We analyze relief graphene gratings by the coordinate transformation method (the C-method). This method is also used for analysis of multilayer gratings with graphene sheets at the interfaces. By using this method, we are able to obtain the eciency of deep graphene gratings with fast convergence rate while previous methods are limited to very shallow graphene gratings. Moreover, a terahertz polarizer is designed by relief graphene grating. Polarization extinction ratio and transmittance of single-layer and double-layer polarizer are simulated by the C-method. Double-layer polarizer gives extinction ratio from 22 dB to 10 dB over a frequency range of 1 GHz to 4 THz.
1. Slipchenko, T. M., M. L. Nesterov, L. Martin-Moreno, and A. Yu Nikitin, "Analytical solution for the di®raction of an electromagnetic wave by a graphene grating," J. Opt., Vol. 15, 114008, 2013. doi:10.1088/2040-8978/15/11/114008
2. Bludov, Y. V., A. Ferreira, N. M. R. Peres, and M. I. Vasilevskiy, "A primer on surface plasmon-polaritons in graphene," Int. J. of Mod. Phys. B, Vol. 27, 1341001, 2013. doi:10.1142/S0217979213410014
3. Peres, N. M. R., A. Ferreira, Y. V. Bludov, and M. I. Vasilevskiy, "Light scattering by a medium with a spatially modulated optical conductivity: the case of graphene," J. Phys.: Condens. Matter, Vol. 24, 245303, 2012. doi:10.1088/0953-8984/24/24/245303
4. Huidobro, P. A., M. Kraft, R. Kun, S. A. Maier, and J. B. Pendry, "Graphene, plasmons and transformation optics," J. Opt., Vol. 18, 044024, 2016. doi:10.1088/2040-8978/18/4/044024
5. Nikitin, A. Y., F. Guinea, F. J. Garcia-Vidal, and L. Martin-Morene, "Surface plasmon enhanced absorption and suppressed transmission in periodic arrays of graphene ribbons," Phys. Rev., Vol. 85, 081405, 2011. doi:10.1103/PhysRevB.85.081405
6. Zhan, T. R., F. Y. Zhao, X. H. Hu, X. H. Liu, and J. Zi, "Band structure of plasmons and optical absorption enhancement in graphene on subwavelength dielectric gratings at infrared frequencies," Phys. Rev. B, Vol. 86, 165416, 2012. doi:10.1103/PhysRevB.86.165416
7. Peres, N. M. R., Y. V. Bludov, A, Ferreira, and M. I. Vasilevskiy, "Exact solution for square-wave grating covered with graphene: surface plasmon-polaritons in the terahertz range," J. Phys.: Condens. Matter, Vol. 25, 125303, 2013. doi:10.1088/0953-8984/25/12/125303
8. Ding, J., F. T. Fisher, and E. H. Yang, "Direct transfer of corrugated graphene sheets as stretchable electrodes," Journal of Vacuum Science and Technology B, Nanotechnology and Microelectronics: Materials, Processing, Measurement, and Phenomena, Vol. 34, 051205, 2016.
9. Wang, M., J. Leem, P. Kang, J. Choi, P. Knapp, K. Yong, and S. Nam, "Mechanical instability driven self-assembly and architecturing of 2D materials," 2D Materials, Vol. 4, 022002, 2017. doi:10.1088/2053-1583/aa62e8
10. Yan, Z. X., Y. L. Zhang, W. Wang, X. Y. Fu, H. B. Jiang, Y. Q. Liu, P. Verma, S. Kawata, and H. B. Sun, "Superhydrophobic SERS substrates based on silver-coated reduced graphene oxide gratings prepared by two-beam laser interference," ACS Applied Materials and Interfaces, Vol. 7, 27059, 2015. doi:10.1021/acsami.5b09128
11. Florio, G. D., E. Brundermann, N. S. Yadavalli, S. Santer, and M. Havenith, "Graphene multilayer as nano-sized optical strain gauge for polymer surface relief gratings," Nano Letters, Vol. 14, 5754, 2014. doi:10.1021/nl502631s
12. Novoselov, K. S., A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, "Electric field effect in atomically thin carbon films," Science, Vol. 306, 666, 2004. doi:10.1126/science.1102896
13. Jablan, M., M. Soljacic, and H. Buljan, "Plasmons in graphene: fundamental properties and potential applications," Proc. IEEE, Vol. 101, 1689, 2013. doi:10.1109/JPROC.2013.2260115
14. Gusynin, P., S. G. Sharapov, and J. P. Carbotte, "Magneto-optical conductivity in graphene," J. Phys.: Condens. Matter, Vol. 19, 026222, 2007. doi:10.1088/0953-8984/19/2/026222
15. Li, Z. Q., E. A. Henriksen, Z. Jiang, Z. Hao, M. C. Martin, P. Kim, H. L. Stormer, and D. N. Basov, "Dirac charge dynamics in graphene by infrared spectroscopy," Nature Phys., Vol. 4, 532, 2008. doi:10.1038/nphys989
16. Alaee, R., M. Farhat, C. Rockstuhl, and F. Lederer, "A perfect absorber made of a graphene micro-ribbon metamaterial," Opt. Express, Vol. 20, 28017, 2012. doi:10.1364/OE.20.028017
17. Fadakar, H., A. Borji, A. Z. Nezhad, M, and Shahabadi, "Improved fourier analysis of periodically patterned graphene sheets embedded in multilayered structures and its application to the design of a broadband tunable wide-angle polarizer," IEEE J. Quantum Electron, Vol. 53, 1, 2017. doi:10.1109/JQE.2017.2696496
18. Khoozani, P. K., M. Maddahali, M. Shahabadi, and A. Bakhtafrouz, "Analysis of magnetically biased graphene-based periodic structures using a transmission-line formulation," JOSA B, Vol. 33, 2566, 2016. doi:10.1364/JOSAB.33.002566
19. Kim, J. T. and S. Y. Choi, "Graphene-based plasmonic waveguides for photonic integrated circuits," Opt. Express, Vol. 19, 24557, 2011. doi:10.1364/OE.19.024557
22. Chandezon, J., D. Maystre, and G. Raoult, "A new theoretical method for di®raction gratings and its numerical application," J. Opt., Vol. 11, 235, 1980. doi:10.1088/0150-536X/11/4/005
23. Chandezon, J., M. T. Dupuis, G. Cornet, and D. Maystre, "Multicoated gratings: a differential formalism applicable in the entire optical region," J. Opt. Soc. Am., Vol. 72, 839, 1982. doi:10.1364/JOSA.72.000839
24. Cao, Y. S, L. J. Jiang, and L. J. Ruehli, "The derived equivalent circuit model for non-magnetized and magnetized graphene," Wireless Information Technology and Systems (ICWITS) and Applied Computational Electromagnetics (ACES), 2016 IEEE/ACES International Conference on, 1, 2016.
25. Petit, R., A Tutorial Introduction, Electromagnetic Theory of Gratings. Springer Berlin Heidelberg, 1980.
26. Li, L., J. Chandezon, G. Granet, and J.-P. Plumey, "Rigorous and efficient grating-analysis method made easy for optical engineers," Appl. Opt., Vol. 38, 304, 1999. doi:10.1364/AO.38.000304
27. David, J. G. and R. College, Introduction to Electrodynamics, Prentice Hall, 1999.
28. Ko, D. Y. K. and J. R. Sambles, "Scattering matrix method for propagation of radiation in stratified media: attenuated total reflection studies of liquid crystals," J. Opt. Soc. Am. A, Vol. 5, 1863, 1988. doi:10.1364/JOSAA.5.001863
29. Chen, P. Y. and A. Alu, "Atomically thin surface cloak using graphene monolayers," ACS Nano, Vol. 5, 5855, 2011. doi:10.1021/nn201622e
30. Hanson, G. W., "Dyadic Green's functions and guided surface waves for a surface conductivity model of graphene," J. Appl. Phys., Vol. 103, 064302, 2008. doi:10.1063/1.2891452
31. Jishi, R. A., M. S. Dresselhaus, and G. Dresselhaus, "Electron-phonon coupling and the electrical conductivity of fullerene nanotubules," Phys. Rev. B, Vol. 48, 11385, 1993. doi:10.1103/PhysRevB.48.11385