The simulation results in the previous section demonstrates that a C‐shaped aperture functions as a ridge waveguide and a peak of PT represents a propagation mode supported by the waveguide for a specific incident condition. Consequently, in this section, we investigate the effect of a corrugation on the transmission through the optimized waveguide. The further transmission enhancement resulting from the hybrid effect that propagation modes and surface plasmons modes coexist is demonstrated accordingly.
3.3.1 Corrugations in Entrance Interface
To yield a coupling effect between SPP modes and propagation modes in a subwavelength aperture, the optimal C‐shaped aperture in a free‐standing silver film is surrounded with a corrugation in the entrance interface of the film.
The configuration of the optical model is shown in Fig. 3‐1 (d). Our simulation, as shown in Fig. 3.6, reveals the power throughput of a C‐aperture surrounded with a corrugation in the entrance interface is higher than that of a single C‐aperture. The power throughput enhancement can reach as high as 3.61.
According to the discussion in section 2.3, if incident light can be coupled into SPP modes in the entrance interface, the field near the interface and inside the aperture will be enhanced by the scattering of evanescent waves in the interface.
As expected, if the aperture is replaced with a ridge waveguide, propagation modes inside the waveguide are also enhanced by this effect. Therefore, the transmission through the C‐shaped aperture is further enhanced with the aid of SPP modes in the entrance interface.
Corrugations in the interface can be treated as an energy well and the width of the energy well determines how many and which modes exist.
Therefore, curves with different tendency in Fig. 3‐6 represent different sets of SPP modes produced by different groove widths. In contrast, interval i changes the field distribution resulting from the superposition of SPP modes which carries different momentum and energy. Thus each curve in Fig. 3‐6 indicates different combination of SPP modes and produce different power throughput.
The higher power throughput implies a more efficient coupling between incident light and SPP modes due to momentum and energy conservation matching conditions.
Fig. 3‐6 The PT as a function of the interval i with various widths w
The groove pitch p dominates the lattice momentum of the groove structure as well as the momentum matching condition of the interaction between the photons and the surface plasmons. It means the probability of the coupling between photons and surface plasmons is determined by the groove pitch. This mechanism explains a concave curve of each power throughput with a peak at pitch of 620 nm in Fig. 3‐7.
Fig. 3‐7 The PT as a function of pitch p with various interval i
Compared to a single C‐shaped aperture, the power throughput can be further enhanced by surrounding the aperture with a corrugation. The enhancement stimulated by the corrugation structure is defined as the ratio of the power throughput of the C‐shaped aperture with a groove to that without a groove. The maximum enhancement of 3.61 can be obtained in our simulation.
It means that the output power through this design is 3.61 times higher than that through a conventional C‐shaped aperture with the same input power. This phenomenon, the power throughput enhancement due to the coupling between propagation modes and SPP modes, is named as the hybrid effect. Moreover, the simulation results also show an ignorable variation on the spot size in near field. Therefore, we can conclude that the hybrid effect significantly increase the power throughput without degrading the spatial resolution.
3.3.2 Corrugations in Exit Interface
Since SPP modes on both sides of a metal film contribute to the
transmission enhancement, after investigating the effect of grooves in the entrance interface, we add a corrugation in the exit interface and study the influence of groove in the exit interface on the power throughput through the C‐shaped aperture. In our optical model, the silver film thickness is 200 nm which is thick enough to suppress the tunneling effect between SPP modes on the opposite side of the metal film. Therefore, the effect of SPP modes in either interface on the transmission can be considered independently. The power throughput with various pitches, intervals, and width of the groove in the exit interface is calculated as the dimensions of the incident‐side groove with the maximum PT obtained in section 3.3.1 are the optimal condition.
Because the thick film prevents the SPP modes in the entrance interface from interacting with the SPP modes at the exit face, the transmitted field through the aperture is primarily responsible for the excitation of the exit SPP modes. The propagation modes inside the aperture enhance the emitted field and thus the SPP modes in the exit interface are induced. The re‐radiation and interference from the SPP modes in the exit interface contribute to the enhancement of the transmitted field out of the aperture. Therefore, the power throughput of the double‐side‐corrugated C‐shaped aperture is as high as 8, which is further enhanced by a factor of 1.17 higher that of the incident‐side‐corrugated C‐aperture. Moreover, the peaks shown in Fig. 3.8 can be considered as a constructive interference of the re‐radiation from the SPP modes in the exit interface while the sharp decline represents a destructive superposition of individual fields. This result indicates that the interval i is a critical factor to the field distribution.
The emitted field profile through the double‐side‐corrugated C‐shaped aperture differs from that of the incident‐side‐corrugated one due to the interference of the SPP modes. This interference alters the field distribution and consequently results in the variation of the spot size. In the case of the
x‐polarized incident light, the spot size in x‐direction is greatly reduced over 15% while the spot size in y direction remains the same. Obviously, the groove in the exit interface functions as a focusing grating at interval i of 240 nm and then causes a more convergent emitted spot. In contrast, a narrower groove width results in a narrower potential well which makes oscillation more strongly thus causes a greater variation in field distribution of the emitted light.
Fig. 3‐8 The PT as a function of the interval i on the exit plane with various widths w
The simulation results in this section demonstrate the hybrid effect induced by the coupling between the SPP modes and propagation modes inside the aperture. With a proper design of the groove surrounding the aperture on the incident plane, the incident light excites SPP modes that resonate in the interface. The interaction between the SPP modes and propagation modes results in the further power throughput enhancement. The highest power throughput occurs at interval i of 420 nm and width w of 240 nm is 6.86 at the spot size of 118x136 nm2. The groove in the exit interface functions as a grating that induces interference of SPP modes and causes a more focusing spot.
Compared to the incident‐side‐corrugated C‐aperture, the power throughput of 8 is enhanced by a factor of 1.17; while the spot size of 102 x136 nm2 is reduced by 30%.