Beam steering with graded index photonic crystal lens and liquid crystal
2013; Institution of Engineering and Technology; Volume: 8; Issue: 1 Linguagem: Inglês
10.1049/iet-opt.2013.0092
ISSN1751-8776
AutoresBabak Bahari, J. Rashed‐Mohassel,
Tópico(s)Optical Coatings and Gratings
ResumoIET OptoelectronicsVolume 8, Issue 1 p. 11-17 ArticleFree Access Beam steering with graded index photonic crystal lens and liquid crystal Babak Bahari, Corresponding Author Babak Bahari [email protected] Center of Excellence on Applied Electromagnetic Systems, School of Electrical and Computer Engineering, College of Engineering, University of Tehran, P.O. Box 14395-515, Tehran, 14399 IranSearch for more papers by this authorJalil Rashed-Mohassel, Jalil Rashed-Mohassel Center of Excellence on Applied Electromagnetic Systems, School of Electrical and Computer Engineering, College of Engineering, University of Tehran, P.O. Box 14395-515, Tehran, 14399 IranSearch for more papers by this author Babak Bahari, Corresponding Author Babak Bahari [email protected] Center of Excellence on Applied Electromagnetic Systems, School of Electrical and Computer Engineering, College of Engineering, University of Tehran, P.O. Box 14395-515, Tehran, 14399 IranSearch for more papers by this authorJalil Rashed-Mohassel, Jalil Rashed-Mohassel Center of Excellence on Applied Electromagnetic Systems, School of Electrical and Computer Engineering, College of Engineering, University of Tehran, P.O. Box 14395-515, Tehran, 14399 IranSearch for more papers by this author First published: 01 February 2014 https://doi.org/10.1049/iet-opt.2013.0092Citations: 2AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Abstract In this numerical study, a new compact and tunable beam-steering device composed of graded index photonic crystal lens and liquid crystal material has been presented and demonstrated. The beam-steering device can work in two modes: First, incident single wavelength beam steers by tuning the refractive index of the liquid crystal material. Second, by fixing the refractive index of the liquid crystal material, incident multi-wavelength beam steers with different off-axis angles for each wavelength. The numerical simulations with finite-difference time-domain method reveal that wide-angle, ± 28.4°, beam steering can be achieved when the length of the liquid crystal layer equals 5.17 μm. Moreover, the wavelengths over λ = 1.518–1.553 μm or λ = 1.487–1.518 μm can be steered to different angles. A special characteristic of the presented structure gives an opportunity to be used as an efficient element in a high integrated optical device for miniaturisation and tuning purposes. 1 Introduction Beam steering is an important concept in optics, with variety of applications such as non-mechanical beam steering, wavelength selector, and so on. Mechanical devices for changing the direction of the beam are bulky and slow, whereas non-mechanical devices are compact and steer the beam rapidly. Sometimes, the separation and redirection of the incident beam to multiple directions according to their wavelengths is highly desired. The non-mechanical beam-steering devices can easily do this. There are several methods for non-mechanical beam steering, such as non-linear optical phased array, acousto-optic modulators, solid crystal-based electro-optic modulators and liquid crystal (LC) optical phased arrays. LC promises an inertia-free operation in non-mechanical beam steerers and deflectors. LC possesses low size and weight, low-cost fabrication [1], fast switching [2] and low operating voltage. The efforts in the development of LC beam steering returns to early 1974 for works of Borel et al. [3]. This approach has been expanded by optical-array beam steerers [4], ferroelectric LC gratings [5], polymer-dispersed LC gratings [6], and so on. To have a compact device for beam-steering application, the spot size of the incident optical beam, which is the Gaussian beam of laser or output of the optical fibre, must be reduced. This spot reduction is performed with optical lenses. One of these optical lenses is the graded index (GRIN) photonic crystal (PC) lens whose refractive index is modulated such that the negative refraction occurs and the parallel incident beam focuses at a focal point [7]. GRIN PC lens is a chip scale lens with high tolerance against the transverse displacements. It means, by displacing the incident beam, the focal point does not displace significantly. By putting a layer of LC behind a GRIN PC lens, we can steer the beam, focused by GRIN PC, in the desired direction. In this work, we have proposed a new design of beam-steering GRIN PC device, showing the advantages of chip scale, high tolerance against the displacement of the incident beam and tunability by using LC. The device works in two modes. First, the incident beam is single frequency and by manipulating the refractive index profile of LC, the beam will steer to a desired off-axis angle. Second, LC is tuned to have a fixed refractive index profile. Therefore, by changing the frequency of the incident beam, each frequency steers with a different off-axis angle. Thus, multiple frequencies are separated at different angles. Until here, all of the simulations are done two-dimensionally, but in the end, we will investigate the possibility of fabrication, and simulate our structure three-dimensionally and observe the amount of changes that will occur in comparison with two-dimensional simulation. 2 Beam-steering device Fig. 1 shows the schematic of a GRIN PC lens, which focuses the incident Gaussian beam at a focal point. For steering the focused beam to the desired direction, a layer of LC is used behind the lens. In fact, there is a Si slab in which some holes with different shapes and dimensions exist. Some holes are circular and filled with air, and some are square filled with LC. The focused beam scans different angles, with the x -axis, using LC. Changing the external voltage of each LC cell, the associated refractive index will change for a specific refractive index profile. This procedure will be clarified in the following. Fig. 1Open in figure viewerPowerPoint Schematic of the beam-steering device The GRIN PC lens is composed of air holes in Si material with a refractive index of 3.46 [8]. The radius of air holes are described by the function, (r (y)/a) = 0.233 + 1.2 × 10−3 (y /a) 2 (approximately like the one in [9]), where a is the lattice constant and is 378.5 nm in this paper, and y is the separation from the centre of the lens. Therefore, the diameters of holes vary from 176.38 to 302.8 nm, which can be created by electron beam lithography (EBL). This technique has been described in [10]. The number of holes in y -direction is 25. There are six cells of LC behind the GRIN PC lens and the dimensions of each cell is L × W. W is 1.2 μm, which is fixed and does not change, but L can be changed depending on the maximum off-axis steering angle. In this work, L is approximately 5 μm, which creates a LC cell with an area of 1.2 × 5 μm2 that is sufficiently large to be filled by LC. This area is reported as 1 × 0.9 μm2 [11]. Also, air holes with areas of 7.84 μm2, filled with LC E7, are fabricated and reported [12]. In Fig. 1, each LC cell is depicted with a different colour showing different refractive indices of the cells. In our analysis, the finite-difference time-domain (FDTD) [13] method is used to calculate the field distribution. The FDTD mesh size and time step are Δx = Δy = 13 nm, and Δt = Cf (Δx/c), respectively, where Cf is the Courant stability factor selected as 0.99 here. The refractive indices of the nematic LC are provided in [14], in which they demonstrate experimentally the refractive indices of the nematic LC E7 at a wavelength of 1550 nm. The extraordinary (ne) and the ordinary (no) indices of refraction of LC are considered to be 1.67 and 1.518, respectively, at room temperature [14]. The incident field to the GRIN PC lens is a Gaussian beam with TM polarisation in which the electric field is parallel to the z -axis. In Fig. 2, the GRIN PC lens has been illuminated by a Gaussian beam source described by (1)where W (x), R (x) and ξ (x) are defined as [15] (2a) (2b) (2c) (2d) Fig. 2Open in figure viewerPowerPoint FDTD results of the field distribution of the GRIN PC lens illuminated by the Gaussian beam for calculating the spot width and DOF W0 is the beam waist that is 10 μm, and xR is the Rayleigh range. At the output of the lens, spot width and depth of focus (DOF) is calculated and results in 1541 nm (spot width ) and 8176 nm , respectively. In Fig. 3, the FDTD simulation of the special field distribution of the GRIN PC lens has been calculated. In Fig. 3 a, LC layer does not exist, but in Fig. 3 b, LC cells are present, but have not been biased with an external voltage, and hence they all have the same refractive indices. As it can be inferred from Fig. 3, the focal point has been formed in the direction of the incident field or off-axis angle of zero. Fig. 3Open in figure viewerPowerPoint FDTD results of the field distribution of the GRIN PC lens illuminated by the Gaussian beam a LC cells are not present b LC cells are present Fig. 4 shows the schematic of a unit cell of LC bounded by two electrode plates on top and bottom. The optical axis of LC is in the n -direction, and the wave is travelling in the x -direction. Without any applied voltage to the plates, n is parallel to x -axis, but by applying appropriate voltage, n starts to change its direction towards y -axis. Fig. 4Open in figure viewerPowerPoint Schematic of a unit cell of LC layer To change the direction of the beam, the refractive index of LC layer must be altered with a different bias voltage for each cell. Fig. 5 shows the refractive index profile of LC layer in the y -direction from no to ne, which is used in this work and can be selected arbitrarily. In fact, we bias each cell with a specific voltage in order to change the effective index of each cell. The effective index is calculated by [16] (3)where θ (tilt angle) is the angle between the optical axis and y -direction. The relationship between θ and the applied voltage is described by [16] (4)where V is the applied rms voltage, Vc is the critical voltage at which the tilting process begins (typically about 1.2–1.6 volts for LC material E7 [17]), and V0 is constant [16]. Therefore, we apply such a voltage to each cell so that the effective index of the cells in Fig. 1 from bottom to top become 1.518, 1.524, 1.543, 1.576, 1.618 and 1.67. Thus, by this refractive index profile for LC layer, if we illuminate the structure, the field distribution shown in Fig. 6 a will result. Fig. 5Open in figure viewerPowerPoint Refractive index profiles of LC cells along a plane perpendicular to x-axis Fig. 6Open in figure viewerPowerPoint FDTD results of the field distribution of the beam steerer a When LC layer have refractive index profile shown in Fig. 5 b When LC layer have an inverted refractive index profile with respect to the y = 5 μm shown in Fig. 5 As shown in Fig. 6 a, the beam steers to an off-axis angle after passing LC layer. As is known, the wave has a higher phase velocity in a low refractive index material. When the wave exits from GRIN PC lens, it has a focal point in the x -direction, as shown in Fig. 3. In LC layer, the cells that have lower refractive indices enhance the speed of the wave, whereas the cells that have a higher refractive indices lessen the speed of the wave in comparison with low refractive index cells. Therefore, the beam steers towards cells with higher refractive indices. If the bias voltages of LC cells are inverted, the refractive index profile will be inverted with respect to the y = 5 μm in Fig. 5, and the beam will steer in the opposite off-axis angle as shown in Fig. 6 b. The maximum angle that the beam can be steered is highly dependent on the length of LC layer, L. If the length of LC layer increases, the beam will steer more than before. Therefore, we expect that by increasing the length of LC layer, the maximum steering angle increases. Fig. 7 a shows the field intensity in a plane normal to the x -direction for different lengths of LC layer. As it can be inferred from the figure, by increasing the length of the layer, the focal point steers more than before. Fig. 7 b shows the amount of the maximum off-axis angle with respect to different lengths of LC layer. For low lengths, the change in θ is approximately linear, which is due to the low interaction length between focused beam at the output of the lens and the LC layer. By increasing L, however, this interaction increases significantly and causes non-linear changes in θ. Fig. 7Open in figure viewerPowerPoint Steering the beam for different lengths of LC layer a Field intensity in a plane normal to the x -direction for different length of LC layer b The maximum off-axis angle for different length of LC layer Now, we investigate the effect of wavelength on the maximum off-axis angle. For this purpose, the length of LC layer is selected as 5.17 μm, which eventuates to maximum off-axis angle from −30.37° to 30.37°, and the power transmission of 58%. The power transmission is defined as (5)where Pout is the transmitted power to the outside of the structure, and Pin is the incident power to the GRIN PC lens. By changing the wavelength of the incident beam, the maximum off-axis angle will change as shown in Fig. 8. These different off-axis angles for different wavelengths are due to the GRIN PC lens. By changing the wavelength of the incident beam, the focal point location from the lens will change [9], causing different length of LC layer to interact with the beam. Thus, for different wavelengths, different maximum off-axis angles will result. The power transmission for the wavelength range shown in Fig. 8 is approximately unchanged and 58%. Fig. 8Open in figure viewerPowerPoint Maximum off-axis angle for different wavelengths of the illumination beam If we fix the refractive index profile of LC layer (Fig. 5), different wavelengths will steer to different off-axis angles. For example, this kind of beam steering can be used over wavelengths of λ = 1.521–1.553 μm or λ = 1.49–1.521 μm for separating different channels with different wavelengths in different directions, or in frequency-dependent nano antennas, the beam can scan different angles by changing the frequency. Fig. 9 shows the field distribution when the length of LC layer is 5.17 μm. The wavelengths of the incident beam in Fig. 9 a is 1525 nm and in Fig. 9 b is 1550 nm, which show the maximum off-axis angles of 21.63° and 30.37°, respectively. Fig. 9Open in figure viewerPowerPoint FDTD results of the field distribution of the beam steerer a Illuminated by a Gaussian beam source with a wavelength of 1525 nm b Illuminated by a Gaussian beam source with a wavelength of 1550 nm 3 Dimensional simulation In this section, we will investigate briefly the possibility of fabrication. Therefore, we make some improvements in the simulation of the proposed structure shown in Fig. 1. As shown in Fig. 10 a, in the first step, a thin layer of gold is deposited on the silicon oxide (SiO2). This gold layer is the ground layer that will be connected to the ground voltage. Fig. 10Open in figure viewerPowerPoint Schematic of the fabrication steps of a beam steerer a Depositing a thin gold layer on the SiO2 b Depositing Si, and creating the GRIN PC lens c Etching LC cells, and then filling them by LC d Depositing a thin parylene layer e Depositing a thin gold layer, and then, etching it in order to create top-gold plates After deposition of the ground layer of gold, in the next step, a silicon layer with 1 μm thickness will be deposited. The GRIN PC lens can be created by using an appropriate chromium mask and EBL technique, which has been described in [10]. The problem that will occur here is that, if we put the top-gold plates, less amount of the focused electric field (from output of the GRIN PC lens) can pass through LC layer, and this is due to the reflection caused by the top-gold layer. Therefore, we select the height of LC layer more than the height of the lens to decrease this reflection. Thus, additional 1 μm silicon is deposited as shown in Fig. 10 b. Meanwhile, we know that LC molecules can be aligned uniformly along the 2 μm thickness. In the next step, the holes of LC cells are created as shown in Fig. 10 c. These holes will be filled by LC. Now by using chemical vapour deposition technique, a thin layer of parylene is deposited [18] (Fig. 10 d) to create a solid layer on top of LC, enabling us to put top-gold plates on LC. In fact, parylene is a material which covers all over the surface including solid or liquid materials [19]. Parylene films can be deposited at room temperature, and the coating process involves no curing, no solvents and no additives [18]. The possibility and fabrication of the deposition of gold on the parylene is investigated and performed in [20]. After creating the top-gold plates, with each plate on the appropriate LC cell, the final structure shown in Fig. 10 e will result. Considering this structure, we utilise 3D-FDTD simulation, and calculate its transmission of power and maximum steering angle. All parameters are like previous ones except some differences. Here, we assume that the power is coupled to the silicon slab (before reaching the GRIN PC lens) in an appropriate way, and then propagating wave in the slab will incident to the GRIN PC lens. Also, the refractive indices of the parylene and SiO2 are considered to be 1.134 [21] and 1.454 [22]. One more thing that we must consider is the refractive index of Si. Considering the fact that the deposited Si on the SiO2 is amorphous silicon, we use its refractive index of 3.73 [8]. Now, we apply the appropriate voltage to have the refractive index profile shown in Fig. 5, however, considering the edge effects of the top-gold plates, the refractive index profile of LC cells will change as shown in Fig. 11. In fact, in a LC cell, with a low applied voltage, molecules are in the x -direction, but by increasing the voltage, molecules begin to change their direction, hence decreasing the refractive index. Therefore, in two adjacent LC cells, the cell with high applied voltage will affect the cell with low applied voltage, resulting in a slight decrease in the refractive index of that cell at the edge. However, the cell with low applied voltage does not have considerable effect on the cell with high applied voltage. Fig. 11Open in figure viewerPowerPoint Refractive index profiles of LC cells along a plane perpendicular to x-axis by considering the edge effect of the plates on voltage distribution To obtain this refractive index profile, first we calculated voltage profile along a plane perpendicular to x -axis, which is in LC region, using CST STUDIO 2011, and then calculated the effective refractive index using (3) and (4). As it can be inferred from Fig. 11, there are little differences in the three left cells; therefore, we assume these cells have uniform refractive indices, but for other cells we take into account the non-uniform refractive indices in the simulation. Thus, calculating the steering angle, and the amount of the power transmission for the proposed structure, the maximum steering angle of 28.4° with a power transmission of 41% is obtained, which are 6.4% and 29.3% lower than the ideal two-dimensional simulation, respectively. In the following, by changing the frequency of the incident beam, the maximum off-axis angle shown in Fig. 12 will result. Comparing Fig. 12 with Fig. 8, there are no considerable differences between them except some decrease in the amount of the maximum off-axis angle for different wavelengths. Therefore, this beam steerer can be used over wavelengths of λ = 1.518–1.553 μm or λ = 1.487–1.518 μm for separating different channels with different wavelengths. The power transmission over the wavelength shown in Fig. 12 is approximately 41%. Fig. 12Open in figure viewerPowerPoint Maximum off-axis angle for different wavelengths of the illumination beam for the structure shown in Fig. 10 e 4 Conclusion We have proposed a new device designed for beam steering. In our device, the GRIN PC lens was used to focus the incident beam in the focal point. For steering the focused beam to an off-axis angle, a layer of LC E7 behind the GRIN PC lens was used, since the GRIN PC lens cannot steer the beam by itself. Controlling the bias voltage of each cell, thus controlling the refractive index profile, the off-axis angle can be controlled. Using the length of LC layer, the maximum off-axis angle will change. Beam steering over wide angles, ± 30.37° or 60.74° in the space with power transmission of 58%, was resulted. By fixing the refractive index of LC layer, but changing the wavelength of the incident beam, each wavelength will steer with a different angle. This kind of application can be used over wavelengths of λ = 1.521–1.553 μm or λ = 1.49–1.521 μm. In addition, fabrication steps were investigated and some improvements such as the refractive index profile were made. Furthermore, the parylene, SiO2 and conducting gold layers were considered in the three-dimensional FDTD simulation, resulting in 6.4 and 29.3% decrease in the steering angle and power transmission, respectively. The corresponding steering angle and power transmission were ± 28.4° and 41%, respectively. Additionally, for separating the wavelengths, there is a little difference in comparison to the two-dimensional simulation. This difference is due to the changes in the maximum off-axis angles for different wavelengths. Therefore, the beam steerer can be used over wavelengths of λ = 1.518–1.553 μm or λ = 1.487–1.518 μm for separating different channels with different wavelengths. This device has an approximate dimension of 10 μm × 9 μm × 2 μm, which is sufficiently compact, and has great applications in near-field scanning, wavelength separators, nano antennas, and so on. 5 References 1Klaus W.: 'Development of LC optics for free-space laser communications', AEU Int. J. Electron. Commun., 2002, 56, pp. 243– 253 (doi: https://doi.org/10.1078/1434-8411-54100104) 2Golovin A.B. Shiyanovskii S.V., and Lavrentovich O.D.: 'Fast switching dual-frequency liquid crystal optical retarder, driven by an amplitude and frequency modulated voltage', Appl. Phys. Lett., 2003, 83, pp. 3864– 3866 (doi: https://doi.org/10.1063/1.1625114) 3Borel J. Deutsch J.C. Labrunie G., and Robert J.: ' Liquid crystal diffraction grating'. US patent 3843231, October 1974 4Jarrahi M. Fabian R. Pease W. Miller D.A.B., and Lee T.H.: 'Optical switching based on high-speed phased array optical beam steering', Appl. Phys. Lett., 2008, 92, pp. 014106-1– 014106-3 (doi: https://doi.org/10.1063/1.2831005) 5Ma Y. Sun J. Srivastava A.K. Guo Q. Chigrinov V.G., and Kwok H.S.: 'Optically rewritable ferroelectric liquid-crystal grating', EPL, 2013, 102, pp. 24005p1– 24005p5 6Sutherland R.L. Tondiglia V.P. Natarajan L.V. Bunning T.J., and Adams W.W.: 'Evolution of anisotropic reflection gratings formed in holographic polymer-dispersed liquid crystals', Appl. Phys. Lett., 2001, 79, pp. 1420– 1422 (doi: https://doi.org/10.1063/1.1399303) 7Kurt H., and Citrin D.S.: 'Graded index photonic crystals', Opt. Express, 2007, 15, pp. 1240– 1253 (doi: https://doi.org/10.1364/OE.15.001240) 8Aspnes D.E.: ' Handbook of optical constants of solids', in: E.D. Palik (Ed.) (Academic, San Diego, California, 1995) 9Wu Q. Gibbons J.M., and Park W.: 'Graded negative index lens by photonic crystals', Opt. Express, 2008, 16, pp. 16941– 16949 (doi: https://doi.org/10.1364/OE.16.016941) 10Jannesary R. Bergmair I. Zamiri S., and Hingerl K.: 'Design and fabrication of Si-based photonic crystal stamps with electron beam lithography (EBL)', Proc. SPIE – Int. Soc. Opt. Eng., 2010, 7637, pp. 763720p1– 763720p8 11Tasolamprou A.C. Zografopoulos D.C., and Kriezis E.E.: 'Liquid crystal-based dielectric loaded surface plasmon polariton optical switches', J. Appl. Phy., 2011, 110, pp. 093102– 093111 (doi: https://doi.org/10.1063/1.3658247) 12Leonard S.W. Mondia J.P., and van Driel H.M. et al. 'Tunable two-dimensional photonic crystals using liquid-crystal infiltration', Phy. Rev. B Condens. Matter Mater. Phys., 2000, 61, pp. R2389– R2392 (doi: https://doi.org/10.1103/PhysRevB.61.R2389) 13Taflove A., and Hagness S.C.: ' Computational electrodynamics: the finite-difference time-domain method' (Artech House, 2000) 14Brugioni S., and Meucci R.: 'Refractive indices of the nematic mixture E7 at 1550 nm', Infrared Phys. Technol., 2007, 49, pp. 210– 212 (doi: https://doi.org/10.1016/j.infrared.2006.06.006) 15Saleh B.E.A., and Teich M.C.: ' Fundamental of photonics' (Wiley, 2007) 16de Gennes P.G.: ' The physics of liquid crystals' (Clarendon Press, Oxford, 1974), Chap. 3 17Tillin M.D. Raynes E.P., and ToWler M.J.: ' Surface mode liquid crystal device and method of making a liquid crystal device'. US patent 6222605, April 2001 18Hsu J.M. Kammer S. Jung E. Rieth L. Normann A.R., and Solzbacher F.: ' Characterization of parylene-C film as an encapsulation material for neural interface devices'. Presented at the Third Annual Conf. Multi-Material Micro Manufacture, Borovets, Bulgaria, 2007 19Sadeghi M.M. Peterson R.B., and Najafi K.: ' High-speed electrostatic micro-hydraulics for sensing and actuation'. IEEE Int. Conf. Microelectromechanical Systems (MEMS), Taipei, 2013 20Sadeghi M.M. Dowling K. Peterson R.B., and Najafi K.: ' High sensitivity, high density micro- hydraulic force sensor array utilizing stereo-lithography fabrication technique'. IEEE Int. Conf. Microelectromechanical Systems (MEMS), Taipei, 2013 21http://www.filmetrics.com/refractive-index-database/Parylene+C, accessed September 2013 22Daldosso N. Melchiorri M., and Riboli F. et al. 'Design, fabrication, structural and optical characterization of thin Si3 N4 waveguides', IEEE J. Lightwave Technol., 2004, 2, p. 1734 (doi: https://doi.org/10.1109/JLT.2004.831182) Citing Literature Volume8, Issue1February 2014Pages 11-17 FiguresReferencesRelatedInformation
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