Squeezing and expanding light without reflections via transformation optics

This paper was published in OPTICS EXPRESS and is made available as an electronic reprint with the permission of OSA. The paper can be found at the following URL on the OSA website: http://dx.doi.org/10.1364/OE.19.003562. Systematic or multiple reproduction or distribution to multiple locations via electronic or other means is prohibited and is subject to penalties under law[EN] We study the reflection properties of squeezing devices based on transformation optics. An analytical expression for the angle-dependent reflection coefficient of a generic three-dimensional squeezer is derived. In contrast with previous studies, we find that there exist several conditions that guarantee no reflections so it is possible to build transformation-optics-based reflectionless squeezers. Moreover, it is shown that the design of antireflective coatings for the non-reflectionless case can be reduced to matching the impedance between two dielectrics. We illustrate the potential of these devices by proposing two applications in which a reflectionless squeezer is the key element: an ultra-short perfect coupler for high-index nanophotonic waveguides and a completely flat reflectionless hyperlens. We also apply our theory to the coupling of two metallic waveguides with different cross-section. Finally, we show how the studied devices can be implemented with non-magnetic isotropic materials by using a quasi-conformal mapping technique. © 2011 Optical Society of America.Financial support by the Spanish MICINN under contract CONSOLIDER EMET (CSD2008-00066) and PROMETEO-2010-087 R&D Excellency Program (NANOMET) is gratefully acknowledged. C. G.-M., R. O. and F.J. R.-F. acknowledge financial support from grants FPU of MICINN, FPI of U.P.V. and FPI of Generalitat Valenciana, respectively.García Meca, C.; Tung, MM.; Galán Conejos, JV.; Ortuño Molinero, R.; Rodríguez Fortuño, FJ.; Martí Sendra, J.; Martínez Abietar, AJ. (2011). Squeezing and expanding light without reflections via transformation optics. Optics Express. 19(4):3562-3575. https://doi.org/10.1364/OE.19.003562S35623575194Yang, R., Abushagur, M. A., & Lu, Z. (2008). Efficiently squeezing near infrared light into a 21nm-by-24nm nanospot. Optics Express, 16(24), 20142. doi:10.1364/oe.16.020142Vivien, L., Laval, S., Cassan, E., Le Roux, X., & Pascal, D. (2003). 2-d taper for low-loss coupling between polarization-insensitive microwaveguides and single-mode optical fibers. Journal of Lightwave Technology, 21(10), 2429-2433. doi:10.1109/jlt.2003.817692Pendry, J. B. (2006). Controlling Electromagnetic Fields. Science, 312(5781), 1780-1782. doi:10.1126/science.1125907Leonhardt, U., & Philbin, T. G. (2006). General relativity in electrical engineering. New Journal of Physics, 8(10), 247-247. doi:10.1088/1367-2630/8/10/247Rahm, M., Cummer, S. A., Schurig, D., Pendry, J. B., & Smith, D. R. (2008). Optical Design of Reflectionless Complex Media by Finite Embedded Coordinate Transformations. Physical Review Letters, 100(6). doi:10.1103/physrevlett.100.063903Rahm, M., Roberts, D. A., Pendry, J. B., & Smith, D. R. (2008). Transformation-optical design of adaptive beam bends and beam expanders. Optics Express, 16(15), 11555. doi:10.1364/oe.16.011555Grzegorczyk, T. M., Chen, X., Pacheco, J., Chen, J., Wu, B.-I., & Kong, J. A. (2005). REFLECTION COEFFICIENTS AND GOOS-HANCHEN SHIFTS IN ANISOTROPIC AND BIANISOTROPIC LEFT-HANDED METAMATERIALS. Progress In Electromagnetics Research, 51, 83-113. doi:10.2528/pier04040901Taillaert, D., Bogaerts, W., Bienstman, P., Krauss, T. F., Van Daele, P., Moerman, I., … Baets, R. (2002). An out-of-plane grating coupler for efficient butt-coupling between compact planar waveguides and single-mode fibers. IEEE Journal of Quantum Electronics, 38(7), 949-955. doi:10.1109/jqe.2002.1017613Roelkens, G., Vermeulen, D., Van Thourhout, D., Baets, R., Brision, S., Lyan, P., … Fédéli, J.-M. (2008). High efficiency diffractive grating couplers for interfacing a single mode optical fiber with a nanophotonic silicon-on-insulator waveguide circuit. Applied Physics Letters, 92(13), 131101. doi:10.1063/1.2905260Tsuchizawa, T., Yamada, K., Fukuda, H., Watanabe, T., Jun-ichi Takahashi, Takahashi, M., … Morita, H. (2005). Microphotonics devices based on silicon microfabrication technology. IEEE Journal of Selected Topics in Quantum Electronics, 11(1), 232-240. doi:10.1109/jstqe.2004.841479Li, J., & Pendry, J. B. (2008). Hiding under the Carpet: A New Strategy for Cloaking. Physical Review Letters, 101(20). doi:10.1103/physrevlett.101.203901Vasić, B., Isić, G., Gajić, R., & Hingerl, K. (2009). Coordinate transformation based design of confined metamaterial structures. Physical Review B, 79(8). doi:10.1103/physrevb.79.085103Shalaev, V. M. (2008). PHYSICS: Transforming Light. Science, 322(5900), 384-386. doi:10.1126/science.1166079Xiong, Y., Liu, Z., & Zhang, X. (2009). A simple design of flat hyperlens for lithography and imaging with half-pitch resolution down to 20 nm. Applied Physics Letters, 94(20), 203108. doi:10.1063/1.3141457Kildishev, A. V., & Narimanov, E. E. (2007). Impedance-matched hyperlens. Optics Letters, 32(23), 3432. doi:10.1364/ol.32.003432Gaillot, D. P., Croënne, C., Zhang, F., & Lippens, D. (2008). Transformation optics for the full dielectric electromagnetic cloak and metal–dielectric planar hyperlens. New Journal of Physics, 10(11), 115039. doi:10.1088/1367-2630/10/11/115039Tichit, P.-H., Burokur, S. N., & de Lustrac, A. (2010). Waveguide taper engineering using coordinate transformation technology. Optics Express, 18(2), 767. doi:10.1364/oe.18.000767Zang, X., & Jiang, C. (2010). Manipulating the field distribution via optical transformation. Optics Express, 18(10), 10168. doi:10.1364/oe.18.010168Chang, Z., Zhou, X., Hu, J., & Hu, G. (2010). Design method for quasi-isotropic transformation materials based on inverse Laplace’s equation with sliding boundaries. Optics Express, 18(6), 6089. doi:10.1364/oe.18.00608