1. Introduction

For many years photorefractive materials have been investigated extensively because of their promise for various applications in photonics [1]. One of these applications is e.g. the spatial and spectral laser beam clean-up. Photorefractive materials with infrared response seem to be key elements for such applications using laser diodes. With photorefractive two-wave mixing it is possible to transfer energy from a high-power laser beam with a poor spatial profile to a diffraction limited beam with Gaussian shape [2, 3, 4]. Placing a photorefractive crystal into the laser cavity [5] or into an external cavity of a laser system [6] one can force the laser to oscillate in a single longitudinal mode. With optical phase conjugation it is possible to injection lock high-power broad-area laser diodes and laser diode arrays to obtain single mode output [7]. In the last few years a remarkable effort was done to improve the photorefractive sensitivity of photorefractive materials in the near-infrared wavelength range due to widely available and powerful near-IR laser sources. One can distinguish two main groups of photorefractive inorganic materials. Semiconductors are relatively fast but have a small nonlinearity and require high external fields. From ferroelectrics oxides the most promising for near-infrared are Rh-doped KNbO₃ [8] and Rh-doped BaTiO₃ [9]. Up to now the material of choice for near infrared photorefractive applications was Rh-doped BaTiO₃ and it was implemented in most of the aforementioned beam cleanup schemes [3, 4, 6]. It shows a photorefractive response up to 1064nm with phase conjugate rise times in the order of 10 s at 5 W / cm² [10]. However, it often suffers of domain formation at this wavelength [11] and, in addition, has a phase transition at ~ 125°C and close to room temperature at ~ 9 °C [12], which most often leads to fatal damage of the crystal and its photorefractive characteristics. Therefore new infrared sensitive photorefractive materials are required for these applications [13].

Tin hypothiodiphosphate (Sn₂P₂S₆) is a photorefractive crystal with high gain coefficients and short response times in the red and near-infrared spectral range [14, 15]. Photorefraction in Sn₂P₂S₆ was first reported in the 1991, however the interest for Sn₂P₂S₆ increased substantially when Odoulov et al. demonstrated photorefraction at 1.06 μm in 1996 [16] using pure crystals with pre-illumination. Conventional nominally pure Sn₂P₂S₆ crystals are grown by vapor-transport technique [17], are of yellow color, and the photorefractive sensitivity substantially depends on pre-illumination. The grating formation shows a strong electron-hole competition leading to a decrease of the steady-state gain coefficients. By changing the growth parameters in the vapor-transport growth technique, modified brown Sn₂P₂S₆ crystals were obtained [18]. These brown crystals are not sensitive to pre-illumination, have no pronounced electron-hole competition as well as they have a much higher two-wave mixing gain and faster response compared to yellow Sn₂P₂S₆ [14, 18]. Brown crystals presumably contain more intrinsic (non-stoichiometric) defects, which are difficult to control in the vapor-transport growth, and up to now only small samples could be grown. Since for the self-pumped optical phase conjugation the theoretical threshold for the product of the two-wave mixing gain coefficient Γ and the length of the crystal L should exceed two [19], self-pumped optical phase conjugation in brown Sn₂P₂S₆ could only be demonstrated up to a wavelength of 980nm [15].

In this paper we present phase conjugation with a new kind of Sn₂P₂S₆ crystals obtained by doping the initial growth compound with Tellurium. Optical quality doped crystals with large dimensions and high gain coefficients could be grown. Using new Te-doped Sn₂P₂S₆ crystals we demonstrate optical phase conjugation at the technologically important wavelength of 1.06 μm with rise times down to 85 ms.

2. Experiment

The Tellurium doped Sn₂P₂S₆ crystal used in our experiment had the dimensions of x×y×z = 10mm × 6mm × 7.44mm along the main x, y, z axes defined as in Ref. [15]. It was grown by the vapor transport growth technique [17] with 1 % Tellurium in the initial compound. The crystal is of homogeneous light brown color. Compared to yellow Sn₂P₂S₆ crystals the absorption edge in Te-doped crystals is shifted from λ ≈ 530nm to higher wavelengths up to λ ≈ 570nm [20]. In all Sn₂P₂S₆ crystals the absorption constant is rather low in the near infrared; in our Sn₂P₂S₆:Te 1 % the absorption constant reaches α = 0.1cm^-1 for the light polarized along the x-axis at 1.06 μm.

 

Fig. 1. Experimental setup for optical self-pumped phase conjugation in a ring cavity scheme using a Te-doped Sn₂P₂S₆ crystal. Additional neutral density filters ND-I and ND-II were used to vary the input beam intensity and the transmission of the loop respectively. The transmission grating in the crystal is written by beam 3 with its self-diffracted beam 4 and by beams 1 and 2 counterpropagating in the loop.

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The experimental setup for ring-cavity self-pumped phase conjugation is shown in Fig. 1. We used a cw Nd:YAG laser with a maximal output power of 400mW(Lightwave Electronics). The light beams were polarized in the plane of the ring-cavity loop and were almost parallel to the x-axis in the crystal and the external angle 2θ was adjusted to 30°. This configuration corresponds to the maximum two-wave mixing gain of the material [15]. To reduce Fresnel losses the crystal was coated with a 190 nm thick Al₂O₃ layer, which gives the lowest reflectivity for an incidence angle β ~ 60° with respect to the sample normal and leads to a single reflection loss of approximately 6 %. An f = 1000-mm lens was placed into the path of the input beam to focus slightly the light into the crystal and decrease beam divergence. The beam had a Gaussian shape with a diameter of approximately 2 mm in the crystal. The used multi-layer dielectric mirrors are optimized for 1064nm and have a reflectivity of more than 99 %. To avoid parasitic reflection gratings one of the mirrors in the cavity was vibrated to ensure incoherency of the beams 1 and 3. The generated phase-conjugated signal is then a result of the coupling via the transmission grating formed by incident beam 3 and its self-diffracted beam 4 as well as by their feedback beams 1 and 2 [19]. The intensity of the phase-conjugated wave 2 is observed by a photodiode placed behind a glass plate used as a beam splitter. The phase-conjugate reflectivity R is defined as the ratio between the measured intensity of the phase-conjugated wave 2 and the input wave 3. The phase conjugate rise time τ ₀ is defined as τ ₀ = τ _90% - τ _10%, where τ _90% and τ _10% are the times needed to reach 90% and 10% of the maximal reflectivity respectively.

3. Results

The temporal evolution of the phase conjugated beam after switching on the pump beam 3 is shown in Fig. 2. For an intensity of 20W/cm² and the above presented configuration we obtained a maximal saturated phase conjugated reflectivity of 42 percent and a rise time of 85 ms. As seen in Fig. 2, after the phase conjugated beam reaches its saturated value it stays stable showing no self-oscillation effects as previously observed in yellow Sn₂P₂S crystals with a strong electron-hole competition [16].

 

Fig. 2. Temporal evolution of the phase conjugated reflectivity R after switching on the pump beam 3 at t = 0. A different time scale between 0.3 s and 2 s is showing the stable phase conjugated reflection.

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To investigate the transmission losses in the ring cavity different neutral density filters ND-II were introduced in the cavity (see Fig. 1). The measured steady-state phase conjugate reflectivity as a function of the loop transmission is shown in Fig. 3. The curves in Fig. 3 were calculated on the base of the four coupled-wave theory described in [19] giving the solution in the form:

where

Here I ₀ is the total incoming beam intensity, Γ the photorefractive gain coefficient, L the length of the crystal and |ρ|² is the theoretical phase conjugate reflectivity. The parameter t ₀ accounts for the changes in beam amplitudes and phases after being reflected by the mirrors in the cavity and transmitted through the crystal surface which is on the side of the cavity. As the loop transmission we define T = |t ₀|². The measured reflectivity is equal to R = |ρ|²|t_L|⁴ where t_L includes the changes in amplitudes and phases after being transmitted through the sample surface which is on the side of the input beam. By inserting Eqs. (2) and (3) into Eq. (1) one gets the transcendental equation for the theoretical reflectivity |ρ|² which depends on the coupling strength ΓL and on the loop transmission T = |t ₀|².

 

Fig. 3. Measured saturated phase conjugate reflectivity R as a function of the loop transmission T. The curves represent calculations for ΓL = 2.9 (solid curve) being in best conformance with the measurement and for ΓL = 2.6 (dashed curve), ΓL = 3.2 (dotted curve) for comparison.

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Following the procedure described in Ref. [14], we first estimated the parameter T|t_L|⁴ by assuming that in first approximation the measured reflectivity is proportional to the transmission of the filter ND-II. From this we obtain T|t_L|⁴ = (0.71±0.05). A direct estimation of T|t_L|⁴ that accounts for absorption and reflection losses is (1 - R ₁)³(1 - R ₂)(1 - A)². For the single reflection losses at the crystal surface for the angles 60 ° and 30° we get R ₁ = 0.06 and R ₂ = 0.1 respectively. A = 0.07 is the absorption loss of the Te-doped Sn₂P₂S₆ crystal at 1064 nm. Therefore T|t_L|⁴ ≈ 0.70, in good agreement with the experimental value. For the loop transmission we get T|t_L|⁴/(1 - R ₁)² ≈ 0.71/(0.94)² = 0.80. This value corresponds to the loop transmission without an additional ND-II filter in the ring cavity, as also taken into account when plotting our data in Fig. 3.

To obtain the coupling strength ΓL from the measurements we calculated the phase conjugated reflectivity as a function of the cavity transmission for different values of ΓL. As one can see in Fig. 3 the measured values agree best for a coupling strength of ΓL = (2.9±0.3), leading to a photorefractive gain of Γ = (3.9±0.4)cm^-1.

Theoretical calculations for the reflectivity R as a function of the coupling strength ΓL for T|t_L|⁴ = 0.71 (no neutral density filter) and T|t_L|⁴ = 0.42 (with a 75% neutral density filter) are presented in Fig. 4. From these calculations one can see that the phase conjugate reflectivity could be increased to R ≈ 70 percent for a crystal thickness of L > 1.2cm.

The phase-conjugate reflectivity will depend also on the input beam intensity due to competing thermal effects (dark generation) and eventual background illumination. This can be modeled by introducing an uniform background intensity I_β which will lead to a change of the parameter κ from (Eq. 3) as [14] :

 

Fig. 4. Dependences of the reflectivity R as a function of the coupling strength ΓL for T|t_L|⁴ = 0.71 (solid curve) and T|t_L|⁴ = 0.42 (dashed curve). The corresponding highest experimental point of Fig. 3 and the point for a loop transmission of 0.6 are included.

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Fig. 5. Saturated phase conjugate reflectivity R as a function of the input intensity. The theoretical curve was calculated with T|t_L|⁴ = 0.71, ΓL = 2.9 and considered an effective background intensity of I_β = 0.9 W/cm².

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To determine I_β we were changing the intensity of the input beam by placing neutral density filters ND-I in the path and measure the phase conjugate reflectivity. The results are shown in Fig. 5. The theoretical intensity dependence with I_β =0.9 W/cm² and the previously obtained parameters T|t_L|⁴ = 0.71 and ΓL = 2.9 is also shown in Fig. 5.

The response rate 1/τ ₀ as a function of the incoming laser intensity I ₀ is presented in Fig. 6 and shows a linear dependence as expected from the simplest one-center charge transport model. For the maximal intensity of I = 20 W/cm² the response rate is 12 s^-1 corresponding to a rise time of about 85 ms. Note that for an intensity of I = 5 W/cm² the rise time is about 300 ms which is more than 30 times faster than reported before in Rh-doped BaTiO₃ at the same wavelength and intensity [10]. As seen in Fig. 6, the response rate in Sn₂P₂S₆:Te is still expected to increase by increasing the intensity above I = 20W/cm².

 

Fig. 6. Response rate 1/τ ₀ versus the incident intensity with a linear curve that corresponds the measurements.

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4. Conclusion

We have demonstrated low-power self-pumped phase conjugation in a ring cavity scheme at a wavelength of 1064nm using Sn₂P₂S₆ crystals doped with Tellurium. Phase conjugate response times as low as τ = 85ms have been measured which is more than 100 times faster than any previously reported value, e.g. τ = 10s in Rh-doped BaTiO₃, without forming any domains, as often seen in BaTiO₃. The experimentally measured phase conjugated reflectivity is 42 percent for a 0.74cm thick crystal. Our estimation shows that the reflectivity can reach about 70 percent for a crystal with a thickness exceeding 1.2cm. Therefore, Te-doped Sn₂P₂S₆ can be considered as one of the most promising material for photorefractive applications at near-infrared wavelengths.