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We report on the confocal Raman characterization of the micro-structural lattice changes induced during the high-repetition rate ultrafast laser writing of buried optical waveguides in lithium niobate (LiNbO3) crystals. While the laser beam focal volume is characterized by a significant lattice expansion together with a high defect concentration, the adjacent waveguide zone is largely free of defects, undergoing only slight rearrangement of the oxygen octahedron in the LiNbO3 lattice. The close proximity of these two zones has been found responsible for the propagation losses of the guided light. Subjacent laser-induced periodic micro-structures have been also observed inside the laser focal volume, and identified with a strong periodic distribution of lattice defects.
©2008 Optical Society of America
1. Introduction
LiNbO3 is one of the most widely used dielectric materials in photonics and optoelectronics due to its excellent nonlinear optical, electro-optical, acousto-optical, piezoelectric and photorefractive properties [1]. In many of these applications compact active components are required that can form into optical waveguides, integrated optical circuits, and other light control systems. LiNbO3 waveguide fabrication processes must therefore induce positive refractive index changes while avoiding crystal defects that increase optical losses or diminish the nonlinear crystal responses. Several methods such as metal and rare earth in-diffusion, ion implantation and proton exchange have, in part, met this criterion by forming low-loss channel waveguides [2–8]. But, these methods still entail complex multi-step procedures that in some cases degrade the LiNbO3 properties [9,10], and in all cases, are limited to forming only near-surface waveguide structures.
Direct laser writing (DLW) has emerged as a unique and flexible method for the fabrication of three-dimensionally (3D) integrated optical devices in glasses and crystals. Buried waveguides are formed by scanning a focused ultrashort pulsed laser beam to induce nonlinear absorption in the transparent media. The DLW technique has outstanding advantages as a single-step and facile process for generating 3D optical devices in processing times of the order of only seconds to minutes depending on the device complexity. The technique was initially demonstrated in glasses [11], and later extended to crystals [12] where extensive laser-writing studies of LiNbO3 have followed [13–22].
Early waveguide laser-writing studies in LiNbO3 centered on low-repetition rate (1–5 kHz) ultrashort-pulsed lasers and optimization of scanning speed, pulse energy, polarization, and temporal pulse width as the writing parameters for tailoring the waveguide properties [13,15,16,18]. Recently, high-repetition rate lasers have been applied over a broader multi-dimensional parameter space for optimizing optical loss, mode symmetry, and processing speed [14,22,23]. Rapid thermal annealing associated with the onset of heat accumulation effects was noted at 700-kHz repetition rate and associated with fewer laser-induced defects [14]. Under these exposure conditions, symmetric waveguides with low 0.6 dB/cm propagation loss in the 1300-nm telecommunication band matched the results of waveguides formed at low repetition rate, but with the significant advantage of a 50-fold faster writing speed of up to 46 mm/s [14].
Despite widespread interest, little is known about the photophysical and photochemical mechanisms responsible for the formation of this laser-induced optical waveguide, and the micro-structural lattice modifications underlying the positive refractive index change. A clear association of the LiNbO3 lattice modifications with the waveguide characteristics together with a detailed morphological characterization would provide fundamental understanding of the processes as well as insights into better controlling the waveguide properties, functionality, and stability that are necessary to broaden the range of LiNbO3 photonic applications. LiNbO3 has a complex crystal structure into which the extreme interactions of ultrashort pulsed lasers can drive defects, incubation processes, local compression and dilatation of the LiNbO3 unit cell, non symmetric heat flow, spontaneous polarization changes, submicron-scale explosions and localized amorphization [14,20,21,24,25]. In this way, a microscopic characterization of the laser-written LiNbO3 waveguides would provide new information about how high repetition-rate ultrashort laser pulses interact with dielectric media in this new processing regime.
In this paper, confocal Raman characterization is systematically applied to low-loss LiNbO3 optical waveguides fabricated by DLW in the regime of high-repetition rate ultrafast processing. A high resolution scanning confocal microscope was used to map the A1(TO) phonon modes in transverse planes to the laser-formed waveguide. A self-consistent interpretation of the frequency shift, linewidth and intensity of each A1(TO) phonon mode to previously identified lattice modifications provided the spatial distribution of defects, changes in unit-cell volume, composition modifications and local disorder. The Raman analysis has been used to elucidate waveguide formation mechanisms and the relationship between waveguide losses and laser irradiation conditions. We also report a periodic modulation of crystal defects that match the optical morphology of previously observed nano-grating structures found in the laser focal volume [14].
2. Experimental details and Raman background
2.1 Waveguide direct laser micro-fabrication
The waveguides under study in this work were fabricated by the DLW technique in z-cut congruent lithium niobate samples (Crystal Technology 99-60011-01). A commercial fiber-chirped-pulse-amplified laser (IMRA America, µJewel D-400-VR) provided ≈600 fs duration pulses at 1045 nm wavelength, and applied at variable repetition rates of 100 kHz up to 1.5 MHz. Waveguides of 9.2 mm length were written in open atmosphere focusing at a position ≈110 µm below the surface and optimized for low propagation losses over exposure conditions of 1 to 80 mm/s writing speed and pulse energies from 120 up to 700 nJ. Sample translation was orthogonal to the laser propagation direction (i.e. perpendicular to the c-axis and along the x-axis of the LiNbO3 lattice). Further details concerning the waveguide fabrication procedure are reported elsewhere [14].
The Raman characterization was focused on the waveguides having the lowest optical loss at the 1300 nm telecom band. A 0.6 dB/cm loss was found for TE polarization (polarized parallel to the crystal y-axis) while the TM modes (polarized parallel to the crystal z-axis) were non-existent or much more lossy. Exposure conditions for this optimum waveguide were a single laser scan at 700 kHz repetition rate, 46 mm/s scan speed, 500 nJ pulse energy, and circularly polarized light [14].
Fig. 1. Optical transmission image of the cross section of the laser modification tracks obtained at the laser exposure conditions of 700 kHz, 46 mm/s and 500 nJ/pulse. The waveguide writing laser was circularly polarized and incident from the top (-c direction), the sample was scanned along the x-direction. Dashed circle indicates the spatial location of the created waveguide whereas Spots 1, 2 and 3 indentifies three modified zones.
Figure 1 shows an optical microscope transmission image of the optimized waveguide in a transverse image. Three distinct modified zones (hereafter spots) appear quasi-periodically along the laser propagation path (top to bottom) inside the sample as labeled (Spot 1, 2 and 3). The Spot 1 position, measured at 106 µm distance from surface (zero position of the vertical scale on Fig. 1), is slightly lower than the expected depth of 110 µm for the laser beam linear focal volume. This discrepancy can be accounted for by the laser power of >0.8 MW, which exceeded the critical power, P c ≈0.3 MW, known for self focusing in lithium niobate at a nearby laser wavelength of 800 nm [21]. Spots 2 and 3 are then expected to be self-formed by the balance of plasma de-focusing from a previous formed spot and self-focusing of the laser pulses in the bulk medium, such as reported, for example, in CaF2 crystal [26]. Further, we note the novel existence of a periodic structure inside the Spot 1, which consists of a laser-induced grating of period ~1.2 µm, as previously reported [14]. The spatial location of the low-loss TE waveguide is not optically visible, but was identified by dual IR-VIS imaging of the waveguide modal profile and surface facet [14]. The waveguide position has also been indicated by a dashed circle (Guiding region) on Fig. 1.
Fig. 2. Typical micro-Raman spectrum recorded from a non-irradiated volume of the LiNbO3 sample and labeled with the three main phonon modes accessible for the x(zz)x Raman configuration.
2.2 Confocal Raman microscopy: Experimental and background
Confocal Raman spectra were recorded with a fiber coupled confocal microscope (Olympus BX-41) integrated with a single-mode 488-nm Argon laser. The laser beam was set to a power of 30 mW and was focused onto the optical-grade polished surface of the sample with 50X MPlan (NA=0.75), and an oil-immersion 100X UPlanSApo (NA=1.4) microscope objective for micron and sub-micron resolution imaging, respectively. The back-scattered Raman signal was collected with the same objective and, after passing through a confocal aperture, was coupled into a 50 µm core fiber connected to a high resolution spectrometer. The sample was positioned on precision xy motorized stages with the written waveguide parallel to the analyzing beam such that a spatial Raman spectral map of the waveguide cross section was generated. A calcite polarizer placed before the microscope objective polarized both the 488 nm laser excitation and the scattered Raman signal along the z-axis (i.e. c-axis) of the LiNbO3 crystal, that in terms of universally adopted Raman notation can be then expressed as x(zz)x configuration [27]. An example of the bulk LiNbO3 Raman spectrum for this arrangement is shown in Fig. 2, and consists mainly of three transverse optical (TO) modes, thus simplifying the ensuing spectral analysis. Following the spectral classification of previous studies [28], the three main phonon modes accessible with this configuration are identified in the figure and summarized as follows:
• A1(TO1) mode.- This phonon mode corresponds to the motion, along the z axis, of Nb ions against the O sub-lattice, while Li ions remain relatively static [28]. This mode is considered especially sensitive to changes in the Nb sub-lattice, and manifested by spectral broadening and low frequency shifting that can quantitatively determine the Li/Nb content ratio as the Li content is locally reduced [28–30].
• A1(TO2) mode.- This mode accounts for displacements along the z axis between Li and Nb ions while the O ions are stationary [28].
• A1(TO4) mode.- This mode corresponds to distortions of the oxygen octahedron only, along the xy plane, and responds with much higher sensitivity to changes in the volume of the LiNbO3 unit cell than the other phonon modes of LiNbO3 [28,31]. This mode is therefore of high relevance in assessing the compaction, and hence the refractive index changes, that may be laser-induced in the LiNbO3 [31]. A reduction in the volume of the unit cell due to a decrease in the lattice parameter shifts this mode to higher frequency [31].
A general response of all the phonon modes of LiNbO3 to the presence of extended defects is a decrease in intensity together with spectral line broadening [32]. This defect-induced reduction of Raman intensity is not restricted to the case of LiNbO3 and has been reported in other similar systems such as KGd(WO4)2 [33]. In addition, the presence of structural disorder in the LiNbO3 lattice (causing density fluctuations) will broaden all the observed Raman modes [34]. As a consequence, Raman spectral analysis is a powerful tool for the detection of local modifications in chemical composition, unit cell volume, ionic displacement, local disorder, and extended defects. Various mechanisms such as local compression/dilatation, compositional change, defect generation, and changes in the spontaneous polarization caused by ionic rearrangement have been previously proposed to underlie changes in the LiNbO3 refractive index [20,28–33]. Each of these mechanisms has a clear signature in the Raman spectrum, and therefore can potentially be isolated by Raman spectral analysis to separate their relative role in the refractive index changes induced by ultrashort pulse laser writing and inferred by waveguide analysis. A summary of the expected Raman spectral response for these various mechanisms is given in Table 1.
Table 1:. Mechanisms of refractive index change in lithium niobate
3. Results and discussion
3.1 Scanning confocal Raman images
Figure 3 shows spatial maps of the intensity, frequency shift and linewidth of the A1(TO1), A1(TO2) and A1(TO4) phonon modes, recorded along the laser irradiated plane as seen on Fig. 1. The Raman shift, bandwidth and intensity values were calculated for each phonon mode by a Lorentzian representation fit of the Raman spectrum recorded at each xy mapping point. A 30 s spectral integration time was used at each point, generating the 250 µm×250 µm map of Fig. 3 in 20 hours of recording time for the 0.5 µm step sizes.
Fig. 3. Spatial map of the intensity, energy shift and spectral linewidth (full width at half maximum; FWHM) of the A1(TO1), A1(TO2) and A1(TO4) phonon modes recorded from the lowest loss laser-formed waveguide (700 kHz, 46 mm/s and 500 nJ). The spatial location of the waveguide (W) and the three laser modified spots (1, 2 and 3) is labeled. Scale bar is 10 µm for all images.
Figure 3 provides further evidence similar to Fig. 1 that the laser-induced micro-structural changes are far away from being spatially homogeneous. The Raman mode intensities (top line images) show two clear ‘damage’ zones labeled Spot 1 (laser focal volume) and Spot 2, which correspond to the spots labeled in Fig. 1. A local reduction in the A1(TO1) phonon mode intensity of up to 48% indicates the formation of a high density of defects both in Spot 1 and Spot 2. This hypothesis is further supported by the strong spectral broadening of the A1(TO1) and A1(TO4) Raman modes (bottom line images in Fig. 3) which indicates a local increase in the lattice disorder at these zones (particularly at Spot 1). This local increase in the density of defects and lattice disorder is consistent with the optical morphology in Fig. 1 and with the underlying assumption that self-focusing of ultrafast laser pulses has created several high intensity excitation focal volumes. Subsequent laser induced nano-explosions are then expected to disrupt the crystal structure at these focal volumes and cause the observed Raman changes. These changes are analogous to the case of high dose ion implantation in LiNbO3 crystals, in which the creation of nano/micro-explosions at the nuclear stopping region leads to a decrease in the Raman intensity and to an increase in the linewidth of the Raman modes [32,33,35].
No appreciable changes in the Raman spectra could be found for the Spot 3 (identified optically in Fig. 1), probably due to the laser energy dissipation into the previous focal spots in the LiNbO3 crystal. Also, there was no appreciable change in the Raman intensity and linewidth at the expected waveguiding position (labeled W in Fig. 3), and thus we can identify this volume to be a defect-free region of positive refractive index change. This observation is in accordance with the low propagation losses (0.6 dB/cm) measured for this waveguide. In addition, and according to References 32 and 36, the absence of any reduction in the Raman signal at the waveguide’s position has also been associated with the preservation of the nonlinear optical properties of the host crystal, presenting a significant advantage here to potentially harness the full nonlinear responses of LiNbO3 in the laser-formed waveguides over other waveguide fabrication procedures that deteriorate the crystal properties [9].
Additional insights in the laser modified volumes are given by the Raman shifts (centre line figures in Fig. 3). Again, the most relevant changes are observed at the main laser focal volume (Spot 1), where a strong decrease in the phonon energies of the A1(TO1) and A1(TO4) modes takes place. However, there is little change in the A1(TO2) phonon mode energy across all the laser modified spots, this indicating that the existing structural changes involve little modification of the corresponding z-axis Nb/Li ions vibration energies [28]. Conversely, the high density of defects in Spot 1 (previously noted by the strong Raman modes intensity decrease) is accompanied by lowered Raman frequencies associated to both the Nb/O z-axis vibrations (A1(TO1) mode) and the oxygen octahedron vibrations within the xy plane (A1(TO4) mode). This combination of Raman modifications has been previously observed in high dose ion-implanted LiNbO3 waveguides, where the nuclear stopping region was characterized with a large density of defects that lead to a local lattice dilatation [5,29]. An equivalent situation has been described by Burghoff et al. who proposed a defect induced lattice expansion at the laser interaction volume [20]. Accordingly to this, we conclude that a large local increase in the LiNbO3 unit cell volume is related to the large densities of defects generated at Spot 1. Note further the opposite response of the phonon energies in the laterally adjacent regions to Spot 1, where the A1(TO1) and A1(TO4) modes have shifted to higher phonon energies (middle row Fig. 3). We attribute this increase to lattice compression along the y axis caused by the lattice dilatation originating in Spot 1. In low repetition rate femtosecond laser writing of Type II waveguides in LiNbO3 crystals, Burghoff et al. have previously associated the positive refractive index change with a similar combination of local lattice compression adjacent to a laser modified volume characterized by a local lattice dilatation [20]. For the present laser tracks, the lattice compression is likely responsible for a local enhancement of the refractive index, but efficient waveguiding has not been observed at these locations, probably because this compression volume is created extremely close to the large defect volume (Spot 1), causing high propagation looses via the evanescent fields.
At the spatial location of the waveguide the Raman images of Fig. 3 indicate that slight decreases in the phonon energies of the A1(TO1) and A1(TO4) frequencies take place, while the A1(TO2) frequency remains unaltered. These phonon energy shifts cannot be attributed to a defect induced local dilatation since neither the Raman intensity nor the linewidth have changed to denote the presence of defects or induced disorder at this location. The absence of any change in the A1(TO2) phonon mode at the waveguide position also eliminates any role for local changes in the Li/Nb ratio content or relative lattice position, since such a change should be accompanied by a frequency shift and an increased linewidth [29]. The observed decrease in the A1(TO1) and A1(TO4) Raman frequencies could be also associated with a local dilatation not assisted by defect formation, but this is unlikely since, according to the Clausius-Mossotti equation, an enlargement of the LiNbO3 unit cell would lead to a decrease in the extraordinary refractive index [20,37], and not to the refractive index increase required for waveguide formation. Since the observed refractive index increase in our study is only in the ordinary index, and we have noted the waveguide region is absent of changes in both the unit volume cell of LiNbO3 and composition, we are left to conclude that the Raman frequency shifts should be attributed to slight ionic rearrangements. The unchanged A1(TO2) response suggests that neither the Nb nor the Li ion lattice positions are distorted, and so, these ionic rearrangements should mainly involve the O ion positions, such as in the oxygen octahedron, along the xy plane. Such O ions displacements can account for the observed frequency shifts of both the A1(TO1) and A1(TO4) phonon modes (Fig. 3). Our assumption is that the oxygen octahedron rearrangement changes the polarizability associated with electronic displacements along this plane, which in turn causes a change in the ordinary refractive index (electric field polarized in the xy plane). A similar assumption of slight ionic rearrangements in the LiNbO3 lattice has been previously accepted as the most plausible mechanism for the origin of waveguide formation under different methods, such as ion implantation [38,39]. Lastly, it is worthy to note that this proposed waveguide formation mechanism entails only very slight Raman modification at the waveguide position and therefore suggests that the LiNbO3 lattice will preserve its original nonlinear and photorefractive properties.
The periodic grating structure noted inside the laser focal volume at Spot 1 in Fig. 1 (see also Fig. 2 in [14]) is a curious and unexplained phenomenon which had not been resolved in the Raman maps of Fig. 3. A higher resolution mode of scanning confocal Raman spectroscopy was therefore applied over the central part of the Spot 1 by using smaller scanning steps of 100 nm, an immersion oil 100X UPlanSApo (NA=1.4) microscope objective, and a reduced confocal aperture of minimum size acceptable in terms of signal-to-noise ratio and exposure time. Figure 4(a) shows the spatial dependence of the Raman intensity of the A1(TO4) mode in the central area of Spot 1. The total measuring time of this image was 35 hours. Figure 4(b) shows the cross-section intensity profile of the A1(TO4) mode along the scan direction indicated by the diagonal arrow in Fig. 4(a). Similar images and Raman intensity profiles have been obtained for the intensity of the A1(TO1) and A1(TO2) phonon modes. These Raman images reveal a strong periodic reduction of the phonon mode intensity that underlies a significant modification in the micro-structural properties of the LiNbO3 lattice. The modification has been observed along three “lines” extending parallel to the 56° cleavage direction of LiNbO3, with an average separation of ≈1.2 µm that matches the periodicity reported previously [14]. No relevant contrast was observable within the signal-to-noise limits of the present Raman spectra to identify periodic modulation in the phonon energy shift or linewidths of any Raman mode. We can attribute the periodic reduction of the Raman signal (Fig. 4) to a periodic density of lattice defects, which extends along the cleavage direction of LiNbO3. This orientation is reasonable since defect creation as well as defect propagation and nucleation are expected to be easier along a crystallographic plane. Further study of such micro- and nano-periodic structural modifications is highly warranted to improve the understanding of basic formation mechanisms and to test for novel optical effects in such spatially modulated media. This understanding would be also required to establish a possible connection between the observed microstructure and the recently reported sub-wavelength nanograting structures induced by ultrashort laser pulses in various other materials [40,43].
Fig. 4. Spatial distribution (a) of the A1(TO4) phonon mode intensity obtained inside Spot 1 for a waveguide yielding the lowest propagation loss (exposure conditions: 700 kHz, 46 mm/s and 500 nJ). The periodic bulk micro-structure is noted by the lowering of the Raman intensity (blue areas), which is clearly periodic in the intensity line profile (b) recorded along the white arrow direction noted in (a).
3.2 Relation between waveguide properties and micro-structural modifications
In this section we have investigated the possible relationship between the micro-structural changes induced in the LiNbO3 lattice and the properties of the obtained waveguides. For this purpose, laser modification tracks were Raman characterized under various exposure conditions of changing writing speed and pulse energy and compared with the changes observed in the waveguide morphology and propagation loss.
In general, waveguide propagation losses in transparent media are associated with the defects created during the fabrication procedure, and include DLW and ion implanted processes in LiNbO3. In the present case of LiNbO3 waveguides fabricated by DLW with ultrafast high repetition rate lasers, the guided light had mode diameter of ≈20 µm which partially overlaps with the area with a high defect concentration in Spot 1 as noted above in the analysis of Figs. 1 and 3 [14]. This spatial overlap has being previously postulated as the main source leading to propagation losses [14], and it follows that the waveguide loss should therefore depend on:
• The spatial overlap of the waveguide mode intensity profile with the laser modified damage zone (Spot 1) which will decrease with the strength of the refractive index modulation but rise with the closer proximity of the defect zone to the waveguide.
• The density of defects induced at the laser modified zone which will increase optical scattering and absorption losses of the overlapping waveguide mode.
The density of defects created in Spot 1 adjacent to the waveguide position was assessed by the reduction in the Raman intensity observed over various laser pulse energy and writing speed conditions. Figure 5(a) shows the Raman intensity of the A1(TO4) phonon mode in Spot 1 as a function of the pulse energy and with repetition rate of 700 kHz and writing speed of 46 mm/s. The large reduction in the Raman intensity for pulse energies below 300 nJ is counterintuitive, predicting higher defect densities as the laser pulse energy is reduced. Two possible mechanisms could be at the origin of this behavior:
• When the pulse energy is reduced, less plasma de-focusing leads to a more confined deposition of pulse energy and hence to a larger density of defects.
• When pulse energy is increased above 300 nJ, a transition from high thermal cycling of laser heating and diffusive cooling to low thermal cycling as heat accumulation effects take hold may provide thermal annealing benefits, for example, via thermal induced defect recombination.
Fig. 5. Intensity of the A1(TO4) phonon mode observed in the first modified zone as a function of the pulse energy (a) for a fixed repetition rate (700 kHz) and translation speed (46 mm/s) and as a function of the writing speed (b) for a fixed pulse energy (500 nJ) and repetition rate (700 kHz). In both graphs, the blue rectangles denote the writing conditions leading to the lowest waveguide propagation losses.
Concomitant with this decreasing density of defects was the generation of low loss waveguides (blue highlighted zone in Fig. 5(a)) only for pulse energies exceeding the same 300 nJ threshold for low defect density. This is, indeed, in agreement with our assumption that the waveguide losses are determined by the density of defects induced in the adjacent damage zone surrounding the waveguide. Figure 5(b) further presents the Raman intensity in Spot 1 as a function of laser writing speed while pulse energy and repetition rate were fixed to 500 nJ and 700 kHz, respectively. Over this range, the waveguide propagation loss was low in the blue highlighted zone of the figure, with a minimum value of 0.6 dB/cm for a writing speed of 46 mm/s. The A1(TO4) Raman intensity was also minimally affected in this same 10 to 50 mm/s low-loss writing zone, but fell at both higher and lower scan speeds where laser interactions may fall respectively into domains of insufficient heat accumulation and over exposure that generated higher densities of defects. This again supports our assertion that the main source of waveguide propagation losses is the spatial overlap of the mode with the adjacent high defect density laser modified zone.
4. Conclusions
In conclusion, we present what is to our knowledge the first systematic study on the micro-structural lattice changes associated with high-repetition rate ultrafast laser-written waveguides in lithium niobate.
From the analysis of the Raman images obtained from the lowest loss waveguides we have been able to determine the spatial location and the extension of local lattice dilatation, defect formation, and ionic rearrangements of the lithium niobate lattice. The relative position of all these changes with respect to the laser focal volume and the waveguide volume has been characterized. We have postulated that the waveguide forms as a consequence of a slight rearrangement of the oxygen octahedron of the LiNbO3 lattice. Although the waveguide has been created in a defect-free zone, its propagating mode can spatially overlap with the nearby directly laser-modified zone, characterized by a large defect concentration, which induces optical losses in the penetrating evanescent tail of the guided mode. This has been further corroborated by the correlation of the micro-structural changes with the waveguide propagation loss obtained over a wide range of laser exposure conditions.
Finally, we have also provided the first Raman study of ultrashort laser-induced bulk periodic micro-structures that reveal periodic modulation of crystal defects oriented along one cleave direction of the lithium niobate crystal.
Acknowledgments
This work was supported by the National Sciences and Engineering Research Council of Canada and the Canadian Institute for Photonic Innovation. A. Ródenas and D. Jaque wish to thank the Spanish Ministerio de Ciencia y Tecnología, the Comunidad Autónoma de Madrid and the Universidad Autónoma de Madrid for financial support (projects MAT2004-03347, MAT2007-6468 and CCG07-UAM/MAT-1861).
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