First measurements of second-order frequency conversion phase-matching conditions in the new CTAS crystal

. We report that Ca 3 TaAl 3 Si 2 O 14 is a positive uniaxial crystal and provides second-order frequency conversion. Indeed, we performed direct measurements of phase-matching conditions for second-harmonic generation and sum-frequency generation up to 3.5 µm. The simultaneous fitting of recorded data provided the Sellmeier equations of the two principal refractive indices and the magnitude of the nonlinear coefficient


CTAS: a crystal from Langasite family
A few years ago, we reported that two bulk nonlinear crystals from the Langasite family, LGT and LGN, well known for their good piezoelectric properties, were also able to generate an optical parametric coherent light especially in the 3-5 µm transmission range of the atmosphere [1,2].In the present work, Ca3TaAl3Si2O14 (CTAS) from the same family has been investigated.It was grown using the Czochralski method and its congruence provided several inches bulk crystals with a very good optical quality (see Fig. 1(a)) [3].From the 32 trigonal point group, it also belongs the uniaxial optical class and exhibits in the dielectric frame (x, y, z) two principal refractive indices, no and ne, where o and e stand for "ordinary" and "extraordinary" respectively.Furthermore, it has a second-order electric susceptibility tensor d (2) with four non-zero coefficients linked by dxxx = -dxyy = -dyxy = -dyyx under Kleinmann assumption.It is d11 using the contracted notation.

Transmission spectra and optical sign
The transmission spectra were recorded between 0.175 µm and 3 µm by combining two commercial spectrometers: a Perkin-Elmer Lambda 900 and a Bruker FT-IR.We used the 0.53 mm thick slab shaped with two parallel faces polished to optical quality, not coated and oriented perpendicular to the y-axis.it is shown in the inset of Fig 2 .The transmission was recorded as a function of wavelength.It was ordinary with the linear polarization parallel to the x-axis, extraordinary with the polarization parallel to the z-axis.The spectra depicted in Fig. 2 without Fresnel corrections, show that CTAS is transparent between 0.25 µm and 6 µm.The magnitude of the two principal refractive indices no and ne of CTAS were determined at  = 0.6328 µm by using a prism shaped with 5 mm x 5 mm entrance and exit faces polished to optical quality but not coated.They were oriented to access the dielectric xy-plane and the angle  = 46°27′ as shown in Fig. 1(b).The prism was centered on a commercial rotating plate graduated over 360° with an angular accuracy of 1′.With the linear polarization of the incoming HeNe beam parallel to the zaxis, the excited refractive index is ne, with the linear polarization perpendicular to the z-axis, it is no.They were determined at the minimum deflection angle of the outcoming beams tracked with a CCD camera.We found  != 1.7100 ± 0.0006 and  " = 1.6690 ± 0.0006 so that the optical sign of CTAS is positive ( " <  ! ).

Birefringence phase-matching angles
With the sphere method, we measured the birefringence phase-matching (BPM) angles of CTAS [1,2].A crystal sphere was shaped with a diameter D = 8.45 mm and an acylindricity Δ  ⁄ of about 1%.It was polished to optical quality and stuck oriented on the goniometric head shown in Fig. 1(c).When mounted at the center of an automatic Kappa circle, all directions of the dielectric yzplane were accessible by rotating the sphere.In the yz-plane, Type I SFG (1/  # !+ 1/  $ != 1/ % " ) with  # ≥  $ >  % and Type I SHG ) are associated to a non-zero effective coefficient.For SFG, one of the two beams was emitted by a 10 ns pulsewidth (FWHM) and 10 Hz repetition rate Continuum OPO tunable between 0.4 and 2.2 µm, the second beam being was part of the pump at 1.064 µm.For SHG, a 15 ps pulsewidth (FWHM) and 10 Hz repetition rate Light Conversion OPA, tunable between 0.4 and 12 µm, provided the incoming beam.By using a proper focusing scheme, normal incidence and a parallel propagation were ensured along any direction of the rotating sphere.Wavelengths, polarization and energies were controlled with great accuracies.Phasematching angles, corresponding to optima of energy conversion efficiencies, were read in spherical coordinates 0°≤  ≤ 90° ( = 90°) on the graduated horizontal rotation stage of the Kappa circle.The accuracy was ± 0.5°.As an example, Fig. 3 shows the type I SHG BPM curve recorded in the yz-plane of CTAS.We will report the first dispersion equations of CTAS from the simultaneous fit of all our recorded data by a Levenberg-Marquardt algorithm, combined with the magnitude of  " and  !given in section 2.

The nonlinear optical coefficient
The magnitude of the nonlinear coefficient  ## of CTAS, was determined using  $' ()* ( $& = 0.66 µ) = 2.37 ± 0.17 / of KTP as a reference.The KTP slab was cut for in the xz-plane at  *+ ()* = 58,5° for type II BPM SHG [4].Then CTAS slab was cut at  *+ ,)-.= 38.5° in the yzplane for Type I BPM SHG at a very close fundamental wavelength  & .Both slabs were polished to optical quality and uncoated.Their same thickness, L=0.5 mm provided a negligible attenuation due to spatial walk-off.
The fundamental wavelength  & was emitted by the tunable OPO beam described in section 3. The same focusing configuration and beam waist radius were used in each slab.It corresponded to a Rayleigh length much larger than L to ensure a parallel beam propagation inside slabs.BPM SHG condition was confirmed in each slab from recording the ratio of the generated energy over the fundamental energy as a function of  & .It is depicted, normalized to its maximal value, in Fig. 4 for CTAS.

Conclusion
We reported for the first time the linear and nonlinear optical properties of the new CTAS crystal.BPM conditions were directly measured for SHG and SFG over its extended transparency range.The analysis of all data led to the wavelength dispersion equations of the two principal refractive indices and the magnitude of the nonlinear coefficient of CTAS that can be used for calculating any OPO configurations.

Fig. 2 .
Fig. 2. Transmission spectra recorded in polarized light through a 0.53-mm-thick y-cut CTAS uncoated slab that is shown in the inset.

Fig. 3 .
Fig. 3. Type I SHG tuning curve in the yz-plane of CTAS.

Fig. 4 .
Fig. 4. Measured and calculated normalized ratio   as a function of fundamental wavelength, in the yz-plane of CTAS for Type I SHG.