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Photorefractive non-linear single beam propagation in LiNbO3 waveguides above the optical damage threshold
Optical Materials 33 (2010) 103–106
Contents lists available at ScienceDirect
Optical Materials journal homepage: www.elsevier.com/locate/optmat
Photorefractive non-linear single beam propagation in LiNbO3 waveguides above the optical damage threshold J. Villarroel a,⇑, O. Caballero-Calero a, B. Ramiro b, A. Alcázar b, A. García-Cabañes a, M. Carrascosa a a b
Dep. de Física de Materiales, Universidad Autónoma de Madrid, E-28049 Madrid, Spain Dep. de Aerotecnia, Universidad Politécnica de Madrid, E-28040 Madrid, Spain
a r t i c l e
i n f o
Article history: Received 31 May 2010 Received in revised form 13 July 2010 Accepted 24 August 2010 Available online 24 September 2010 Keywords: Lithium niobate Waveguides Non-linear optical materials Photorefractive materials
a b s t r a c t The effect of photorefractive optical damage on single laser beams in undoped LiNbO3 waveguides has been thoroughly investigated. The experiments have been carried out in soft proton exchanged planar LiNbO3 waveguides covering a wide range of intensities (10–5000 W/cm2). Different non-linear behaviours such as self-defocusing, beam break-up and temporal instabilities have been observed as the light intensity increases. X- and Z-cuts have been compared showing similar behaviours at low intensities although at higher intensities they present relevant differences. Some comments on the influence of these results in LiNbO3 devices have been also included. Ó 2010 Elsevier B.V. All rights reserved.
1. Introduction It is well known that the photorefractive (PR) nonlinearity [1,2] causes beam degradation, i.e. optical damage (OD), during propagation of single beams of moderate or high light intensity [1,3,4]. This effect is particularly strong in some photorefractive crystals such as LiNbO3 with high technological relevance. A considerable effort has been devoted to characterize optical damage and to find methods to reduce it such as Mg or Zn doping [5] or moderate heating (up to 100–150 °C) [6]. However, photorefractive OD is still considered an important drawback of photorefractive materials for developing high power photonic devices such as frequency converters or laser oscillators [7,8]. In fact, very outstanding recent works are devoted to find new methods to get a further reduction of optical damage effects [9,10]. A number of papers investigate the so-called OD threshold in bulk LiNbO3 crystals and waveguides [6,11–13]. Above this light intensity threshold the optical beam undergoes a distortion during propagation that becomes more severe as the light intensity increases. This distortion roughly consists in a self-defocusing effect [1,14,15] that in some cases becomes a more complicated behaviour including asymmetric profiles and temporal instabilities [16,17]. The OD effects are often enhanced in waveguide configuration, of high technological interest, because of the high confined light intensities and propagation lengths that are reached. However, in spite of the negative impact in practical devices, the infor⇑ Corresponding author. E-mail address: [email protected] (J. Villarroel). 0925-3467/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.optmat.2010.08.024
mation about beam distortion in undoped LiNbO3 above the OD threshold, particularly in waveguide configuration, is scarce and sometimes confusing. Then, a further understanding and a detailed characterization of the propagation behaviour should be very useful to control or avoid OD. In addition, from a more positive point of view, a good knowledge of the structure of the spatial non-linear beam dynamics might open perspectives for photonic applications such as beam deflection or optical switching. In this work we address a detailed experimental investigation of the non-linear behaviour of a laser beam propagating in undoped LiNbO3 planar waveguides as a function of light intensity. Two different geometries, polar c-axis parallel (X-cut) and normal (Z-cut) to the guide plane, have been considered to investigate the possible influence of the direction of main charge transport mechanism contributing to the photorefractive effect in LiNbO3, i.e. the photovoltaic effect [2], in the optical beam distortion. A number of qualitatively different behaviours are observed and characterized showing significant differences between both cuts. Finally, we discuss the observed non-linear behaviours and give some comments on their implications on practical LiNbO3 devices. 2. Experimental method X- and Z-cut 1 mm-thick congruent pure LiNbO3 substrates, purchased from Photox Optical Systems (Oxford, UK), have been used to prepare the waveguides. They were fabricated by immersion (24 h) in a benzoic acid melt buffered with 3% lithium benzoate at 300 °C within a sealed ampoule. This treatment (soft proton exchange) produced a highly homogenous layer of a thickness of
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2 lm with a Gaussian-like refractive index profile and a surface index change of Dne = 10 2 at k = 532 nm, supporting two TM or TE modes for Z- or X-cut, respectively. The experimental set-up used to investigate the effect of OD on single beam propagation is depicted in Fig. 1. A 5 W laser beam at 532 nm is focused and coupled inside the waveguide through a rutile prism. At the focus the waist is 80 lm with a focus depth of about 20 mm so that the beam is approximately collimated inside the waveguide where it propagates 4 mm. It is decoupled by a second prism being the output profile analyzed by a beam profiler (CCD head) placed at 8 cm from the output prism. The actual light intensity coupled into the planar waveguide, a key magnitude in the non-linear characterization, is determined using the method proposed in [18] that requires a measurement of the light output power from the second prism. To this end, a small fraction of the output beam power is directed to a photodiode by a beam splitter. From this relative measurement, after calibration, the absolute output power is continuously monitored along the experiments. 3. Results Output beam profiles have been studied in X- and Z-cut optical waveguides for intensities ranging between 10 and 5000 W/cm2. For each light intensity I, the output profiles are monitored after they reach the steady state when it exists. The time response that decreases with I, ranges between 50 and 0.5 s for intensities between 10 and 1000 W/cm2, respectively. These values are typical of the photorefractive response for soft proton exchange waveguides [19]. A variety of degradation patterns have been observed depending on the intensity region. Let us first describe the results for Z-cut waveguides for which nearly no information about beam degradation has been previously reported.
3.1. Z-cut samples In this cut the input beam propagates along the X-axis being free to undergo a distortion along the Y-axis, which is monitored with the beam profiler. In Fig. 2 the output beam profiles for several increasing intensities ranging between 75 and 500 W/cm2 are plotted. At low intensities, below I 200 W/cm2, the beam profile is unaltered i.e. the beam exhibits a linear propagation behaviour. For I > 200 W/cm2 the beam profile, shows a progressively increasing self-defocusing effect up to I 500 W/cm2. Then, at about I 200 W/cm2, would be the OD threshold at which beam degradation effects start to be observed. This value is in good accordance with that previously recorded [13]. In order to better appreciate this self-defocusing behaviour the normalized beam width at half maximum w has been plotted versus the beam intensity (see Fig. 3 solid circles). Note that w monotonously increases up to a width 2.5 times greater than the value for low intensity. Above 500 W/cm2 the beam breaks up showing initially two symmetric filaments. However, as I increases the number of filaments progressively grows as shown in Fig. 4, where a sequence of beam spot images at increasing intensities is presented. Up to 11 filaments can be distinguished exhibiting a clearly symmetric pattern with regard to the central point y = 0. To our knowledge this specific symmetric beam break-up behaviour had not been observed so far in lithium niobate. To investigate in more detail this process, the intensity evolution of the beam profiles up to the generation of four filaments has been recorded and is shown in Fig. 5. As I increases the light beam broadens and a well appears at the centre (profile f) giving rise to a pair of symmetric filaments. At higher
Fig. 1. Schematic of the experimental set-up: L, lens; P, TiO2 prism; D, Photodiode power detector; BS, beam splitter; CCD, CCD detector head of the laser beam profiler. Fig. 3. Full width at half maximum (FWHM) w of the beam intensity profile as a function of its light intensity I for Z- and X-cuts. The w values have been normalized to value corresponding to the lowest intensity. The dashed lines are just guides to the eye.
Fig. 2. Output intensity profiles for a Z-cut waveguide along the guide plane (Yaxis) corresponding to the linear and self-defocusing stages. The light intensities specified in figure are in W/cm2.
Fig. 4. Steady state spot images taken by the beam profiler at increasing light intensities for the Z-cut waveguide illustrating the beam break-up spatial dynamics.
J. Villarroel et al. / Optical Materials 33 (2010) 103–106
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Fig. 7. Time evolution of the light intensity at one fixed point of the beam profile.
Fig. 5. Output intensity profiles for a Z-cut waveguide along the guide plane (Yaxis) at different light intensities (specified in W/cm2 in the figure) showing the beam break-up dynamics.
intensities a new filament grows at the central I minimum (profile h) always keeping the symmetry. The process progresses further following the same pattern: new wells or peaks always appear at the centre. Furthermore, the process is reversible, so that when I is reduced back the beam filaments disappear following the opposite light intensity evolution. 3.2. X-cut samples Similar experiments have also been carried out in X-cut waveguides. Now light propagates along the Y-axis and distorts along the polar Z-axis. The results are shown in Fig. 6 where some of the observed output beam spots (a) and profiles (b) are presented. Again the same regions of linear behaviour, self-defocusing and beam break-up can be distinguished but the whole sequence is shifted to slightly lower intensities. In fact, it can be seen from Fig. 6b that the light intensity threshold separating the linear behaviour from self-defocusing appears at a similar but slightly lower intensity of about I 150 W/cm2. The self-defocusing process is analogous to that of Z-cut guides (profiles f, g) with similar a beam broaden-
Fig. 6. (a) Spot images obtained by the beam profiler at increasing light intensities for the X-cut waveguide. (b) Output intensity profile along the guide plane (Z-axis). The light intensities specified in the figure are in W/cm2.
ing factor better illustrated in Fig. 3 (solid triangles). Then, beam break-up is clearly observed up to four filaments (profiles h–j) showing roughly the same separation between filaments than in Fig. 5 (see profiles g, k, Fig. 5 and profiles h, j, Fig. 6b). However, significant differences with Z-cut can be seen in this region. Symmetry is no longer kept and filaments for positive Z-values become broader and noisier. Finally, at still higher intensities I > 3000 W/cm2, and at difference with the Z-cut, temporal instabilities, probably chaotic, appear in the asymmetric profile. To illustrate this behaviour we have recorded, and plotted in Fig. 7, the evolution of the light intensity at a fixed point of the profile. Similar dynamics are found at other profile points. Moreover, at variance with the Z-cut, the intensity evolution is not reversible and when I is reduced back to low intensity (linear behaviour region) the beam remains distorted for time periods much higher than the photorefractive time response (at least after 1 h). 4. Discussion and conclusions Let us briefly summarize and discuss the obtained results. Our study allows distinguishing a rich variety of non-linear beam behaviours (self-defocusing, beam break-up and temporal instabilities) that appear as the intensity increases. Self-defocusing and temporal instabilities were previously observed in bulk [6] and X-cut lithium niobate waveguides [16] whereas to our knowledge the observed beam break-up had not been reported and characterized so far. Besides, in this work the range of intensities and the influence of the substrate orientation (X or Z-cut) were characterized. Beam break-up is typical of positive non-linear refractive index changes leading to self-focusing and, due to modulational instabilities, to filamentation effects [20]. In fact, a similar sequence to that observed in this work but with a first step of self-focusing instead of self-defocusing has been reported in SBN planar waveguides [21]. There, the authors invoke a quite complex thermal nonlinearity combining thermooptic and piroelectric effects to qualitatively explain the phenomenon. In our case, the optical absorption of our undoped LiNbO3 waveguides is so low (optical losses are lower than 0.3 dB/cm) that thermal effects can be discarded and only the photorefractive non linearity can be responsible for the observed behaviour. The origin of the obtained differences between X- and Z-cut i.e. symmetric versus asymmetric break-up patterns and appearance of temporal instabilities also deserves some attention. In the first geometry the polar axis and so, the photovoltaic current, is inside the waveguide plane, whereas in the Z-cut it is perpendicular to the guide. Then, only this latter configuration is symmetric with regard to the polar axis, in good correlation with the symmetry properties of the observed profiles. Moreover, asymmetrical selfdefocusing has been explained invoking directional beam amplification via noise gratings in some PR crystals [16,22]. This should be the case in our X-cut waveguides, where according to a two-centre PR model, recently reported for undoped LiNbO3 [23], the directional beam amplification coefficient C for grating K-vectors parallel to the c-axis dramatically increases with I for values in the range (200–10,000 W/cm2), just covering our regions of asymmetric break-up and time instabilities (see Fig. 6b.) This dramatic increase
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of C can also explain the existence in X-cut of a chaotic evolution as due to multi-beam coupling via these noise PR gratings with spatial periods of about a few microns. However, in Z-cut the guide thickness along the Z-axis is of only 2–3 lm and there is not enough space to record those noise gratings avoiding asymmetric effects and instabilities. Furthermore, the absence of noise gratings is consistent with the higher stability and reproducibility showed by this geometry that allows observing clearly the stage of symmetric break-up. Anyhow, to definitely clarify the origin of the observed behaviours detailed theoretical calculations of beam propagation in photorefractive LiNbO3 waveguides should be addressed. Further work in this direction using the cited two-centre PR model [23] for both Z- and X-cut configurations is now in progress. Regarding optical devices such as frequency converters, laser cavities or even holographic applications the impact of the variety of non-linear beam behaviours could be very different. While in the self-defocusing region the beam only moderately spreads lowering its peak intensity, at higher intensities the non-linear effects should be much more dramatic for any device, particularly in Xcut guides where temporal instabilities develop. Finally, the study shows the more stable, reversible and reproducible performance of Z-cut planar configurations so that they are very likely more suitable to control negative effects of optical damage or even to take advantage of it. For instance, the observed non-linear behaviour generates a refractive index profile that would affect the propagation of a second probe beam. This effect might be potentially used for applications such as beam deflection or switching in the line of some reported proposals [24]. Acknowledgements This work was supported by the Ministerio de Ciencia e Innovacion (MICINN) under grant MAT2008-06794-C03. J. Villarroel acknowledges his FPI fellowship from MICINN. We also thank Prof. J.M. Cabrera for useful discussions and comments.
References [1] A. Ashkin, G.D. Boyd, J.M. Dziedzic, R.G. Smith, A.A. Ballman, J.J. Levinstein, K. Nassau, Appl. Phys. Lett. 9 (1966) 72–74. [2] F. Agulló-López, G.F. Calvo, M. Carrascosa, in: P. Günter, J.P. Huignard (Eds.), Photorefractive Materials and their Applications 1, Basic Effects, Springer, New York, 2006, pp. 43–82. [3] D. Kip, M. Wesner, in: P. Günter, J.P. Huignard (Eds.), Photorefractive Materials and their Applications 1, Basic Effects, Springer, New York, 2006, pp. 281–315. [4] T. Volk, L. Wöhlecke, Lithium, Niobate Defects, Photorefraction and Ferroelectric Switching, Springer Series in Materials Science, Berlin Heidelberg, 2008. p. 115. [5] T. Volk, N. Rubinina, M. Wöhlecke, J. Opt, Soc. Am. B 11 (1994) 1681–1687. [6] J. Rams, A. Alcazar-de-Velasco, M. Carrascosa, J.M. Cabrera, F. Agulló-López, Opt. Commun. 178 (2000) 211–216. [7] L. Arizmendi, Phys. Stat. Sol. (a) 201 (2004) 253–283. [8] C.Q. Xu, H. Okayama, Y. Ogawa, J. Appl. Phys. 87 (2000) 3203–3206. [9] M. Falk, Th. Woike, K. Buse, Appl. Phys. Lett. 90 (2007) 251912. [10] M. Kösters, B. Sturmann, P. Werheit, D. Haertle, K. Buse, Nature Photon. 3 (2009) 510–513. [11] E. Glavas, J.M. Cabrera, P.D. Townsend, J. Phys. D: Appl. Phys. 22 (1989) 611–616. [12] O. Caballero-Calero, A. Alcázar, A. García-Cabañes, J.M. Cabrera, M. Carrascosa, J. Appl. Phys. 100 (2006) 93103. [13] F. Luedtke, J. Villarroel, A. García-Cabañes, K. Buse, M. Carrascosa, Opt. Express 17 (2009) 658–665. [14] Y. Kong, J. Wen, H. Wang, Appl. Phys. Lett. 66 (1995) 280–282. [15] R. Mouras, S.M. Kostriskii, P. Bourson, M. Aillerie, M.D. Fontana, Opt. Mat. 18 (2001) 127–130. [16] A. Alcazar de Velasco, J. Rams, J.M. Cabrera, F. Agulló-Lopez, Appl. Phys. B 68 (1999) 989–993. [17] R. Jerominek, R. Tremblay, C. Delisle, J. Light. Techno. LT-3 (1985) 1105–1109. [18] O. Caballero-Calero, J. Carnicero, A. Alcazar, G. de la Paliza, A. García-Cabañes, M. Carrascosa, J.M. Cabrera, J. Appl. Phys. 102 (2007) 074509. [19] J. Villarroel, M. Carrascosa, A. García-Cabañes, J.M. Cabrera, J. Opt. A: Pure Appl. Opt. 10 (2008) 104008. [20] R.W. Boyd, Nonlinear Optics, Elsevier, Burlington, MA, 2008. [21] D. Kip, E. Krätzig, V. Shandarov, P. Moretti, Opt. Lett. 23 (1998) 343–534. [22] M. Goulkov, K. Bastwöste, S. Möller, M. Imlau, M. Wöhlecke, J. Phys.: Condens. Matter 20 (2008) 075225. [23] M. Carrascosa, J. Villarroel, J. Carnicero, A. García-Cabañes, J.M. Cabrera, Opt. Express 16 (2008) 115–120. [24] D. Kip, M. Wesner, E. Krätzig, V. Shandarov, P. Moretti, Appl. Phys. Lett. 72 (1998) 1960–1962.
Contents lists available at ScienceDirect
Optical Materials journal homepage: www.elsevier.com/locate/optmat
Photorefractive non-linear single beam propagation in LiNbO3 waveguides above the optical damage threshold J. Villarroel a,⇑, O. Caballero-Calero a, B. Ramiro b, A. Alcázar b, A. García-Cabañes a, M. Carrascosa a a b
Dep. de Física de Materiales, Universidad Autónoma de Madrid, E-28049 Madrid, Spain Dep. de Aerotecnia, Universidad Politécnica de Madrid, E-28040 Madrid, Spain
a r t i c l e
i n f o
Article history: Received 31 May 2010 Received in revised form 13 July 2010 Accepted 24 August 2010 Available online 24 September 2010 Keywords: Lithium niobate Waveguides Non-linear optical materials Photorefractive materials
a b s t r a c t The effect of photorefractive optical damage on single laser beams in undoped LiNbO3 waveguides has been thoroughly investigated. The experiments have been carried out in soft proton exchanged planar LiNbO3 waveguides covering a wide range of intensities (10–5000 W/cm2). Different non-linear behaviours such as self-defocusing, beam break-up and temporal instabilities have been observed as the light intensity increases. X- and Z-cuts have been compared showing similar behaviours at low intensities although at higher intensities they present relevant differences. Some comments on the influence of these results in LiNbO3 devices have been also included. Ó 2010 Elsevier B.V. All rights reserved.
1. Introduction It is well known that the photorefractive (PR) nonlinearity [1,2] causes beam degradation, i.e. optical damage (OD), during propagation of single beams of moderate or high light intensity [1,3,4]. This effect is particularly strong in some photorefractive crystals such as LiNbO3 with high technological relevance. A considerable effort has been devoted to characterize optical damage and to find methods to reduce it such as Mg or Zn doping [5] or moderate heating (up to 100–150 °C) [6]. However, photorefractive OD is still considered an important drawback of photorefractive materials for developing high power photonic devices such as frequency converters or laser oscillators [7,8]. In fact, very outstanding recent works are devoted to find new methods to get a further reduction of optical damage effects [9,10]. A number of papers investigate the so-called OD threshold in bulk LiNbO3 crystals and waveguides [6,11–13]. Above this light intensity threshold the optical beam undergoes a distortion during propagation that becomes more severe as the light intensity increases. This distortion roughly consists in a self-defocusing effect [1,14,15] that in some cases becomes a more complicated behaviour including asymmetric profiles and temporal instabilities [16,17]. The OD effects are often enhanced in waveguide configuration, of high technological interest, because of the high confined light intensities and propagation lengths that are reached. However, in spite of the negative impact in practical devices, the infor⇑ Corresponding author. E-mail address: [email protected] (J. Villarroel). 0925-3467/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.optmat.2010.08.024
mation about beam distortion in undoped LiNbO3 above the OD threshold, particularly in waveguide configuration, is scarce and sometimes confusing. Then, a further understanding and a detailed characterization of the propagation behaviour should be very useful to control or avoid OD. In addition, from a more positive point of view, a good knowledge of the structure of the spatial non-linear beam dynamics might open perspectives for photonic applications such as beam deflection or optical switching. In this work we address a detailed experimental investigation of the non-linear behaviour of a laser beam propagating in undoped LiNbO3 planar waveguides as a function of light intensity. Two different geometries, polar c-axis parallel (X-cut) and normal (Z-cut) to the guide plane, have been considered to investigate the possible influence of the direction of main charge transport mechanism contributing to the photorefractive effect in LiNbO3, i.e. the photovoltaic effect [2], in the optical beam distortion. A number of qualitatively different behaviours are observed and characterized showing significant differences between both cuts. Finally, we discuss the observed non-linear behaviours and give some comments on their implications on practical LiNbO3 devices. 2. Experimental method X- and Z-cut 1 mm-thick congruent pure LiNbO3 substrates, purchased from Photox Optical Systems (Oxford, UK), have been used to prepare the waveguides. They were fabricated by immersion (24 h) in a benzoic acid melt buffered with 3% lithium benzoate at 300 °C within a sealed ampoule. This treatment (soft proton exchange) produced a highly homogenous layer of a thickness of
104
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2 lm with a Gaussian-like refractive index profile and a surface index change of Dne = 10 2 at k = 532 nm, supporting two TM or TE modes for Z- or X-cut, respectively. The experimental set-up used to investigate the effect of OD on single beam propagation is depicted in Fig. 1. A 5 W laser beam at 532 nm is focused and coupled inside the waveguide through a rutile prism. At the focus the waist is 80 lm with a focus depth of about 20 mm so that the beam is approximately collimated inside the waveguide where it propagates 4 mm. It is decoupled by a second prism being the output profile analyzed by a beam profiler (CCD head) placed at 8 cm from the output prism. The actual light intensity coupled into the planar waveguide, a key magnitude in the non-linear characterization, is determined using the method proposed in [18] that requires a measurement of the light output power from the second prism. To this end, a small fraction of the output beam power is directed to a photodiode by a beam splitter. From this relative measurement, after calibration, the absolute output power is continuously monitored along the experiments. 3. Results Output beam profiles have been studied in X- and Z-cut optical waveguides for intensities ranging between 10 and 5000 W/cm2. For each light intensity I, the output profiles are monitored after they reach the steady state when it exists. The time response that decreases with I, ranges between 50 and 0.5 s for intensities between 10 and 1000 W/cm2, respectively. These values are typical of the photorefractive response for soft proton exchange waveguides [19]. A variety of degradation patterns have been observed depending on the intensity region. Let us first describe the results for Z-cut waveguides for which nearly no information about beam degradation has been previously reported.
3.1. Z-cut samples In this cut the input beam propagates along the X-axis being free to undergo a distortion along the Y-axis, which is monitored with the beam profiler. In Fig. 2 the output beam profiles for several increasing intensities ranging between 75 and 500 W/cm2 are plotted. At low intensities, below I 200 W/cm2, the beam profile is unaltered i.e. the beam exhibits a linear propagation behaviour. For I > 200 W/cm2 the beam profile, shows a progressively increasing self-defocusing effect up to I 500 W/cm2. Then, at about I 200 W/cm2, would be the OD threshold at which beam degradation effects start to be observed. This value is in good accordance with that previously recorded [13]. In order to better appreciate this self-defocusing behaviour the normalized beam width at half maximum w has been plotted versus the beam intensity (see Fig. 3 solid circles). Note that w monotonously increases up to a width 2.5 times greater than the value for low intensity. Above 500 W/cm2 the beam breaks up showing initially two symmetric filaments. However, as I increases the number of filaments progressively grows as shown in Fig. 4, where a sequence of beam spot images at increasing intensities is presented. Up to 11 filaments can be distinguished exhibiting a clearly symmetric pattern with regard to the central point y = 0. To our knowledge this specific symmetric beam break-up behaviour had not been observed so far in lithium niobate. To investigate in more detail this process, the intensity evolution of the beam profiles up to the generation of four filaments has been recorded and is shown in Fig. 5. As I increases the light beam broadens and a well appears at the centre (profile f) giving rise to a pair of symmetric filaments. At higher
Fig. 1. Schematic of the experimental set-up: L, lens; P, TiO2 prism; D, Photodiode power detector; BS, beam splitter; CCD, CCD detector head of the laser beam profiler. Fig. 3. Full width at half maximum (FWHM) w of the beam intensity profile as a function of its light intensity I for Z- and X-cuts. The w values have been normalized to value corresponding to the lowest intensity. The dashed lines are just guides to the eye.
Fig. 2. Output intensity profiles for a Z-cut waveguide along the guide plane (Yaxis) corresponding to the linear and self-defocusing stages. The light intensities specified in figure are in W/cm2.
Fig. 4. Steady state spot images taken by the beam profiler at increasing light intensities for the Z-cut waveguide illustrating the beam break-up spatial dynamics.
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Fig. 7. Time evolution of the light intensity at one fixed point of the beam profile.
Fig. 5. Output intensity profiles for a Z-cut waveguide along the guide plane (Yaxis) at different light intensities (specified in W/cm2 in the figure) showing the beam break-up dynamics.
intensities a new filament grows at the central I minimum (profile h) always keeping the symmetry. The process progresses further following the same pattern: new wells or peaks always appear at the centre. Furthermore, the process is reversible, so that when I is reduced back the beam filaments disappear following the opposite light intensity evolution. 3.2. X-cut samples Similar experiments have also been carried out in X-cut waveguides. Now light propagates along the Y-axis and distorts along the polar Z-axis. The results are shown in Fig. 6 where some of the observed output beam spots (a) and profiles (b) are presented. Again the same regions of linear behaviour, self-defocusing and beam break-up can be distinguished but the whole sequence is shifted to slightly lower intensities. In fact, it can be seen from Fig. 6b that the light intensity threshold separating the linear behaviour from self-defocusing appears at a similar but slightly lower intensity of about I 150 W/cm2. The self-defocusing process is analogous to that of Z-cut guides (profiles f, g) with similar a beam broaden-
Fig. 6. (a) Spot images obtained by the beam profiler at increasing light intensities for the X-cut waveguide. (b) Output intensity profile along the guide plane (Z-axis). The light intensities specified in the figure are in W/cm2.
ing factor better illustrated in Fig. 3 (solid triangles). Then, beam break-up is clearly observed up to four filaments (profiles h–j) showing roughly the same separation between filaments than in Fig. 5 (see profiles g, k, Fig. 5 and profiles h, j, Fig. 6b). However, significant differences with Z-cut can be seen in this region. Symmetry is no longer kept and filaments for positive Z-values become broader and noisier. Finally, at still higher intensities I > 3000 W/cm2, and at difference with the Z-cut, temporal instabilities, probably chaotic, appear in the asymmetric profile. To illustrate this behaviour we have recorded, and plotted in Fig. 7, the evolution of the light intensity at a fixed point of the profile. Similar dynamics are found at other profile points. Moreover, at variance with the Z-cut, the intensity evolution is not reversible and when I is reduced back to low intensity (linear behaviour region) the beam remains distorted for time periods much higher than the photorefractive time response (at least after 1 h). 4. Discussion and conclusions Let us briefly summarize and discuss the obtained results. Our study allows distinguishing a rich variety of non-linear beam behaviours (self-defocusing, beam break-up and temporal instabilities) that appear as the intensity increases. Self-defocusing and temporal instabilities were previously observed in bulk [6] and X-cut lithium niobate waveguides [16] whereas to our knowledge the observed beam break-up had not been reported and characterized so far. Besides, in this work the range of intensities and the influence of the substrate orientation (X or Z-cut) were characterized. Beam break-up is typical of positive non-linear refractive index changes leading to self-focusing and, due to modulational instabilities, to filamentation effects [20]. In fact, a similar sequence to that observed in this work but with a first step of self-focusing instead of self-defocusing has been reported in SBN planar waveguides [21]. There, the authors invoke a quite complex thermal nonlinearity combining thermooptic and piroelectric effects to qualitatively explain the phenomenon. In our case, the optical absorption of our undoped LiNbO3 waveguides is so low (optical losses are lower than 0.3 dB/cm) that thermal effects can be discarded and only the photorefractive non linearity can be responsible for the observed behaviour. The origin of the obtained differences between X- and Z-cut i.e. symmetric versus asymmetric break-up patterns and appearance of temporal instabilities also deserves some attention. In the first geometry the polar axis and so, the photovoltaic current, is inside the waveguide plane, whereas in the Z-cut it is perpendicular to the guide. Then, only this latter configuration is symmetric with regard to the polar axis, in good correlation with the symmetry properties of the observed profiles. Moreover, asymmetrical selfdefocusing has been explained invoking directional beam amplification via noise gratings in some PR crystals [16,22]. This should be the case in our X-cut waveguides, where according to a two-centre PR model, recently reported for undoped LiNbO3 [23], the directional beam amplification coefficient C for grating K-vectors parallel to the c-axis dramatically increases with I for values in the range (200–10,000 W/cm2), just covering our regions of asymmetric break-up and time instabilities (see Fig. 6b.) This dramatic increase
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of C can also explain the existence in X-cut of a chaotic evolution as due to multi-beam coupling via these noise PR gratings with spatial periods of about a few microns. However, in Z-cut the guide thickness along the Z-axis is of only 2–3 lm and there is not enough space to record those noise gratings avoiding asymmetric effects and instabilities. Furthermore, the absence of noise gratings is consistent with the higher stability and reproducibility showed by this geometry that allows observing clearly the stage of symmetric break-up. Anyhow, to definitely clarify the origin of the observed behaviours detailed theoretical calculations of beam propagation in photorefractive LiNbO3 waveguides should be addressed. Further work in this direction using the cited two-centre PR model [23] for both Z- and X-cut configurations is now in progress. Regarding optical devices such as frequency converters, laser cavities or even holographic applications the impact of the variety of non-linear beam behaviours could be very different. While in the self-defocusing region the beam only moderately spreads lowering its peak intensity, at higher intensities the non-linear effects should be much more dramatic for any device, particularly in Xcut guides where temporal instabilities develop. Finally, the study shows the more stable, reversible and reproducible performance of Z-cut planar configurations so that they are very likely more suitable to control negative effects of optical damage or even to take advantage of it. For instance, the observed non-linear behaviour generates a refractive index profile that would affect the propagation of a second probe beam. This effect might be potentially used for applications such as beam deflection or switching in the line of some reported proposals [24]. Acknowledgements This work was supported by the Ministerio de Ciencia e Innovacion (MICINN) under grant MAT2008-06794-C03. J. Villarroel acknowledges his FPI fellowship from MICINN. We also thank Prof. J.M. Cabrera for useful discussions and comments.
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