1. Introduction

The demonstration of extraordinary optical transmission through subwavelength apertures has renewed the interest in resonant structures using metals that support surface plasmon polaritons (SPPs) [1,2]. Wavelength-dependent enhanced transmission has been demonstrated for periodic hole arrays [1–3], and for a single hole or a slit surrounded by periodic surface structures [4–6]. Both those approaches used Bragg resonances to couple the normally incident light into the SPPs. Another approach is to use Bragg resonances to act as a SPPs reflector in the plane [7–9], which has been used to enhance the subwavelength aperture array optical transmission [10].

For an even more compact reflector device with resonant transmission, here we propose using the highly reflective gold as a simple mirror, and thereby forming a compact surface plasmon (SP) microcavity. The SP microcavity is created by trench milling in a gold film. Other narrower trench structures have been proposed for channel plasmon polaritons waveguides [11–13]; those structures used a different polarization state and they relied on lateral guiding the SPPs [14], which is not the topic of this work. Here, the trench is used simply to form mirror side-walls, and thereby to create a microcavity. Due to the surface localization of the SPPs, the trench side-walls are good reflectors, even for depths of only a few hundred nanometers [15]. As a result, compact SP microcavities can be easily created using this approach. Recently, a theory was presented for enhanced coupling between plasmonic transmission lines by using a gold microcavity [16]. In that work, the transverse resonances of a corresponding periodic slit-array were considered to explain the enhanced coupling. Here, we present experimental observations and calculations of a SP microcavity enhanced transmission through a slit for the case of free-space coupling.

In this paper, we demonstrate the use of a SP microcavity formed in a gold film to resonantly enhance the transmission of light through a slit. The optical transmission is measured experimentally for SP microcavities fabricated with various widths, each having a central slit. The observed resonant transmission peak wavelengths agree well with finite-difference time-domain (FDTD) calculations. The FDTD calculations allow for near-field visualization of the SP standing waves within the SP microcavity. These near-field images elucidate the interaction between the SP microcavity and the slit in the center of the microcavity.

2. Experimental and calculation methods

2.1 Focussed-ion beam fabrication

Figure 1 shows the scanning electron microscope image of a fabricated SP microcavity with a slit and a schematic representation of the structure. Focussed ion beam (FIB) milling was used to fabricate the SP microcavity structures. The FIB milled through a 300 nm deep gold film evaporated on a glass substrate. There was a 5 nm thick chromium layer deposited to assist adhesion between the gold layer and glass substrate. A gallium beam current of 30 pA at 30 kV was used for milling. The gallium beam spot size was 7 nm. The mill rate of the gold film was calibrated using energy-dispersive x-ray analysis and it was found to be 110 nm/ms.

We fabricated six SP microcavity structures of 200 nm depth and of variable widths from 800 nm to 1300 nm. The length of these structures was 15 µm. In the middle of each structure, a 180 nm slit was milled entirely through the gold film. From past work, the 200 nm high walls of the microcavity were estimated to give 50% reflection, while having strong coupling to the input radiation through scattering [15].

 

Fig. 1. Scanning electron microscope image of w=1300 nm wide SP microcavity (200 nm depth) with central slit (180 nm width, 100 nm depth) and a schematic representation.

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2.2 Optical transmission setup

The transmission spectra were recorded using a fiber-optic coupled spectrometer. The source was focused with normal incidence onto the SP microcavity structure with a slit. An illumination spot size of 30 µm was obtained using a combination of an iris and a 20× microscope objective. A polarizer was used to control the polarization of the incident light. The zeroth order transmission was collected with a 100 µm diameter core fiber placed 1.5 mm from the sample. Positioning of the fiber core and gold slide were achieved using XYZ translation stages.

2.3 FDTD calculations

FDTD was used to calculate electromagnetic transmission characteristics of the SP microcavity structure with a slit [17]. The dispersion of the gold was captured using a Drude model. A small mesh-size of 2 nm was chosen to accurately capture SP effects, as was verified by finite-difference mode calculations and repeating the calculations with varying grid sizes (both smaller and larger). Perfectly matched layer boundary conditions were used on all sides of the calculation domain. The Courant stability factor was 0.99. To reproduce the conditions of the experiment, a broadband plane wave source (500 nm to 900 nm) was normally incident on the top surface of the SP microcavity structure, with electric field polarization in the x-direction. Near-field and transmission monitors were used to visualize standing waves within the microcavity and to quantify the transmission spectrum.

3. Results and discussion

3.1 Measured transmission spectra

Figure 2 shows the measured transmission spectra from different width SP microcavities, with incident polarization in the x-direction, normalized to the white-light source spectrum. There was no additional normalization to account for the width of the microcavity; however, the lengths of all the structures were the same. All of the structures were measured under the same conditions and the results were repeatable. The transmission for a single slit in a 100 nm gold film without a microcavity is also shown for direct quantitative comparison. (For the orthogonal polarization, no transmission was detectable, which is expected because of the reduced TE transmission through a subwavelength slit.) Resonant transmission peaks were observed with wavelength that increases as cavity width increases. For example, for a cavity width of 1300 nm, the transmission peak was at 750 nm wavelength (shown with the blue curve in Fig. 2). This resonant transmission peak was approximately 170 nm wide. There appears to be some additional structurally-dependent transmission features for shorter wavelengths (below 600 nm); however, these effects were obscured by the transmission of gold close to the plasma frequency. The measured transmission is reduced at longer wavelengths due to greater diffraction from the slit. This is an experimental artifact that arises because the 100 µm core fiber collects the transmitted light 1.5 mm from the slit. In essence, this is a zeroth-order transmission measurement.

 

Fig. 2. Measured transmission spectra for different surface plasmon microcavity widths.

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3.2 Calculated transmission spectra

Figure 3 shows the FDTD calculated transmission spectra for different SP microcavity widths for normal incidence and polarization in the x-direction. The transmission was normalized to the incident power on the width of the slit. There is good quantitative agreement between this calculation and the experimental results for the long wavelength transmission peak. For example, the 1300 nm wide SP microcavity had a calculated transmission peak at 730 nm, whereas the experimentally measured peak was at 750 nm. The small discrepancy can be attributed to fabrication tolerances and experimental error. As in the experiment, the peak transmission wavelength red-shifted when the SP microcavity width increased. The calculated transmission spectra also showed small short-wavelength transmission peaks below 600 nm; however, for these wavelengths, the Drude model does not accurately represent the gold dispersion and so the agreement with experiment is not as good [18]. For the 1100 nm, 1200 nm and 1300 nm wide structures, both experiments and calculations show transmission peaks below 600 nm. These peaks are expected as the the next higher order standing wave resonances of the microcavity structure. For example, for the 1300 nm structure, the magnetic field has two nodes for the 730 nm wavelength, and four around 550 nm. The minima in transmission occurs around where there is a node in the region of the slit, as will be discussed in more detail later (see Fig. 4(a)).

The calculated resonant transmission peak widths were smaller than in the experiments, which may be attributed to additional losses from surface roughness that is present in real fabrication. We have repeated our calculations without the slit and we still observe strong SPPs resonances inside the cavity; for example, the 1300 nm wide slit showed 72% as large a transverse magnetic field without the slit as compared to with the slit. This implies that the side walls play an important part in coupling to the input radiation, as well as the coupling as the central slit.

 

Fig. 3. FDTD calculated transmission spectra, normalized to power incident on slit, for different SP microcavity widths.

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3.3 Discussion

From the experimental and calculation results, the SP microcavity shows a resonant enhancement of the optical transmission through a slit. The experiment showed a maximum transmission enhancement of 2× with respect to the single slit and the calculations showed a maximum enhancement of 2.6×, both for the 1100 nm array. The discrepancy can be mostly attributed to fabrication tolerances (see Fig. 1). There is good quantitative agreement in the wavelength of peak transmission between experiment and calculations. The resonant enhancement is expected from coupling of the slit to standing-wave resonances of the SP microcavity, which is formed by the 200 nm tall side walls.

The SP microcavity is similar to the plane-wave microcavity, except that plane-waves are replaced with SPPs. This should shift the resonances to longer wavelengths; however, the transmission peak resonances were actually observed at shorter wavelengths. To explore this further, we consider the field distribution within the cavity for different wavelengths.

Figure 4 shows the near-field distribution of the transverse magnetic field squared magnitude for the 1300 nm cavity. It should be noted that similar features have been observed in a complimentary plasmonic cavity structure [19]. Figure 4(a) shows the near-field for 640 nm – a wavelength that is shorter than the transmission resonance peak. It is clear from this figure that the intensity maxima are away from the slit (on each side), which reduces the coupling to the slit and the overall transmission. Figure 2(b) is at the transmission resonance peak wavelength of 730 nm. It is clear from this figure that the slit introduces a strong negative phase-shift and reflection to the SPPs mode [20], which produces 3 peaks near the slit. There is also a strong intensity variation seen within the slit, which corresponds to resonances within the slit from the reflection at each end. These features are associated with the slit, and they perturb the cavity to blue-shift the resonant wavelength away from the expected values of a regular microcavity. Figure 4(c) shows the near-field distribution at 840 nm, where the SPPs is closely matched to the second order resonance of the 1300 nm wide cavity. While this does not give the largest transmission, since the coupling to the slit is not optimized, the standing wave within the cavity is seen clearly.

There may be additional resonance effects from changing the height of the cavity side-walls coming from modes in the vertical z-direction in addition to resonant modes we observe in the horizontal x-direction [16]. This influences only slightly the resonance wavelength for the short and wide cavities considered here – the resonances are mainly from the transverse SPPs propagation. For example, we varied the depth of the side-walls by 100 nm for the 1300 nm cavity in the FDTD calculations and found that the peak shift was only 20 nm.

 

Fig. 4. Transverse magnetic field (perpendicular to imaging plane) profile of 1300 nm structure for three wavelengths: (a) 640 nm, (b) 730 nm and (c) 840 nm. Scale bar is the same for all three images.

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The reflection of a 200 nm step for a gold surface was calculated using FDTD. For 750 nm wavelength, the reflection was 0.76 and the phase of reflection was 171° (close to 180° expected for a perfect electric conductor, which contributes a 1.7% shift to the resonant wavelength). For the 1300 nm cavity, ignoring the influence of the slit and the SPPs loss, this gives an optimal quality factor (Q) of 6.6. Considering this, the FWHM of the transmission resonances should be approximately 110 nm. In the FDTD calculations for the 1300 nm cavity, the transmission peak FWHM (subtracting the slit-only transmission) was 150 nm, which is larger due to material loss and scattering loss from the slit. In the experiment, the FWHM of the 1300 nm cavity peak transmission (subtracting the slit-only transmission) was 15% larger still, likely due to roughness from fabrication. The transmission resonance has an asymmetric shape, which is characteristic of Fano resonances found in similar plasmonic systems [21]. The present structure was not optimized for achieving a large quality factor because of the additional losses necessary from the slit to measure the transmission. Without the slit, the quality factor (from calculations) increases to 14.3; however, there is an intrinsic limitation from metal losses that limits plasmonic microcavities. The SPPs propagation length divided by the SPPs wavelength is an approximate upper bound for the quality factor imposed by plasmonic damping.

4. Conclusions

The optical transmission through a slit was resonantly enhanced, by a factor of 2, by forming a SP microcavity around the slit. Wavelength tuning of the transmission maxima was achieved by varying the width of the microcavity. FDTD calculations were also performed that agreed quantitatively with the experiments. The resonance transmission wavelength was dependent on the cavity width, and influenced by the presence of the slit. The compact SP microcavity geometry proposed here is easily fabricated and it may be used to provide wavelength-sensitive transmission. By extending the SP microcavity approach presented here, it is easy to envision future devices for enhancing local electromagnetic fields and for providing refractive index sensitive peak shifts. Those optimized SP microcavity structures can be applied to surface-enhanced Raman scattering, nonlinear optics and surface plasmon resonance sensors [22–27].