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We report numerical analysis of the coupling of localized surface plasmons to the modes of U-shaped cavities. The coupling results in intense resonance for which the electric field is strongly enhanced on the cavity surfaces. As a result, an optical vortex in the power flow is formed in the cavities and a sharp and strong resonance dip is observed in the reflectance spectrum. High sensitivity of the dip wavelength to change in the refractive index of the surrounding medium is reported. The high sensitivity is realized with a small number of cavities, thus enabling miniaturization of detectors based on U-shaped cavities.
©2013 Optical Society of America
1. Introduction
Metallic nanostructures have received significant attention due to their ability to sustain surface plasmons. The interaction of light with the metallic nanostructures results in the collective oscillations of free electrons at a specific wavelength. The electron oscillations are confined within the nanostructures, so that the phenomenon is referred to as localized surface plasmon resonance (LSPR) [1]. LSPR properties are determined by the nanostructure parameters that can be designed to suit the requirements of a wide range of applications. Recently, biosensors based on LSPR have become an intensively researched topic thanks to the superior sensitivity and small surface requirement of LSPR [2,3]. Indeed, detection based on conventional propagating surface plasmon resonance (SPR) requires large surface and complicates the optical systems resulting in bulky detection systems. In contrast, LSPR sensors can be designed with simple optical systems and do not require large propagation area due to the localized nature of the resonance. Thus, LSPR-based sensors with their simple designs and miniaturization ability have potential to be integrated in micro-fabricated devices [4].
For the purpose of biosensing, the same principle of detection is applied in both the conventional propagating SPR and the localized LSPR, namely, the sensor response is recorded as a variation in the reflectance spectrum upon change in the surrounding refractive index. A robust and widely used response is in the form of a shift in the resonance wavelength. The amount of shift is determined by the refractive index sensitivity, the difference in the refractive index between the adsorbate and the surrounding material, the thickness of the adsorbate layer, and the characteristic decay length of the electromagnetic field [5,6]. Although the refractive index sensitivity in the LSPR sensors is not as high as in the SPR sensors, the LSPR sensors have higher sensitivity to adsorbate because of stronger light confinement and smaller decay length of the electromagnetic field. That is, the LSPR sensors have high sensitivity performance in the region near the surface of the nanostructures and thus provide superior detection performance for adsorbates.
Nanoparticles have been used in LSPR sensing in the form of suspensions in solutions and layers on substrates. The shape and size of the nanoparticles have been varied to excite LSPRs at different resonance wavelengths [7]. Among nanoparticles, nanospheres were first reported to have high sensitivity to refractive index and offer control over the resonance wavelength with density and size [8,9]. Nanobars and nanorices showed clear dependence of the resonance with geometrical parameters [10–13]. High-aspect-ratio nanorods were found to sustain different plasmonic modes in the longitudinal and transverse directions and were applied to the detection of mixtures of biomolecules [14,15].
The LSPR biosensors have the same merits as the SPR biosensors, namely real-time and label-free detection [3,9,16]. The main demerit of the LSPR based biosensors lies in the difficulty in tuning the LSPR wavelength with nanoparticle parameters such as permittivity and size, as there exists no simple relation between the LSPR wavelength and LSPR extinction magnitude of nanoparticles and their parameters such as size and shape [17,18]. A different approach is to fabricate nanostructures on a substrate by lithography to obtain a wide variety of shapes and an accurate control of dimensions [19–23]. Among the nanostructures, cavities are promising because cavities not only support LSPRs but also cavity modes [24,25]. Moreover recent reports show that vertical (in relation to the substrate) surfaces of cavities can support surface plasmon polaritons [26,27]. To achieve superior properties for sensing, the coupling of LSPR to cavity modes seems to be a promising design.
In this report, a U-shaped cavity structure is proposed to achieve the coupling of LSPRs to cavity modes. The coupling to the cavities results in a sharp and strong resonance for which the electric field is strongly enhanced on the cavity surfaces. A clear optical vortex in the power flow of the cavity is generated. Thus, the U-shaped cavity structure offers large surface for sensing and has potential to increase sensitivity to variation in refractive index of the surrounding medium. A sensitivity S to refractive index of 1929 nm/RIU and a figure of merit FOM of 35.7 were obtained. The values for the sensitivity S*, defined as the variation in reflectance intensity per RIU, was 25.4 per refractive index unit (RIU) and the figure of merit FOM*, defined as the ratio between sensitivity S* and reflectance, was larger than 106. The resonance wavelength is tunable by modifying the geometry of the cavities; therefore, a wide range of applied wavelengths is available for sensing. With the efficient coupling of LSPRs to cavity modes, the light is found to be well confined in a single cavity, so that a small number of cavities forming an array performed equally to an infinite array of cavities in terms of sensitivity and FOM. Sensors fabricated with a small number of cavities are very promising for practical integration and miniaturization in biosensing applications. Finally, it should be noted that metallic cavities with high-aspect-ratio walls such as those of the U-shaped cavities can be fabricated by a low-cost technique [28].
2. Coupling of localized surface plasmons to U-shaped cavity
2.1 Optical behavior
The schematic of the studied U-shaped Au cavity structure on a silicon (Si) substrate is given in Fig. 1(a) together with the cavity parameters, namely, the period p, the height h and the thickness t of the Au layers. The Au permittivity is described by the Lorentz-Drude dispersion model [29]. Light is incident on the structure surrounded by a medium of refractive index n at an angle θ with p-polarization. A reflectance spectrum of a cavity structure having p = h = 1 μm, t = 50 nm performed at θ = 35 degrees in air (n ≅ 1) simulated with the rigorous coupled-wave analysis (DiffractMOD, Rsoft Design Group, Ossining, USA) is presented in Fig. 1(b). A sharp dip in the reflectance spectrum is observed at the resonance wavelength of 1891 nm having a low reflectance below 0.01 and a full width at half maximum (FWHM) of 42 nm.
Fig. 1 (a) Schematic of the studied U-shaped cavity together with the direction and polarization of the incident light. The parameters are the period p, the height h, the Au layer thickness t, the incident angle θ, and the refractive index of the surrounding medium n. (b) Simulated total reflectance spectrum performed with periodic boundary conditions for p = h = 1 μm, t = 50 nm, θ = 35°, and n = 1 (the total and the zero order reflectance spectra are the same in the region of the resonance dip).
The light behavior in the cavity structure exhibiting a sharp and strong dip is first examined with simulation of the enhancement of the electric field density computed using the finite-difference time-domain technique (FullWAVE, Rsoft Design Group, Ossining, USA). The electric field density (relative to free space) calculated at the resonance wavelength of 1891 nm (Fig. 1(b)) is presented in Fig. 2(a) . Strong excitation of LSPRs is observed at the top and bottom of the vertical walls. Also, strong field confinement is seen on both the wall and bottom surfaces of the cavity. The electric field density enhancement relative to free space reaches 8000 (800) at the top (bottom) corners of the walls, and ranges from 200 to 900 on other surfaces of the walls and bottoms. Next, the components Ex and Ez of the electric field are shown in Fig. 2(b). It is found that adjacent walls have symmetric distribution for the Ex component and adjacent bottoms have antisymmetric distribution for the Ez component. Finally, the time-averaged Poynting vector field at the resonance wavelength of 1891 nm is shown in Fig. 2(c). A clear vortex pattern is observed in the simulated power flow of the cavity. The optical vortex results from the coupling of the LSPRs to a cavity mode with symmetric Ex and antisymmetric Ez distributions of the electric field components. As a result of the optical vortex, light is efficiently trapped in the cavity and thus a sharp and strong dip is observed in the reflectance spectrum. Moreover, the intense power flow is confined on the surfaces of the vertical walls and the horizontal bottoms.
Fig. 2 (a) Simulated time-averaged electric field density in a cavity at the resonance wavelength of 1891 nm performed with periodic boundary conditions (the density relative to free space is shown on a log scale). The insets show high resolution images of the simulated field density. (b) Distributions of the electric field components Ex and Ez. (c) Time-averaged Poynting vector field at the resonance wavelength of 1891 nm. Optical vortices are clearly seen near the cavity center and the tops of the vertical walls. The parameters have the same values as those in Fig. 1(b).
In conclusion, the sharp and strong reflectance dip is explained by the presence of LSPRs that are coupled to cavity mode, thus forming an optical vortex in the cavity. The calculated power flow suggests that high sensitivity to refractive index can be achieved in U-type cavities, not only because the U-cavities offer large surface for sensing due to the high-aspect-ratio of the structure, but also because the electric field is strongly enhanced and confined on the cavity surfaces. This unique property of light trapping and field enhancement and confinement on the surfaces of a structure is obtained thanks to the combination of LSPRs and cavity properties. Owing to the huge variation in the electric field magnitude within small distances from the cavity surfaces and the optical vortex of the power flow, the U-shaped cavity structure has potential to increase sensitivity to change in the surrounding medium refractive index, especially for molecular sensing based on change in surface conditions caused by anchored molecules.
2.2 Discussion
Since the incident light is trapped at specific wavelengths in the U-shaped cavities, the relation between the resonance frequencies and the period of the cavity should give evidence for the presence of cavity modes. Reflectance variation of the arrayed U-shaped cavities with the period (p = h) and the incident wave frequency is shown in Fig. 3(a) for the following parameters t = 50 nm, θ = 35 degrees and n = 1. The reflectance results of Fig. 3(a) reveals a 1/p dependence with the incident light frequency and the occurrence of more than one resonance wavelength in a U-shaped cavity structure. This is evidence for the formation of standing waves at different cavity modes. Thanks to the 1/p dependence, the resonance wavelength can easily be controlled by varying the period of the cavities, thus enabling sensing for a wide range of wavelengths.
Fig. 3 (a) Reflectance variation with the incident light frequency and the cavity period p (p = h) at a fixed angle θ = 35 degrees. (b) Reflectance variation with the incident light wavelength and the incident angle θ for p = h = 1 µm. All calculations were done with t = 50 nm.
Another remarkable behavior is found in the dip resonance wavelength dependence with the incident angle. Figure 3(b) shows that the dip wavelength is little affected by change in the incident angle over a wide range of angles. This rather counter intuitive behavior means that U-type cavities realize light trapping with little constraint on the incident angle. Under the Fig. 3(b) conditions (p = h = 1 μm, t = 50 nm and n = 1), the resonance wavelength varies by less than 6% from the lowest value of 1888 nm at θ = 45 degrees to the highest value of 1997 nm at θ = 89 degrees. The incident angle has also only a slight effect on the magnitude of the reflectance dip in the range from θ = 25 to 75 degrees, the lowest reflectance being at θ = 35 degrees. In conclusion, light is effectively trapped in the cavities at resonance wavelengths with little dependence on the incident angle. In contrast to the conventional SPR for which the incident angle plays a major role to control the resonance wavelength, the U-type cavities exhibit resonance wavelengths almost independent of the incident angle which could be an advantage for the design of detectors.
From the above discussion, it is clear that incident light is trapped in the cavities and follows the behavior of a standing wave by forming an optical vortex in each cavity. For this reason, a structure consisting of a finite number of cavities is expected to behave similarly to a structure made of an infinite number of cavities. This property is promising for miniaturization of detectors based on U-shaped cavities. The behavior of a finite number of U-shaped cavities is investigated using perfectly matched layer (PML) boundary conditions. The simulation results are shown for structures consisting of 5 and 10 cavities in Fig. 4 and compared with an infinite array of cavities simulated with periodic boundary layer conditions. The time-averaged Poynting vector magnitude distributions of the infinite array of cavities and the 5 and 10 cavity structures have all very similar patterns with optical vortices, as reported in Fig. 2(c). The magnitude of the Poynting vector differs between the infinite and finite arrays, with larger values for the maximum magnitudes obtained in the case of the finite array. Thus, the incident light is trapped in the 5 and 10 cavity structures as efficiently as or even more efficiently than in the infinite structure. It is concluded that structures consisting of a finite number of U-shaped cavities have potential to realize small size detector with high sensitivity for use in micro-integrated analysis systems.
Fig. 4 Time-averaged Poynting vector magnitude distribution of (a) a 5 cavity structure, (b) a 10 cavity structure, and (c) an infinite array of cavities. The parameters have the same values as those in Fig. 1(b). The resonance wavelengths were 1886 nm, 1885 nm and 1891 nm for the 5, 10, and infinite number of cavities, respectively.
3. Application of U-shaped cavity structures
3.1 Sensitivity and figure of merit
For biosensing applications, the sensitivity S to refractive index is defined as the sensor response (shift value of the resonance wavelength in this report) per refractive index unit (RIU). The sensitivity S is typically evaluated by measuring the sensor response with varying the refractive index of the surrounding medium. Here, the variation of the reflectance spectrum of the U-shaped cavities (p = h = 1 μm and t = 50 nm) under different surrounding media (n = 1.333 and n = 1.361) with light incident angle at θ = 35 degrees are computed and examined.
The results shown in Fig. 5(a) reveal a shift of the resonance dip to longer wavelengths when the refractive index of the surrounding medium increases. The refractive index sensitivity is calculated to be 1929 nm/RIU. In practical measurements, the sensitivity performance is not only dependent on the shift magnitude of the resonance wavelength, but also on the width of the dip. That is, a sharp dip of the resonance is essential for sensing. The effect of the dip width is typically modeled with the full width at half maximum (FWHM), which in our case is 54 nm (Fig. 5(a)). Both the resonance FWHM and the sensitivity S are known to strongly depend on the geometry of nanostructures. Thus, S and FWHM are combined to calculate an index that better represents the performance of sensors: the figure of merit (FOM), defined as FOM = S/FWHM [30]. FOM is found to be 35.7 for our U-shaped cavities. The reported U-shaped cavities achieve high sensitivity in terms of absolute shift (1929 nm/RIU) and figure of merit (35.7), with performances that are among the best for detectors based on cavity designs.
Fig. 5 (a) Simulated reflectance spectra of the Au U-shaped cavities for p = h = 1 μm, t = 50 nm and θ = 35 degrees. The solid and dashed curves show the results for two surrounding media of different refractive indices (n = 1.333 and 1.361). (b) Calculated S* with a maximum value reaching 25.4. (c) Calculated FOM* with a maximum value over 106.
A different methodology for the evaluation of the performance of biosensors was recently proposed to better take account of practical sensing techniques that often rely on the variation of reflectance at a specific wavelength. In this methodology, the sensitivity S* was defined as the variation of the reflectance R per RIU (S* = ΔR/Δn), and the figure of merit FOM* is defined as FOM* = (ΔR/Δn)/R [31]. The sensitivity S* and the figure of merit FOM* for the U-shaped cavities are shown in Fig. 5(b) and Fig. 5(c), respectively. We found S*max to be 25.4 per RIU and FOM*max larger than 106. The large values of S*max and FOM*max are achieved thanks to the very low resonance reflectance that is a consequence of the efficient light trapping in the cavities.
3.2 Tunable ability of the resonance wavelength
Utilizing the U-shaped cavities offer a wide range of resonance wavelengths for sensing. From the results of Fig. 3(a), the resonance wavelength is controlled by varying the period of the cavities. A systematic analysis of the performance of the U-shaped cavities over a wide range of wavelengths is presented in the following. The resonance wavelength of the cavities and the corresponding FOM are shown as a function of the period of the cavities in Fig. 6 . The resonance wavelength varies linearly with the cavity periods in the range from 0.4 to 5 μm. Moreover, FOMs above 28 were obtained for cavity periods from 0.4 to 5 μm, thus enabling high sensitivity over a wide range of resonance wavelengths (1062 to 12326 nm). The most sensitive region is found in the short wavelength region for which FOM above 31 are achieved with periods smaller than 2 μm.
Fig. 6 FOM (open circle) and resonance wavelength (filled square) variations with the period of the U-shaped cavities when n is varied from 1.333 to 1.361. The ratio between period and height of the cavities is kept constant (p = h), θ = 35 degrees and t = 50 nm.
3.3 Miniaturized sensors based on finite arrays of cavities
To apply the U-shaped cavities as sensors in micro integrated analysis systems, the miniaturization of the cavity structure is an essential issue. The results of Fig. 4 show clear light trapping with a small number of cavities and therefore suggest the possibility of realizing a sensor less than 10 µm in size. In this section, the performance results of the finite arrays of Fig. 4 are quantified using the indices for sensitivity and figure of merit. The indices calculated from the normalized (to effective area) reflectance spectra of the structures having 5 and 10 cavities are listed in Table 1 and compared with the indices of an infinite array of cavities. It is found that high sensitivity and figure of merit were achieved with the finite arrays without significant degradation of performance. The sensitivities S and S* and the figure of merit FOM are not affected significantly by the use of a finite number of cavities. The figure of merit FOM* decreases to 300 due to a slight increase in the reflectance (from 10−4 to 10−1) at the resonance. In summary, high sensitivity is achieved with a small number of cavities (less than 10) and the performance of the finite cavity array is not significantly degraded over that of the infinite cavity array, except for the FOM* index. We conclude that the U-shaped cavities enable the fabrication of small size detector with high sensitivity for use in micro-integrated analysis systems.
Table 1. Sensitivities and figure of merits for infinite and finite arrays of cavities
3.4 Local refractive index sensing with finite arrays of cavities
In order to apply the U-shaped cavity structure to molecular sensing through the formation of a layer of adsorbed molecules, numerical simulations were performed to evaluate the effect of a change in refractive index localized near the surface of the cavities. For this purpose, a biomaterial layer representing human IgG with an average thickness of 10 nm and a refractive index n = 1.450 was added on the cavity surfaces [32–35]. The refractive index of the surrounding medium was n = 1.333. The effect of the added layer of biomaterial shifted the resonance dip by ∆λ = 6 nm toward longer wavelengths. Experimental shifts obtained with gold nanoparticles (spheres and core-shell nanorods) fall in the range from 5 to 14 nm [36,37]. We note that using a smaller period of the cavity of 0.5 µm results in an increased shift of 7 nm. Moreover, it is found that the shift magnitude of the U-shaped cavities is not changed when the number of cavities is decreased to 10 or even 5. This is evidence for the ability of the U-shaped cavities to detect local refractive index and realize small size detectors with high sensitivity.
4. Conclusion
We proposed a new structure consisting of metallic U-shaped cavities that efficiently trap light by confining the power flow near the cavity surfaces. This property is realized by coupling the localized surface plasmons to cavity modes, thus forming a resonance that is clearly seen as a sharp and strong dip in the reflectance spectrum of the U-shaped cavities. Strong electric field enhancement is found on the cavity surfaces, both walls and bottoms. The distribution of the electric field exhibits dipolar distribution on adjacent walls and bottoms. As a consequence, an optical vortex in the power flow is formed in the cavity. The light trapping efficiency and its associated reflectance dip have little dependency with the incident angle and the number of cavities. Also, the resonance wavelength of the U-shaped cavities is easily tuned over a wide range of wavelengths thanks to the control of the cavity modes with the cavity dimensions. The sharp and strong resonance dip of the reflectance spectrum is found to be highly sensitive to variation in the refractive index of the medium surrounding the cavities. The performance of the cavities in sensing was evaluated by simulation of infinite and finite arrays of cavities. For the infinite array, the simulated results of sensitivities to refractive index give values as large as S = 1929 nm/RIU, S* = 25.4, FOM = 35.7, and FOM* > 106. Finite arrays with 5 and 10 cavities do not degrade the performance except for FOM*, which was still larger than 300. In overall, the performance of the finite arrays of cavities was the same as that of an infinite array. The results of this study shows that a small number of cavities (<10) is enough to obtain a sharp and strong resonance, so that a detector based on the U-shaped cavities can be fabricated within a few micrometers and thus integrated in micro-fabricated devices. Furthermore, the shift of the resonance dip is also confirmed for the change in the local refractive index near the cavity surfaces. Our investigation shows that the U-shaped cavities have potential to realize small size detectors with high sensitivity to local change in refractive index and thus open new possibilities in micro-integrated analysis systems.
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