Nematic liquid crystal waveguide arrays

Transcription

1 OPTO-ELECTRONICS REVIEW 13(2), th International Workshop on Nonlinear Optics Applications Nematic liquid crystal waveguide arrays K.A. BRZD KIEWICZ *1, M.A. KARPIERZ 1, A. FRATALOCCHI 2, G. ASSANTO 2, and E. NOWINOWSKI-KRUSZELNICKI 3 1 Faculty of Physics, Warsaw University of Technology, 75 Koszykowa Str., Warsaw, Poland 2 NooEL-Nonlinear Optics and Optoelectronics Laboratory, University Roma Tre, Via della Vasca Navale 84, Rome, Italy 3 Institute of Applied Physics, Military University of Technology, 2 Kaliskiego Str., Warsaw, Poland We investigate linear and nonlinear light propagation in a voltage-tunable array of waveguide channels in undoped nematic liquid crystals. This novel geometry, based on a photonic structure with a periodic modulation of refractive index controlled by an electric field, offers a wealth of possibilities for the study of discrete optical phenomena. The structure, in conjunction with a giant, non-resonant and voltage-dependent reorientational nonlinearity, allows us to drive the system from bulk diffraction to discrete propagation. Theoretical and experimental investigations, carried out with near infrared light wavelength and powers of a few milliwatts, show the possibility of transverse light localization, resulting in discrete spatial solitons. Such array, with its voltage- and light-adjustable guided-wave confinement and coupling, exhibits potentials for the realization of multifunctional routers and all-optical signal processors with nematic liquid crystals. Keywords: nonlinear optics, solitons, self-action effects, optical nonlinearity in liquid crystals, discrete diffraction. 1. Introduction Linear and nonlinear effects in discrete systems such as photonic structures with a periodic modulation of the refractive index have became the subject of intensive investigations. Particular attention has been devoted to the generation of discrete solitons [1,2] which are excellent candidates for novel all-optical switching devices and networks [3 6]. Similarly to continuous systems, stable spatial solitons can be formed in discrete structures when self focusing is strong enough to balance discrete diffraction. Moreover, discrete solitons can be viewed as due to a nonlinear response which detunes a waveguide from the neighbouring ones. General properties of discrete optical solitons were first described by Christodoulides et al. referring to a cubic Kerr nonlinearity [7] and later studied with reference to other nonlinear materials, including photorefractive and parametric crystals [1,8]. To the date, they were observed experimentally in AlGaAs [9 12], in silica [13,14], in SBN-crystals [15,16], in Lithium Niobate [17], and recently also in nematic liquid crystals (NLC) [18]. The latter were proven to be very promising for nonlinear optics [19 21]. Their inexpensive and consolidated technology, huge birefringence, giant reorientational nonlinearity and low power requirements, have allowed us demonstrating that spatial solitons can be effectively generated at mw power levels, in bulk as well as in planar waveguide configurations, with propagation distances of a few millimeters [20]. Moreover, the large electro-optic response of NLC allows for creation of flexible and voltage-tunable architectures, useful for the study of discrete phenomena. In this communication, we illustrate a one-dimensional periodic photonic structure with refractive index contrast controlled by an external electric field. We present experimental and theoretical analyses of both linear and nonlinear discrete propagation of infrared-light in arrays of identical weakly-coupled waveguides in undoped nematic crystals, paying particular attention to the choice of geometric parameters. A sketch of the device is drawn in Fig. 1. A few-micron thick layer of PCB (4-cyano-4'-n-pentylbiphenyl) nematic liquid crystal is sandwiched between two glass plates, forming a planar waveguide in the absence of an applied voltage. The anchoring conditions at the top and bottom glass surfaces determine the planar alignment of the molecules in the z-direction. To introduce a spatially periodic refractive modulation inside of NLC layer and to obtain a voltage-adjustable response, a set of regularly-spaced, transparent indium-tin-oxide (ITO) electrodes (as thin as 50 nm) is placed on the top surface to apply a reorientational bias across the cell. The comb-shape of this electrode (with equal finger widths and spacing) allows us the formation of identical channels and provides confinement in the transverse x-y plane. In our samples, the electrode set had the periods ranging from 4 to 8 µm depending on the cell thickness. * kasia@if.pw.edu.pl Opto-Electron. Rev., 13, no. 2, 2005 K.A. Brzd¹kiewicz 107

2 Nematic liquid crystal waveguide arrays Fig. 1. Sketch of the liquid crystal waveguide array. The period of the electrode distribution L varies from 4 to 8 µm and the cell thickness d from 3 to 7 µm (depending on the cell). 2. Numerical results The application of an appropriate voltage causes the reorientation of the NLC molecules which, as a result of free- -energy minimization, tend to align parallel to the direction of the electric field. The angular molecular distribution can be theoretically calculated from the Euler-Lagrange equation describing reorientation through an applied bias [21]. The numerical results shown in this communication were obtained for the liquid crystal PCB, with low-frequency anisotropy De if = Owing to a new arrangement of the orientation angle, a periodic spatial modulation of the refractive index occurs. Figure 2 shows an example of refractive index distribution (for x-polarized light) obtained in the 5-µm-thick sample and for electrode period of 6 µm. Figure 2(b) presents numerical results of refractive index distribution in the middle of the NLC layer (i.e., for x =0) and three different values of bias. As one can see, the refractive index increases mainly in the regions under the electrodes and thereby the channel waveguides are well defined through lateral confinement. In general, the higher refractive index is obtained for a higher bias, and better light guiding is expected. In this case, the coupling length, defined as the propagation distance at which whole energy goes from one waveguide to the neighbouring ones [23], gets longer. Numerical simulations of light propagating in the NLC layer were carried out with BPM injecting a TM-polarized Gaussian beam. Additionally, in each propagation step the molecular orientation distribution was recalculated based on minimization of the total free-energy of the liquid crystal under the influence of both the low-frequency (bias) and the optical electric field [21]. The refractive indices characteristic of PCB are n 0 = 1.52 and n e = 1.69 at a wavelength of 1064 nm. Figure 3 displays light propagation in the linear (low input optical power) regime. In this case, the electric bias plays a crucial role in the reorientation process, leading to the periodic modulation of a refractive index, as shown in Fig. 2. While standard diffraction (in the homogenous medium) takes place in the transverse y-z plane in the absence of bias, discrete diffraction [1,2,22] sets-in and can be tuned in strength as the voltage increases and the array is formed. As a consequence of discrete diffraction, energy redistributes among the guiding channels, as clearly visible in Figs. 3(b) 3(e) showing the cross-sections in x = 0 and beam transverse profiles in the x-y plane along propagation. In the analysed geometry, the optimisation of such parameters as the optical properties (especially birefringence) of NLC, the NLC layer thickness, the electrode spacing and width, allows us to obtain properly coupled and well defined waveguides. Moreover, the magnitude of discrete diffraction can be easily tuned by controlling the voltage. Figure 4 shows how the coupling between channels and the resulting discrete diffraction changes with the applied voltage. An increase in bias reduces angular divergence of the beam; light is more confined within the core region of the channels, and the coupling length increases. As intuitive, by increasing the bias it is possible to progressively Fig. 2. Spatial distribution of the refractive index for light linearly polarized along x, NLC layer 5-µm thick and electrode width and spacing of 3 µm. Three-dimensional map for the bias V = 1.35 V (a), refractive index in the middle of the NLC cell (i.e., for x = 0) for three different applied voltages (b). 108 Opto-Electron. Rev., 13, no. 2, COSiW SEP, Warsaw

3 7 th International Workshop on Nonlinear Optics Applications Fig. 3. Numerical results for a low-power Gaussian optical input of waist 2 µm and wavelength 1064 nm, for a 5-µm-thick NLC-cell, electrode period of 6 µm and applied voltage V = 1.35 V. Discrete diffraction for the beam launched into one input waveguide (a). Beam transverse profiles (for x = 0) (b) and (c), spatial distribution of light intensity (d) and (e) after 1- and 2-mm propagation distances, respectively. reduce light transfer between channels. By using a proper bias the difference between refractive indices in each channel and in the gaps between the finger electrodes can be maximized. However, the saturating character of this reorientation process causes an excessive voltage to flatten the index profile and thereby weaken the spatial definition of each channel. The non local response of NLC, in fact, is such that an electric field increases the index not only under electrodes but also between them. For high enough applied voltages, the NLC elastic response mediates reorientation in the regions between neighbouring waveguides, thereby reducing the refractive index modulation. This is also visible in Fig. 5(a) where, for a fixed cell thickness, the coupling length first increases with applied voltage until saturation and non locality makes it decrease again. Figure 5 shows how discrete diffraction can be modified by varying the sample geometry. By reducing the thickness of the NLC layer it is possible to obtain better defined waveguides, i.e., an increased coupling length, Fig. 5(b). Figure 5(c) shows how the light beam injected in a 2.5-µm-thick sample for low bias (1.2 V) is confined within 3 channels after 1-mm propagation. Conversely, for thicker NLC layers, the change in coupling length versus voltage is negligible and discrete diffraction is hardly affected. As expected, the coupling length can be also reduced by decreasing the electrode periodicity. However, a close proximity of the stripe electrodes reduces the coupling length dependence with bias. For example, in a 5-µm-thick sample with 4-µm electrode period, by varying the voltage from 1.1 to 1.9 V, the change in coupling distance is around 60 µm. The analyses demonstrate that, in the process of sample designing, it is important to find the optimum ratio between electrode width and sample thickness in order to obtain a well tunable structure for suitable values of the applied voltage. Fig. 4. Linear coupling between channels and its dependence on applied voltage for NLC thickness of 5 µm and electrode period of 6 µm. The optical intensity distribution is colour-inverted (i.e., darker corresponds to a higher intensity) and evaluated after 1 mm propagation. Opto-Electron. Rev., 13, no. 2, 2005 K.A. Brzd¹kiewicz 109

4 Nematic liquid crystal waveguide arrays Fig. 5. Linear coupling between channels versus NLC thickness. Dependence of a coupling length on applied voltage for three cell thicknesses d (a). Coupling length versus NLC thickness at a voltage V = 1.2 V (b). Spatial intensity distribution calculated after 1 mm propagation and V = 1.2 V for different values of NLC thickness d (c). Going from the linear to the nonlinear regime, as the power of the propagating beam increases, the refractive index of the excited waveguides is modified by the nonlinearity, and discrete diffraction can be effectively counteracted by the power-induced detuning of the launch channel. As shown in Fig. 6, as the light power gets higher, the beam narrows in space. Finally, when the input beam is intense enough, nonlinearity completely balances diffraction and light propagates (transversely) localized in a limited region of the array or, for high enough excitations, in a single channel. Such a beam, which propagates maintaining an invariant transverse profile, is called discrete spatial soliton [1,2,18,22]. It is possible to consider either partially localized or wide solitons with energy in a few channels, or totally localized narrow solitons, with energy essentially confined in the input waveguide. It is worth to underline that, due to light confinement, discrete systems require less power for solitons than comparable slab waveguide or bulk media. Fig. 6. Beam distribution versus input beam power calculated for V = 1.35 V after 1-mm propagation. Discrete diffraction is limited and discrete spatial solitons are generated due to increase in input light power. 3. Experimental results We performed experiments in NLC cell of a thickness of 5 6 µm and with an array period of 6 µm. The beam from a Nd:YAG laser (l = 1064 nm) was focused to a diameter of approximately 4 µm at the entrance of the sample. The beam evolution in the NLC cell was observed through a CCD camera detecting the photons scattered above the cell. Photographs were taken at various biases, as shown in Fig. 7. The pictures show the change in discrete beam propagation for a fixed input power of 5 mw and a propagation distance of 1 mm. As one can see, by increasing the applied voltage the coupling length becomes longer and beam spatial localization is enhanced. For low voltages [Figs. 7(a) and 7(b)], the beam is guided in a few channels, whereas V = 1.45 V it essentially propagates in just one of them. As predicted theoretically, however, spatial light localization can be also obtained by increasing the beam power, leading to discrete soliton generation. Figure 8 shows the experimental photographs of light propagation depending on optical power in the structure. When no voltage is applied, the beam diffracts in the y-z plane, progressively reducing its intensity and becoming hardly visible after a few Rayleigh ranges, see Fig. 8(a). Figure 8(b) shows discrete diffraction of the excitation injected into a single channel for a bias V = 1.1 V, large enough to create an array of well-defined channels. In z = 1.4 mm, the input has spread over 13 adjacent waveguides. Compared to standard diffraction in a homogeneous 1D geometry [planar waveguide, Fig. 8(a)], discrete diffraction [Fig. 8(b)] gives rise to the smaller divergence. Figures 8(c) 8(e) present the successive changes of the 110 Opto-Electron. Rev., 13, no. 2, COSiW SEP, Warsaw

5 7 th International Workshop on Nonlinear Optics Applications 4. Conclusions Fig. 7. Experimental results showing a 5-mW Nd:YAG beam after 1-mm propagation for three different applied voltages. character of discrete propagation obtained due to increment of the beam evolution versus optical power. As expected, a high excitation mismatches the input waveguide, resulting in a narrow discrete soliton [Fig. 8(e)]. Figures 8(f) 8(i) show the corresponding beam transverse profiles in z = 1.4 mm. In conclusions, we have presented nonlinear waveguide arrays in undoped nematics. The investigated geometry takes advantage of both the electro-optic and all-optical response of liquid crystals in a planar arrangement, offering considerable flexibility both in the linear and nonlinear regimes by voltage tuning the relevant parameters. The giant nonlinear response characteristic of molecular reorientation in such medium, allows for observation of discrete spatial solitons at mw levels, paving the way to multifunctional routers and signal processors in liquid crystals. The theoretical predictions are in excellent agreement with the experimental results, and further work is underway to enlighten a variety of additional fascinating phenomena including gap solitons and discrete breathers. Acknowledgments This work was partially supported by the State Committee for Scientific Research under grant No. 4 T11B Fig. 8. Linear propagation (standard diffraction) of the beam in the homogenous planar waveguide (i.e., at zero voltage) (a). Light propagation (for voltage of 1.1 V) for different input powers of the beam launched into one channel (b e). Acquired transverse profiles (solid line) in z = 1.4 mm, corresponding to the cases (b e) (f i). The dashed-line graphs are calculated profiles matching the experimental conditions. Opto-Electron. Rev., 13, no. 2, 2005 K.A. Brzd¹kiewicz 111

6 Nematic liquid crystal waveguide arrays References 1. F. Lederer, S. Darmanyan, and A. Kobyakov, Discrete solitons, in Spatial Solitons, edited by S. Trillo and W. Torruellas, Wiley, New York, A.A. Sukhorukov, Y.S. Kivshar, H.S. Eisenberg, and Y. Silberberg, Spatial optical solitons in waveguide arrays, IEEE J. Quantum Electron. 39, 31 (2003). 3. D.N. Christodulides and E.D. Eugenieva, Blocking and routing discrete solitons in two-dimensional networks of nonlinear waveguide arrays, Phys. Rev. Lett. 87, (2001); E.D. Eugenieva, N.K. Efremidis, and D.N. Christodoulides, Minimizing bending losses in two-dimensional discrete soliton networks, Opt. Lett. 26, 1876 (2001), Design of switching junctions for two-dimensional discrete soliton networks, Opt. Lett. 26, 1978 (2001), Minimizing bending losses in two-dimensional discrete soliton networks: errata, Opt. Lett. 27, 369 (2002). 4. R. Morandotti, U. Peschel, J.S. Aitchison, H.S. Eisenberg, and Y. Silberberg, Dynamics of discrete solitons in optical waveguide arrays, Phys. Rev. Lett. 81, 2726 (1999). 5. W. Królikowski and Y.S. Kivshar, Soliton-based optical switching in waveguide arrays, J. Opt. Soc. Am. B13, 876 (1996). 6. O. Bang and P. Miller, Exploiting discreteness for switching in waveguide arrays, Opt. Lett. 21, 1105 (1996). 7. D.N. Christodoulides and R.I. Joseph, Discrete self-focusing in nonlinear arrays of coupled waveguides, Opt. Lett. 13, 794 (1988). 8. C. Etrich, F. Lederer, B. Malomed, T. Peschel, and U. Peschel, Optical solitons in media with a quadratic nonlinearity, in Progress in Optics, Vol. 41, pp. 483, edited by E. Wolf, Elsevier Science Publishers 2000; T. Peschel, U. Peschel, and F. Lederer, Discrete bright solitary waves in quadratically nonlinear media, Phys. Rev. E57, 1127 (1998). 9. J. Meier, G.I. Stegeman, Y. Silberberg, R. Morandotti, and J.S. Aitchison, Nonlinear optical beam interactions in waveguide arrays, Phys. Rev. Lett. 93, (2004). 10. R. Morandotti, H.S. Eisenberg, Y. Silberberg, M. Soler, and J.S. Aitchison, Self-focusing and defocusing in waveguide arrays, Phys. Rev. Lett. 86, 3296 (2001). 11. H.S. Eisenberg, Y. Silberberg, R. Morandotti, A.R. Boyd, and J.S. Aitchison, Discrete spatial optical solitons in waveguide arrays, Phys. Rev. Lett. 81, 3383 (1998); Diffraction management, Phys. Rev. Lett. 85, 1863 (2000). 12. P. Millar, J.S. Aitchison, J.U. Kang, G.I. Stegeman, A. Villeneuve, G.T. Kennedy, and W. Sibbett, J. Opt. Soc. Am. B14, 3224 (1997). 13. D. Cheskis, S. Bar-Ad, R. Morandotti, J.S. Aitchison, H.S. Eisenberg, Y. Silberberg, and D. Ross, Strong spatiotemporal localization in a silica nonlinear waveguide array, Phys. Rev. Lett. 91, (2003). 14. T. Pertsch, U. Peschel, F. Lederer, J. Burghoff, M. Will, S. Nolte, and A. Tunnermann, Discrete diffraction in two-dimensional arrays of coupled waveguides in silica, Opt. Lett. 29, 468 (2004). 15. N.K. Efremidis, S. Sears, D.N. Christodoulides, J.W. Fleischer, and M. Segev, Discrete solitons in photorefractive optically induced photonic lattices, Phys. Rev. E66, (2002). 16. J.W. Fleisher, T. Carmon, M. Segev, N.K. Efremidis, and D.N. Christodoulides, Observation of discrete solitons in optically induced real time waveguide arrays, Phys. Rev. Lett. 90, (2003); J.W. Fleisher, M. Segev, N.K. Efremidis, and D.N. Christodoulides, Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices, Nature 422, 147 (2003). 17. R. Iwanow, R. Schiek, G.I. Stegeman, T. Pertsch, F. Lederer, Y. Min, and W. Sohler, Observation of discrete quadratic solitons, Phys. Rev. Lett. 93, (2004). 18. A. Fratalocchi, G. Assanto, K.A. Brzd¹kiewicz, and M.A. Karpierz, Discrete propagation and spatial solitons in nematic liquid crystals, Opt. Lett. 29, 1530 (2004). 19. I.C. Khoo and S.T. Wu, Optics and Nonlinear Optics of Liquid Crystals, World Scientific Publ., Singapore 1997; F. Simoni, Nonlinear Optical Properties of Liquid Crystals, World Scientific Publ., London, M. Peccianti, G. Assanto, A. De Luca, C. Umeton, and I.C. Khoo, Electrically assisted self-confinement and waveguiding in planar nematic liquid crystal cells, Appl. Phys. Lett. 77, 7 (2000); M. Peccianti, K.A. Brzd¹kiewicz, and G. Assanto, Nonlocal spatial soliton interactions in nematic liquid crystals, Opt. Lett. 27, 1460 (2002); G. Assanto and M. Peccianti, Spatial solitons in nematic liquid crystals, IEEE J. Quantum Electron. 39, 13 (2003); M.A. Karpierz, Solitary waves in liquid crystalline waveguides, Phys. Rev. E66, (2002); M.A. Karpierz, M. Sierakowski, M. Œwi³³o, and T.R. Woliñski, Self focusing in liquid crystalline waveguides, Mol. Cryst. Liq. Cryst. 320, 157 (1998). 21. N.V. Tabiryan, A.V. Sukhov, and B.Ya. Zel'dovich, Orientational optical nonlinearity of liquid crystals, Mol. Cryst. Liq. Cryst. 136, 1 (1986); P.J. Collings, M. Hird, Introductions to Liquid Crystals Chemistry and Physics, Taylor & Francis, London F. Lederer and Y. Silberberg, Discrete solitons, Opt. Photon. News 2, 49 (2002); D.N. Christodoulides, F. Lederer, and Y. Silberberg, Discretising light behaviour in linear and nonlinear waveguide lattices, Nature 424, 817 (2003). 23. A. Yariv, Optical Electronics in Modern Communications. Oxford Press, New York Opto-Electron. Rev., 13, no. 2, COSiW SEP, Warsaw