1. Introduction

Recently we predicted possibility for photoactive dipolar centers in noncentrosymmetric crystals to be aligned in polar way by linearly polarized light [1]. Such an alignment should produce macroscopic electric polarization of a sample, which was supposed to be measurable in experiment. Microscopic structure of dipolar centers can be different: in particular we have considered donor-acceptors associates in our theoretical model where we estimated the magnitude of new nonlinear optical effect to be comparable with optical rectification [1].

In this paper experimental observation of the predicted effect of optical orientation of dipolar centers (OODC) is reported for the first time to the best of our knowledge. The effect was observed as alternating electric current generated in Bi₁₂SiO₂₀ crystal under its illumination by continuous-wave light of constant intensity but with modulated in time polarization state. Measured dependence of the ac-current on the modulation frequency in the range of 40 Hz–40 kHz allows us to reveal at least three different types of dipolar centers contributing into OODC effect. Additional measurements of the light-induced dichroism and photoconductive characteristics of our crystal support proposed interpretation of the experimental results.

2. Phenomenological description

As it was shown, dc polarization P induced due to OODC is described by phenomenological expression similar to that for the effect of optical rectification [1]:

where d_ijk is the third rank material tensor existing only in crystals without inversion symmetry, I is the light intensity, (e_je_k*+e_j*e_k)/2 is the symmetric part of the polarization matrix describing the degree of linear polarization, P_lin, of incident photons. Despite similarity of phenomenological description of both effects they are different in their physical origins. Optical rectification is not generally related with resonant optical transitions and it exists in the region of optical transparency of a crystal. In contrast, OODC effect requires real optical transitions of electrons accompanied by the relaxation process towards the equilibrium state.

Two main microscopic mechanisms of OODC: (i) orientation-sensitive optical excitation of centers (including intra-center transitions) combined with their real reorientation, which occurs with different rates in ground and excited states; and (ii) repopulation of differently oriented centers resulting from orientation-sensitive release of electrons from the centers due to charge-transfer transitions and their subsequent orientation-insensitive trapping, were considered [1]. A model of OODC-effect in which both mechanisms of the relaxation were taken into account was proposed in our theoretical work [1].

3. Experimental setup

The most efficient technique for experimental study of the OODC-effect is detection of displacement current, J_d, caused by transient polarization generated at non-steady-state illumination. To distinguish J_d from other currents (for example, photovoltaic) also capable to be generated in a crystal under illumination we use specific feature of OODC that generated polarization P of the crystal depends on the polarization state of the incident light. Sketch of experimental setup is shown in Fig. 1(a).

 

Fig. 1. (a) Configuration of the experimental setup, (b) Orientation of Bi₁₂SiO₂₀ crystal: electrodes are in the faces (110), the unit polarization vectors e_k and e_j make angle 330 with[001] and [1 1̄ 0] axes, respectively.

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Electro-optic phase modulator was used to modulate the polarization state of continuous-wave radiation emitted by diode-pumped Nd:YVO₄ laser at the wavelength of 532 nm with output power up to 2 W. By applying to the modulator electric field of square-wave form, we switch the polarization of the light beam between two mutually orthogonal linear states with frequency ω keeping the power of light beam non-modulated in time. Electric current generated in sample under such modulated illumination was measured by lock-in amplifier at the same frequency ω. The reference signal for the amplifier was provided by the generator, which controls the driver of electro-optic modulator. In this experiment we vary the modulation frequency from 40 Hz to 40 kHz. Intrinsic resistance of all measured samples was much higher than the input resistance of the lock-in amplifier. Therefore, short-circuit condition was satisfied allowing us to measure generated current, not a voltage.

Several crystals with sillenite structure of Bi₁₂SiO₂₀ (BSO) and Bi₁₂TiO₂₀ were tested in the experiment but the frequency-dependent ac current (see below) was observed only in BSO crystal grown by Chokhralsky method in oxygen-free atmosphere namely, in argon. The sample has shape of plate with thickness of 2 mm and area of 5×10 mm². Silver-paste electrodes were deposited on the medium faces of the crystal. Crystallographic orientation of the sample in respect to the polarization of incident light and direction of photo-induced current are shown in Fig. 1(b). It should be noted that the plane of polarization of linearly polarized beams makes angle 33° (or 57°) with the <111> axis on account of optical activity of the crystal. Transverse geometry of the experiment allows further diminishing of unwanted photovoltaic current. Optical transitions excited in the crystal at the wavelength of 532 nm are in the region of so called “absorption shoulder” featured for sillenite crystals [2]. Electrons are assumed to be raised by these transitions from deep levels (created by intrinsic defects) into the conduction band [2].

4. Results

Dependencies of currents observed at different light intensities on the modulation frequency ω are shown in Fig. 2. Graphs in Fig. 2(a) were measured by lock-in amplifier synchronized in phase with voltage applied to electro-optic modulator (in-phase component of the current) while the curves in Fig. 2(b) were measured with 90°-phase-shifted reference (quadrature component).

 

Fig. 2. Dependencies of (a) the in-phase and (b) quadrature components of the J_d - current on the modulation frequency (ω/2π) measured at incident light intensity of 0.065 W/cm² (squares), 0.13 W/cm² (diamonds), and 0.26 W/cm² (triangles). Laser beam was expanded to overlap the space between electrodes. RC of electrical circuit was about 7·10^-7 s.

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As one can see, both components are evidently of the relaxation type. In the geometry of the experiment, two known nonlinear optical effects, optical rectification and linear photogalvanic effect [3] may also be the reason of current appearance in crystal illuminated by light with temporally modulated polarization state. However, both these effects cannot have any resonance in the frequency range used in the experiment. For example, linear photogalvanic effect in sillenite crystals is characterized by the relaxation time of the electron’s momentum, τ_P~10^-14÷10^-12 [3]. Relaxation of polarization P irrespectively of its physical origin leads to the following expression of displacement current, J_d, in the case of harmonic modulation of P_lin~sinωt:

Here τ_d is relaxation time of P (or OODC-current) and d is the respective component of the d_ijk-tensor. It follows from Eq.2 that the quadrature component of the J_d-current has a relaxation peak at ω^p=τ^-1_d. The frequency dependence of the qudrature component in Fig. 2(b) manifests at least three similar peaks with ω^p being different from each other by the order of value. At light intensity of 0.26 W/cm² we get the following relaxation times: τ⁽¹⁾_d=5.3·10^-4 s, τ(2)_d⁽²⁾=4.0·10^-5 s, and τ⁽³⁾τ=3.5·10^-6 s (see Fig. 2(b)) Besides difference of relaxation times, the sign of the second peak is opposite to others. These data indicate that there are at least three kinds of dipolar centers contributing into J_d in the sample. Behavior of the in-phase component (Fig. 2(a) correlates with the proposed interpretation. At low frequencies (<400 Hz) we observe superposition of frequently-independent photogalvanic current, J_PG, and opposite-sign component of J_d (which increases with ω) due to dipolar centers of the first type. At higher frequency signal diminishing is replaced by its growth, which could be explained by contribution of dipolar centers of the second type. Thereafter, the current amplitude again diminishes because the third type of dipolar centers is coming into effect, whose contribution in J_d is comparable with that of second-type centers. It is worth noting that relaxation time τ⁽ⁱ⁾_d is a function of the light intensity (see Fig. 2). Moreover, the amplitude of J_d grows up nonlinearly with intensity, which is in conflict with Eq.2. In contrast, photogalvanic current has linear dependence on the intensity in full agreement with the theory and vast experiments [2].

 

Fig. 3. Dependence of light-induced dichroism on the pump intensity. The intensity of probe beam was 0.02 W/cm². Both beams were focused into 1-mm² area on the crystal surface. Arrows indicates incident light intensities in OODC experiments.

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We carried out additional experiments to confirm our interpretation of observed current as a consequence of optical orientation of dipolar centers. To be oriented dipolar centers should have different absorption cross-sections for orthogonal linear polarizations [1]. Therefore, linear dichroism induced in our crystal by the linearly polarized light should be measurable. To do these measurements we split laser beam into probe and pump parts. Linearly polarized pump beam was directly sent to the sample while the probe beam was repeatedly switched between two orthogonal linear states as for the J_d-current measurements (see Fig. 1(b)) but beams were focused in a spot of 1 mm² area. The probe beam transmitted through the sample was detected by a photodiode, and its power was measured by lock-in amplifier. Without pump, small signal was observed at the modulation frequency, which is probably caused by not perfect adjustment of the phase modulator. Switching on the pump beam led to appreciable increase of the signal so that photons with polarization vector parallel to that of pumping light were less absorbed. After switching off the pump, the signal exponentially disappeared with characteristic time, which depends on the probe beam intensity as the square-root. Figure 3 shows the light-induced difference of absorption coefficients, Δα, for the light beams with two mutually orthogonal linear polarizations as a function of the pump intensity. As seen the curve is clearly nonlinear. Within the interval of 0.01–0.3 W/cm² it can be well fitted with the square-root dependence. Note that the same range of intensities is used in measurements of J_d-current. Observed light-induced dichroism evidently shows that there are anisotropic centers in the crystal capable to be optically aligned.

 

Fig. 4. Frequency (ω/2π) dependencies of (a) the in-phase and (b) quadrature components of the photoconductive current at the light intensity of 0.065 W/cm² (squares), 0.13 W/cm² (diamonds), and 0.26 W/cm² (triangles).

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We also measured photoconductivity (J_ph) of our BSO crystal as a function of light intensity and modulation frequency. The same setup (Fig. 1(a)) was used in this experiment except for installing a polarizer to modulate light intensity and applying bias voltage to the crystal. Dependence of the photocurrent on the frequency modulation of input light intensity (in-phase and quadrature components) is shown in Fig. 4. Note that the relaxation time, τ_ph, of photoconductivity is almost the same as τ_d⁽²⁾. Moreover, both τ_ph and photocurrent J_ph sublinearly change with light intensity. These features were previously reported for BSO crystals grown in the argon atmosphere and explained by nonlinear (bimolecular) recombination of carriers, which is caused by high degree of compensation of deep (acceptor) levels [4]. It was suggested that electrons from relatively shallow donors (most probably oxygen vacancies, which are natural for oxygen-deficient BSO) are delivered to fill these deep levels. Therefore, formation of impurity associates possessing dipole moment (which is the necessary condition for OODC effect) is quite probable within this microscopic model especially at high concentration of donor centers.

5. Discussion

Peculiarities of J_d-current and light-induced dichroism observed in experiments can be explained by using theoretical model of the OODC-effect proposed in Ref. [1]. According to this model, donor-acceptor pairs have prominent dipole moment when both centers, which form the pair, are ionized. There are at least two types of pairs in the crystal, denoted as pairs of type I and II in Ref. [1], which have two non-equivalent orientations of permanent dipole moment in respect to the plane of polarization of the incident light and, as result, different absorption cross-sections. Owing to such a distinction of the light absorption, difference of concentrations of pairs arises in illuminated crystal that leads to its polarization. The non-equivalency of orientations is the best pronounced in the geometry when the plane of polarization of the incident light is either parallel or perpendicular to the <111> axis (remember that the effect of optical activity of the crystal was taken into account in our experiments). To explain the set of obtained experimental data two additional assumptions have to be incorporated in the model in comparison with Ref. [1]. First, concentration of nonionized acceptors, N_A 0 is suggested to be close to the concentration of photoexcited electrons in illuminated crystal. Second, the concentration of ionized donors, N_D +, is diminishing with increasing light intensity due to trapping of photoexcited electrons. These assumptions require modification of one of the balance equations for the case of bimolecular recombination and addition of the equation, which describes trapping of photoexcited electrons by the donors and their release due to thermal generation. After these modifications, the system of the equations describing reorientation of donor-acceptor pairs becomes following:

Here n is concentration of photoexcited electrons in the conduction band; N ₁ and N ₂ are concentration of pairs of type I and II, respectively and σ₁ and σ₂ are their absorption cross-sections, respectively; hν is photon energy; γ is recombination coefficient; Γ is the hopping rate accompanied by the reorientation of one type of the pairs to another; N is the total number of pairs including pairs with non-ionized donors; β is the thermal generation rate of electrons; and η is the rate of electron trapping. Using this system of equations it is easy to derive expression for the steady-state concentration difference, ΔN=N ₁-N ₂:

where Δσ=|σ₁-σ₂|. It should be noted that Eq.8 is obtained by neglecting real reorientation of dipolar centers (Γ=0) and filling of donor levels by the dark electrons. As one can see, nonlinear behavior of the current J_d versus light intensity and dependence τ_d(I) are clearly following from Eq.8. Moreover, observed growth of light-induced Δα with light intensity proportional to √I at relatively small I and its decreasing at the high intensity are in good agreement with Eq.8. Therefore, the model based on the idea of donor-acceptor pairs as dipolar centers participating in OODC-effect explains main features of the observed non-steady- state current in BSO crystal. However, further research is needed in particular for interpretation of contribution to the current J_d by the first and the third types of dipolar centers.

It is worth comparing the magnitude of the observed current with known photogalvanic current. To this end we calculate the coefficient K=J_d α/I considering the maximal value of the in-phase component diminished by the current at low frequency, which is attributed to the photogalvanic effect. It yields K=0.9·10^-9 cm/V at I=0.26 W/cm². This value is two-folds higher than previously reported Glass constant for linear photogalvanic effect in BSO crystals [3], which is in good agreement with the OODC-effect estimations presented in Ref. [1].

6. Conclusion

In conclusion, we have experimentally observed optical orientation by a polar way of centers with permanent dipole moment, which is new nonlinear optical effect to our knowledge. The effect was observed in a Bi₁₂SiO₂₀ crystal grown in the argon atmosphere and it manifests itself as electrical current generated in the crystal illuminated by light, which polarization state is modulated in time. Specific features of the observed current as a function of the modulation frequency allow us to certainly attribute this current with OODC effect, which was also supported by the experimental data on the photoconductivity and light-induced linear dichroism. A model of donor-acceptor pairs as dipolar centers is shown to be able to explain all main peculiarities of the optical orientation of dipolar centers in the BSO crystal.