Widely tunable nonlinear liquid crystal-based photonic crystals

Transcription

1 Widely tunable nonlinear liquid crystal-based photonic crystals I. C. Khoo a, Yana Zhang a, A. Diaz a, J. Ding a, I. B. Divliansky c, Kito Holliday b, T. S. Mayer a, V. Crespi b, D. Scrymgeour c, V. Gopalan c. a Department of Electrical Engineering, The Pennsylvania State University, PA16802, USA b Department of Physics, The Pennsylvania State University, PA16802, USA c Department of Material Science and Engineering, The Pennsylvania State University, PA16802, USA ABSTRACT We report theoretical and experimental studies of 1-D and 2-d tunable nonlinear photonic crystals made of liquid crystal or liquid crystal infiltr ated periodic structures. Theoretical modeling shows that such structures exhibit tunable bandgap, and super -prism effect. Experimentally, we have demonstrated the possibility of writing dynamic or permanent [but switchable] index gratings in dye-doped LC films that act as planar waveguides. Keywords: Nonlinear Liquid Crystals, photonic crystals, filters, switches, waveguides, super-prism effect. 1. INTRODUCTION Nematic liquid crystals (NLC) possess very broadband birefringence and transparency, and extraordinarily large optical nonlinearity ; the optical dielectric constant anisotropy is on the order of unity for the entire spectrum from 400 nm to 20 microns [1, 2]. Furthermore, liquid crystals by virtue of the fluid nature are also compatible with various optoelectronics structures. There have been attempts [3, 4] to infiltrate photonic crystals fabricated with other materials with liquid crystals to device tunable devices. Recently, Tondiglia et al [5] has demonstrated fabrication of a 3-D polymer-liquid crystal photonic crystal structure. For optical applications, 2-D PC s are more practical and versatile and easier to fabricate. Also the number of modes is smaller and there is no mixing of the TE and TM modes. In this paper, we report a novel approach of fabricating tunable photonic crystals by writing permanent [but electrically switchable] 2-D holographic gratings in liquid crystals. Our theoretical an alysis shows that such structures exhibit tunable bandgap, and will also enable super-prism beam steering effects [6, 7]. 2. LIQUID CRYSTAL PHOTO NIC CRYSTAL PLANAR WAVEGUIDS Fig. 1a shows a planar aligned nematic liquid crystal (NLC), in which the director axis is aligned parallel to the enclosing windows. The NLC film functions as an optical waveguide if the refractive indexes of the two enclosing surfaces are lower than the liquid crystal (LC), which possesses typical extraordinary refractive index n e ~ 1.7 and ordinary refractive index n o ~ 1.5. Recent studies have shown that it is possible to optically realign the director axis, using a variety of mechanisms [8, 9]. In particular, experiments with methyl-red dye doped or Fullerene C60 doped liquid crystals [9-11] show that robust permanent realignment

2 of the director axis can be achieved, with resolution down to microns. It is thus possible to impart a 2-D intensity grating on the film, and write a 2-D pattern of realigned director axis, as shown in fig. 1b. The schematic of the experimental set up for writing 2-D grating on a planar nematic film is shown in Fig. 1b. The liquid crystal sample is made by sandwiching 5CB or E7 between rubbed PVA coated glass slides. Sample thicknesses range from 6 µm to 25 µm. The sample is mounted so that the director axis is at 45 degrees to the optical electric fields. The laser used is either a cw Argon laser [488 nm] or a 10 ns third harmonic of a Nd: Yag laser [355 nm]. The intersecting angle of the three linearly polarized beams, obtained by beam splitting from the laser, is 2.64 o ; the optical intensity grating constant is 3.9 µm. TM TE TE 1a 1b UV laser (355nm) (MR+E7)Planer Sample He-Ne Laser Tek Oscilloscope High Power mirror Screen for Diffraction Pattern mirror Wedge Fig. 1. (a) Linearly polarized laser incident on a planar aligned nematic liquid crystal where director axis lies in the plane of the slab.(b) Experimental set up for writing 2-D grating on the LC sample. Photo above shows the self-diffraction pattern of the nanosecond UV pulse [right], and the He-Ne diffraction [left].

3 We notice that using lasers of different wavelength could create quite different results. In general, with cw Argon laser wavelengths [497 nm, 488 nm, nm] or 2 nd Harmonic of nanosecond pulsed Nd:YAG [532 nm], permanent grating are easily written [9-11]. On the other hand, with near UV radiation [3 rd Harmonic of nanosecond pulsed Nd:Yag 355nm], the gratings tend to be of the dynamic kind [with a short rise times of a few nanosecond as the laser pulse duration, and a short relaxation times on the order of several 100 s nanoseconds], c.f. Fig. 2a-b. This is probably due to different mechanisms involved, including excited dye adsorption on the surface, photo-induced trans-cis isomerization and order parameter modification, thermal/density effects [1, 9]. In the case of 355 nm nanosecond laser pulse induced effects as shown in Fig. 2, the likely mechanisms are LC-order parameter modification by the photo-excited trans -cis isomerization of the dye dopant molecules, and/or density effects. Both mechanisms are characterized by relaxation times of the order of several 100 s of nanoseconds as observed here [1, 9]. Further studies and measurements are clearly needed to identify the exact mechanisms, including experiments on un-doped LC samples, use of other optic al gratings functions [instead of intensity grating, we employ polarization gratings]. These experiments are currently underway. Laser Pulse Dynamic of the 2D grating(25um sample) 2a 2b Fig. 2. (a) Oscilloscope trace of UV ns laser pulse. Time scale 10 ns/div (b) Oscilloscope trace of He-Ne diffraction. Time scale: 100 ns/div. 3. LIQUID CRYSTAL PHOTONIC CRYSTAL BAND STRUCTURE AND ELECTR O-OPTICAL BEAM STEERING. Such 2-D grating structures act as 2-D photonic crystals for TE/TM modes propagating in the plane of the sample, c.f. Fig. 1. The TM modes does not see the grating as its optical field polarization is perpendicular to the director axis [which lie on the plane of the film], i.e. it sees n o. On the other hand, the TE modes will see a periodic variation of refractive index as it propagates as an e-wave inside the film. We have calculated the band-structure of such liquid crystal 2-D grating. Fully-vectorial eigenmodes of the Maxwell's equations with periodic boundary conditions are computed by preconditioned conjugate-gradient minimization of the block Rayleigh quotient in a plane wave basis, using a freely available software package [12]. The ε xx and ε yy components of the principal-axis dielectric tensor are chosen to vary sinusoidally α cos k x cos k y ) with maxima and minima of 3.01 [n e = 1.734] and 2.25 [n o = 1.5], the ε xx component ( ( ) ( ) x y is taken as the minimum value. The resultant photonic band structure in Fig. 3 shows a small isotropic gap for TM modes in the Γ X direction. The smallness of the gap is due simply to the small dielectric anisotropy ε xx ε yy.

4 If the planar liquid crystal is made with ITO coated windows, an external field can be applied to switch the liquid crystal alignment from planar to homeotropic [i.e. director axis perpendicular to the windows]. In this case, the grating disappear for both TE and TM waves, and the gap closes, i.e. the liquid crystal 2-D grating functions as an electro-optical switch. Fig. 3. PC band structure for all-lc structure with reorientational grating 0.8 Such small bandgap is typical of liquid crystalline structures involving low index materials. Fig. 4b, for example, shows the band structure calculated for a nematic liquid crystal dispersed as 2D hexagonal arrays of liquid crystal rods in a background of polymer. The refractive index of the polymer is typically ~1.52 and the effective refractive index of the liquid crystal is 1.63 when the external applied field is off, and is about 1.52 when the external field is on [the clearing state]. By appropriate choice of incident light propagation directions, the switching of the refractive index and the resultant modification of the dispersion of light in the photonic crystal allows one to switch the direction of the light, c.f. Fig. 4b X 0.4 Γ a J Fig. 4a Fig. 4b Fig. 4a Energy-wave vector diagram for TE mode polarizations of an electromagnetic wave through a hexagonal photonic crystal with rod radius R = 0.35a where a is the unit cell length shown in the first Brillouin zone in Fig. 4b. For both figures, the solid lines are for the rods εa = 2.65 (LC nanodroplets) in a matrix of polymer (εb = 2.3) [13], while the dashed lines are for same structure with an 11 V/µm field applied to the structure (εa 2.3, εb = 2.3). The normalized energy is ωa/(2πc) where ω is the angular frequency of incident wave, c is the velocity of light in free space, and a is a lattice parameter as shown in 4b. The symmetry points X, J, and Γ along the wave vector k in the reciprocal lattice in the first Brillouin zone are depicted on the dispersion surface in 4b. The dispersion surface is shown for a normalized energy of 0.42 (horizontal broken line in 4a). The vertical line in 4b shows the momentum line, and the two arrows represent the angle of light exiting the structure, one for the unperturbed case the othe r for application of an electric field. 49.1

5 If the input light is He-Ne wavelength of nm, propagating into a structure with a lattice spacing, a, of µm with a rod diameter of 0.09 µm, one can get a change of input light direction of 49.1 if the input light is incident light at 12.26, with the application of an electric field across the photonic crystal as shown in Figure 3b. Much larger switching angle can be obtained for larger refractive index difference. Furthermore, since the index of the liquid crystal can be modified by the incident light itself [1], the switching effect described here can also be optically self-induced. In recent studies, we have shown that a polarized laser will have its polarization converted into the orthogonal polarization component by all-optical self action via the laser induced liquid crystalline axis reorientation dynamic grating effect, i.e. SOS [Stimulated Orientational Scattering] [15,16]. If a film of aligned nematic liquid crystal is placed adjacent to a 2-D P C as described here, it is possible to have very large all-optical angular switching of the laser beam as its polarization changes from one state to the other. Since feedback is naturally present in such PC structures, one could also expect novel self -starting optical phase conjugation processes to occur in these novel material structures. 4. CONCLUSION We have demonstrated the feasibility of writing permanent but switchable 2-D index gratings in aligned nematic liquid crystal slab. Calculation of the band structure of such liquid crystalline structure shows that it exhibits a small but sizeable bandgap that can be switched on and off. We have also demonstrated the possibility of using such structure for large-angle switching. 6. ACKNOWLEDGEMENT This work was supported by the Center for Collective Phenomena in Restricted Geometries (Penn State MRSEC) under NSF grant DMR , and the Army Research Office. 7. REFERENCES 1. I. C. Khoo, Liquid Crystals: Physical Properties and Nonlinear Optical Phenomena ( Wiley Interscience, NY 1995). 2. I. C. Khoo and S. T. Wu, Optics and Nonlinear Optics of Liquid Crystals (World Scientific, Singapore, 1994). 3. K. Yoshino, Y. Shimoda, Y. Kawagishi, K. Nakayana, M. Ozaki, Appl. Phys. Lett. 75, 932, (1999). 4. D. Kang, J. E. Maclennan, N. A. Clark, A. A. Zakhidov, R. H. Baughman, Phys. Rev. Lstt. 86, 4052 (2001). 5. V. P. Tondiglia, L. Natarajan, R.L. Sutherland, D. Tomlin, and R. J. Bunning, Holographic formation of electro-optical polymer-liquid crystal photonic crystals, Adv. Mater. 14, No (2002). 6. S.-Y. Lin, V. M. Hietala, L. Wang and E. D. Jones, Highly dispersive photonic band-gap prism, Opt. Lett. 21, 1771 (1996) 7. H. Kosaka, T. Kawashima, A. Tomina, M. Notomi, T. Tamamura, T. Sato and S. Kawakami, Superprism phenomena in photonic crystals, Phys. Rev. B 58, (1998) 8. I. C. Khoo, P. H. Chen, M. Y. Shih, A. Shishido, S. Slussarenko, Supra Optical Nonlinearities of Methyl-Red and Azobenzene Liquid Crystal doped Nematic Liquid Crystals, Molecular Crystals Liquid Crystals, Mol. Cryst. Liq. Cryst. 358, 1-13 (2001). 9. See for example, I. C. Khoo, Min-Yi Shih, M. V. Wood, B. D. Guenther, and P. H. Chen, F. Simoni, S. Slussarenko*, O. Francescangeli, L. Lucchetti, Dye-doped photorefractive liquid crystals for dynamic

6 and storage holographic grating formation and spatial light modulation Invited Paper - IEEE Proceedings Special Issue on Photorefractive Optics: Materials, Devices and Applications. IEEE Proceedings Vol. 87, no. 11, pp (1999). 10. I. C. Khoo, Optics Letters, 20, 2137 (1996). Photorefractivity and storage holographic gratings in dyeand fullerene-doped nematic liquid crystal film. I.C. Khoo, Invited paper, Liquid Crysals, Devices, and Applications, IS&T/SPIE, 2651 p68-78 (1996). 11. Malgosia Kaczmarek, Min-Yi Shih, Roger S. Cidney and I. C. Khoo, Electrically tunable, optically induced dynamic and permanent gratings in dye-doped liquid crystals, Accepted for publication in IEEE J. Quantum electronics, JQE [5/2002]. 12. Steven G. Johnson and J. D. Joannopoulos, Optics Express 8, (2001). 13. A configuration similar to the PDLC system reported by R.L. Sutherland, V.P. Tondiglia, L.V. Natarajan, T.J. Bunning and W.W. Adams, Electrically switchable volume gratings in polymer - dispersed liquid crystals, Appl. Phys. Lett. 64 (9) (1994). 14. W. Park and C. Summers have also performed similar calculation for a 2-D slab PC with Si as the background matrix and obtained a switching angle of about 70 o if the incident light angle is varied by a few degrees. [Optics Letters, In Press, 7/2002]. 15. I. C. Khoo and Y. Liang, Stimulated Orientational and Thermal Scatterings and Self -Starting Optical Phase Conjugation with Nematic Liquid Crystals, Phys. Rev. E62, pp (2000). See also, I. C. Khoo and Yu Liang, Self-starting phase conjugation with cross-polarization stimulated orientational scattering in liquid crystal, Optics Letters, 20, 130 (1995). 16. Paper by I.C. Khoo et al in this proceeding reporting observation of stimulated orientational scattering and polarization rotation of cw 1.55 µm laser by aligned nematic film.