1. Introduction

Photorefractive optical damage in lithium niobate (LiNbO₃) waveguides continues to be a crucial problem for applications at light powers above 10 mW. Although great effort has been devoted to characterize [1, 2, 3, 4], understand [5, 6] and reduce [7, 8] optical damage, many experimental and theoretical aspects remain open, and the definite method for optical damage inhibition is still lacking. For the development of even more efficient methods of optical damage reduction a reliable and well-understood model of the effect is desired. So far it is unclear which index changes Δn are acceptable, i.e. do not cause critical beam distortions, and which values are unacceptable. Also more information is needed about the origin of the Δn, in particular the role of secondary centers and of the dark conductivity

To work on these tasks we take advantage of an interferometric technique we developed for the measurement of the refractive index change in planar waveguides. The method is described in detail in [9]. The main advantage of this technique is that, compared to holographic approaches [10], it measures the change of the effective mode index Δn_eff for single-beam propagation, the case more appropriate to investigate optical damage. Moreover, it is applicable to z-cut guides for which very scarce measurements of Δn_eff have been z-axis being normal to the guide plane, the typical holographic method fails. In this work we study planar proton-exchanged (PE) waveguides. The obtained data for Δn_eff will be related to complementary measurements of the intensity threshold for the onset of beam distortion, thus getting more complete information about optical damage. Furthermore, we study the dark conductivity in these waveguides.

2. Experimental Methods

2.1 Sample preparation

Three different z-cut LiNbO₃ substrates have been used: congruently melting undoped, congruently melting thermo-electrically oxidized [11], and 5.0 % mol Mg-doped material. Every sample undergoes the same treatment of immersion for 24 h at 300 °C in benzoic acid buffered with 3 wt. % lithium benzoate in a sealed glass ampoule [10]. This procedure results in formation of a-phase proton-exchanged LiNbO3 (PE:LiNbO₃) waveguides with extraordinary index jumps at the surface of Δn_e ≈ 0.01 and smooth Fermi-like index-profiles with effective depths in the 1-2 μm range [10]. These guides support one or two modes at the wavelengths 532 and 633 nm. One of the edges of each sample is polished to optical grade in order to enable decoupling of light via the waveguide edge in the interferometer setup described below.

Slight differences with respect to the waveguide fabrication are noticed between the different substrates. Both, the waveguides in the thermo-electrically oxidized substrate and in the magnesium-doped substrate tend to guide rather one than two modes at the two wavelengths mentioned above. For magnesium-doped LiNbO₃ it is known that the proton-exchange process is slower than in undoped material [12].

2.2 Determination of the threshold intensity for beam degradation

In order to measure the threshold intensity for the onset of appreciable distortion of the out-coupled light we use a simple setup schematically shown in Fig. 1 and described in [3]. While continuously illuminating the waveguide with light at λ = 532 nm, the output power passing through a diaphragm placed 30 cm behind the waveguide is monitored. The size of the diaphragm is chosen such, that at low intensities (no light-induced scattering) about 70% of the total out-coupled power is transmitted. The light intensity inside the waveguide has been estimated (to a ±15% accuracy) by following the procedure described in [13].

 

Fig. 1. Schematic sketch of the single-beam setup that is used for the determination of optical damage thresholds via the detection of significant beam distortion.

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2.3 Measuring optical damage with the interferometric method

The interferometric technique for characterizing the optical damage in waveguides is based on the measurement of relative phase changes between two weak He-Ne laser beams that propagate along the two arms of a Mach-Zehnder interferometer (Fig. 2). The key feature of the setup is the fact that both interferometer beams (represented in Fig. 2 by a dotted and a dashed line, respectively) propagate separately, but next to each other in the same planar waveguide. Thus, the setup is insensitive to changes of the external parameters, such as the ambient temperature, since both interferometer arms are equally influenced. Optical damage is induced in one of the arms by intense collinear illumination with visible light (532 nm in our case). The probe beam and the pump beam interact over the whole propagation length from the incoupling prism to the end face of the waveguide. The measured quantity is the modulation of the red light-intensity pattern at the output of the interferometer. The use of chopped probe light and a lock-in amplifier enable us to detect changes in the interference pattern with a high signal-to-noise ratio. Our realization of the Mach-Zehnder interferometer in planar waveguides together with its features and limitations have been previously described in [9].

 

Fig. 2. Experimental setup for the interferometric measurement of photorefractive index changes in planar waveguides. The dashed and the dotted lines on the lower left-hand side represent the two arms of the interferometer. These two lines are separated in the direction perpendicular to the plane of the paper.

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The experimental procedure is as follows: With the green beam blocked, the coupling angles for the weak red beams are adjusted to the best interference signal. Afterwards, the coupling angle for the green beam is adjusted at very low in-coupled power to avoid optical damage before the actual measurement starts. Then, with the red beam going through and a green blocking-filter placed in front of the detector, the green intensity is increased up to the value the measurement is supposed to be conducted with. The measuring time starts when the shutter for the green light is opened. Depending on the in-coupled intensity, and therefore on the expected rise time of the photorefractive effect, the modulated intensity is recorded for a few minutes up to one hour.

In order to compare the relative importance of dark and photoconductivity, we have also ≈ 10^-4). In this case, the measuring time starts when the green shutter is closed. In order to determine the dark conductivity σ_d from these decay measurements, it is necessary to decrease the intensity of the red probe light to be sure that the induced optical erasure is negligible compared with σ_d (I_red ≈ 0.05 Wcm^-2 inside the waveguide). Doubling of the probe intensity does not accelerate the decay, ensuring that the 0.05 Wcm^-2 are small enough to monitor purely the dark relaxation. Since these dark decays are much slower than the production of optical damage upon illumination, the typical measurement times here are several hours. All measurements described in this section are performed with the temperature of the sample holder being stabilized to (25.0 ± 0.1) °C.

3. Experimental results

3.1 Single-beam setup

The results of the measurements of the threshold intensity are summarized in Fig. 3. As long as the in-coupled beam does not cause appreciable optical damage in the guiding layer, the out-coupled beam maintains its shape and the power detected behind the diaphragm is proportional to the in-coupled power. The loss of this proportionality marks the threshold intensity for the onset of optical damage. It can be seen in Fig. 3 that the waveguides on the congruent substrate, either untreated or thermoelectrically oxidized, exhibit very similar thresholds around 270 Wcm^-2. This value is a little higher than the threshold intensity I_thr measured for the same type of waveguide (i.e. produced by the same fabrication procedure) and with the same experimental method, but fabricated in x-cut congruent substrates (I_thr ≈ 100 Wcm^-2) [4]. In the Mg-doped sample no significant degradation of the out-coupled beam could be measured up to the highest intensity available, 10⁵ Wcm^-2. The threshold intensities I_thr for all the samples used can be found in Table 1. The criterion that we apply to determine I_thr is as follows: I_thr is the intensity where for the first time the derivative dI_out/dI_in is smaller than 0.15. This value is arbitrarily chosen, but the result is in good accordance with the intuitive impression given by Fig. 3, thus it provides a reasonable criterion for quantitative comparison of different waveguides.

 

Fig. 3. Results of the measurements with the single-beam setup: outcoupled intensity I_out versus incoupled intensity I_in

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Table 1. Intensity thresholds for the different types of waveguides

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3.2 Mach-Zehnder interferometer

In the standard photorefractive model [14], the time dependence of Δn_eff (t) involves a saturating exponential function as follows:

where Δn_eff,sat is the effective index change at saturation and τ is the rise time. This dependence is valid for our data (see the fit in Fig. 4(a)). Beyond the threshold intensity for significant beam distortion, the interferometric method becomes problematic. This is because, due to increasing beam divergence, the intensity inside the waveguide is no longer well defined.

We measure the development of the change of the effective mode index with time, Δn_eff(t), for all types of waveguides guides (see Section 2) for an intensity range of 10 – 2000 Wcm^-2. From the interferometer signals we extract the time evolution of the refractive index changes as described in [9]. Thus we obtain values for the saturation index change Δn_eff,sat and the rise constant τ^-1 as functions of the intensity inside the waveguide. With regard to τ^-1, it turns out to be of the same order of magnitude as those values obtained by the holographic method for congruent samples [15].

 

Fig. 4. Typical measurement results obtained with the Mach-Zehnder interferometer for the build-up (a) and dark-decay (b) of optical damage. The solid lines correspond to exponential fits of Eq. (1) and Eq. (2), respectively.

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The dependence of Δn_eff,sat on the intensity has been plotted in Fig. 5 for all the guides. All curves show an increase of Δn_eff,sat with the light intensity I inside the waveguide that seems to saturate for higher intensities. In the low-intensity-region (< 60 Wcm^-2) the curves appear to have also a lower sensitivity to the variation of light intensity. In accordance with the behavior present in Fig. 3, the thermo-electrically oxidized and the congruent guides exhibit very similar Δn_eff,sat(I). It is worthwhile noticing that the intensity thresholds from Fig. 3 roughly coincide with the region in which Δn_eff,sat seems to saturate with I. Finally, for the MgO-doped samples, the measured index changes are too small to detect a reliable Δn_{eff, sat} increase within the intensity range used, in agreement with the much higher intensity threshold seen in Fig. 3.

Since the competition of dark conductivity σ_d and photoconductivity σ_ph in photorefractive charge transport was often used in early papers [5] to explain dependences similar to that of Fig. 5, we have also measured the dark decay time of Δn_eff in order to determine σ_d. In analogy to Eq. (1), we expect the decay of the index change to behave like

where τ_d is the time constant of the dark decay. It is connected to the dark conductivity via

In Eq. (3), ε ₀ and ε are the vacuum permittivity and the relative permittivity, respectively. We take ε ≈ 27 [16] to calculate σ_d from the measured decay times. These are σ_d (corresponding to ad of a few 10^-16 Ω^-1 cm^-1). Comparing this to the optical damage rise-time of a few seconds, it becomes unambiguously clear that the dark conductivity plays no role for the suppression of optical damage for our experimental conditions. An example of the measured time evolution of the index change during a dark decay is displayed in Fig. 4(b).

 

Fig. 5. Saturation values of the refractive index changes Δn_eff,sat for all three types of waveguides versus incident light intensity I_in. Solid and dashed lines are just guides to the eye, in analogy to presentations in [6, 17, 18].

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5. Discussion

The Mach-Zehnder interferometric technique applied to measure photorefractive index changes in planar waveguides has proved to be a complementary useful tool for characterizing the optical damage. First, it has confirmed previous experimental data on a strong increase of the induced saturation index change Δn_eff,sat at high intensities obtained by the holographic method in x-cut planar guides [15] or the Mach-Zehnder method in channel guides [5]. Also measurements of the photorefractively induced birefringence in x-cut bulk crystals with a Senarmont compensator setup showed an enhancement of Δn with I up to values of about 10^-4 [19]. Moreover, comparing the results with those from the single-beam technique, it is observed that the optical damage threshold occurs when the Δn_eff,sat(I) starts to saturate. We interpret this result as follows: For low enough intensities the photorefractive index changes, independently of their possible increase with I, are too small to appreciably affect the light propagation inside the guide. For increasing intensity, Δn_eff,sat becomes sufficient for modifying the beam profile and generating noticeable self-defocusing along the propagation direction causing the sublinear dependence seen in Fig. 3. This should occur for Δn_eff,sat ≈ 10^-4 as shown in Fig. 5. For higher in-coupled intensities the actual intensity inside the guide can hardly increase due to the self defocusing. Hence, in our case the onset of serious beam distortion is at Δn_eff,sat of about 1 × 10^-4. This threshold, however, may depend on several parameters like the interaction length and the beam diameter. Finally it is worth to mention that waveguides fabricated in Mg-doped substrates exhibit Δn_eff,sat well below 1 × 10^-4 even for the highest intensities used. This result is in good accordance with the absence of measurable optical damage thresholds in the intensity region checked.

The dark conductivity measurements achieved with the Mach-Zehnder technique clearly indicate that its contribution to charge transport is negligible when compared with the photoconductivity. Consequently, models based the on the role of dark conductivity to explain the increase of Δn_eff,sat with I are not applicable, and different approaches should be invoked. Conversely, our results are in good semi-quantitative accordance with the intensity dependence for the Δn_eff,sat predicted based on a two-center model for undoped LiNbO₃ applied to α-phase waveguides [6]. In particular, Δn_eff starts to grow sharply at similar light intensities. In this model the intensity dependence of Δn_eff,sat is attributed to the increasing importance of the highly bulk photovoltaic defect of niobium on lithium lattice sites (Nb_Li) in the charge transport.

Regarding the different crystals used we have fabricated α-phase PE waveguides on thermoelectrically oxidized LiNbO₃ substrates. Unfortunately, the PE treatment seems to alter the oxidation state of the waveguide layer so that the obtained waveguide has an optical damage resistance similar to that of standard α-phase guides. This result is indirectly a further confirmation of the conclusions of a recent work that reports a significant reduction of the samples during the PE treatment [20]. This effect should cancel the previous strong oxidation obtained by the thermoelectric technique.

6. Summary

In summary, we applied the recently developed interferometric Mach-Zehnder technique for characterizing photorefractive optical damage in planar waveguides. The study of α-phase PE:LiNbO₃ guides, fabricated in different z-cut substrates, has shown that the steady-state index change monotonously increases with the light intensity up to a saturating value. This last value coincides with serious beam divergence, i.e. the threshold for the onset of optical damage. Dark conductivity appears negligible compared with photoconductivity within the light intensity range used. Up to saturation, measured values compare well with results of simulations performed within the two-center model which considers the anti-site or Nb_Li-site defect as a secondary photorefractive center.