0733-8724 (c) 2013 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/JLT.2014.2350481, Journal of Lightwave Technology JLT-XXXXX-2014 1 Plasmonic rainbow trapping by a silica-graphene-silica on a sloping silicon substrate Xiang Yin, Tian Zhang, Lin Chen, Member, IEEE, Member, OSA, Xun Li, Senior Member, IEEE, Member, OSA Abstract—We give a proposal for plasmonic rainbow trapping based on a novel structure comprised of a silica-graphene-silica on a sloping silicon substrate, which, importantly, overcomes the intrinsic constraints that are required by metal/dielectric interface. As compared with previous plasmonic grating structures for rainbow trapping, the adiabatic control of the dispersion curve for the present one is achieved by gradually changing the equivalent permittivity of the graphene monolayer via the gap separation between the graphene monolayer and the silicon substrate. We attribute the rainbow trapping effect to the correlative dispersive relation between the slow plasmonic mode and the gap separation between the graphene monolayer and silicon substrate, which leads to localization of light waves of different frequencies at different positions on the graphene surface. The group velocity can be reduced to be 1000 times smaller than light velocity in air, which is 1～2 smaller than that was previously reported in dielectric gratings based plasmonic strutures. Index Terms—Plasmons, optical waveguides, nanophotonics. I. INTRODUCTION or decades slow light has attracted tremendous research interest because of a number of potential applications, including optical buffers [1], filters [2], and enhanced light-matter interactions [3]. Ultraslow light can be obtained by use of quantum interference effects [4, 5], photonic crystals [6], stimulated Brillouin scattering [7, 8] and electromagnetically induced transparency [9]. It is known that the group velocity ( g υ ) of surface plasmon polaritons (SPPs) at metal/dielectric interface can be reduced significantly as light frequency approaches 1 p d ω ε + [ ] 10 , where p ω denotes the bulk plasma frequency and d ε is the relative dielectric constants of dielectric layer. But for a given metal, the slow SPP mode can only occur at a fixed frequency, which typically lies in the ultraviolet domain. To achieve slow SPP modes in the long wavelength region, plasmonic grating structures have been widely proposed to engineer the dispersion relations at will by engraving a metal surface with a groove array or covering a metal layer with a dielectric grating Manuscript received May 4, 2014. X. Yin, T. Zhang, and L. Chen are with Wuhan National Laboratory for Optoelectronics, Huazhong University of Science and Technology, Wuhan 430074, China (e-mail: chen.lin@mail.hust.edu.cn). X. Li is with the Department of Electrical and Computer Engineering, McMaster University, Hamilton, ON L8S 4K1, Canada. [ ] 11-14 . Further adiabatic control of the dispersions of plasmonic grating structures allows for recent demonstration of optical rainbow trapping at visible, infrared, and THz frequencies, which is also realized in other architectures, including insulator-metal-insulator (IMI) [ ] 15 , insulator-negative-index-insulator [ , ] 16 17 , metal-insulator-metal [ , ], hyperbolic metamaterial [ ] 15 18 19 waveguide tapers. II. RAINBOW TRAPPING ON A GRAPHENE MONOLAYER Fig.1. (color online) The g υ of the anti-symmetric SPP mode in IMI structures versus light frequency for different values of ρ : ρ =1.0001 (blue line), ρ =10 (cyan line), ρ =100 (red line), ρ =1000 (black line). The inset shows the magnified region bounded by the black rectangle for ρ =10, 100, and 1000. The thickness of metal is assumed to be 20 nm. We first consider the anti-symmetric SPP mode for the case ρ >1 ( m d ρ ε ε = − ) supported by a IMI waveguide [ ] 20 , where m ε is the relative dielectric constant of metal. The mode dispersion relation can be obtained by solving the Maxwell's equations [20]. Figure 1 shows the dependence of the group velocity, g υ , of the anti-symmetric SPP mode on light frequency for different values of ρ . Here, the thickness of F