In this study, the optical properties of a plasmonic multilayer structure, consisting of tw6o longitudinally cascaded gratings with a half pitch off-set, are investigated. The proposed structure, which is a system mixing extended and localized surface plasmon, forms transversely cascaded metal/insulator/metal cavities. The angle dependent reflection spectrum of the proposed structure displays a resonance peak at a specific angle. The full-width at half maximum (FWHM) of the resonant peak is smaller than 3°. The angular dispersion of the cascading plamonic gratings is about dθ/dλ, =0.15 °/nm. The cascading plasmonic gratings can be used as a spatial filter to improve the spatial coherence of a light source.
©2009 Optical Society of America
Plasmonic multilayer structures, essentially consisting of a textured metallic film neighboring a flat metallic film, have potential applications in both passive and active optical devices, such as notch filters  and narrowband infrared emitters . The electromagnetic responses of the neighboring metallic structures are strongly coupled via evanescent fields [3–4]. The coupling depends strongly on the separation between the two metallic layers . When the separation is small, the coupling is strong. The plasmonic multilayer structures form metal-insulator-metal (MIM) cavities which allow optical mode volumes to be reduced to subwavelength scales with an extraordinarily high confinement factor [6–7]. At least four surface plasmon (SP) modes, which are both symmetric and antisymmetric in nature, exist for the finite thickness MIM structure due to splitting of the coupled plasmon modes of the two interacting metallic structures . In addition, the so-called magnetic atoms [9–12], formed by periodic arrangement of metallic grating pairs, have been found to have negative permeability, due to the presence of plasmonic modes with opposite electric dipole moments. These MIM cavities have versatile applications, such as for wavelength selection  and the omni-directional light emission .
In this study, we investigate longitudinally cascading plamonic gratings, which form a series of transversely cascaded MIM cavities. The proposed multilayer structure forms a system consisting of a propagating SP and a localized surface plasmon (LSP) coupled system. The free-space light undergoes a series of the coupling and decoupling processes via SP as it impinges on the periodic grating. It is suggested that the resonant optical properties of the cascading plasmonic gratings can be used as a free-space spatial filter to improve the spatial coherence of a light source.
2. Description of the device
The plasmonic multilayer structure is illustrated in Fig. 1. It is comprised of two plasmonic gratings cascading with a separation of tg. The slit portion of the bottom grating is symmetrically aligned to be right under the metal ridge of the upper grating. The grating periodicity and the thickness of the two grating, denoted by Λ and tm, respectively, are identical. The widths of the slits in the gratings are S1 and S2. The structure under the metal ridge of the first grating can be seen as transversely butt-jointed MIM waveguides with an air gap of width S2. The material of the plasmonic grating is silver and its dielectric constant is denoted by εAg. The wavelength-dependent optical constant of silver is taken from the tabulated data in the reference . The structure is illuminated with an incident plane wave at an angle of θi. Here, the reflection properties are simulated by using Rigorous Coupled Wave Analysis (RCWA) . The incident light is assumed to be TM-polarized in which the magnetic vector is parallel to the grating grooves (i.e., parallel to the y-axis).
3. Spatial filtering properties
The polar plot of the specular reflection spectrum (i.e. the zeroth-order reflection spectrum) is shown in Fig. 2. The geometric parameters of the cascading plasmonic gratings are denoted as follows: Λ=500nm, S 1=250nm, S 2=40nm, tg=20nm and tm=50nm. The results for the five wavelengths (from 815nm to 895nm in step of 20nm) are shown in Fig. 2. It can be seen that the resonant peaks for 785nm, 805nm, 825nm, 845nm and 865nm are at 34°, 37°, 40°, 43° and 46°, respectively. The longer wavelength has a resonant peak at larger specular angle. The full-width at half maximum (FWHM) of the peaks are all smaller than 3°. The angular dispersion of the cascading plamonic gratings is about dθ/dλ=0.15°/nm. The resonance wavelength can be predicted roughly according to the conservation of momentum for SPs
where kSP is the wave vector of the surface plasmon polariton; kx is the wave vector parallel to the grating surface; G=2πm/Λ is the reciprocal lattice vectors of the grating; m is an integer. The wavelengths of the resonance peaks simulated by RCWA are slightly longer than the predicted value based on the conservation of momentum for m=-1.
Figure 2(b) and 2(c) show the Hy 2 distribution within one pitch of the cascading plasmonic gratings for λ=825nm and an incident angle of θi=30° (away from the peak position) and θi=40° (at the peak position), respectively. It can be seen in Fig. 2(b) that the H-field is localized within the MIM cavity. The structure under the metal ridge of the first grating can be seen as transversely butt-jointed MIM waveguides with an air gap of width S 2. The length of the MIM waveguide is (Λ-S 1-S 2)/2=105nm. The standing wave interference pattern shows that both of the MIM waveguide support only one fundamental Fabry-Perot-like mode, i.e., the LSP mode. Under this condition, the light is coupled into LSP and the reflectance is low. It can be seen in Fig. 2(c) that most of the H-field is concentrated at the upper surface of the structure. In this case, it is easier for the localized field to leak into free-space to form a resonant peak. Moreover, the leaky modes have significantly higher field intensities in the air region above the structure.
When a source of focused broadband light source is incident on the device, the reflected light forms a divergent beam with a rainbow-like pattern, with long wavelength light located at the outer ring and short wavelength light at the inner ring. The color pattern is similar to the transmission of a focused white light after passing through a Fabry-Perot Etalon filter. However, with a focused monochromatic light, most of the incident light is coupled into LSP. Only the light closed to the resonant condition of the grating-coupled SP radiates into free-space. Thus, the reflected light is a collimated light with a small divergence angle.
To discuss the efficiency of the device, a practical example is demonstrated here: a focused beam with a wavelength of 825nm and a numerical aperture of 0.13 impinges onto the device. The included angle between the chief ray of the focused beam and the normal of surface is 40°. Assuming that its intensity distribution within the corresponding incident angle, 40° ± 7.5°, is uniform, 25.1% of the total input power can be filtered as a collimated beam. 67.2% is coupled into the MIM waveguides. However, as shown in Fig. 2(a), the sideband of the spectrum is not low enough. Therefore, there is 7.7% of light leaked into free-space with a divergent property.
4. Angle-dependent reflectance spectrum
Figure 3 shows the zeroth-order far-field reflectance of the cascading plasmonic gratings as a function of the photon energy and of the in-plane wavevector kx, ko sinθi, where ko indicates the wave vector in free-space. The incident angle, θi, is calculated from 5° to 60°. The geometric parameters of the cascading plasmonic gratings are denoted as follows: Λ=500nm, S1=250nm, S2=40nm, tg=20nm and tm=50nm. The red and blue colors mark the high and low reflectance, respectively. The black line indicates the SP dispersion according to Eq. (1) for m=-1. The angle-dependent reflectance spectrum shows that there is an angle-independent resonance dip at 1.52eV and an angle-dependent resonance peak. The angle-independent resonant dip has a FWHM of 65nm. This resonant dip is formed due to the LSP which is a fundamental Fabry-Perot-like mode shown in Fig. 2(a). The angle-dependent resonance peak red shifts from 1.7eV to 1.4eV when θi changes from 25° to 43°. The position of the resonance peak is in good agreement with the Eq. (1). This reveals that the dispersion curve is due to the excitation of grating-coupled SPs at Air/Ag interfaces, although the linewidth of the reflection peak is much wider than the common grating-coupled SP.
In Fig. 3, it can also be seen that the proposed cascading plasmonic structure is that of an SP/LSP combined system. The SP and LSP correspond to the angle-dependent peak and angle-independent dip, respectively. The formation of the reflection peak is described as follows. First, the free-space light obtains an additional momentum provided by the grating and the nanostructure. It is coupled into the MIM cavity through the generation of the LSP. The LSP is resonant inside the cavity and form a standing-wave interference feature. Once the wavelength is close to the resonant wavelength of the grating-coupled SP, the LSP is coupled to the upper layer and radiated into free-space. A reflection peak is formed.
Through the understanding of the formation of the reflection peak, the optical properties of the cascading gratings can be easily modified. First, the resonant wavelength can be easily designed according to Eq. (1). However, a pure propagating SP resonance usually leads to a resonant dip rather than a peak in the reflection spectrum. Through cascading plasmonic layers, new coupled SP modes, the LSP, can be formed. In this study, the LSP is coupled within a MIM waveguide. The resonant wavelength of the LSP can be easily adjusted by modifying the length of the MIM waveguide (Λ-S 1-S 2)/2. The longer the MIM waveguide, the longer the LSP resonant wavelength is. When the resonant wavelength of the LSP is in the regime of Λ/2 to Λ, the LSP can be decoupled via the grating-coupled SP for m=-1. However, when the LSP wavelength is longer than Λ, there is no overlap between the SP and the LSP. At this time, the LSP cannot be coupled out by the grating.
The coupling effect between the two cascading MIM waveguides is also investigated. Figure 4(a) shows the zeroth-order far-field reflectance of the cascading plasmonic gratings with geometric parameters of Λ=500nm, S1=180nm, S2=110nm, tg=20nm and tm=50nm. The incident angle, θi, is calculated from 5° to 60°. The red and blue colors indicate the high and low reflectance, respectively. The length of the MIM waveguide is identical to the case shown in Fig. 3 but with a larger air separation, S2=110nm. The angle-dependent reflectance spectrum also shows an LSP resonant dip at 1.54eV which is slightly blue-shifted from that in Fig. 3. In addition, the LSP resonance dip becomes red-shifted when it is close to the grating-coupled SP mode. Fig. 4(b) shows the H-field distribution of the corresponding structure for λ=825nm at an incident angle of θi=30°. It can be seen that the field is localized in one of the cascaded MIM waveguides and hence the two MIM waveguides are not coupled. In addition, the 40-time localized field enhancement is lower than that shown in Fig. 2(a).
In this study, we have investigated the optical properties of longitudinally cascading plasmonic gratings. Two plasmonic gratings with a half pitch off-set form a series of transversely cascading MIM cavities supporting LSP modes. The H-field distribution shows that the localized field leaks into free-space when it is close to the resonant condition of the grating-coupled SP. After a series of coupling/decoupling processes through the formation of the SP/LSP combining system, a resonance peak is formed. It is shown that the reflected light can be collimated with high spatial coherence by illuminating the proposed structure with a focused monochromatic light. The illuminating of the device with a focused white light produces a reflected beam displaying a rainbow-like pattern.
This work was supported by the National Science Council of Taiwan, R.O.C., under project number NSC 97-2218-E-259 -004 -.
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