## Abstract

We directly measured the phase-matching angles of second-harmonic generation and difference-frequency generation up to 6.5 *µ*m in the Langanate crystal La_{3}Ga_{5.5}Nb_{0.5}O_{14} (LGN). We also determined the nonlinear coefficient and damage threshold. We refined the Sellmeier equations of the ordinary and extraordinary principal refractive indices, and calculated the conditions of supercontinuum generation.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

## 1. Introduction

We identified the Langatate La_{3}Ga_{5.5}Ta_{0.5}O_{14} (LGT) as a serious candidate for the parametric generation between 3 and 6.5 µm [1]. We then focused on a new compound of the same family, *i.e.* the Langanate La_{3}Ga_{5.5}Nb_{0.5}O_{14} (LGN). We reported in a previous paper that when the transmittance is half its maximal value, the ultraviolet cut-off is down to 0.35 *µ*m and the infrared cut-off is up to 6.5 *µ*m, in very high quality and large-size crystals grown with the Czochralski method [2]. Since LGN crystallizes in the *32* trigonal point group, there is only one nonzero element of its second-order electric susceptibility tensor under Kleinman symmetry, *i.e. d _{xxx} = - d_{xyy} = - d_{yxy} = - d_{yyx}* (

*= d*) where

_{11}*d*stands for the contracted notation. We found that the absolute magnitude of

_{11}*d*is equal to 3.0 ± 0.1 pm/V at 0.532

_{11}*µ*m using the Maker fringes method [2]. We also reported a damage threshold of 1.41 GW/cm

^{2}at 1.064 µm in the nanosecond regime [2]. LGN is a positive uniaxial crystal, so that the ordinary principal refractive index (

*n*) is smaller than the extraordinary one (

_{o}*n*). Both indices were previously measured as a function of the wavelength using an oriented prism, which enabled to determine Sellmeier equations valid between 0.36 and 2.32

_{e}*µ*m [3]. Using the same method, we proposed an alternative set of equations valid between 0.43 and 2.3

*µ*m [2].

Using sets of equations from [2] and [3], we did not find the same calculated phase-matching tuning curves in the principal dielectric planes of LGN for all the possible quadratic processes associated with a non-zero conversion efficiency [2]. Then we decided to directly record these curves, which is described in the present paper. We report for the first time to the best of our knowledge the direct measurement in LGN of the phase-matching tuning curves of second harmonic generation (SHG) and difference frequency generation (DFG). A simultaneous fit of all our data allowed us to refine the Sellmeier equations of the two principal refractive indices of LGN. We also determined the nonlinear coefficient *d _{11}* at another wavelength from [2] and the damage threshold. We could then calculate the conditions of supercontinuum generation.

## 2. Phase-matching angles and Sellmeier equations

The LGN crystal was cut and polished as a sphere with a diameter of 10.8 mm and asphericity below 1%. It was stuck on a goniometric head as shown in Fig. 1(a). It was successively oriented along the *x*- and *y*- dielectric axes with an accuracy better than 0.5°, using the X-ray backscattered Laue method. Then the LGN sphere was placed at the center of an Euler circle to be rotated in any direction. Thus any directions of the two (*y, z*) and (*x, z*) principal dielectric planes can be addressed successively in the same sample.

Only one incoming beam tunable between 0.4 and 11 µm is used for studying SHG. It was emitted by a Light Conversion optical parametric generator (OPG) with 15-ps FWHM and 10-Hz repetition rate. The OPG is pumped by the third-harmonic of a beam at 1.064 *µ*m emitted by a Excel Technology Nd:YAG laser. Thus for the study of DFG, we can combine the OPG beam with part of the 1.064 *µ*m beam directly in the sphere as shown in Fig. 1(b).

A 100-mm-focusing lens (f) placed at the entrance side of the sphere ensured normal incidence and quasi-parallel propagation of all the input beams along any diameter of the sphere. The polarization was adjusted by using achromatic half-wave-plates (HWP).

The energy of the incoming beams was measured with a J4-09 Molectron pyroelectric joulemeter placed behind a beam splitter (BS) and a lens with a focal length of 50 mm. The energy of the generated beam was measured simultaneously at the exit of the sphere by a J3-05 Molectron pyroelectric joulemeter associated with a PEM531 amplifier. A filter removed all input beams. The phase-matching wavelengths were controlled by monitoring the wavelengths of the input beams between 0.4 and 1.7 *µ*m with accuracy of ± 1 nm using HR 4000 and of ± 3 nm with NIRquest 512 Ocean Optics spectrometer. The phase-matching angles were read on the Euler circle with an accuracy of ± 0.5°. A phase-matching direction is detected when the conversion efficiency reaches a maximal value.

The recorded SHG and DFG phase-matching tuning curves are shown in Figs. 2 and 3, respectively. We studied type I SHG ($1/{\lambda}_{2\omega}^{o}=1\u2044{\lambda}_{\omega}^{e}+1\u2044{\lambda}_{\omega}^{e}$) and type II DFG $\left(1/{\lambda}_{i}^{e}=1/{\lambda}_{p}^{o}-1/{\lambda}_{s}^{e}\right)$ in the (*y, z)* plane, and type III DFG $\left(1/{\lambda}_{i}^{o}=1/{\lambda}_{p}^{o}-1/{\lambda}_{s}^{e}\right)$ in the (*x, z*) plane. Superscripts *o* and *e* stand for the ordinary and extraordinary waves, respectively. ${\lambda}_{\omega}$ and ${\lambda}_{2\omega}$ are the fundamental and second harmonic wavelengths. ${\lambda}_{p}$, ${\lambda}_{s}$ and ${\lambda}_{i}$ are respectively the pump, signal and idler wavelengths verifying ${\lambda}_{p}<{\lambda}_{s}\le {\lambda}_{i}$.

Figures 2 and 3 also show the calculated phase-matching curves using the Sellmeier equations from Refs [2]. and [3]. It highlights discrepancies between our experimental data and both sets of calculations, even if calculations using [3] are closer to our experimental data. It is true especially above 2.3 *µ*m that corresponds to the limit of the spectral range over which the ordinary and extraordinary principal refractive indices were determined in Refs [2]. and [3]. As shown in Fig. 4, by performing our measurements up to 6.5 µm, we widely extended the wavelength range where the two principal refractive indices of LGN are involved. Such a difference might explain the discrepancies shown in Fig. 2 and 3.

We refined the Sellmeier equations of LGN by the simultaneous fit of all our SHG and DFG experimental data shown in Fig. 2 and 3. We used the Levenberg-Marquardt algorithm encoded with Matlab. Among the several possible forms of Sellmeier equations to fit the ordinary and extraordinary refractive indices, the best one was that used in Refs [2, 3], *i.e*:

*λ*is in

*µ*m and

*j*stands for

*o*or

*e*. The precision of our angular measurements is ± 0.5°, leading to a relative accuracy $\Delta {n}_{j}/{n}_{j}$ better than 10

^{−4}. The numerical values of the best fit parameters

*A*,

_{j}*B*,

_{j}*C*and

_{j}*D*are summarized in Table 1. Our interpolated tuning curves using the Sellmeier equations of the present work correspond to the continuous red lines shown Figs. 2 and 3. They clearly show a much better agreement with our experimental data than using the calculations from Refs [2]. and [3].

_{j}## 3. Nonlinear coefficient and damage threshold

The absolute value of *d _{11}* of LGN can be determined from angle critical phase-matched type I SHG in the (

*y, z*) plane. The corresponding effective coefficient is expressed as:

We chose the nonlinear coefficient of KTP ${d}_{24}^{KTP}$(${\lambda}_{2{\omega}_{2}}$ *=* 0.66 *µ*m) = 2.37 ± 0.17 pm/V as a reference [4] for the determination of *d _{11}* of LGN. The coefficient ${d}_{24}^{KTP}$ governs type II SHG $(1/{\lambda}_{{\omega}_{2}}^{e}+1/{\lambda}_{{\omega}_{2}}^{o}=1/{\lambda}_{2{\omega}_{2}}^{o})$ in the (

*x, z*) plane of KTP, the corresponding effective coefficient being ${d}_{eff}^{KTP}={d}_{24}^{KTP}\left({\lambda}_{2{\omega}_{2}}\right)\mathrm{sin}\left[{\theta}_{P{M}_{2}}-{\rho}^{e}({\theta}_{P{M}_{2}},{\lambda}_{{\omega}_{2}})\right]$ with ${\theta}_{P{M}_{2}}=\text{}58.5\xb0$ and ${\rho}^{e}\left({\theta}_{P{M}_{2}},{\lambda}_{{\omega}_{2}}\right)$ = 2.57° at the fundamental wavelength ${\lambda}_{{\omega}_{2}}$ = 1.32

*µ*m. A LGN slab was then cut at $({\theta}_{P{M}_{1}}$ = 70.4°, ${\phi}_{P{M}_{1}}$ = 90°) according to our refined Sellmeier equations, the goal being to study the SHG in LGN at a fundamental wavelength the closest as possible to that of KTP. It has the advantage that we could get rid of the spectral response of the experimental setup. The LGN and KTP slabs were cut with the same small thickness $L$ = 0.52 mm. The fundamental beam emitted by the OPG was focused with a 100-mm-focal length CaF

_{2}lens. Then the beam waist diameter was ${w}_{o}$ = 120

*µ*m on the two slabs surface, with a Rayleigh length of 30 mm that is much longer than

*L*. Then parallel beam propagation was ensured, and the spatial walk-off attenuation is minimized.

The fundamental beam energy was measured with the J4-09 Molectron pyroelectric joulemeter placed behind a beam splitter and a lens with a focal length of 50 mm. The SHG energy was measured at the exit of each slab by the J3-05 Molectron pyroelectric joulemeter combined with a PEM531 amplifier, while a filter removed the input beam. Then we can determine the corresponding SHG conversion efficiency of type I SHG in LGN (${\text{\eta}}_{\text{I}}^{\text{LGN}}$), and that of type II SHG in KTP (${\text{\eta}}_{\text{II}}^{\text{KTP}}$).

Figure 5 shows the ratio ${\text{\eta}}_{\text{I}}^{\text{LGN}}/{\text{\eta}}_{\text{II}}^{\text{KTP}}$ recorded as a function of the fundamental wavelength ${\lambda}_{\omega}$. The peak wavelength is ${\lambda}_{{\omega}_{1}}$ = 1.317 *µ*m for LGN, which is very close to the targeted value ${\lambda}_{{\omega}_{2}}$. The spectral acceptance *L.δλω _{1}* is equal to 19.8 mm nm. It is in very good agreement with the calculation using our refined Sellmeier equations. In these conditions, we can calculate ${d}_{eff}^{LGN}$ relatively to ${\text{d}}_{\text{eff}}^{\text{KTP}}$ as follows:

*n*and

_{o}*n*are the ordinary and extraordinary refractive indices. They were calculated at ${\lambda}_{{\omega}_{1}}$ = 1.317

_{e}*µ*m for LGN using Eq. (1) and Table 1, and at ${\lambda}_{{\omega}_{2}}$ = 1.320

*µ*m for KTP using respectively the phase-matching angles ${\theta}_{P{M}_{1}}$ and ${\theta}_{P{M}_{2}}$ defined above and [4].

*T*and

_{o}*T*are the corresponding Fresnel transmission coefficients. For LGN, the spatial walk-off angle ${\rho}^{e}({\theta}_{P{M}_{1}},{\lambda}_{{\omega}_{1}})$ = 0.55° and the spatial walk-off attenuation ${G}_{I}^{LGN}=\mathrm{0.999.}$ ${G}_{II}^{KTP}=0.987$ for KTP [4,5]. Note that Fig. 5 shows a conversion efficiency of KTP that is two orders of magnitude higher than that of LGN: it is due to the relative value of their trigonometric functions that weigh differently on the nonlinear coefficients at the considered phase-matching angles. According to Eq. (2), we found that $\left|{\text{d}}_{11}(0.659\mu \text{m})\right|$ = 2.9 ± 0.5 pm/V and ${\delta}_{11}=$ 0.284 ± 0.049 pm/V, the Miller index [6], which corroborates the result obtained using the Maker fringes technique [2]. Furthermore it is also very close to $\left|{d}_{24}(0.660\text{\xb5m})\right|$ = 2.37 ± 0.17 pm/V of KTP [4], and a little bit larger than $\left|{d}_{11}(0.659\text{\xb5m})\right|$ = 2.4 ± 0.4 pm/V of LGT [1].

_{e}We also determined the surface damage threshold of the same LGN and KTP slabs. Both crystals were illuminated by the same Nd:YAG laser at 1.064 µm with a very high beam quality, a pulse duration of 5 ns (FWHM) and repetition rate of 10 Hz. By using a 100-mm-focal BK7 lens, we measured a beam waist diameter of 60 ± 3 *µ*m at their input surface using the standard knife-method. In these conditions, LGN was damaged at an incoming energy of 500 ± 10 $\mu $J, corresponding to a peak power density of 2.8 ± 0.7 GW/cm^{2}. It is a little bit lower than that of KTP where the damage was observed at 760 ± 10 $\mu $J, *i.e.* 4.3 ± 1.1 GW/cm^{2}. Using the same setup and same KTP crystal as a reference, LGT had been damaged for an input energy of 480 ± 10 $\mu $J, which corresponds to a peak power density of 2.7 ± 07 GW/cm^{2} [3]. In our previous work, we reported a surface damage threshold of 1.41 GW/cm^{2} in a 1-mm thick LGN slab using KDP as a reference [2]. They were illuminated by a Nd:YAG laser at 1.064 µm with a pulse duration of 10 ns (FWHM) and a repetition rate of 1 Hz. Moreover, the experimental protocol was different than the one we used here since the average power had been set at 20 mW and the beam waist diameter at the entrance surface of the slab was equal to 200 *µ*m. Furthermore, the slabs were moved toward the focal point until damage was observed at their input surface. All these differences could explain the different result.

## 4. Calculation of the supercontinuum generation by phase-matched OPG

Using our refined Sellmeier equations and the method described in ref [7], we showed that a supercontinuum can be generated using a type II phase-matched OPG *i.e. $1/{\lambda}_{P}^{o}\to 1/{\lambda}_{s}^{e}+1/{\lambda}_{i}^{e}$* when pumped at *λ _{p}* = 0.982 µm in the (y, z) plane of LGN. Figure 6 shows that the emission could range between 1.4 and 3.45

*µ*m, the LGN crystal being cut at (

*θ*= 52°,

_{PM}*φ*= 90°). According to the value of

_{PM}*d*determined above, the calculated corresponding figure of merit ${\left({d}_{eff}^{yz}\right)}^{2}/{n}^{o}({\lambda}_{P}){n}^{e}({\lambda}_{i}){n}^{e}({\lambda}_{s})$ is equal to $0.15\frac{p{m}^{2}}{{V}^{2}}$ in LGN, which is a relatively low value. However, the supercontinuum range and the figure of merit are both larger in LGN compared with LGT [1]. Concerning the pump laser to use, Fig. 6 shows that the tuning curve of LGN exhibits a quasi-supercontinuum behavior when the crystal is pumped at

_{11}*λ*= 1.064

_{p}*µ*m, while it is not anymore the case at

*λ*= 0.8

_{p}*µ*m.

## 5. Conclusion

We measured the SHG and DFG phase-matching tuning curves of LGN as well as the absolute magnitude of the associated nonlinear coefficient. These data can be used *per se* for designing any parametric device, but we also used them for refining the Sellmeier equations of the crystal. Using these equations, we found the possibility of generating a super continuum in the mid-IR by pumping LGN at the standard wavelength of emission of the Nd:YAG laser. This interesting feature combined with the ability of this crystal to be grown in large size and high optical quality put LGN in the category of the best nonlinear crystals for practical applications.

## Acknowledgment

The authors thank the China Scholarship Council (CSC) for the financial supports of Feng Guo and Dazhi Lu.

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