A T-shaped plasmonic array is proposed for application as an effective thermal emitter or biosensor. The reflection and thermal radiation properties of a T-shaped array are investigated theoretically. The angular dependent reflectance spectrum shows a clear resonant dip at 0.36eV for full polar angles. No other significant localized resonant mode is found in the investigated spectral range from 0.12eV to 0.64eV. According to the Kirchhoff’s law, the thermal radiation of the proposed structure can lead to a sharp peak at 3.5µm with low sideband emission. We have also found that the T-shaped structure filled with organic material such as PMMA with different thicknesses (10 nm -50 nm) can lead to significant shift of the resonance wavelength. Thus, the T-shaped structure can also be used as a good sensor for organic materials.
© 2009 Optical Society of America
According to the well-known Kirchhoff’s law , good light absorbers are good light emitters when they are heated. At structured surfaces, the absorption may strongly depend on the angle of incidence and the polarization of the impinging light. Strong grating anomalies, where the absorption of a metallic surface rises up to nearly 100% of the impinging light flux, are expected to behave like a black body which leads to a perfect emitter . Thermal radiation of structured surfaces, such as laminated structures [3,4], 2D/3D photonic crystals (PhC) [5–8], nanoparticle arrays [9,10], and plasmonic crystals [11–13], has been widely investigated. In addition, the grating anomaly highly depends on the incident angle of the impinging light so that the enhanced thermal radiation is observed only at a specific observation polar angle, the so-called Wolf effect [14,15]. Recently, we demonstrated a narrow band thermal radiation of a plasmonic multilayer structure  which can be fabricated more easily than the PhC structure. The thermal radiation peaks coincide with angular-independent localized surface plasmon polariton (LSPP) modes of the structure. Thus, reducing the unwanted LSPP mode becomes an alternative for suppressing the sideband of the thermal radiation.
In this paper, we demonstrate the thermal radiation properties of a T-shaped array. Comparing to our pervious work , the multiple LSPP peaks of the metal/dielectric/metal cavity are suppressed. The reflectance spectrum of the proposed structure shows only one resonance dip, which leads to a sharp thermal radiation peak with a low sideband emission.
2. Thermal radiation and angular-dependent reflectance spectrum
Although the thermally induced radiation of a structured surface cannot be quantitatively related to the reflectivity, a qualitative description is possible by investigating the angular-dependent reflectance spectrum. In the angle-dependent reflectance measurement, at a specific wavelength and angle of incidence, a minimum occurs, which is attributed to the incoming light being transformed into a surface wave which dissipates the energy in the metal that is eventually converted to thermal energy. The thermal radiation integrated over all polar and azimuthal angles of the hemisphere for a sub-wavelength structure can be regarded as the product of the black-body radiation profile and the emissivity, given by
where R(λ, θ, ϕ) is the reflectance of the proposed structure at an incident angle, (θ,ϕ) confined in the upper hemisphere, and 1-R(λ,θ,ϕ) is the absorption efficiency of the structure, assuming the effect of higher-order reflectivities is negligible. B(λ,T) denotes the thermal radiation spectrum at temperature T without the grating structure. Through Eq. (1) one can quickly obtain an estimate of the thermal radiation spectrum of a structured surface by investigating the reflectance properties.
3. Device descriptions
In this paper, we study the thermal radiation and reflection properties of T-shaped plasmonic structures. Figure 1 shows a schematic picture of the analyzed structures. For reference, a plasmonic multilayer structure, which has been extensively investigated [12,13,16], is shown in Fig. 1(a). The proposed T-shaped array on a metallic substrate is depicted in Fig. 1(b). The material of T-shaped array and the substrate is Ag. The periodicity of the T-shaped array is denoted by Λg. The widths at the top and the bottom of the T-shaped metallic line are wAg and wT, respectively. The thickness of the top of the T-shaped metallic line is tAg. To make the structure more robust, the bottom of the T-shaped metallic line are buried in a thin SiO2 layer with a thickness of tw. The substrate thickness is assumed to be infinite. The structure is illuminated with an incident plane wave at an angle θi. The reflectance of the structure is calculated by using the Rigorous Coupled Wave Analysis (RCWA) as described in ref. . The input light is TM (or TE) polarized in which the magnetic (electric) field is parallel to the grating grooves (i.e., parallel to the y-axis). The frequency-dependent complex dielectric constants of SiO2 and Ag are taken from ref. . It is found that around 50 plane waves are needed to obtain convergent results due to the localized nature of the solutions.
4. Angle-dependent reflectance spectrum and thermal emission
Figure 2(a) shows the angle-dependent reflectance spectra of the plasmonic multilayer structure with geometric parameters of Λg=3000nm, wAg=1500nm, tAg=100nm and tw=50nm. The red and blue colors respectively represent high and low reflectance. Figure 2(a) displays three resonant dips at 0.21eV, 0.37eV and 0.55eV. Figures 2(b) and 2(c) shows the Hy 2 distribution within one pitch of the periodic structure respectively for 0.37eV (θi=89°) and 0.55eV (θ i=0°). From these nodal structures, we can identify the three resonant dips at 0.21eV, 0.37eV and 0.55eV as the n=1, n=2 and n=3 Fabry-Perot cavity modes, respectively.
With the same geometric parameters, the T-shaped array with wT=800nm displays a very different property. As shown in Fig. 3, the TM mode angle-dependent reflectance spectrum shows only one clear resonant dip at 0.36eV within a wide spectrum range from 0.12eV to 0.64eV for full polar incident angles. The geometric parameters of the T-shaped array are adopted as follows: Λg=3000nm, wAg=1500nm, tAg=100nm, tw=50nm and wT=800nm.
Figure 3(b) shows the Hy 2 distribution within one pitch of the periodic T-shaped array at 0.36eV for θi=0°. The Hy 2 field distribution is symmetric with respect to the center plane (x=0nm) and localized under the cap of the T-shaped line. The Hy 2 field is localized within a one-closed-end cavity under the cap of the T-shaped, with a cavity length of Lc=(wAg-wT)/2. The wave function has a node at the open end and an antinode at the closed end. Ideally, the resonant wavelength satisfies the relation, λ=4neffLc. Here, the effective index of the resonant cavity, neff is a function of resonant wavelength and the dimensions of the cavity, so the relation is not quite linear. The Lc-dependent resonant wavelength will be discussed later. The TE mode reflectance spectra and mode pattern for the resonance dip are shown in Figs. 3(c) and 3(d). For the TE mode, there is no SPP mode since it follows different boundary conditions as the TM mode, and the Ey 2 field distribution at the resonance dip is not localized under the cap of the T-shaped line as illustrated in Fig. 3 (d).
Figure 4(a) shows the absorption spectrum for both TE and TM modes. It is clear in the figure that for TE mode most of the wave is reflected for all wavelengths, while for TM mode, there is strong absorption near the resonance wavelength. The thermal radiation spectra of the above mentioned structures are also calculated according to Eq. (1). The integration was done over 18 polar angles and 18 azimuthal angles (with 5 degree steps between 0 and 90 degrees) and B(λ,T) is taken to be the idea blackbody radiation curve at 500°C and it shows a maximum around 3.75µm. Figure 4(b) shows the simulated thermal radiation spectra of the structures. The solid and the dot-dashed lines represent the thermal radiation of the T-shaped array and plasmonic multilayer structure, respectively. The ideal blackbody radiation at 500°C is shown as dotted line. The plasmonic multilayer structure gives three thermal radiation peaks at 2.2µm, 3.1µm and 6µm, which correspond to the Fabry-Perot resonant dips at 0.55eV, 0.37eV, and 0.21eV shown in Fig. 2(a). The radiation spectrum of T-shaped array shows a single peak around 3.5µm. The other peaks due to the Fabry-Perot resonant dips, at 2.2µm and 6µm, are suppressed. Both the normal-incidence absorption spectrum and the thermal emission spectrum (integrated over all solid angles) display a strong peak near 3.5µm with similar lineshapes. This indicates that the emission pattern is nearly independent of angles, consistent to what’s displayed in Fig. 3(a). There is also a very narrow resonance peak in the normal-incidence absorption spectrum, which is caused by the angle-dependent SPP mode and it merges with the LSPP mode after the average over solid angles.
From the point of view for applications, one can modify the resonant wavelength of the T-shaped array, i.e. engineer the thermal emission peak wavelength, through adjusting the cavity length, Lc. Figure 5(a) shows the resonant wavelength as a function of Lc. wT is fixed at 800nm, while wAg is allowed to vary from 1000nm to 2000nm in steps of 20nm. Two different SiO2 thickness, tw=20nm (black square) and tw=50nm (red circle), were considered. It can be seen that the resonant wavelength red shifts almost linearly with increasing Lc. The slopes for tw=20nm and tw=50nm are 9.21 and 7.35, respectively. For a thinner tw, the effective index of the cavity (defined as the slope divided by 4) is larger. Therefore the slope for tw=20nm is larger than that for tw=50nm. The single-mode behavior remains as the cavity length changes. However, the resonance peak is less sharp as the cavity length reduces. Besides the cavity length, the refractive index inside the cavity also plays a crucial role for tuning the reflection/emission properties. Thus a T-shaped structure without SiO2 could be used as material sensor, since the reflectance spectra would be sensitive to the refractive index of the filling material.
6. Sensitivity to organic materials
The T-shaped structure without SiO2 may also be used as a biosensor, since its reflectance spectra is sensitive to the refractive index or thickness of the filling material. For example, if we fill the open area of the T-shaped structure (i.e. the region which was previously occupied by SiO2) from the bottom with an organic material, PMMA (with refractive index of ~1.49 ) and vary the PMMA thickness from 10nm to 50nm, the resonance wavelength of the reflectance spectrum can shift from 2.78µm to 3.64µm as illustrated in Fig. 5(b). The geometric parameters of the simulated T-shaped structure are: Λg=3000nm, wAg=1500nm, tAg=100nm, tw=50nm and wT=800nm. Note that we have also observed a sharp absorption at wavelength (4.52 um) due to absorption by the carbonyl bond of PMMA  and this resonance is independent of the PMMA thickness, t. The sensitivity (defined as the slop, dλ/dt) varies from 11 to 35.5 when t varies from 10 nm to 50 nm. For a PMMA thickness of 30 nm we observe a shift in resonance of 470 nm as illustrated in the inset of Fig. 5(b), which is much better than the sensor used in a previous work .
In summary, reflection and thermal radiation properties of a T-shaped array are investigated. The angular dependent reflectance spectrum shows a clear resonant dip at 0.36eV for all polar angles. Comparing to our previous work , the multiple LSPP peaks of the metal/dielectric/metal cavity are suppressed. According to the Kirchhoff’s law, the thermal radiation of the proposed structure can have a sharp peak at 3.5µm with low sideband emission. We showed that the T-shaped structure has good sensitivity to organic materials such as PMMA. This kind of radiation property with narrow bandwidth emission and low sideband could be very useful for studies of reactions of biological systems, environmental surveillance, and other industrial applications.
The authors acknowledge fruitful discussions with Ming-Wei Tsai, Yi-Han Ye, Chia-Yi Chen, Yu-Wei Jiang, Yi-Tsung Chang and Si-Chen Lee. This work is supported by Academia Sinica.
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