A simple method for photoconductivity measurement in lithium niobate

A simple and effective technique to characterize the photoconductivity (PC) of lithium niobate is presented. The technique is based on the modulation of the external field and on the observation of the optical response of the material as a function of the intensity of a gaussian beam using a Tardy’s polarimetric setup in the r 22 configuration. When the temporal period of the modulation is larger than the Maxwell time of the material, the effect of the PC can be detected observing the kinetics of the screening effect of the external applied field. This approach allows measuring a wide dynamic range up to high light intensities with good accuracy using a standard oscilloscope and with no need for charge collection electrodes. The technique is demonstrated by comparing two samples, the first possessing a standard congruent composition, the second being doped with Zn in order to boost the PC.


Supplementary information
The application of our method to lithium niobate is based on electro-optic modulation in the so-called r 22 conguration: the light propagates along the z-axis and the electric eld is applied on the y-axis. This conguration is favorable because the inuence of thermo-optic eects can be neglected. However, due to the photogalvanic eect (sometimes dubbed also as Bulk Photovoltaic Eect) there exist a photogalvanic (PG) current J P G induced by the light in the crystal bulk. Thus a PG eld builds up in the illuminated area. As our method is based on the time dependence of the internal elds, as probed by the electro-optic refractive index change, it is important to assess whether the internal PG eld can aect the results of our measurement.
The photogalvanic current in lithium niobate can be written as: where E k(l) are the optical eld polarization components and β S jkl and β A jkl are the symmetric and anti-symmetric parts of the PG tensor, respectively. For the three components of the current, this can be rewritten explicitly taking into account the form of the PG tensor in the Voigt notation for lithium niobate: (1) For a beam propagating along z with polarization amplitude components E x(y) = A x(y) e −i(kz+ϕ x(y)) we have: with I = A 2 x + A 2 y the total power density and ∆ϕ(z) = ϕ y (z) − ϕ x (z) the phase dierence between the two polarization components. The rst component, J x , is zero for a circularly polarized beam like the one here used in the Tardy setup because in this case ∆ϕ = π/2 = ϕ 0 . This result is in agreement with Neumann's principle, since a circular polarization cannot break the three-fold symmetry of the crystal inducing a current along one specic direction other than the z axis. However, as the beam propagates along the sample, the circular polarization prepared at the input of the sample (see Fig. 1) is in general transformed into elliptical along the sample, either due to the birefringence ∆n = n x −n y = n 3 o r 22 E 2 induced by the external electric eld applied along the y-axis, either due to other disturbances or misalignment of the propagation direction of the beam with respect to the z axis. In this case the phase dierence increases with the propagation distance z: In the worst case, for z 2π λ ∆n = ±π/2, the phase dierence becomes equal to 0 or ±π. The beam polarization would then be linear and |J x | would be maximal. The maximum attainable internal eld generated at equilibrium by such a current is given by: where σ is the photoconductivity. Since σ is here taken to be proportional to I, E P G max is not dependent on the beam intensity. It should be noted here that this is a rough majorant because the externally applied eld, after being switched on, decreases monotonously to zero due to the screening eects mentioned in the paper. Thus the polarization has the tendency to go back to circular all along the sample and the PG eects are thus frustrated during the measurement.
On the other hand, the J y component remains always close to zero as long as the amplitude of the two polarization components remains close to each other (see eq. (5)), as it is the case here. Finally, the J z component of the PG current creates some charges on the input and output faces of the sample that are in air and separated of several millimeters. We can therefore safely consider that they are screened by ambient charges before they can buildup a signicant eld and in the following we will neglect this contribution.
In summary we have to evaluate the potential eect of an x-directed E P G space charge with an upper limit E P G max compared to the externally applied eld. Unfortunately, to the best of our knowledge, there are not detailed data on the value of the β S 22 PG coecient in undoped or Zn-doped LN, so we cannot perform an a priori estimate. However we empirically determine that the PG-generated eld is not perturbing our measurement as it follows.
Taken into account the form of the electro-optic tensor of lithium niobate it can be seen that, while the externally applied eld E 2 squeezes the optical indicatrix along thex andŷ directions, the internal eld directed alongx does the same but along the diagonal directionŝ u =x +ŷ andv =x −ŷ (see Fig. 2 (a) and (b)). In our setup the polarization reading is achieved by means of a quarter wave plate placed after the sample and oriented at 45 degrees, thus along the diagonalsû orv. This design guarantees the maximum sensitivity to birefringence changes of the type described in Fig. 2 (a). However, for an applied eld along x, the situation is as depicted in Fig. 2 (b). In those conditions the quarter wave plate is no longer working correctly and we should observe a marked change in the response function of our setup corresponding to a measurable alteration of the extinction ratio I max /I min after the analyzer.
We checked several times the extinction ratio of our system, in dierent illumination conditions and at dierent times, with and without an applied eld on both the samples: in all cases we did not notice any signicant variation in the contrast, which proves that the eld along x is negligibly small. Thus we conclude that our experiment is sensitive only to the externally applied eld.