Linear and nonlinear optical properties of the ... - OSA Publishing

Segonds et al.

Vol. 21, No. 4 / April 2004 / J. Opt. Soc. Am. B

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Linear and nonlinear optical properties of the monoclinic Ca4 YO(BO3 ) 3 crystal Patricia Segonds and Benoıˆt Boulanger Laboratoire de Spectrome´trie Physique, 140 avenue de la Physique BP 87, 38402 St. Martin d’He`res Cedex, France

Jean-Philippe Fe`ve JDS Uniphase Commercial Lasers, 31 Chemin du Vieux Cheˆne, Zone pour I’Innovation et les Reálisations Scientifiques et Techniques 4101, 38941 Meylan, France

Bertrand Meńaert and Julien Zaccaro Laboratoire de Cristallographie, 25 Avenue des Martyrs BP 166, 38042 Grenoble Cedex 09, France

Ge´rard Aka Chimie Appliqueé de l’Etat Solide, 11 rue Pierre et Marie Curie, 75231 Paris Cedex 05, France

Denis Pelenc LETI-CEA Technologies Avanceés DOPT/SCMDO CENG, 17 avenue des Martyrs, 38054 Grenoble Cedex, France Received September 12, 2003; accepted October 23, 2003 We report that the optical frame orientation is wavelength independent over the entire transmission range of the nonlinear monoclinic crystal Ca4 YO(BO3 ) 3 (YCOB). We used a new method based on internal conical refraction associated with x-ray diffraction on a single crystal cut as a sphere. Direct phase-matching-angle measurements of second-harmonic generation were performed in the principal planes of the spherical crystal for fundamental wavelengths up to 3.5 ␮m, and three absorption peaks were measured above 2.4 ␮m. By fitting all data simultaneously, we found new dispersion equations of the refractive indices of YCOB. © 2004 Optical Society of America OCIS codes: 190.4400, 190.2620.

1. INTRODUCTION In the past few years, the literature has widely reported a new biaxial crystal belonging to the calcium-rare-earth oxoborate family, Ca4 YO(BO3 ) 3 (YCOB), which is characterized by good nonlinear coefficients, a high damage threshold, and the possibility to be doped with Nd3⫹. Large and good optical-quality crystals have been grown from a melt by use of the Czochralski pulling method.1 YCOB crystallizes in the monoclinic biaxial crystal system and belongs to the Cm space group. The unit cell contains a mirror that is perpendicular to the b axis; the angles between the unit-cell axes are1 ab d ⫽ 90°, bc d ⫽ 90°, and ac d ⫽ 120.26°. The optical frame (x, y, and z) does not correspond to the main axes of the crystallographic coordinate system (a, b, and c). For the crystal class m, the y axis is considered parallel to the b axis, and the x – z axes are tilted around b (or y) from the a – c ones. Their relative orientation had been measured for YCOB by use of the x-ray Laue technique associated with the conoscopic method under white light,1 leading to az d ⫽ 24.7° and cx d ⫽ 13.5°. The three principal refractive indices n i , the index i standing for the axes of the optical 0740-3224/2004/040765-05$15.00

frame x, y, and z, had been measured on a prism in the visible and the near infrared, to as much as 1.1 ␮m, by use of the minimum-deviation technique. They had been fitted with a single-pole Sellmeier equation of the form n i 2 ⫽ A i ⫹ B i (␭ 2 ⫺ C i ) ⫺1 ⫺ D i ␭ 2 , where ␭ is in micrometers. The values of the parameters A i , B i , C i , and D i are different according to the index i, which stands for x, y, or z: A x ⫽ 2.7663, B x ⫽ 0.02076, C x ⫽ 0.01757, D x ⫽ 0.00553; A y ⫽ 2.8724, B y ⫽ 0.02281, C y ⫽ 0.01634, D y ⫽ 0.00906; and A z ⫽ 2.9122, B z ⫽ 0.02222, C z ⫽ 0.01930, D z ⫽ 0.01355.1 Type I phasematching angles had been measured on slabs cut in the principal planes x – z, y – z, and x – y for second-harmonic generation (SHG) with the fundamental wavelength ranging between 0.75 and 1.5 ␮m.1 The agreement between experiment and calculation by use of the Sellmeier equations of Ref. 1 is reasonable in the visible and in the near-infrared ranges. The objectives of the present study were to propose a new method for the determination of the orientation of the optical frame of a monoclinic crystal as a function of the wavelength and to perform direct measurements of

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types I and II phase-matching SHG directions in order to determine reliable dispersion equations of the refractive indices in the whole transmission domain of YCOB.

2. OPTICAL FRAME ORIENTATION AS A FUNCTION OF WAVELENGTH Checking the possible wavelength dispersion of the az d and cx d angles of a monoclinic or a triclinic crystal is of prime importance for the characterization of its optical properties. For example, in the case of SHG or sum- and difference-frequency generations, the different interacting waves may have optical frames with different orientations. It would be then necessary to calculate the phase-matching directions in a fixed orthonormal frame that is not the optical frame and whose relative orientation with the crystallographical frame is defined arbitrarily. We propose a method for the study of the optical frame that is different from the one based on prisms with different orientations as described in Ref. 2. In a previous paper we had shown that it is possible to measure with accuracy the position of the optical axes of KTiOPO4 (KTP) by observation of the internal conical refraction at the exit of a crystal cut as a sphere.3 Because YCOB is also a biaxial crystal, we can use such an observation for the measurement of az d and cx d angles as a function of the wavelength. This is, to our knowledge, the first measurement of that kind. For that purpose, a YCOB sphere with a diameter of 5.54 mm was cut and polished and then stuck on a goniometric head. In the first step, the head was mounted on an x-ray automatic diffractometer. We performed a single wavelength measurement by coupling the diffractometer with a He–Ne laser beam at ␭ ⫽ 0.6328 ␮ m, which was focalized through the sphere by use of a lens. The sphere was oriented to propagate the He–Ne beam in any direction of the a – c plane. From the x-ray orientation, we marked out the goniometric positions of the a axis and c axis. Then, by rotating the sphere through 360° in that plane, we can observe the four hollow cones that correspond by pairs to the two optical axes of internal conical refraction as shown in Fig. 1. Because these two axes are symmetrical in comparison with the principal axes of the optical frame z and x, we are also able to mark out the corresponding goniometric positions of the z axis and x axis. The precision of the measurement is approximately ⫾0.1°. Then we get the angles az d ⫽ 24.7° and cx d ⫽ 13.4°, at ␭ ⫽ 0.6328 ␮ m. The three pictures of Fig. 1 show the typical patterns that are observed on a screen placed 10 cm behind the sphere when the incident laser beam propagates in three characteristic directions of the x – z plane of YCOB: The hollow cone, which has allowed us to perform the previous measurements, corresponds to an optical axis; the single spot is relative to an axis of the optical frame, for which the ordinary and extraordinary Poynting vectors are joint; and the two spots show the double-refraction effect that exists for a crystallographical axis, x or z, or for any other direction that is neither an optical axis nor an axis of the optical frame. In the second step, the YCOB sphere was placed at the center of an Euler circle and coupled to a tunable laser,

Fig. 1. Relative orientation between the crystallographical frame (a, b, and c) and the optical frame (x, y, and z). V z is the angle between the z axis and the optical axes denoted by OA. The three pictures correspond to the refracted beams observed on a screen placed behind the YCOB sphere when the wave vector of an incident He–Ne unpolarized beam is along an optical axis, an axis of the optical frame, and an axis of the crystallographical frame in the x – z plane.

Fig. 2. (a) Angle between the a axis and the z axis as a function of wavelength. (b) Angle between the optical axes and the z axis as a function of wavelength. The circles are relative to our experimental data. The dashed–dotted curve refers to the calculation from the Sellmeier equations of Ref. 1, and the solid curve is relative to the calculation performed in the present study.

emitting between 0.4 and 10 ␮m. We took the same goniometric head as the one mounted previously to keep the goniometric positions of the crystallographic axes a and c and of the principal axes z and x found with the diffractometer and the He–Ne laser. The incoming tunable laser beam was allowed to propagate in any direction of the x – z plane, since the sphere can be rotated around the y axis. First, a measurement was performed at ␭ ⫽ 0.6328 ␮ m to verify the conservation of the absolute angles between a and z and between c and x. Second, the position of the z axis was measured as a function of the wavelength up to 2.2 ␮m. We still used the observation of the four hollow cones. The observation was made directly on a screen in the visible and with a visual card in the infrared. The corresponding results for az d(␭) are reported in Fig. 2 with an accuracy that reaches ⫾0.5°.

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The error was mainly due to the quality of the observation in the infrared and to the asphericity of the sample, the relative variation of the diameter being around 1%. It clearly appears from Fig. 2(a) that the angle between the a axis and the z axis can be considered wavelength independent within the accuracy of our measurements and that az d ⫽ 24.7 ⫾ 0.5°. This nondispersion explains that our method and the conoscopic technique under white light lead to the same result. The previous set of experimental data also leads to the determination of the dispersion of the angle V z (␭) between the optical axes and the z axis. The measured angle V z (␭) is plotted in Fig. 2(b) and compared with the calculation V z (␭) ⫽ Arcsin兵关 n y ⫺2 (␭) ⫺ n x ⫺2 (␭) 兴 1/2 ⫺2 ⫺2 ⫻ 关 n z (␭) ⫺ n x (␭) 兴 ⫺1/2其 , where n x , n y , and n z are the three principal refractive indices at ␭. There is a strong disagreement between the experiment and the calculation that uses the Sellmeier equations of Ref. 1, especially above 1.1 ␮m where the refractive indices were only extrapolated.

3. PHASE-MATCHING PROPERTIES AND DISPERSION EQUATIONS OF THE PRINCIPAL REFRACTIVE INDICES Because the optical frame is completely characterized, the second part of the present study was devoted to the establishment of dispersion equations of the refractive indices of YCOB, reliable over the entire transmission range, on the basis of the optical axis data given above and of SHG phase-matching angles also measured on the sphere as described below. This study is necessary because the equations previously determined in Ref. 1 are satisfactory only over a limited wavelength range, as shown in Fig. 2(b), which corresponds typically to the range for which the refractive indices had been measured on a prism, i.e., in the visible and near-infrared domains. In the first step, unpolarized optical transmission spectra have been recorded between 0.32 and 3.3 ␮m. As an example, the y-axis spectrum of a 5-mm-long YCOB slab is given in Fig. 3(a): It shows a transmission reaching 80% from 0.3 to 2.4 ␮m, followed by three large infrared absorption peaks observed at 2.7, 2.9, and 3.2 ␮m, referred to as P1 , P2 , and P3 , respectively. The corresponding transmission coefficients are equal to approximately 40% for P1 , 10% for P2 , and 25% for P3 . In the second step, we performed direct and accurate measurements of phase-matching angles by using the same sphere and tunable source as for the optical frame study. We already used such a technique with success on arsenate isomorphous4 KTiOAsO4 , RbTiOAsO4 , and CsTiOAsO4 . The quality of the results relies on the implication of the three principal refractive indices over a wavelength range as large as possible. It was sufficient to perform only SHG phase-matching measurements, since we used a tunable source as the fundamental beam, which allowed us to reach the infrared cutoff. It was also enough to consider the three principal planes of YCOB. The corresponding SHG phase-matching relations with nonzero effective coefficients are established by following Ref. 5 and are given in Table 1. The sphere was rotated around the x, y, and z axes successively to scan the prin-

Fig. 3. (a) Y-axis unpolarized transmission spectrum of a 5-mmlong YCOB slab as a function of the wavelength. P1 , P2 , and P3 are the three infrared absorption peaks. (b) Type I SHG phasematching angles of YCOB in the x – z plane. The symbols are relative to our experimental data. The dashed–dotted curve refers to the calculation from the Sellmeier equations of Ref. 1, and the solid curve is relative to the calculation performed in this study.

cipal planes y – z, x – z, and x – y: Measurements performed out of the principal planes would bring no more information. The experimental curves are given in Figs. 3(b), 4, and 5; the accuracy of the measurements are approximately ⫾0.3°. The phase-matching curve of type II SHG in the x – z plane was not measured because the associated effective coefficient is nil. The measurements were performed with fundamental wavelengths up to 3.5 ␮m, and we notice that the curves’ behavior is never affected by the three absorption peaks despite their strong magnitude. Figures 3(b), 4, and 5 also give theoretical curves that are calculated by use of the Sellmeier equations of Ref. 1 and phase-matching relations of Table 1. The calculations were performed in the optical frame, since it is not wavelength dependent, as demonstrated above. There is often a disagreement between these calculated curves and our experimental data. The discrepancy appears essentially above 1.5 ␮m: It is small for types I and II SHG in the x – y plane; it is more significant in the x – z plane for type I SHG; and the disagreement is strong for types I and II SHG in the y – z plane. This comparison between calculation and experiment shows that it could be risky to test the validity of dispersion equations with a small number of interactions. As is shown in Table 1, it is due to the different levels of implication of the three principal refractive indices according to the different phase-matching types, even if the wavelength ranges are close. In the third step, we determined new dispersion equations of the refractive indices: We considered not only the phase-matching angles’ data but also the optical axes’ angle measurements as a function of the wavelength, given in Fig. 2(b). Furthermore, to have the absolute

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Table 1. SHG Phase-Matching Relations Associated with a Nonzero Effective Coefficient in the Principal Planes x – y, y – z, and x – z a Principal Planes

Types

xy

Phase-Matching Relations

␸ ⫽ arcsin

I

冋

II

yz

2 cos2共␸兲 ny2共␭/2兲

⫹

sin2共␸兲 nx2共␭/2兲

册

1/2

⫺ n z共 ␭ 兲 ⫺

nz⫺2共␭兲 ⫺ ny⫺2共␭/2兲 n x ⫺2 共 ␭/2兲 ⫺ n y ⫺2 共 ␭/2兲

冋

1 cos2共 ␸兲

␪ ⫽ arcsin

I

␪ ⫽ arcsin

II

xz: 0 ⬍ ␪ ⬍ Vz

再冋

冠再

再冋

⫹

n i2 ⫽ A i ⫹

Bi

⫹

Ci

⫺ D i␭ 2 ⫺ E i␭ 4,

册

ny⫺2共␭兲 ⫺ nx⫺2共␭/2兲 n y ⫺2 共 ␭ 兲 ⫺ n z ⫺2 共 ␭ 兲

n y ⫺2 共 ␭ 兲 ⫺ n z ⫺2 共 ␭ 兲

再冋

ny⫺2共␭兲 ⫺ nx⫺2共␭/2兲 n z ⫺2 共 ␭/2兲 ⫺ n x ⫺2 共 ␭/2兲

a The principal refractive indices n x , n y , and n z are at the fundamental and second-harmonic wavelengths, ␭ and ␭/2, respectively. corresponding phase-matching angles. The analytical solution of the type II SHG phase-matching relation in the x – y plane does not exist. between the optical axes and the z axis.

magnitude of the refractive indices, it is necessary to add the value of one refractive index at a given wavelength to the previous angular data set: We took the value of n z measured by the prism technique1 at 1.064 ␮m, i.e., n z ⫽ 1.708. All the data were simultaneously fitted by use of a gradient algorithm. We tried different forms of the dispersion equation, but no combination of ultraviolet and infrared oscillators was able to give satsfactory fitting of all our data. This may be due to the absorption peaks, especially in the infrared. We have been able to fit the data only with a five-parameter polynomial development of the form

nx2共␭兲

1/2

n y ⫺2 共 ␭ 兲 ⫺ 关 2n x 共 ␭/2兲 ⫺ n x 共 ␭ 兲兴 ⫺2

␪ ⫽ arcsin

I

ny2共␭兲

sin2共 ␸兲

册冎 1/2

⫽0

册冎冎冡册冎 1/2

1/2

1/2

␪ or ␾ are the V z is the angle

where i stands for x, y, or z and ␭ is in micrometers. We get from the fitting the set of the five parameters, A i , B i , C i , D i , and E i , which are listed in Table 2. The mean accuracy is of the order of 0.1%. The corresponding calculated phase-matching curves are shown in Figs. 3(b), 4, and 5, where we can see the very good agreement with experiments at any wavelength. The fitting is also very satisfactory in the case of the dispersion curves of the optical axes, as is shown in Fig. 2(b), despite the very narrow angle range.

4. CONCLUSION (1)

We have shown in this paper that it is possible to study the wavelength dispersion of the optical frame of a mono-

Fig. 4. Types (a) I and (b) II SHG phase-matching angles of YCOB in the x – y plane. The symbols are relative to our experimental data. Dashed–dotted curves refer to the calculation from the Sellmeier equations of Ref. 1, and solid curves are relative to the calculation performed in the present study.

Fig. 5. Types (a) I and (b) II SHG phase-matching angles of YCOB in the y – z plane. The symbols are relative to our experimental data. Dashed–dotted curves refer to the calculation from the Sellmeier equations of Ref. 1, and solid curves are relative to calculations performed in this study.

␭2

␭4

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Table 2. Fitting Parameters of the Dispersion Equations of the Principal Refractive Indices n x , n y , and n z of YCOB at Room Temperature Parameters

i⫽x

i⫽y

i⫽z

Ai Bi Ci Di Ei

2.6629 0.034508 0.0009115 0.010944 0.000016415

2.846 0.038086 0.00098163 0.020364 0.00010088

2.9027 0.0423 0.00068559 0.020262 0.00029925

B. Boulanger, the corresponding author, can be reached by e-mail at [email protected].

REFERENCES 1.

2.

3.

clinic crystal with a single sample cut as a sphere. Using the same sphere, we have also performed phase-matching measurements. This powerful method applied to YCOB has allowed us to determine new dispersion equations of the refractive indices that are reliable over the entire transmission range. By combining our results with the knowledge of the second-order electric susceptibility tensor ␹ ( 2 ) , 6,7 we have the basis for a complete description of the three-wave parametric properties of YCOB.

4.

5.

6.

7.

ACKNOWLEDGMENT We thank Mission Ressources et Compe´tences Technologiques (MRCT) for financial support.

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