Surface plasmons (SPs) are electromagnetic waves that propagate along a conductor surface, whose electric field has a maximum at the surface and decays exponentially. SPs are excited generally through a coupling of an evanescent field generated by a TM-polarized light in attenuated total reflection (ATR).^[1,2] Owing to the resonant condition, the excited SP that is very sensitive to the variation in refractive index of the surrounding environment. ATR offers a potential for exploring a sensor based on surface plasmon resonance (SPR). Over recent decades, since the dramatic progress made in micro-nano-fabrication technology,^[3–5] ATR has became a useful tool in many areas, such as biology, chemistry, and environment.^[6–9] The most commonly used setup of SPR sensor is the so-called Kretschmann,^[10] in which a thin metal film is deposited on the base of a coupling prism and the sample is placed over the metal film. When we use a TM-polarized light that impinges from the base side at a certain incident angle, the light gets transferred to SP mode and will create a dip point in the reflectance curve. In order to make the sensor work in a sensitive and stable manner, till now, studying single or multilayer metal films (with different thicknesses, stacked positions, and compositions) on the resonant angle, spectrum and intensity have been reported.^[11–14] The sample’s refractive index smaller than that of the base of setup is required for ATR, or it will not work. In some cases, given a sample with a high refractive index, to choose a base with a much higher refractive index is needed. However, because of a poor chemical stability and dispersive characteristics of the base introduced, such a method is unacceptable in practice. In the face of such a situation, it is necessary to restudy the basic mechanism and rule of the sensor based on SPR.

In this paper, an improved SPR sensor is proposed to investigate the sample with a refractive index higher than that of the base. The sensor configuration is similar to the Kretschmann, but the metal film has been patterned into a subwavelength-metal grating. We will study and summarize the performance of the sensor, more detailed information is organized as follows.

The designed sensor configuration is shown in Fig. 1, which consists of two parts: one is a subwavelength-metal grating (made of silver) deposited on a SiO₂ substrate (or base), the other is the sample placed over the grating. The thickness, gap width, and period of the grating are denoted as h, w, and p, respectively. The refractive index is for the substrate and the gap filling, and for the sample. A TM-polarized laser beam (the magnetic field is perpendicular to the x–z plane, |E₀| = 1) with a wavelength of λ₀ = 632.8 nm is incident from the substrate. A two-dimensional finite-difference time-domain (FDTD) method is used to accomplish the simulation. In order to ensure accuracy, the simulated space is meshed into cells with a uniform scale of 1 nm×1 nm. The frequency dispersion of silver is modified by Drude mode as

Fig. 1.

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	Fig. 1. The designed sensor configuration.

At the very beginning of the studying, the simulation accuracy is evaluated by resorting to the sensor style of Kretschmann for h = 50 nm. In Fig. 2(a), the reflectance (R) is defined as the ratio of total energy flux reflected by the sensor to that of incidence, then the absorption (A) can be calculated by A = 1 − (R + T), where the transmission (T) is defined as the ratio of total energy flux going through the sensor to that of incidence. According to the Kretschmann mode, the resonant incident angle of θ can be obtained by

Fig. 2.

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	Fig. 2. (a) The sensing properties of Kretschmann for h = 50 nm; (b1) and (b2) the reflectance for ns = 2 at different gap widths.

As the sensor of Kretschmann is confronted with the challenge mentioned above, a feasible way of etching the metal film on it into a subwavelength grating is proposed. For learning its sensing characteristics in depth, the influence of reflectance on the grating’s gap width is studied for p = 260 nm first. In Fig. 2(b1), when a narrow gap is given, one can find that the grating has no contribution to the sensing. With the gradual increase of the gap width shown in Fig. 2(b2), a resonant dip point performance similar to that in Fig. 2(a) is observed, however, the physical mechanisms behind them are different. For the sensor with a grating, the gap serves as a channel. When the gap is tiny enough, its cut-off frequency is too high to stop the incident light coupled by the grating going through it, and while the gap is increased to satisfy with Fabry–Perot (F–P) resonance,^[17–19] it becomes open for the maximal transmission. In that case, as the increment of the grating thickness goes on, a dip in reflectance curve will emerge periodically. A vivid illustration of F–P resonance is depicted in Fig. 3, where a period changing of reflectance is shown in Fig. 3(a). With the energy flux shown in Fig. 3(b1) for h = 260 nm, from where one can find clearly that the channel offered by the gap to guide the incident light through it is correct, SPs at the grating/sample interface are generated. A phase of E_z is shown in Fig. 3(b2), which is distributed periodically for the interference of gap mode of SPs.^[20] For each phase difference of π, as the dashed lines show, the positions of what distributed are consistent with the maximal transmission positions in Figs. 3(b1) and 3(a).

Fig. 3.

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	Fig. 3. (a) Reflectance versus the grating thickness h for w = 18 nm, 8.2°; (b1) and (b2) the distribution of energy flux and the phase of Ez for h = 260 nm.

Besides the gap effects, the effects of grating period on reflectance are shown in Fig. 4(a). For one thing, if we estimate the sensing resolution by full width at half maximum (FHWM) of the reflectance curve, except for the influence of gap width on it, which is also influenced by the grating period, the best resolution gives rise to the largest period. For another thing, as the grating period is increased, in response to the dip points emerged in Fig. 4(a), the resonant incident angle is decreased. For the grating with the largest period, that means the amount of gaps etched on it is less. When the light wave goes through the gaps, it will be scattered and absorbed by the gaps to result in energy losses. The less gaps are etched on the grating, the less energy loss is, as a result of it, the best resolution is obtained for the largest period case. In addition, based on the excited SPR theory, it is well known that when a light wave is incident to a metal nanograting, except for k_x, an extra wave vector of k_g = 2π/p can be provided by the grating. The dispersion relation of k_x, k_g, and k_sp is

Fig. 4.

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	Fig. 4. (a) Reflectance curves in different grating period p cases; (b) the comparison between the theoretical and simulated results.

The dip in reflectance curve based on F–P resonance and SPR has been studied successively. Finally, with the optimized parameters of w = 18 nm and p = 260 nm, the sensing properties are discussed. For the reflectance curves shown in Fig. 5(a), there are some phenomena that should be of interest. For the sample with a higher refractive index, in reply to the incident angle, this is the same as the cases of grating period and can also be explained well for SPR by Eq. (5). The next, as seen in the figure, for the improved sensor of Kretschmann, the sensing properties of which are different from those of the traditional one, that is, no matter whether the sample’s refractive index is smaller or larger than the substrate’s, it can always work. We define the sensing sensitivity as

Fig. 5.

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	Fig. 5. (a1) and (a2) Reflectance curves in different sample refractive index ns cases; (b) the comparison between theoretical and simulated results.

A subwavelength metal-grating assisted sensor of Kretschmann has been proposed. With the study of the grating’s gap and period effects on reflectance, a cause of the dip point in reflectance curve based on F–P resonance and SPR has been proved. The sensor is able to work when the refractive index of a sample is smaller or higher than that of the substrate. A constant sensing sensitivity of 51.484°/RIU has given rise to the samples with refractive index higher than that of the substrate, and in the lower cases, the value gets higher. Our studies provide a guideline for sensing application based on the subwavelength-metal grating.