Measurements of birefringence, second-harmonic phase-matching conditions, and nonlinear coefficient d31 are performed for a set of Hafnium-doped congruent lithium niobate (Hf:cLN) crystals as functions of dopant concentration. The data highlight that the threshold concentration, above which there is a change in the Hf incorporation mechanism, is slightly above 2mol% and that, up to this value of concentration, the efficiency of nonlinear processes is not affected by the dopant insertion. Combining these results with those already present in literature, Hf:cLN crystals appear to be very promising candidates for the development of photorefractivity-free wavelength converters working at room temperature.
© 2007 Optical Society of America
Lithium niobate is a very interesting material for the realization of nonlinear optical devices because of a combination of several favorable properties, such as high nonlinear optical coefficients, wide transparency window, well established technology for fabricating channel waveguides and periodically poled structures. After the first demonstration of wavelength conversion based on the cascade of two second-order processes in a periodically-poled lithium-niobate (PPLN) crystal , several authors have shown that wavelength converters based on PPLN waveguides can be very efficient and versatile and may have important applications in optical communication systems [2–5].
At present, a strong limitation to the applications of wavelength converters based on ferroelectric crystals comes from the fact that, under illumination with visible or near-infrared light, there are semi-permanent changes in the index of refraction of the crystal, causing beam distortion and dramatically decreasing the device efficiency, unless some strategy to tackle the photorefractivity is implemented . Such an effect, called photorefractive effect (or, “optical damage”), is caused by the photoionization of impurities. The resistance to optical damage can be increased considerably by changing the lithium niobate (LN) composition from congruent (cLN; [Li]/[Nb]=0.94) to stoichiometric (sLN: [Li]/[Nb]=1) or by adding to LN an appropriate dopant. Among the many dopants that have been tested, the most utilized is, at present, MgO that is known to be effective in molar concentrations above 5 mol% [7,8]. The main problem with sLN and MgO-doped LN (Mg:cLN) is that it is very difficult to grow large homogeneous crystals. Interesting results have been recently obtained by using periodically-poled waveguides of MgO-doped stoichiometric Lithium Tantalate (LT) . In any case, since the nonlinear optical coefficients of LT are smaller than those of LN and the guided wave technology for LT is not mature, it is still important to explore the possibilities offered by doped LN. It is known that the main source of photorefractivity in congruent LN crystals is due to the occupation of missing-lithium sites by Nb ions. The NbLi sites can act as donors and/or acceptors of the photogenerated electrons. Dopant ions can reduce the photorefractivity by removing the NbLi sites . In the case of doping with MgO, the threshold concentration, that is, the minimum concentration necessary to remove all NbLi sites is about 5 mol%. The doping level chosen for reducing photorefractivity is usually kept slightly above the threshold concentration. In fact, when all NbLi sites are removed, there is no further advantage in increasing the dopant concentration. On the contrary, too high dopant concentrations may be detrimental for the optical quality of the crystals.
Recently, some investigations of the properties of cLN doped with HfO2 (hereafter called Hf:cLN) were undertaken, in view of the possibility of using Hf:cLN instead of Mg:cLN for wavelength conversion. Since Hf is tetravalent, the threshold concentration for Hf:cLN is expected to be lower than that of Mg:cLN [6,10]. Measurements of the photorefractivity-induced birefringence change , in a set of congruent LN crystals doped with increasing concentrations of HfO2, have shown that a significant reduction of the photorefractive effect can be obtained at HfO2 concentrations cHf above 4 mol.%. Successively, measurements performed at different light intensities have indicated that the threshold concentration cHf * is below 3mol%  and that the curve of photorefractivity as a function of light intensity tends to saturate when the doping level is above threshold [12,13]. Important steps toward the possible utilization of Hf:cLN in wavelength converters are the precise evaluation of cHf * and the measurement of the effect of Hf doping on the nonlinear optical properties of the crystals. In this work we present experimental results concerning the dependence of different optical parameters on cHf, so as to have a complete set of data describing the overall physical properties of Hf:cLN crystals. In Section 2 we report the behaviour of the crystal birefringence, showing that the threshold concentration for Hf:cLN is around 2mol%. In Section 3 we give the behavior of the phase-matching parameters and of the nonlinear coefficient d31, as obtained by second-harmonic-generation (SHG) measurements, highlighting that the nonlinear coefficients are little modified as long as the level of Hf doping does not substantially exceed the threshold value. Section 4 is devoted to the discussion of the experimental results.
2. Birefringence measurements
We studied a series of Hf:cLN crystals grown by the Czochralski technique. Hf4+ impurity ions were introduced into the melt in the form of HfO2 in increasing amounts going from 0 to 5 mol%. Information about the growth process is given in . The grown Hf:cLN crystals were found to possess a very good uniformity, as verified by microRaman investigations .
It is known that the birefringence of doped LN crystals, plotted as a function of the dopant concentration, shows a kink in correspondence of the threshold concentration . This is due to the fact that the dopant ions can occupy distinct positions in the crystal lattice depending whether their concentration is below or above threshold, so the contribution to the electric susceptibility of the crystal given by the ions in excess with respect to threshold is different from that of the ions occupying NbLi sites. The crystal birefringence measurement was performed by using a broadband optical source, linearly polarized at 45° between the x and the z axis of the crystal. The field component polarized along the z axis experiences the extraordinary refractive index ne, while the x component experiences the ordinary refractive index no. A polarizer with axis at 45° is positioned at the crystal output. The polarizer transmission is maximum for the spectral components that have accumulated a phase difference (Δφ) multiple of 2π in the crystal propagation, whereas it is minimum when Δφ is an odd multiple of π. As a result, the transmission is a periodical function of wavelength.
The measurements have been performed in the 1550-nm and in the 800-nm range using respectively the amplified spontaneous emission (ASE) of an Erbium-Yitterbium doped fiber amplifier and the output of a mode-locked Ti:sapphire laser producing 100-fs pulses centered at 806 nm. We show in Fig. 1 the optical spectra measured at the crystal input (a), and at the polarizer output (b) in the 1550-nm range. The ratio (b)/(a) is shown in Fig. 1(c). By taking two wavelengths λA and λB corresponding to two consecutive maxima of the curve and calling L the crystal length, the crystal birefringence, Δn = ne - no, can be calculated from the relation:
As discussed in  for the case of Mg:cLN, no is a very weak and smooth function of the dopant concentration, so that, by similarity, it can be assumed that the observed birefringence behavior of Hf:cLN crystals essentially reflects the behavior of ne. Recalling that the nonlinear interactions occurring in PPLN crystals usually involve waves with an extraordinary polarization, the fact that ne is, above threshold, a growing function of the Hf concentration (cHf) could give the possibility of fabricating channel waveguides for cascaded wavelength conversion by indiffusing Hf into an already Hf-doped substrate (e.g. 2 mol%).
3. Second-harmonic generation measurements
In order to measure the effect of Hf-doping on the phase-matching parameters and on the nonlinear properties, we performed SHG experiments by using the tunable picosecond pulses of an optical parametric oscillator (OPO) pumped by the second harmonic of an amplified mode-locked Q-switched Nd:YAG laser . Around 1100 nm, the pulse duration is 20 ps and the maximum pulse energy is about 50 μJ. The vertically polarized beam coming from the OPO, re-collimated by a 1 m focal-length lens, is impinging on the Hf:cLN samples with a spot size of about 1 mm. The crystals have the shape of a parallelepiped, cut along the dielectric axes. The beam enters perpendicularly to the xz face and propagates as an ordinary beam, in order to satisfy type I phase-matching. The data acquisition system records at the same time, for each pulse train, both pump and second-harmonic (SH) output energy. This is important because the pulse energy presents some shot-to-shot fluctuation, arising from the pulse-pumped nature of the wide-gain-bandwidth OPO . In order to explore a wide range of pump intensities (typically from 1 to 100 MW/cm2), a variable attenuator is inserted before the focusing lens. The crystals temperature is controlled with a 0.1°C accuracy.
By tuning the OPO output in the range 1080–1200 nm, we measured for each sample the phase-matching wavelength λpm at the temperature of 110°C. The obtained results are shown in Fig. 3(a). It is found that λpm is weakly decreasing when 0 mol%≤ cHf ≤2 mol%; conversely both the sign and magnitude of the curve slope change drastically at higher concentrations. Subsequently, we fixed the operating wavelength at 1130 nm and we measured the phase-matching temperature, obtaining the data shown in Fig. 3(b). The data obtained at fixed OPO wavelength are more reliable than those of Fig. 3(a) that could be affected by some errors arising from variations of the spectral and temporal emission occurring when the OPO is tuned over a wide wavelength range. An evident kink at an Hf concentration slightly above 2mol%, exactly coincident with that reported in Fig. 3(a), is shown by the data of Fig. 3(b).
The SHG measurements are performed in a non-depletion regime for the pump intensity Ip, so that, at phase-matching, the SH intensity Ish is given by:
where npm the index of refraction of the crystal at λpm, and A is an instrumental constant. As an example of the quality of data, we show in Fig. 4(a) the SH intensity versus pump intensity, obtained at phase-matching with the 4 mol% Hf:LN crystal. The dashed line represents a parabolic fit. The dependence of d 31 on the Hf concentration was studied by fixing the operating wavelength at 1120 nm and changing the temperature in order to satisfy the phase-matching condition for each Hf concentration. Considering that the estimated change of npm over the whole temperature variation is about 0.5%, we neglected such an effect in the data analysis. We only performed relative measurements, that is, the nonlinear coefficient of the Hf:cLN crystals was derived by comparison with a congruent LN crystal. Values of L in our experiment were in the range 2–3 mm.
The values of d 31, as derived from the experimental data with an uncertainty of about 5% are given in Fig. 4(b). We see that the normalized d 31 is nearly constant at small dopant concentrations, and starts slightly decreasing above 2mol% (d 31 >0.95 @ 3mol% Hf:cLN). We recall that, by using the Maker-fringe method, Shoji et al.  measured both d 31 and d 33 for Mg-doped congruent LN, finding that doping does not change the nonlinear coefficients for MgO molar concentrations up to 5mol%, that is the threshold concentration for Mg.
It should be recalled that the nonlinear coefficient exploited in PPLN wavelength converters is d 33 and not d 31. However, the chemical-bond model developed by Xue and Zhang  for the calculation of effect of doping on the linear and nonlinear optical properties of crystals shows that the two coefficient have a parallel behavior. This is also confirmed by experimental data about the nonlinear coefficients of Mg:cLN crystals .
The above presented data indicate that the threshold concentration for the removal of Nb ions from Li sites in Hf:cLN crystals is slightly above 2mol%, as measured in the crystal melt. In order to compare this experimental result with the theoretical ones reported in literature it is important to underline that Hf concentration in the grown crystal can be different from that in the melt. In particular, considering a segregation coefficients of 0.77, for an Hf concentration close to 2 mol% , the range 2 – 2.5 mol% of Hf in the melt corresponds to a range of 1.54 – 1.925 of Hf in the grown crystal. In the scientific literature slightly different values of the threshold concentration are proposed, depending on the method employed for its assessment. In the case of tetravalent dopants the charge compensation method predicts a value of the threshold concentration equal to half of the Nb excess concentration, that is: cHf * = 0.5([Nb]-[Li]) . Typically, the Nb excess is in the range between 3 and 4mol%, and thus cHf * is predicted to be, in the crystal, in the range between 1.5 and 2mol%. Anyway, it should also be taken into account that the precise value of the Nb excess depends also on the dopant concentration, as shown in  for the case of Mg:cLN. A different method, based on a chemical bond analysis for the evaluation of the global instability index , sets the value of cHf * in the crystal to 1.7mol%. We conclude that the measured value of cHf * is consistent with the theoretical predictions. It should be noted that the knowledge of the threshold concentration for Hf:cLN crystals is useful not only for wavelength conversion, but also for optical data storage applications. In fact Fe:LN crystals with HfO2 co-doping present enhanced response speed and sensitivity when the HfO2 concentration exceeds cHf * .
Concerning the measurement of the nonlinear coefficient d 31 as a function of cHf, we have found that d 31 is unchanged, within experimental uncertainty, up to the concentration of 2 mol%. At higher concentrations, the experimental data show a slight reduction of the SHG efficiency. Such a decrease can have two distinct causes: an intrinsic one consisting in the modification of crystal properties, introduced by the presence of Hf ions in the LN lattice, and an extrinsic one related to the increase in the crystal disorder due to the technological difficulties of crystal growth in presence of high dopant concentration .
As a conclusion, we have presented a linear and nonlinear optical characterization of Hf:cLN crystals showing that the threshold concentration cHf * for the complete removal of NbLi sites is close to 2mol% and that the nonlinear coefficients are little affected by the Hf-doping. The obtained value of cHf * is much lower then the value derived in  on the basis of photorefractivity measurements, but it is consistent with the successive data presented in . The fact that cHf * is rather low (less then half with respect to cMg *) should facilitate the growth of high quality photorefractive-resistant crystals. The overall picture emerging from the present data and from previous works is that Hf:cLN crystals are very promising candidates for the realization of efficient cascaded wavelength converters working at room temperature.
This work was partially supported by the project FIRB-MIUR RBIN043TKY, and by a grant from Fondazione CARIPLO. The authors would also like to thank L Tartara and A. Poletto for their help in carrying out the measurements.
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