N. Fressengeas a b, J. Maufoy b, D. Wolfersberger a b & G. Kugel a a MOPS/CLOES/Université de Metz-Supélec. Published online: 07 Mar 2011.

Transcription

1 This article was downloaded by: [INASP - Pakistan (PERI)] On: 21 March 2014, At: 23:58 Publisher: Taylor & Francis Informa Ltd Registered in England and Wales Registered Number: Registered office: Mortimer House, Mortimer Street, London W1T 3JH, UK Ferroelectrics Publication details, including instructions for authors and subscription information: Experimental transient self-focusing in Bi 12 TiO 20 crystal N. Fressengeas a b, J. Maufoy b, D. Wolfersberger a b & G. Kugel a a MOPS/CLOES/Université de Metz-Supélec b SEL/Supélec 2 rue E. Belin, 57078, METZ Cedex 3, FRANCE Published online: 07 Mar To cite this article: N. Fressengeas, J. Maufoy, D. Wolfersberger & G. Kugel (1997) Experimental transient self-focusing in Bi 12 TiO 20 crystal, Ferroelectrics, 202:1, , DOI: / To link to this article: PLEASE SCROLL DOWN FOR ARTICLE Taylor & Francis makes every effort to ensure the accuracy of all the information (the Content ) contained in the publications on our platform. However, Taylor & Francis, our agents, and our licensors make no representations or warranties whatsoever as to the accuracy, completeness, or suitability for any purpose of the Content. Any opinions and views expressed in this publication are the opinions and views of the authors, and are not the views of or endorsed by Taylor & Francis. The accuracy of the Content should not be relied upon and should be independently verified with primary sources of information. Taylor and Francis shall not be liable for any losses, actions, claims, proceedings, demands, costs, expenses, damages, and other liabilities whatsoever or howsoever caused arising directly or indirectly in connection with, in relation to or arising out of the use of the Content. This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden. Terms & Conditions of access and use can be found at page/terms-and-conditions

2 Ferrouk~rrrrr Vol 202. pp Reprints avdilahk directly from the publisher Photocopying permitted b) license only!c 1997 OPA (Overseas Publishers Association) Amsterdain B.V Published undcr license in The Netherlands under thc Gordon and Bredrh Science Publisher., iniprint Printed in lndiii EXPERIMENTAL TRANSIENT SELF-FOCUSING IN Bi12TiOzo CRYSTAL N.FRESSENGEAS*", J.MAUFOY", D.WOLFERSBERGER*", G.KUGEL* *MOPS/CLOES/Universite de Metz-Supelec "SEL/Supdec 2 rue E.Belin, METZ Cedex 3, FRANCE (Recriced2.l August 1996: In,finalform 3 March Abstract An experimental study of both transient and steady state bi-dimensional photorefractive bright spatial solitons in Bi12TiOzo is presented. The results are compared to previous theoretical work, showing qualitative agreement concerning both the transient and the steady soliton widths. INTRODUCTION Photorefractive materials have recently been the focus of many theoretical and experimental studies regarding their self-focusing properties. In particular, bright spatial solitons have been predi~ted''~ and ~bserved~'~ in properly biased photorefractive media. They are quite different from their Kerr counterpart" for they can be obtained at low power levels on the order of the rnw/cmz and because they are stable in two transverse dimensions". The major drawback of the photorefractive effect is its slow time response and some theoretical studies have been recently conducted on the temporal behavior of the self-focusing process'2s". According to theoretical prediction, the self-focusing process is highly sensitive to the thermal carrier generation and to the dark conductivity: these effects are essential in order to allow charge transport is the dark regions around the beam ; it prevents the electric field to be uniformly screened out to zero on the spot of the beam. These dark phenomena can be modeled as the result of a (( dark irradiance )): a fictitious uniform illumination of the crystal generating the same charge generation and transport as the thermal effects do. [509]1193

3 19445 I 01 N. FRESSENGEAS et al. In this paper, the results of an experimental study of the behaviors of both steadystate and transient self-focusing as a function of the ratio of the beam peak power over the dark irradiance are presented, providing a partial experimental validation of the above theoretical considerations. THEORETICAL BACKGROUND The self-focusing process sterns from a partial masking of an externally applied electric field at the spot of the beam, inducing, via the Pockels effect, a refractive index change. If the electric field is properly polarized, the sensitivity of the refractive index upon the electric field is negative. This induces an increase in the refiactive index, namely, a waveguide. The analytical expression of the space charge field temporal evolution can be derived from the Kukhtarev model14 restricted to one dimension and under some assumptions detailed in Ref 13. The space-charge field temporal evolution is plotted in ESC FIGURE 1 Normalized space-charge field evolution for a centered Gaussian beam, for the normalized time t/t, = 0,0.1,0.2, 0.5, 1, 2, 5, 10, 00 from top to bottom, with respect to the normalized transverse dimension X. T, = Z/Zd is the normalization constant with Z being the soliton energy density defined in Ref. 13 and Zd the dark irradiance.

4 TRANSIENT SELF-FOCUSING Bi,,TiOz,, [511]/195 Fig. 1 as obtained from an analytical expression expressed in Ref. 13. A Wave Propagation Equation (WPE) can thus be derived from the expression of the space charge field, knowing the behavior of the refractive index change through the Pockels effect. Assuming the WE allows the propagation of spatial solitons, the soliton Half Width at Half Maximum (HWHM) can be numerically evaluated. Steady-state The width of the induced waveguide depends on the trapped charge camers distribution. If the dark irradiance is considered null, all the charge carriers are trapped in the dark regions : the electric field is zero on the spot of the beam, inducing a clipped waveguide too wide to properly confine the beam. On the contrary, it is straightforward that if the dark irradiance is too intense with respect to the beam itself, the charge carriers cannot be trapped and no waveguide is induced. Therefore, an optimal waveguide is induced if the ratio of the beam peak optical power over the dark irradiance is correct. The OC IOOO. Peak Dower to dark irradiance ratio r FIGURE 2 Normalized soliton Half Width at Half Maximum (HWHM) as a function of the beam peak power to dark irradiance ratio r. The plain line shows the steady state whereas the dotted line shows the minimum HWHM achieved during transient state. The normalization constant is an arbitrary length as defined in Ref. 13.

5 196/[512] N. FRESSENGEAS ef al. theoretical predictions of Refs. 13 and 15 suggest that this ratio should be equal to unity, for the self-focusing process to be the strongest ( i.e. soliton to be the narrowest ) as is shown in Fig. 2. However, in order to achieve self-focusing with a beam too powerful in comparison with the dark irradiance, it is possible to artificially raise the latter with a continuous background light, incoherent with the beam itself. Transient state If the beam peak power is larger than the dark irradiance -whether it is natural or artificially raised -, it is sufficient to partially saturate the photorefractive effect and to induce a waveguide too wide to confine the beam. However, the process of photorefractive saturation is not immediate. At the time the external electric field is turned on, the process of saturation begins. Fig. 1 shows the theoretically evaluated evolution of the space-charge field13 when the charge diffusion mechanism of transport can be neglected : starting from a uniform refractive index, the waveguide deepens and broadens with time. While neither the initial nor the final state is able to trap the beam, our calculations show that there is a transient shape of the waveguide that is exactly the width of the beam. Therefore, the beam should undergo transient stronger self-focusing p=~mw equipped with beam cleaner and expander Bi,,TiO,, Band-pass filter tunedto633 Photodetector He-Nelaser P=4mW Rotating polarizers Focusing lenses 1 mmaperture (circular hole or slit) h=633nm FIGURE 3 Experimental apparatus.

6 and then relax to a less focused state. TRANSIENT SELF-FOCUSING Bi,,TiO,, [513]/197 EXPERIMENTAL SETUP Our experiments were conducted using a linearly polarized conventional 4 mw 633 nm He-Ne laser, equipped with a monomode fiber beam cleaner, focused on a BilzTiOzo photorefractive crystal'6 to a beam waist of 30pm. As suggested in the previous section, a continuous background illumination, incoherent with the He-Ne laser, is provided by a 670 nm laser diode equipped with a beam cleaner and expander, shedding its light upon the whole crystal. A 7.5 kv/cm external electric field is applied to the crystal, in the direction of the beam polarization, in order to induce a drift charge transport mechanism. The measurement method is shown in Fig. 3. It consists of a far field spatial filtering of the beam. If a spatial soliton state is reached, the beam outputs from the crystal with a beam waist identical to the input waist and a plane wave surface*. Simple Gaussian beam considerations show that the light power passing through a hole of the 3. Time Electric field turned on I I I I I FIGURE 4 Typical raw measurement: the initial state is the rest state, that we consider as homogeneous.

7 N. FRESSENGEAS et al. correct diameter ( 1 mm ) in the far field region ( 120 mm away from the crystal ) is directly proportional to the output beam waisti3. The light passing through that hole is collected on a photodetector using a lens. The optical power measured by the photodetector is proportional to the output beam diameter. EXPERZMENTAL RESULTS The raw measurement of the optical power transmitted through the aperture yields curves presented as typical measurement in Fig. 4. The results are compared to the notions introduced in the theoretical section. The value corresponding to the initial state of the unperturbed crystal gives a reference to which to compare self-focused states. We see two other characteristic values, one corresponding to the steady state and a minimum value characteristic of the transient state, corresponding to the minimum diameter achieved during the transient. * I a I I I be** O4.01 I I r FIGURE 5 Output beam waist normalized to the input one as a function of the peak power to dark irradiance ratio r, measured using the circular hole spatial filtering method. The squares show the steady-state and the circles show the transient. The solid line shows the output beam waist resulting of linear diffraction.

8 TRANSIENT SELF-FOCUSING Bi,,TiO, [5 15yl99 Overall focusing results The measurement through a circular hole yields a measure of the overall beam selffocusing, neglecting a potential asymmetry of the process, making particularly no distinction between potentially different focusing in the direction of the electric field or perpendicular to it. Fig. 5 shows the output beam diameter as a hnction of the beam peak power to dark irradiance ratio r. It confirms the predictions that the steady-state overall self-focusing is the highest for r around 1 '', 15. Fig. 2 shows the predictions made by Refs. 13 and 15 for the spatial soliton HWHM. It is important to understand that the predictions shown in Fig. 2 carry the assumption that a spatial soliton state is reached. On the opposite, Fig. 5 shows the half width of the beam on the output face of the crystal, providing an analysis of the self-focusing process rather than of the spatial soliton phenomenon. Although these two phenomena are closely linked, they are not identical. Figs. 2 and 5, though they are both quantitative, can therefore only be compared qualitatively. For instance, while the expected soliton diameter widens, the expected output beam diameter cannot be much wider than the input one, inducing the clipping of the curve in Fig. 5. Fig. 5 shows that the transient beam diameter is constant if the beam is more powerful than the dark irradiance, as predicted earlier13, 17. This is only true for r<5. The points corresponding to the transient state for r>5 do not fit with these theoretical predictions. They are due to the fact that our measuring apparatus is too slow to catch the fast transient state. Self-focusing parallel to the electric-field One way to study a potential asymmetry of the self-focusing process is to spatially filter the far field beam with a slit rather than with a circular hole. The theory" predicts different diameters in the two directions, making the output beam elliptical. Fig. 6 shows the self-focusing process in the direction parallel to the electric field, in the same conditions as Fig. 5. As can be seen, a qualitative difference appears. For intensity ratios smaller than 1, a defocusing takes place. We do not have an explanation for this feature but we suspect

9 N. FRESSENGEAS et al. that this is due to oscillations of the beam diameter inside the crystal, as predicted by Zozulya and Anderson". For intensity ratios around unity and greater, the same qualitative behavior is obtained. Even though no measurement concerning self-focusing in the direction perpendicular to the field is displayed here, an analysis of Figs. 5 and 6 can give good hints of the results it would lead to. Fig. 5 shows the self-focusing phenomenon averaged in all the directions, because the measurement is made using a circular hole. Fig. 6 shows it in the direction parallel to the field. Therefore, because the averaged beam width is smaller than the width in the direction of the electric field, we can deduce that the width in the direction perpendicular to the field is smaller than the averaged one. The resulting output beam profile is elliptical, as predicted previously". The analysis of the transient state leads to the same conclusions as above. The asymmetry of the self-focusing process is confirmed. A quantitative comparison 5 1,25 Q s.l s 1,2 9 1,15 0 w '0 1,l 5 1,05 he 1 1 I I I I z 0,Ol 0, r FIGURE 6 Output beam waist normalized to the input one as a function of the peak power to dark irradiance ratio r, measured using the slit spatial filtering method. The squares show the steady-state and the circles show the transient. The transient state measurements for large r are not displayed. The solid line shows the output beam waist as a result of linear diffraction.

10 TRANSIENT SELF-FOCUSING Bi,,Ti02, [5 I 71/20 1 between the measurements shown in Fig. 5 and 6 show that the ratio between the averagd beam width and the beam width perpendicular to the field is not a constant : the ellipse undergoes changes in its shape throughout the build-up of the self-focusing process. Further measurements are on the way, in order to completely validate this first observation. CONCLUSION Our experiments provide a partial validation of the previously developed theory, both for steady state self-focusing" and screening soiiton~l~~'~*'~ as well as for transient self- focusing'2 and quasi-steady solitons". More complete study under are way about the influence of the electric field and concerning the predicted oscillations of the beam diameter in the crystal". ACKNOWLEDGMENTS The authors wish to thank D.Rytz, from the Forschunginstitut fiir Mineralische und Mettallische Werkstoffe Edelsteine / Edelmetalle GmbH ( D Idar-Oberstein, Germany), for useful discussion and for his Bi12Ti020 crystal on which our experimental studies have been conducted REFERENCES 1. M.Segev,B.Crosignani, A.Yariv, Phvs.Rev.Lett,%, 923, (1992) 2. B.Crosignani, M. Segev, D.Engin, P.Di Porto, A.Yariv, G.Salamo, Journ.ODt.Soc.Am.B, 446, (1993) 3. M.Segev, B.Crosignani, P.Di Porto, G.C.Duree, G.Salamo, E.Sharp, Opt.Lett., l9-1296, (1994) 4. D.N.Christodoulides, M.I.Carvalho, Opt.Lett., l9-1714, (1994) 5. G.C.Duree, J.L.Shultz, G.J.Salamo, M.Segev, A.Yariv, B. Crosignani, P.Di Porto, E.J.Sharp, R.R.Neurgaonkar, Phvs.Rev.Lett., - 7l 533, (1993) 6. G.C.Duree, G.Salamo, M.Segev, A.Yariv, B.Crosignani, P.Di Porto,E.Sharp, Opt.Lett., 19, 1195, (1994)

11 202/[518] N. FRESSENGEAS et al. 7. M.D.Iturbe Castillo, P.A.Marquez Aguilar, J. J.Sanchez Mandragon, S. Stepanov, V.Vysloukh, Appl.Phys.Lett., , (1994) 8. M.F.Shih, MSegev, G.C.Valley, G.Salamo, B.Crosignani,P.Di Porto, Elec.Lett., 3l- 826, (1 995) 9. M.T.Taya, M.C.Bashaw, M.Segev, G.C.Valley, Phys.Rev.A, , (1995) 10. S.Maneuf, R.Desailly, C.Froehly, Opt.Commun., 65, 193, (1988) 11. A.A.Zozulya, DZAnderson, Phys.Rev.A,5l, 1520, (1995) 12. A.A.Zozulya, D.Z.Anderson, Opt.Lett.,20,837, (1995) 13. N.Fressengeas, J.Maufoy, G.Kugel, Phys.Rev.E, 54,6866 (1996) 14. N.V.Kukhtarev, V.B.Markov, S.G.Odulov, M.S.Soskin, V.L.Vinetskii, Ferroelectrics, 22,949, (1 979) 15. D.N.Christodoulides, M.LCarvalho, Journ.Opt.Soc.Am.B, l2, 1628, (1995) 16. Crystal provided by D.Rytz, FEE, Strutlistrasse 2, D Idar-Oberstein, Germany 17. M.Morin, G.Duree, G.Salamo,M.Segev, ODt,Lett.,20,2066, (1995) 18. M.Segev, G.C.Valley, BCrosignani, P.Di Porto, A.Yariv, Phys.Rev.Lett., , (1 994) 19. S.R.Singh, D.N.Christodoulides, Opt.Commun., 118,569, (1995)