1. Introduction

Waveguides are the basic elements in integrated optical applications [1]. Many of these applications like optical switching, routing or dynamic optical interconnections require fast switching between waveguide channels. This is normally done electro-optically by applying complicated electrode configurations on permanently structured waveguides [2,3]. Several techniques based on light-induced refractive index changes have been recently proposed [4–9]. The most interesting feature of these waveguides is that they can be dynamically reconfigured, and thus signals can be routed by solely changing the light illumination.

Periodic dielectric structures such as photonic crystals or photonic lattices have recently gained a lot of interest due to their exciting features like controlling and manipulating the propagation and manage the diffraction of optical beams [9–11]. In photorefractive crystals, a periodic modulation of the refractive index can be induced dynamically by interfering two or more light beams inside the crystal. Beam steering in such a 1 dimensional optically induced lattice has recently been demonstrated using a third controlling beam [12]. For investigations of light propagation in periodic lattices, strontium-barium-niobate (SBN) is the most extensively employed material due to its high electro-optic activity (r ₃₃ = 235 pm/V for SBN:60, r ₃₃ = 1340 pm/V for SBN:75 at λ = 0.5 μm) [13]. However, the photorefractive response times of SBN in the visible are in the order of a few seconds [13], which makes this material not suitable for applications, where short waveguide formation times are required.

In this work, we investigate the potential of tin hypothiodiphosphate (Sn₂P₂S₆) for dynamic waveguide applications. Sn₂P₂S₆ is a semiconducting ferroelectric material with interesting optical and nonlinear optical properties: high photorefractive efficiency in the infrared up to the telecommunication wavelength 1.55 μm [14–16] and a large electro-optic coefficient (r ₁₁₁ = 174 pm/V at 633 nm [17]). Furthermore, the photorefractive response of Sn₂P₂S₆ in the near-infrared is very fast, more than two orders of magnitude faster than in any other photorefractive ferroelectric crystal as e.g. Rh-doped BaTiO₃ [18]. Recently, photorefractive self-focusing at 1.06 μm was demonstrated in bulk Te doped Sn₂P₂S₆ crystals with 15 ms response time at peak intensities of 160 W/cm² [19].

The photorefractive response time can be decreased, if light with photon energy larger than the band gap of the material is used [20]. In this so-called interband photorefractive effect, refractive index structures can be generated by charge redistribution between the bands, which in general provides 2-3 orders of magnitude faster response than the conventional effect.

So far, light induced waveguides were demonstrated in KNbO₃ [5] and Mg doped LiTaO₃ [6] by interband photorefraction with controlling light at ultraviolet (UV) wavelengths. However, there are some drawbacks of using UV light such as availability of laser sources, need of special optical elements and coatings to mention a few. Sn₂P₂S₆ has a band gap energy of E = 2.3 eV, which is lower than in conventional photorefractive crystals and enables interband photorefraction already in the visible at λ = 514 nm [21].

In this work we show that fast reconfigurable waveguides and waveguide arrays can be induced beneath the surface of Sn₂P₂S₆ crystals by using band-to-band excitations. The waveguiding structures are written beneath the surface in regions illuminated by 514 nm light by drift or diffusion of charge carriers, dominated by hole charge transport. They are probed nondestructively in transverse direction.

2. Light induced waveguides

The experiments were performed in a 6.8 mm long Sn₂P₂S₆ crystal oriented as shown in Fig. 1. The sample was nominally pure, to minimize the possibility of deep level trapping [20]. The use of interband light provides a faster effect, but on the other hand also a higher absorption for the controllling light. The absorption in Sn₂P₂S₆ is α = 490 cm^-1 at the controlling wavelength of λ _CL = 514 nm [21]. Therefore, the waveguide reaches a depth of only a few ten micrometers below the surface and the crystal needs sharp edges for in- and out-coupling of the guided light. Since the structures are written between the bands, readout at sub band-gap wavelengths as e.g. red or telecommunication wavelengths, does not disturb the waveguide structures.

The illumination of the crystal is shown in Fig. 1(a). The controlling light (Argon Ion Laser @ 514 nm) homogeneously illuminated a mask that was imaged onto the crystal z-surface by appropriate optics (not shown in the figure). The probe beam (HeNe @ 633 nm) traveled along the crystalline y-direction and was focused onto the input face of the crystal by a spherical lens (f = 40 mm) to a diameter of 2w ₀ = 22 μm. An out-coupling lens imaged the output face onto a CCD-camera. In order to excite an eigenmode, the readout beam was polarized along the dielectric 3-axis at an angle of Ψ = 43° with respect to the x-axis according to the orientation of the indicatrix in Sn₂P₂S₆ [16,17]. The controlling light was polarized in x-direction and an electric field was applied along x as well. For this configuration, we get an effective electro-optic coefficient of r _eff = r ₁₁₁ sin² Ψ+r ₃₃₁ cos² Ψ + r ₁₃₁ sin2 Ψ = 183pm/V at 633 nm using the coordinate system as defined in [16]. Uniform background illumination at 514 nm produced a homogeneous conductivity that is needed for a better confinement of the waveguides [6].

The basic process for inducing a step index profile in photorefractive crystals is schematically shown in Fig. 1(b). i) is the unperturbed state with a uniform refractive index n ₀. In a first step (ii) an electric field E ₀ is applied, which homogeneously decreases the refractive index via the electro-optic effect to a value of $n\text{'}=n_0-\genfrac{}{}{0.1ex}{}{1}{2}{n}_0^3{r}_{\mathrm{eff}}{E}_{0.}$ Finally, the controlling light is switched on (iii) and electrons are excited to the conduction band. Free charges, electrons in the conduction band and holes in the valence band, drift and screen the applied electric field in the illuminated region. This results in an electric field pattern that is correlated to the pattern of the controlling light. Thus, a refractive index structure is produced, which has its maximum in the illuminated regions. For the simple case of a slit mask, we get a 1D planar waveguide [5,6].

 

Fig. 1. (a) Arrangement for recording light induced waveguide structures. (b) Simplified electric field (dashed red) and refractive index (solid green) distribution in a photorefractive crystal during the formation of the waveguides. Explanation is given in the text.

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Fig. 2. (a) CCD-images of the output face of a 6.8 mm long SPS crystal without (left) and with (right) a photoinduced waveguide. (b) Build-up times τ_b of the light induced waveguide as a function of the controlling light intensity.

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Figure 2(a) shows the output of a 6.8 mm long pure Sn₂P₂S₆ crystal. A straight slit was imaged onto the crystal z-surface to a width of 17 μm in x-direction. Compared to previous experiments in KNbO₃ or LiTaO₃, much smaller fields are required due to the large electro-optic coefficient of Sn₂P₂S₆ (Table 1). In our experiments, the applied electric field was E = 900 V/cm, which resulted in a refractive index change of Δn = 2.3 × 10^-4 for the HeNe probe Beam. The profile of the guided light perfectly matches a cos²-function, for the first waveguide-mode, with a FWHM of 12 μm, which is in good agreement with the expected FWHM of 11 μm for the given index profile.

The build-up times τ_b, of light induced waveguides in Sn₂P₂S₆ as a function of the controlling light intensity are shown in Fig. 2(b). The response is very fast, with τ_b < 200 μs for intensities above 0.1 W/cm². As listed in Table 1, this is two times faster than the build-up times observed in KNbO₃ [5] and more than one order of magnitude faster than the build-up times measured in LiTaO₃ [6] for recording with the same intensity but in the UV. The build-up times were determined by recording the temporal evolution of the peak intensity of the output light. This was measured using a photodiode and a 100 μm pinhole in the image plane of the out-coupling lens. The square-root intensity dependence of the build-up times confirms the interband nature of the structure formation [20].

3. Light induced waveguide arrays

We further demonstrated optically induced waveguide arrays in Sn₂P₂S₆ at the interband wavelength λ _CL = 514 nm. For this we used a crystal with a length of 15 mm along the propagation direction (y). The array was induced by interfering two light beams that generated an interband photorefractive grating beneath the z-surface of the crystal. Such a structure represents a waveguide array with a waveguide spacing equal to the grating spacing Λ. In our set-up we had Λ ≈ 7 μm which yielded a modulation depth in the x-direction of δn = 1.0 × 10^-4 for the readout light at λ ≈ 633 nm, as determined by Bragg diffraction measurements [21].

Different than in the single waveguide experiments described above, the array structures could be created only by diffusion of charge carriers without the background illumination. If an additional electric field was applied to the crystal, a combination of diffusion and drift was responsible for the formation of the waveguide arrays.

Table 1. Parameters for the recording of interband light induced waveguides in LiTaO₃ [6], KNbO₃ [5] and Sn₂P₂S₆[this work]

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λ _CL: Recording wavelength, n ₀: Refractive index, r _eff: Electro-optic coefficient, α: Absorption @ λ _CL, E ₀: Electric field, Δ_n: refractive index change, τ_b: Build-up Time at I_CL=0.1W/cm². n ₀, r _eff, Δn and τ_b are values for readout at 633 nm in the respective configuration.

We probed the array in transverse direction since the structures are written in a layer a few ten micrometers beneath the surface, similar to the light induced waveguide experiments in the previous section. The light was coupled into the array with a 20x microscope objective. A cylindrical lens (f = 200 mm) was placed into the path of the probe beam, to minimize diffraction in the z-direction. The size of the read-out beam in the x direction was 2w_x = 12μm, so that the input-beam covered about two waveguides. The output after 15 mm propagation was again monitored by the CCD - camera and is shown in Fig. 3(a). Without the array, the beam diffracted to 2w_x = 330μm. With the array, the input beam was distributed among several waveguides, as shown in Fig. 3(a). The build-up time of these waveguides was τ_b = 225 μs for controlling light intensity of 0.1 W/cm².

An additional electric field E ₀ = 1 kV/cm applied in the +x-direction of the crystal shifted the whole waveguide array by an amount of Δx ≈ - 1.52μm = -0.21 Λ (Fig. 3(b)), Λ = 7.25 μm being the waveguide spacing. This can be explained by the fact, that the refractive index grating is phase shifted with respect to the light illumination. This phase shift strongly depends on the applied electric field and on the type of dominant charge carriers (e^- or h⁺). Measuring this phase shift allows us to give an estimation for the free carrier density n ₀ responsible for the generation of the photorefractive grating, as well as for the direct recombination constant γ_dir describing electron-hole recombination between the bands. For this we use the free carrier model from Ref. 20, which describes the space charge field E_sc in the trap-free approximation valid for high light intensities. The expression for E_sc can be further simplified for large grating spacing Λ ≳ 1 μm and an applied electric field smaller than the recombination field of the dominant charge carriers, i.e. the average internal electric field in which the charges drift for an average distance K ^-1 = Λ/2π before recombination. In our configuration this is true for E ₀ ≪ 20 kV/cm considering the results of the Bragg diffraction measurements [21]. We furthermore consider only one type of charge carriers. This is eligible if one of the mobilities is much larger than the other one, i.e. μ_e ≫ μ_h or μ_h ≫ μ_e for electron or hole dominated charge transport respectively. This simplification yields the following relation for the space charge field:

 

Fig. 3. (a) Output of a 15 mm long pure Sn₂P₂S₆ crystal without (left) and with (right) the induced photorefractive waveguides. (b) Measured profiles along the x-direction without an external applied electric field (red open squares) and with an applied electric field of 1kV/cm (blue solid circles). The lines are drawn for the guidance to the eyes.

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where E_D = Kk_BT/e is the diffusion field and $E_{qf}=\genfrac{}{}{0.1ex}{}{e}{\epsilon {\epsilon }_{0}K}{n}_0$ is the maximum electric field that can be created by free charge carriers; m grating modulation depth, k_B Boltzmann constant, T absolute temperature, e elementary charge, ϵ ₀ vacuum permittivity and ϵ = 230 [16] the dielectric constant of Sn₂P₂S₆. The upper signs in Eq. (1) are for electron and the lower signs for hole dominated charge transport respectively. The phase shift ϕ between the waveguide array and the interference pattern can then be calculated from Eq. (1) and is given by:

Taking into account the negative sign of the electro-optic effect (Δn ∝ -E), positive and negative values of ϕ correspond to dominant electron and hole charge transport respectively. The spatial shift of the array in the negative x direction after applying an electric field to the array implies a reduced negative phase shift in our experiment. This proves that the hole mobility in our Sn₂P₂S₆ crystal is larger than the electron mobility, in agreement with two-wave mixing experiments at this wavelength [21].

Without applied electric field, a maximum shift of ${\varphi }_0=-\genfrac{}{}{0.1ex}{}{\pi }{2}$ is reached. After applying an electric field of E ₀ = 1 kV/cm, the array is phase shifted by ϕ_E = 1.32 rad. This corresponds to a phase shift of ϕ = ϕ_E + ϕ ₀ = -0.25 rad between the array and the light fringes. Using the above definitions of E_D and E_qf, the charge density can be estimated from Eq. (2) to n ₀ ≈ 2 · 10¹⁶ cm^-3 for a writing light intensity of I ₀ = 100 mW/cm². Assuming a quantum efficiency close to 1, we can give an estimation for the direct recombination constant of Sn₂P₂S₆: γ _dir = α I ₀/(hv n ^{2 0}) ≈ 4 · 10^-13 cm³s^-1, with absorption constant α and photon energy hv.

By applying a modulating electric field, it may be possible to modulate such arrays in realtime. The arrays may also be shifted by a modulated phase-difference between the two writing beams, which can be realized with an additional electro-optic modulator or a piezo-controlled mirror in the path of one of the writing beams, as used for moving photorefractive gratings [15].

4. Conclusions

We have demonstrated for the first time to our knowledge waveguides and waveguide arrays induced by band-to-band excitation at visible wavelengths. In the electro-optic material Sn₂P₂S₆ we measured the fastest build-up of light induced waveguide structures (τ = 200 μs at I ₀ = 0.1 W/cm²) reported up to now. This is more than four orders of magnitude faster than for previously studied waveguides induced at visible wavelengths, which were produced by the conventional potorefractive effect [13]. The presented technique allows the generation of different straight and bent dynamic waveguide structures by using external masks or a spatial light modulator. Due to the fast response of Sn₂P₂S₆, these structures can be reconfigured in a sub-millisecond time-scale.