Coupled surface plasmon polaritons on thin metal slabs corrugated on both surfaces

A modelling study of the effect of coupled surface plasmon polaritons (SPPs) on the optical response of a thin metal film corrugated on both surfaces is presented. Initially the case of conformally corrugated metal films (the corrugations on each surface are identical and in phase with each other) is considered. Sinusoidal structures, and those having an additional first harmonic, $2k_g$ (where $k_g$ is the grating vector) component, are investigated. This $2k_g$ component opens up significant band gaps in the SPP dispersion curves, and also causes anticrossing behavior between the long range SPPs and short range SPPs. It is shown that this anticrossing, and the band gap, have a common explanation. Following this, nonconformally corrugated films are examined, and strongly enhanced resonant transmission is shown to occur, which can be almost independent of the in-plane wave vector. The results presented show that, though the enhanced transmission through hole arrays which has provoked extensive recent investigation is of great interest from a physics viewpoint, other structures which exhibit enhanced transmission may provide more benefits, including higher transmission, for some applications.

Figure 1

The optical response as a function of frequency and slab thickness for $k_x=0$ on a conformal, sinusoidally corrugated, silver slab of $10\mathrm{nm}$ amplitude and $400\mathrm{nm}$ pitch, in the classical mount. (a) Reflectivity, (b) transmissivity (log scale), and (c) absorption.

Figure 2

The optical response of the same system as described for Fig. 1 (the film thickness is $30\mathrm{nm}$) as a function of frequency and in-plane wave vector. (a) The dispersion of the modes obtained from the scattering matrices, (b) the reflection, (c) the transmission, and (d) the absorption of the system.

Figure 3

The optical response of the same system as Fig. 1, but with an additional $5\mathrm{nm}$ amplitude $2k_g$ component ($+90°$ out of phase with the $k_g$ component) in the grating profile description, as a function of frequency and slab thickness. (a) The position of the modes in frequency obtained from the scattering matrices, (b) the reflectivity, and (c) the transmissivity (log scale) of the system.

Figure 4

The band structure of the SPPs of the system (obtained from the scattering matrices) for the same structure as for Fig. 3 but for different slab thickness. (a) $d=70\mathrm{nm}$, (b) $d=50\mathrm{nm}$, and (c) $d=30\mathrm{nm}$.

Figure 5

$H_z$ profiles for normal incidence of the long range (a) and short range (b) surface plasmon modes which can be excited on a conformal grating structure with a $2k_g$ component. The modes correspond to those shown in Fig. 3, with a metal slab thickness of $30\mathrm{nm}$.

Figure 6

The zeroth order normal incidence reflectivity (a), transmissivity (b), and absorption of the system (c), for a $30\mathrm{nm}$ thick silver slab corrugated on both surfaces with a $400\mathrm{nm}$ pitch, $10\mathrm{nm}$ amplitude, sinusoid as a function of frequency and phase between the corrugations on the two surfaces.

Figure 7

Schematic of the structure being investigated. There is a $10\mathrm{nm}$ amplitude $k_g$ component, and a $5\mathrm{nm}$ amplitude $2k_g$ component. The grating pitch is $400\mathrm{nm}$. In this case the average film thickness is $50\mathrm{nm}$.

Figure 8

The band structure (a), reflectivity (b), and transmissivity (c) (log scale) of the zeroth order, for normally incident light as a function of frequency and slab thickness for the structure shown in Fig. 7.

Figure 9

Schematics showing the positions of maximum surface charge density of the four possible standing wave coupled SPP modes for normal incidence that may be excited on the structure. (a) The LRSPP from the high energy band edge, (b) the LRSPP from the low energy band edge, (c) the SRSPP from the high energy band edge, and (d) the SRSPP from the low energy band edge.

Figure 10

Field profiles ($H_z$ where $z$ is into the page) of the four possible first order SPP modes excitable on the structure shown in Fig. 7, but with an average thickness of $80\mathrm{nm}$, that can be excited on this structure for $2k_x∕k_z=0.05$. (a) The LRSPP developing from the high energy band edge, (b) the LRSPP developing from the low energy band edge, (c) the SRSPP developing from the high energy band edge, and (d) the SRSPP developing from the low energy band edge.

Figure 11

The reflectivity as a function of frequency and in-plane wave vector for the same system described for Fig. 7, and for film thickness of (a) $80\mathrm{nm}$, (b) $50\mathrm{nm}$, (c) $40\mathrm{nm}$, and (d) $30\mathrm{nm}$.

Figure 12

The transmissivity as a function of frequency and in-plane wave vector for the same system described for Fig. 7, and for film thickness of (a) $80\mathrm{nm}$, (b) $50\mathrm{nm}$, (c) $40\mathrm{nm}$, and (d) $30\mathrm{nm}$.