-axis, however, only one measurement was performed at normal incidence since strong second harmonic generation was observed in the Z-cut BIBO (obviously related to type ee–o interaction in the Y–Z plane and outside it [14]). A substantially larger value of n2 was obtained for polarization parallel to the Z-axis, roughly two-times the result for polarization parallel to the X-axis. The three principal values of the nonlinear refractive index obtained are in the same relation as the linear parts of the refractive index [14]. Although no information is available on the polarization dependence of the band-gap, since no index crossing trends were observed in [14] down to 360 nm, it can be expected that the differences in the obtained nonlinear refractive values correspond to different band-gaps, the smallest band-gap being associated with EkZ.

Fig. 3. Closed-aperture z-scan traces, obtained in (a) Y- and (b) Z-cut BIBO crystals for beam polarization parallel to the X-axis.

1.20 1.15

Normalized transmittance

Fig. 2. Closed-aperture z-scan traces, obtained in (a) X- and (b) Y-cut BIBO crystals for beam polarization parallel to the Z-axis.

0

X-cut BIBO E // Y-axis

1.10 1.05 1.00 0.95 0.90 0.85 0.80 -20

-15

-10

-5

0

5

10

15

20

z [mm] Fig. 4. Closed-aperture z-scan trace, obtained in X-cut BIBO for beam polarization parallel to the Y-axis.

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Table 1 Principal values of the nonlinear index of refraction of BIBO obtained at 1064 nm Polarization

Propagation

n2 (1016 cm2/W)

EkX

kY kZ kX kX kY

8.00 7.39 9.21 15.2 16.5

EkY EkZ

The obtained results can be compared with the nonlinear refractive index values determined previously for crystals having similar band-gap. Other borates have larger band-gaps and exhibit smaller n2 as can be expected. The band-gap of BIBO is actually very close to those of two other, widely spread nonlinear optical crystals, KTP and LiNbO3. The value of the n2 of BIBO is higher than that of LiNbO3 but smaller than that of KTP at 1064 nm [17]. This could be an advantage over KTP (in addition to the higher effective nonlinearity and the type-I interaction) for intracavity frequency doubled lasers operating in the green. Moreover, our measurements have shown that n2 of BIBO is strongly anisotropic; unfortunately the values reported in the literature for other nonlinear crystals are normally for unspecified orientation. Acknowledgements F.R. was supported by the Korea Science and Engineering Foundation grant funded by the Korea government (No. R0A-2007-000-20113-0).

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