Physics Chat
Transverse electric surface plasmon polariton modes in periodic graphene-based structure
Speaker: Zeeshan Ahmad (SS Oh)
Date: Friday 1 April 2022
Time: 15:00
Venue: Zoom
Surface plasmon polaritons (SPPs) are charge-density oscillations coupled with electromagnetic waves that propagate along an interface between dielectric and conductor [1,2]. While surface plasmons in a metal-dielectric interface can have transverse-magnetic (TM) polarisation only, graphene can allow SPP modes with transverse-electric (TE) polarisation to propagate along its surface due to the interband transition contributions to its permittivity [3]. While the TM SPP modes in graphene are frequency-capped, the TE modes are free from such a restricted frequency range at a finite temperature [4]. In addition to existence of TE SPPs, graphene allows tunability with temperature and gate-voltage to control dispersion-dependent temporal loss of the SPP modes. In this work, we present numerical results using a complex-frequency approach with an aim to use for temporal analysis of SPP modes. Figure 1 (a, b) illustrates the dispersion relation for TE SPP mode in a graphene sheet in vacuum. The red lines are the imaginary part of frequencies, while blue solid lines correspond to the real part. This is done by solving TE secular equations for a complex frequency # while setting in-plane wavenumber q to be real. This approach, as opposed to complex q and real #, is better equipped to describe the temporal loss and spectral properties of graphene. Furthermore, permitting frequency # to be complex, in addition to a finite temperature, reveals an extended frequency range for TE SPP mode, compared to the limited range (1.667 < ##/#< 2) reported earlier in the literature [3]. Interestingly, the TE SPP modes, in comparison to TM SPP modes, can propagate along planar graphene with extremely small loss. This can be shown analytically by approximating the dispersion relation under the assumption that the real frequency is close to the light line. Experimental methods have been found to excite the TE SPP mode in multilayer graphene structures thus proving its existence [5]. Another promising structure is an adjacent dielectric grating which could affect the TE SPP modes of graphene. For example, one could expect a coupling between TE SPPs in graphene and waveguide mode in the grating which might provide a new way to control the TE SPP modes via bandgap opening.
References [1] E. N. Economou, Surface plasmons in thin films, Phys. Rev. 182, 539 (1969) [2] H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings, Springer Berlin Heidelberg (1988) [3] S. A. Mikhailov and K. Ziegler, new electromagnetic mode in graphene, Phys. Rev. Lett. 99, 016803 (2007) [4] Z. Ahmad, E. A. Muljarov and S. S. Oh, Extended frequency range of transverse-electric surface plasmon polaritons in graphene, Phys. Rev. B 104, 085426 (2021) [5] S. Menabde, D. Mason, E. Kornev, et al. Direct Optical Probing of Transverse Electric Mode in Graphene, Sci Rep 6, 21523 (2016)
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