Trapping of surface-plasmon polaritons in a graded Bragg structure: Frequency-dependent spatially separated localization of the visible spectrum modes

We theoretically demonstrate that a metallic film covered by a dielectric grating of graded thickness can strongly slow light as the propagation velocities of surface plasmon polaritons (SPPs) are reduced over a large frequency bandwidth at visible frequencies. Since the dispersive relation of SPPs is dependent on the dielectric grating thickness, the guided SPPs at different frequencies can be localized at different spatial positions of the plasmonic grating. We numerically demonstrate that a true rainbow from violet to red colors can be separately localized, resulting in the spatial separation of the visible spectrum on a chip.

Figure 1

(Color online) Dependence of the real part $n_{eff}^{\prime }$ of effective refractive index of SPPs on wavelength $\lambda$ for different grating thicknesses $h$. Inset A: metal-dielectric-air model ($h\ne 0$, silver-${\text{Si}}_3{\text{N}}_4$-Air). Inset B: metal-air model ($h=0$, silver-air). Inset (i): optical properties of silver in the visible domain. Blue solid line: the refractive index $n$, and red dashed line: the extinction coefficient $k$.

Figure 2

(Color online) (a) Calculated band dispersion of a metallic film coated with a binary dielectric grating with thickness $h=5\text{nm}$ (blue solid line) and 350 nm (red dashed line), respectively. The widths of the dielectric and air layers are set at $w_1=70\text{nm}$ and $w_2=110\text{nm}$, respectively. Inset: schematic of the structure. (b) Schematic of the designed graded plasmonic structure (infinite along the $x$ axis) for trapping rainbow in the visible domain. (c) Calculated transmittance of SPPs passing through the structure of (b). In the calculations, the grating thickness $h$ increases linearly from 5 to 350 nm with the step of 2.5 nm, and the total length of the structure is approximately $25\mu \text{m}$. Other parameters are the same as that of (a).

Figure 3

(Color online) FDTD simulated magnetic field intensity distributions $\left({\left|H_x\right|}^2\right)$ of SPPs through the graded plasmonic structure shown in Fig. 2b as the incident light is at 390 (violet), 490 (blue), 560 (green), 585 (yellow), 610 (orange), 635 nm (red), respectively. Other parameters are the same as that of Fig. 2c.

Figure 4

(Color online) (a) Calculated gray distribution of SPP field intensity $\left({\left|H_x\right|}^2\right)$ in time-position plane (along the $z$ axis, 5 nm above the metal surface). Inset: arrival time of SPP wave packets at eight spatial positions, with an equal spacing of $2.5\mu \text{m}$ along the propagation direction. The first position is $1.5\mu \text{m}$ away from the input port. (b) Time evolution of SPP wave packets at the above eight spatial positions of the structure. In the calculations, the incident light is a TM-polarized Gaussian pulse with a pulse width $\left(\sigma \right)$ of 90 fs and 635 nm central wavelength [magnetic field is parallel to the $x$ axis]. All the geometrical parameters are the same as that of Fig. 3c.

Figure 5

(Color online) (a) Calculated magnetic field intensity distribution $\left({\left|H_x\right|}^2\right)$ of SPPs in the time-position plane (along the $z$ axis, 5 nm above the metal surface) as the grating thickness and the total length of the structure are 270 nm and 100 periods, respectively. The incident pulse is the same as that used in Fig. 4 but centering at 645 nm. Inset: time evolution of the SPP intensity at two spatial positions (blue solid line: $1.5\mu \text{m}$ and red dashed line: $6.5\mu \text{m}$ away from the incident port). (b) and (c) Dependence of the (b) attenuation coefficient $\alpha$ and group velocity ${\upsilon }_g$ and (c) lifetime of SPPs on grating thickness $h$.