1. Introduction

In 2007, we synthesized and studied the crystal structure of the new acentric crystal NaI₃O₈ [1]. Three years later, another group showed that this material is a negative uniaxial crystal with potential nonlinear optical properties. They performed powder second harmonic generation (SHG) measurements and calculations based on the density functional theory (DFT) [2]. Recent advances in crystal growth allowed us to get single crystals of very high quality suited for the first exhaustive study of linear and nonlinear optical properties described in the present letter. We recorded the transmission spectra in polarized light and determined the damage threshold in NaI₃O₈ slabs polished to optical quality. We directly measured phase-matching tuning curves of SHG and difference frequency generation (DFG) by using a method where NaI₃O₈ was cut as a cylinder polished on its curved surface [3]. From these experimental data we determined accurate Sellmeier equations describing the dispersion of the ordinary and extraordinary principal refractive indices, n_o and n_e (n_o > n_e), as a function of the wavelength. We also determined the absolute values of the two independent nonlinear coefficients d₁₄ and d₁₅ using a phase-matching technique [4].

2. Crystal growth, transmission spectra and damage threshold

NaI₃O₈ single crystals were grown by slow evaporation of Nitric Acid aqueous solutions (7M) at fixed temperature ranging between 60 and 70 °C. We obtained samples of several millimeter dimensions as the one shown in the insert of Fig. 1(a). While NaI₃O₈ displays a significant solubility in acidic solutions of lower molarity, such solutions were proved to be unstable toward the reduction of the iodate species into iodine. The later gets incorporated in the growing crystals giving them a yellow tint. Since NaI₃O₈ belongs to the $S4(\overline{4})$ tetragonal point group, its crystallographic frame (a, b, c) is orthonormal and fully coincides with the dielectric frame (x, y, z) [1, 2].

 

Fig. 1 NaI₃O₈: (a) Transmission spectra of the 3-mm-thick slab shown in insert; (b) Setup used for phase-matching measurements in the 4.13-mm-cylinder shown in insert.

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The transmission spectra depicted in Fig. 1(a) were recorded in polarized light through a 3-mm-thick slab. The two faces were cut perpendicularly to the x-axis, polished but uncoated. The linear polarization of light oriented successively perpendicularly and collinear with the z-axis, led to the ordinary and extraordinary transmission coefficients respectively. We used a Perkin-Elmer Lambda 900 spectrometer to record spectra as a function of the wavelength between 0.175 and 3.300 µm, and a Bruker FT-IR above 3.3 µm. Figure 1(a) shows that NaI₃O₈ is transparent between 0.32 and 6 µm despite strong absorption bands above 4 µm.

We determined the surface damage threshold of NaI₃O₈ compared with that of KTiOPO₄ (KTP). The two slabs were illuminated by a 1.064-µm laser with 5-ns FWHM, 10-Hz repetition rate and 30-µm beam waist radius. NaI₃O₈ was damaged at an input energy of 140 J, corresponding to a peak power density of 0.79 GW/cm². It was only 5 times lower than the damage threshold in KTP, which has been observed at 760 µJ i.e. 4.29 GW/cm².

3. Phase-matching properties, Sellmeier equations and nonlinear coefficients

Under Kleinman symmetry, the second-order electric susceptibility tensor of the NaI₃O₈ crystal has two independent nonzero coefficients, i.e. d_xyz = d_xzy = d_yzx = d_yxz = d_zxy = d_zyx ( = d₁₄); d_xzx = d_xxz = d_zxx = - d_yzy = - d_yyz = - d_zyy ( = d₁₅), where d₁₄ and d₁₅ stand for the contracted notation [5]. The five following types of SHG and DFG processes can be phase-matched with a nonzero effective coefficient identically in the xz- and yz-plane: type I SHG$(1/{\lambda }_{\omega }^o+1/{\lambda }_{\omega }^o=1/{\lambda }_{2\omega }^e)$, type II SHG $(1/{\lambda }_{\omega }^o+1/{\lambda }_{\omega }^e=1/{\lambda }_{2\omega }^e)$, type I DFG $\left(1/{\lambda }_P^e-1/{\lambda }_s^e=1/{\lambda }_i^o\right),$type II DFG $(1/{\lambda }_P^e-1/{\lambda }_s^o=1/{\lambda }_i^o)$ and type III DFG $(1/{\lambda }_P^e-1/{\lambda }_s^o=1/{\lambda }_i^e)$. Superscripts o and e stand for the ordinary and extraordinary waves, respectively. ${\lambda }_{\omega }^k$ and ${\lambda }_{2\omega }^k$ (with k being o or e) are the fundamental and second harmonic wavelengths, respectively. ${\lambda }_P^k$ and ${\lambda }_s^k$ are the pump and signal input wavelengths, and ${\lambda }_i^k$ is the idler wavelength generated by DFG, with the following relation of order: ${\lambda }_p^k$ $<{\lambda }_s^k\le {\lambda }_i^k$ . The corresponding tuning curves were directly measured by using a method where the NaI₃O₈ crystal was cut as a cylinder with a diameter D = 4.13 mm and an acylindricity ΔD/D below 1%. The curved surface was polished to optical quality as shown in the insert of Fig. 1(b). We previously used this sample shape to study many nonlinear crystals, as RTP for example [3].

Using an X-ray backscattered Laue method, the cylinder was cut with its rotation axis oriented along the y-axis with a precision better than 0.5°. Then it was stuck on a goniometric head along this axis. When placed at the center of an Euler circle, the cylinder can rotate on it-self to access any direction of the xz-plane. Note that this plane is equivalent to yz-plane, since NaI₃O₈ belongs to the $S4(\stackrel{}{\overline{4}})$tetragonal point group. Using a focusing 100-mm-focal length lens properly placed, an incoming beam remains in normal incidence and propagates parallel to the diameter of the rotating cylinder as shown in Fig. 1(a) [3].

One incoming tunable beam was necessary for SHG. It was emitted by a 5-ns (FWHM) and 10-Hz repetition rate optical parametric oscillator (OPO) from Continuum Company. The OPO was pumped at 1.064 µm and tunable between 0.4 µm and 2.4 µm. The OPO beam and part of the 1.064-µm beam were collinearly combined for achieving DFG. They were put in spatial and temporal coincidence inside the cylinder using mirrors and the delay line shown in Fig. 1(b). All beams being linearly polarized, achromatic half-wave plates (HWP) provided their polarization rotation, in order to achieve the different types of phase-matching, i.e. type I, II and III. Input energies were measured at the entrance of the cylinder using a J4-09 Molectron pyroelectric joulemeter coupled to a beam splitter and a 50-mm focal length CaF2 lens. They were removed at the output of the cylinder by using a polarizer and a filter. Thus only beams generated by SHG and DFG were measured on the J3-05 Molectron joulemeter combined with a PEM531 amplifier. Phase-matching angles corresponding to maximum values of the conversion efficiency were directly read on the Euler circle with an accuracy of ± 0.5°. The corresponding phase-matching wavelengths were recorded with a precision of ± 1nm using a HR 4000 Ocean Optics spectrometer. Figures 2 show the measured types I and II SHG tuning curves, types II and III DFG being given in Figs. 3. For SHG, it was not possible to record phase-matching angles for fundamental wavelengths lower than 0.7 µm because the corresponding generated wavelengths were below the ultra-violet cut-off wavelength. Similarly, we did not study type I DFG tuning curve since the incoming tunable pump wavelength being below 0.5 µm, it could damage the surface of the cylinder. The tuning curves of Figs. 2 and 3 indicate that NaI₃O₈ allows phase-matching conditions over its entire transparency range, which is also the spectral range of reliability of its two principal refractive indices. These data can be used directly to cut the crystal at a phase-matching angle corresponding to the targeted parametric process and phase-matching wavelength. But the combination of the simultaneous fit of all the phase-matching curves with the magnitude of the ordinary refractive index n_o at a given wavelength, can lead to the determination of the Sellmeier equations [3]. We used n_o(λ = 0.671 µm) = 1.6 that we determined from the direct measurement of a Brewster angle of 58° in the xy-plane of NaI₃O₈ cut as a slab. For that purpose, we used the Levenberg-Marquardt algorithm encoded with Matlab. We tried different dispersion equations, the best result being obtained with the following dual oscillator model:

 

Fig. 2 Measured (dots) and fitted (line) (a) Type I- and (b) type II- SHG tuning curves in NaI₃O₈.

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Fig. 3 Measured (dots) and fitted (line) (a) Type II- and (b) type III- DFG tuning curves in NaI₃O₈.

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Table 1. Sellmeier Coefficients for the Two Principal Refractive Indices n_o and n_e of NaI₃O₈.

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Table 2. Refractive Indices and Nonlinear Coefficients of NaI₃O₈: Comparison between our work and [2].

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The following step was to determine the magnitude of the two independent nonlinear coefficients of NaI₃O₈, $d_{14}$and$d_{15}$. For that purpose, we measured conversion efficiencies in NaI₃O₈ slabs cut at critical phase-matching angles for types I-SHG and type II-SHG, and for type II-SHG in KTP that was taken as a reference [4]. We chose all fundamental wavelengths as near as possible, to get rid of the experimental setup spectral response. With ρ^e as the spatial walk-off angle, the corresponding effective coefficients are in NaI₃O₈ [4,5]:

Using Eq. (1) and Tab. 2, we calculated the corresponding phase-matching and walk-off angles in NaI₃O₈ at the phase-matching wavelength ${\lambda }_{\omega }^{PM}=1.064 \mu m$. We found for type I SHG that ${\text{θ}}_{\text{PM}}=32.1°$and ρ^e(${\text{θ}}_{\text{PM}},{\lambda }_{\omega }^{PM})$ = 1.38°; ${\text{θ}}_{\text{PM}}=49°,$ ρ^e(${\text{θ}}_{\text{PM}},{\lambda }_{\omega }^{PM})$ = 1.52° and ρ^e(${\text{θ}}_{\text{PM}},{\lambda }_{2\omega }^{PM})$ = 1.51° in the case of type II SHG. We chose type II SHG$(1/{\text{ λ}}_{\text{ω}}^{\text{e}}+1/{\text{ λ}}_{\text{ω}}^{\text{o}}=1/{\text{λ}}_{2\text{ω}}^{\text{o}})$ in the xy-plane of KTP as a reference. The absolute value of the associated effective coefficient is$\left|{\text{d}}_{\text{eff}}^{\text{KTP}}\right|$ = 2.43 pm/V, the corresponding phase-matching and walk-off angles being φ_PM = 23.1°, ρ^e(${\text{θ}}_{\text{PM}},{\lambda }_{\omega }^{PM})$ = 0.17° and ρ^e(${\text{θ}}_{\text{PM}},{\lambda }_{2\omega }^{PM})$ = 0.29° [6]. We cut two NaI₃O₈ slabs $({\text{L}}_{\text{I }}^{{\text{NaI}}_3{\text{O}}_8}=$800 µm, ${\text{L}}_{\text{II }}^{{\text{NaI}}_3{\text{O}}_8}=$680 µm) and one KTP slab $({\text{L}}_{}^{KTP}=$ 800 µm) at the phase-matching angles given above. We took such a small interacting length in order to avoid any spatial walk-off attenuation. Since the incoming fundamental beam was focused through a 100-mm focal length CaF₂ lens, the corresponding beam waist radius was around w_o = 60 µm. It leads to a Rayleigh length 2xZ_R = 22 mm, which is much longer than the thickness of the slabs and ensures a parallel beam propagation. Types I and II SHG conversion efficiencies of NaI₃O₈, recorded relatively to KTP as a function of the fundamental wavelength are shown in Fig. 4: ${\text{η}}_{\text{I}}^{{\text{NaI}}_3{\text{O}}_8}$ and ${\text{η}}_{\text{II}}^{{\text{NaI}}_3{\text{O}}_8}$ correspond to types I and II SHG conversion efficiencies of NaI₃O₈ respectively, and ${\text{η}}_{\text{II}}^{\text{KTP}}$ stands for type II SHG conversion efficiency of KTP.

 

Fig. 4 Calculated (line) and measured (dots) conversion efficiencies in NaI₃O₈ of (a) type I SHG and (b) type II SHG as a function of the fundamental wavelength.

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The absolute value of the effective nonlinear coefficient ${\text{d}}_{\text{eff}}^{{\text{NaI}}_3{\text{O}}_8}$ relatively to ${\text{d}}_{\text{eff}}^{\text{KTP}}$ of KTP can be determined from the maximum of each curve shown in Fig. 4 and by using:

With

Reliable NaI₃O₈-OPG tuning curves can be calculated using our Sellmeier equations. Thus, we found that a supercontinuum can be generated from type II OPG $(1/ {\lambda }_p^e-1/ {\lambda }_s^o=1/{\lambda }_i^o)$in the dielectric xz-plane of NaI₃O₈. The supercontinuum is the broadest one, ranging between 2.55 µm and 4.65 µm, when the pump wavelength is equal to 1.16 µm and the crystal oriented at θ = 18.5° from the z-axis as shown in Fig. 5. A supercontinuum can also be generated when the crystal is pumped by the Ti:Sapphire at 0.8 µm and the Nd:YAG at 1.064 µm, also shown in Fig. 5.

 

Fig. 5 Calculated OPG tuning curve in the xz plane of NaI₃O₈ with λ_P = 1.16, 1.064 and 0.8 µm.

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4. Conclusion

We measured for the first time to the best of our knowledge the transmission spectra in polarized light, the damage threshold, and the phase-matching conditions of SHG and DFG in the new acentric uniaxial NaI₃O₈ crystal. It allowed us to determine the Sellmeier equations and the absolute value of the two nonzero second-order nonlinear coefficients. Our data show that NaI₃O₈ is very attractive since using our Sellmeier’s equations we showed that a NaI₃O₈-based OPG can generate a supercontinuum in the mid-IR when pumped in the near-IR. We also bring a new input to refine the modelling of the second-order electric susceptibility in iodates compounds.