Quasi-phase-matching devices are usually fabricated by electric field poling over photolithographically defined electrode patterns on ferroelectric crystal substrates. For the optimal nonlinear optical performance of such devices, the micro-poled domain structure must ensure good fidelity to the designed grating structure. We present a nondestructive diffraction method to evaluate the quality of periodically poled lithium niobate crystals, by utilizing index modulation caused by the internal field effects. Our proposed method is much simpler than the conventional second-harmonic generation experiment, and provides a fast, low-cost but accurate means for micro-poling quality evaluation.
©2009 Optical Society of America
Quasi-phase-matching (QPM) devices based on ferroelectric crystals are widely used as highly efficient optical frequency conversion devices . Typically a QPM device is fabricated by applying a dc electric field after forming a desired electrode pattern on the positive surface of a crystal substrate defined by a photolithographic mask . When the applied field exceeds the coercive field, nucleation sites are formed, which initiate polarization-reversal followed by the domain-wall motion to extend the reversed region in order to achieve desired duty cycle [3,4]. For the optimal performance of a QPM device, the poled domain structure must ensure good fidelity to the designed grating structure. However, local deviations from the ideal domain-wall locations inevitably occur, which can lead to a decreased efficiency or undesired function of the devices . For stable fabrication of high-fidelity QPM devices, it is essential to monitor the poling quality and give a quick feedback to the poling processes.
Several methods [5–7] have been proposed to examine the periodically poled domain structure during and after poling process, which provide information on local domain structures. Although these methods are appropriate for visualizing the microscopic domain structures, they do not easily provide quantities which are directly related to the final device performance. Thus, the second harmonic generation (SHG) tuning curve is usually measured to assess the final quality of a QPM device, as it provides direct estimation of overall performance of the device. For example, the QPM bandwidth of the SHG tuning curve is a fundamental quantity that is directly related to the quality of poling . However, it is not an easy task to measure the SHG tuning curve unless an appropriate coherent light source is available.
As an alternative, linear diffraction methods were utilized to investigate poling quality of QPM devices [8–11]. Jin et al. obtained the duty-cycle information by measuring the far-field diffraction orders from a surface-etched periodically poled lithium niobate (PPLN) device . Gao et al. also used diffraction to investigate the intrinsic index modulation and the duty-cycle in a Mg-doped PPLN device . In both works, binary phase grating models were used. Müller et al. studied the electro-optic (EO) diffraction effects as a function of applied electric field by introducing continuous phase distribution over the periodically reversed domains . Recently, we proposed a simple method to quantify the statistical information about the duty-cycle error, and to test the final performance of PPLN by applying an improved far-field diffraction method on surface-etched PPLN devices . In that work, however, we etched the original –z face of the device in order to create a phase modulation for diffraction as in our previous work , which takes time and risk of damage to the sample. In principle, diffraction cannot be observed from as-poled PPLN because in an ideal ferroelectric crystal with 180° domains periodic domain reversal creates only a periodic modulation of the nonlinear optical tensor components, without affecting any linear index of refraction. However, as-poled PPLNs produce significant diffraction which is caused by the intrinsic index modulation after periodic poling as demonstrated in Refs. 9 and 10. A possible cause of this intriguing phenomenon is the EO index change due to the very slowly relaxing internal field component [12–15].
In this work, by utilizing this intrinsic EO index modulation and by extensive application of the methods of Fourier optics, we propose simple and systematic nondestructive quality checking methods for QPM devices. As a demonstration of the nondestructive quality evaluation methods, we illuminated a low-power cw laser beam on as-poled PPLNs, and the diffraction patterns were taken for two different experimental arrangements. First, an expanded laser beam uniformly covering the whole sample was used in order to check the overall nonlinear optical performance of the device, and the results were compared with SHG. Next, the laser beam was focused on PPLN to obtain the Fourier transform of the local phase profile at the sample. From the diffraction measurements for many sampled locations, we could obtain the statistics on the local duty-cycle, which directly affects the overall device performance . For both experiments, we compared the EO diffraction results with those of the etched PPLN, to assure that the EO diffraction method provides accurate information on the micro-poling quality.
2. Theoretical model
First, we assume that the intrinsic index modulation in PPLN forms a binary phase grating with a period same as the QPM period Λ. This model is supported by the fact that the typical domain wall in congruent lithium niobate is mostly parallel to the crystalline z-axis, and the width is very small (< 100 nm) . This will be further verified by comparing the experimental data for the as-poled PPLNs and the etched ones. According to the model, all theories follow the results of our previous work with surface etching . We would like to highlight some of the results: If a plane optical wave is normally incident on the binary phase grating, the phase of the exiting wave is modulated according to the phase structure. The electric field amplitude pattern of the Fraunhofer diffraction would be the convolution of the Fourier transform of the phase structure and that of the input field distribution . When the QPM device is uniformly illuminated on the grating region, the diffraction pattern will be equivalent to the SHG tuning curve , because the output QPM SHG amplitude spectrum can be expressed as a Fourier transform of the nonlinearity modulation function in the case of negligible depletion of the fundamental . On the other hand, when the sample is illuminated with a focused beam, each diffraction order has a finite envelop which is the Fourier transform of the focused beam shape, but the intensity ratios among the orders remain unchanged from the infinite grating case . In particular, the intensity ratio between the 2nd order and the 1st order is given by I2/I1 = cos2(πR), where R is the local duty ratio [8,9]. We note that the intensity ratio I 2/I 1 is a function of R exclusively, giving a good measure for the duty ratio.
3. Experiment and discussion
For the demonstration of the proposed methods, a 0.5 mm thick z–cut wafer of congruent lithium niobate crystal (Yamaju Ceramics) was used for electric field poling. Diffraction patterns were measured for the as-poled PPLNs as described below. The poled channels were 0.5 mm wide and 10.0 mm long. In order to check the validity of the proposed nondestructive method, we also carried out the same experiments after etching the original –z faces of the samples. Before etching, the samples were annealed to reduce the internal field effects.
3.1 Far-field diffraction with expanded beam
In the first diffraction experiment, we measured the diffraction pattern of the whole sample illuminated by an expanded laser beam, in order to check the overall nonlinear performance of the device. A He-Ne laser (Melles Griot, λ = 543.5 nm, 1 mW cw-power) beam was expanded and collimated by a telescope to uniformly illuminate a 10.0 mm-long PPLN crystal with a QPM period of 18.5 µm. The PPLN has an aperiodic domain whose width is Λ (twice the average domain width) in the middle of the device as schematically described in Fig. 1(a) . A CCD camera captured the + 1st (or 1st) order far-field diffraction pattern, at the focal plane of a lens placed just after the sample .
For comparison, we also measured the SHG-tuning curve. The pump source was an optical parametric oscillator (OPO) system using a β-BBO crystal, which was pumped by the third harmonic (355 nm) of a Q-switched Nd:YAG laser (pulse duration ~7 ns, repetition rate ~10 Hz). The idler output of the OPO was focused into the PPLN crystal. The SHG output energy was measured with a photodiode while scanning the idler wavelength around the QPM point by rotating the β-BBO crystal. Type-0 interaction was used for our measurement.
For the as-poled aperiodic PPLN, the 1st order diffraction pattern agrees well with the theoretical prediction as shown in Fig. 1(b). Figure 1(c) shows that the diffraction pattern remained the same after etching the sample, except the diffraction efficiency. The EO diffraction efficiency was much smaller (~3%) than the etched case (~24%). Both diffraction patterns agree with the SHG tuning curve in Fig. 1(d), although the measured SHG spectrum is slightly broader than the theoretical curves due to the finite line-width (~0.7 nm) of the OPO source. These experiments verify that the diffraction measurement on the as-poled PPLN provides equivalent information as the SHG tuning curve. However, the SHG tuning curve measurement requires a narrow line-width tunable source or uniform temperature control along the whole length of the device, and cutting and polishing the fabricated device. On the other hand, our proposed EO diffraction method is much simpler and fast. It can be used not only for the periodic structures, but also for the samples with more complex structures, for which SHG may not easily resolve the details of the QPM spectral structure.
3.2 Far-field diffraction with focused beam
Although the above expanded beam diffraction experiment provides equivalent information to the SHG tuning curve in terms of Fourier transform, it lacks of information on the strength of the nonlinear optical coefficient modulation, and detects the average duty ratio only. We observed that the expanded beam diffraction shape is not sensitive to the duty ratio fluctuation unless it is significant, while local duty ratio fluctuation does affect the nonlinear optical performance of the QPM device . Thus, we carried out the diffraction experiment with a focused beam in order to check the local duty cycle error. The He-Ne laser used in the first experiment was focused to a spot (~62 μm at FWHM) on a PPLN with a QPM period of 29.5 µm. In this case, the Gaussian beam waist acts as an aperture function. The far-field diffraction patterns were obtained by using a lens between the sample and the detector plane  for 60~80 locations throughout the poled region of 10.0 mm.
A typical diffraction pattern is shown in Fig. 2(a) . While scanning the sample through the focused spot, small intensity changes were observed in the 1st and the 2nd order peaks, which were caused by the local duty cycle fluctuation. For each location, the intensity ratio between the first and the second orders were measured to calculate the duty ratio as described in Section 2. Since the focused spot contains 2~3 periods in the FWHM area, the intensity ratio between the first and the second order provides a locally averaged duty ratio within the focused spot region. If the spot gets smaller, the averaging effect will be reduced. On the other hand, the width of each diffraction order broadens as a result of Fourier transform, and the neighboring peaks will overlap each other for the spot size smaller than the grating period, hindering the analysis. From the statistical analysis of the intensity ratio of all the locations, we obtained an average duty ratio of 0.416, with a standard deviation of 0.017 for this particular PPLN sample. The average value (<1/2) means that the PPLN was underpoled or overpoled by 8.4% of a period. But it was confirmed that the PPLN was underpoled by calculating the total charge flowed during the poling process. The small standard deviation assures that the duty ratio is quite uniform throughout the poled channel. The histogram is provided in Fig. 2(b) to visualize the statistical distribution.
By the same token, for the etched sample the average duty ratio and the standard deviation were measured to be 0.410 and 0.015, respectively, both of which are very close to the EO diffraction results. A typical diffraction pattern and the histogram for the etched PPLN are given in Figs. 2(c) and (d), respectively. The two histograms in Figs. 2(b) and (d) are not exactly the same because the sampling locations were not identical for the two cases. From the similar statistical results obtained from the as-poled and the etched PPLNs, we can conclude that the binary phase grating model works well in analyzing the first few diffraction orders with a small index modulation in the as-poled PPLN . (For the etched PPLN, the validity of the model has been justified in our previous work .) However, more complicated phase models should be used when one is dealing with the higher orders and a large index modulation caused by an external field .
Our proposed methods can be applied to check the poling quality of other ferroelectric QPM devices. Although we performed non-destructive analyses by utilizing the intrinsic internal field of the PPLN, the same methods can also be used for the QPM devices made of materials with small internal fields, such as stoichiometric lithium niobate (SLN), stoichiometric lithium tantalate (SLT), and MgO-doped SLN and SLT, by applying an electric field smaller than the coercive field through transparent electrodes.
On the other hand, we also want to point out the limits of our method: we note that a QPM device with a much smaller period would require a laser with a shorter wavelength and a Fourier transform lens with a large numerical aperture for the focused-spot diffraction experiment, which can make the experimental conditions critical. This method may not be appropriate for the QPM devices with very small periods (a few micrometers or smaller). On the other hand, for the expanded-beam diffraction experiment, a lens with a large diameter would be necessary for a long QPM device. The availability of a well-corrected large-aperture lens would limit this application.
Finally, regarding the physics involved in the intrinsic index modulation in PPLN, congruent lithium niobate is known to have strong internal electric fields, due to the intrinsic defects of the crystal [12–15]. After periodic poling, the unrelaxed internal fields in the reversed domains seem to produce the index modulation through the electro-optic effect, resulting in the similar diffraction as in the surface-relief grating case. However, the detailed mechanism of the index modulation in as-poled PPLNs needs further investigation. (strengths and directions of the internal field components, etc.)
We proposed simple nondestructive methods to check the quality of PPLN by analyzing the far-field diffraction pattern. With the expanded beam diffraction patterns we estimated the overall nonlinear optical performance of the device. On the other hand, by the diffraction experiment with a focused beam, we quantitatively estimated the duty ratio fluctuation, which is an important indicator of the micro-poling quality. Our proposed methods provide fast, low-cost, but accurate tools for evaluating the macroscopic and microscopic quality of QPM devices, and can give quick feedback to the fabrication process.
This work was supported by the Korea Research Foundation grant funded by the Ministry of Education, Science and Technology (No. 2009-0068995), and by the Ministry of Knowledge and Economy of Korea through the Ultrashort Quantum Beam Facility Program.
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