1. Introduction

Surface plasmon resonance (SPR) sensors have been extensively explored for biochemical or biomedical applications [1]. Refractive index variations in the analyte, as the result of a bio-molecular interaction, are rapidly monitored with SPR techniques providing a high sensitivity and a label-free analysis. Various types of SPR sensors have been investigated. Prism coupling is the most widely used method among the SPR platform [2], but the prism is too bulky to integrate. Other types of SPR sensors have been proposed, including a nanoparticle-based sensor [3,4], an EOT-based sensor [5], a ring resonator-based sensor [6], and so on.

In recent years, there has been a growing tendency to incorporate SPR sensors within a photonic integrated circuit to form lab-on-chip systems [7]. Such an integrated system would bring the benefits of a high level of automation, improved performance and low-cost large-scale production. Some integrated SPR solutions have been realized. Galina Nemova and associates proposed a Mach-Zehnder interferometer based SPR sensor to detect phase variation [8]. The sensitivity of the sensor was ~250 nm/RIU. Yang Hyun Joo and associates proposed a Bragg grating resonance sensor based on long-range SPR excited on an asymmetric double-electrode waveguide structure with a μ-fluidic channel [9]. The sensitivity was about ~120 nm/RIU, and the bulk index resolution was of the order 10⁻⁷-10⁻⁶ RIU. Yifen Liu and associates numerically presented SPR sensors based on an asymmetric metal-insulator-metal (MIM) waveguide structure as a solution to enhance the coupling between SPPs and optical waves propagating along dielectric waveguides [10]. They obtained SPR sensing resolutions of 1.53$\times$10⁻⁵ RIU. Yi-Shin Chu and associates investigated SPR sensors made by multi-mode silica-on-silicon channel waveguides with a sensitivity of ~683 nm/RIU in the 1.333-1.348 index range [11].

In this paper, we propose a tiny SPR sensor integrated on a Si waveguide based on vertical coupling into a finite thickness MIM (f-MIM) plasmonic waveguide structure acting as a Fabry-Perot (FP) resonator. MIM waveguides use gap surface plasmons that allow extremely tight mode confinement and high field enhancement [12], and are thereby especially suitable for sensing applications. The development of a silicon-based SPR on-chip platform also allows for potential integration of existing CMOS technology with nanophotonic structures and devices. We theoretically and numerically investigate the resonant characteristics of a vertically coupled f-MIM plasmonic waveguide, and then show the sensing characteristics of a tiny SPR sensor integrated on Si waveguide.

2. Structure design and calculation based on fabry-perot resonator

As shown in Fig. 1(a) , the proposed tiny SPR sensor structure is simply composed of a f-MIM plasmonic waveguide vertically coupled with a Si waveguide. At a resonant wavelength, for the TM-polarization (magnetic field along the y-axis), the evanescent field of the Si waveguide was coupled into a f-MIM plasmonic waveguide structure acting as a FP resonator. The resonant wavelength was dependent on various external parameters, such as the core (analyte) thickness, the length of the f-MIM plasmonic waveguide, and the refractive index of analyte. The refractive index of the Si and SiO₂ was assumed to be 3.24 and 1.45, respectively, and the height of the Si waveguide (h) was set to be 250 nm. For a f-MIM plasmonic waveguide, t_a, t_m, and L_FP stand for the core (analyte) thickness, the metal thickness, and the length of the f-MIM plasmonic waveguide, respectively. The refractive index of the analyte, n_a, was set to be 1.33, and the complex relative permittivity of gold was described by the well-known Drude model${\epsilon }_{Au}(\omega )={\epsilon }_{\infty }-{\omega }_p{}^2/({\omega }^2+i\gamma \omega )$, with${\epsilon }_{\infty }=1.1431$,${\omega }_p=8.69\text{eV}$ and $\gamma =0.071\text{eV}$(parameters obtained by fitting the experimental data [13] at the infrared frequencies). The contour profile of the magnetic (H_y) field distribution, which is calculated from the two-dimensional (2D) finite-difference time-domain (FDTD) method, in the proposed structure at λ = 1.55 μm in which L_FP=250 nm, t_a=50 nm, and t_m=50 nm is depicted in Fig. 1(b).

 

Fig. 1 (a) Schematic of the proposed tiny SPR sensor integrated on a Si waveguide. (b) The magnetic (H_y) field distribution at λ=1.55 um in which L_FP=250nm, t_a=50nm, and t_m=50nm.

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To understand the resonant characteristics of the proposed structure, we theoretically investigated the characteristics based on a three-layer FP structure, which was composed of an air (n_air=1)/f-MIM waveguide (n_{eff, f-MIM})/Si waveguide (n_{eff, Si}). First, to obtain the effective refractive index of the f-MIM plasmonic waveguide, we derived the expressions for the dispersion of the SPP modes in the f-MIM waveguide. The f-MIM waveguides support the four geometry modes – two symmetric and two antisymmetric - because of the coupling between the four metal-dielectric interfaces in the geometry [14, 15]. We define the mode symmetry in terms of the magnetic field (H_y) with respect to the waveguide median. Solving the Maxwell equation using the boundary condition for the symmetric modes, we find the following dispersion relation:

The dispersion relation for the antisymmetric modes is given by replacing $\coth (k_{z1}{t}_a/2)$with $\tanh (k_{z1}{t}_a/2)$in the left hand side of Eq. (1)-(2). Figure 2(a) shows the dispersion relation of the f-MIM waveguide with t_a=t_m=50 nm and the MIM waveguide with semi-infinite metal thickness. As shown in Fig. 2(a), the dispersion relations for the two symmetric modes of the f-MIM waveguide were nearly identical to that of the MIM waveguide. The results in Fig. 2(b) indicate the mode profile of the f-MIM SPP and the MIM SPP at λ=1.55 μm, and Fig. 2(c) shows the effective refractive index (n_eff) for the S+ mode of the f-MIM waveguide as a function of wavelength as the core thickness (t_a) was varied from 30 nm up to 100 nm, and in which t_m was kept as 50 nm. For a wavelength of 1.55 μm, the effective refractive indices of the f-MIM waveguide with t_a=30, 50, 70, and 100 nm were 2.13, 1.85, 1.72, and 1.61, respectively.

 

Fig. 2 (a) The dispersion relation of the f-MIM plasmonic waveguide (n = 1.33 and 1 are the waveguide core and cladding indices, respectively) and the MIM waveguide. The antisymmetric modes of the f-MIM waveguide do not appear in this wavelength range. The inset shows (top) the enlarged view of the dispersion relation in the 1.5–1.6 μm wavelength range and (bottom) the geometry of the f-MIM waveguide. (b) The H_y field patterns (λ=1.55 μm) of the f-MIM SPP modes with t_a=t_m=50 nm and the MIM SPP mode as a function of z. (c) Effective refractive indices (n_eff) of the Si waveguide (dashed line) and the f-MIM waveguide (solid line) as a function of wavelength when t_m is 50 nm. The inset shows the schematic of the Si waveguide structure used for calculation of the effective refractive indices. The resonant wavelength from the calculated results (d) as a function of L_FP when t_a and t_m are both 50 nm, (inset) as a function of t_a when L_FP and t_m are 250 nm, 50 nm, respectively.

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The effective refractive index of the Si waveguide was calculated based on three-layer planar waveguides, which comprised the f-MIM waveguide (n_{eff, f-MIM})/Si (n_Si)/SiO₂ (n_SiO2) as shown in the inset image of Fig. 2(c). Figure 2(c) shows the effective refractive index of the Si waveguide as a function of wavelength as core thickness (t_a) was varied from 30 nm up to 100 nm, in which t_m was kept as 50 nm. For a wavelength of 1.55 μm, the effective refractive indices of the Si waveguide with t_a=30, 50, 70, and 100 nm were 2.28, 2.17, 2.13, and 2.11, respectively. As the core thickness (t_a) increased, the effective refractive index (n_eff) of the f-MIM waveguide and the Si waveguide decreased.

Based on the calculated results of the effective refractive indices, the resonant wavelength of the f-MIM plasmonic waveguides vertically coupled with a Si waveguide can be simply estimated with the following equation:

Figure 2(d) shows the resonant wavelength calculated from Eq. (4) as a function of L_FP when t_a and t_m are both 50 nm and the inset of Fig. 2(d) as a function of t_a when L_FP and t_m are 250 nm, and 50 nm, respectively. The operating wavelength of the proposed structure can be effectively modulated by altering the length and the core thickness of the f-MIM waveguide.

3. Simulation results

The 2D FDTD method was used to obtain the spectral response of an f-MIM plasmonic waveguide vertically coupled with a Si waveguide. Figure 3(a) shows the transmission spectra when L_FP ranged from 200 nm to 300 nm and t_a and t_m were both kept as 50 nm, and the resonant wavelength as a function of a L_FP is shown in Fig. 3(c). Figure 3(c) reveals that the resonant wavelength had a linear relationship with the length of the f-MIM plasmonic waveguide and exhibited a redshift with an increasing value of L_FP, which agrees with the solution of Eq. (4). For a resonant wavelength of 1.55 μm, we calculated the length (L_FP) of the f-MIM waveguide with Eq. (4) and found it to be 245 nm, which is quite close to the value of 250 nm from FDTD simulated result. Figure 3(b) shows the transmission spectra when t_a equals to 30 nm, 50 nm, 70 nm, 100 nm and L_FP and t_m are kept as 250 nm, 50 nm, respectively, and the resonant wavelength as a function of a t_a is shown in Fig. 3(d). For a core thickness (t_a) of the f-MIM waveguide of 50 nm, the resonant wavelength is 1.576 μm from calculated results, as compared to 1.55 μm from the 2D FDTD results.

 

Fig. 3 Transmission spectra for the proposed tiny SPR sensor integrated on a Si waveguide (a) with L_FP ranging from 200 nm to 300 nm, in increments of 20 nm (exception: 10 nm between 240 nm and 260 nm), in which t_a and t_m are both kept as 50 nm, (b) with t_a equaling 30 nm, 50 nm, 70 nm, and 100 nm, in which L_FP and t_m are kept as 250 nm, 50 nm, respectively. The resonant wavelength from calculated (black dots and line) and 2D FDTD simulated (red dots and line) results (c) as a function of L_FP with t_a=t_m=50 nm, (d) as a function of t_a with L_FP=250 nm and t_m=50 nm.

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4. SPR sensor

We investigated the sensitivity of a f-MIM plasmonic waveguide vertically coupled with a Si waveguide to change the refractive index of analyte (n_a) at 1.33-1.35 RIU. Figure 4(a) shows the transmission spectra for the proposed tiny SPR sensor integrated on a Si waveguide in which L_FP=250 nm, t_a=t_m=50 nm, and Fig. 4(b) shows the resonant wavelength shift when the refractive indices of the analyte are varied from 1.33 to 1.35. The slope of the resonant wavelength shift is nearly constant, ~635 nm/RIU, which is moderate as compared with other SPR on-chip platforms [8,9,11]. Assuming the ability to detect 0.03% change in power, the sensing resolution around λ=1.5 um was ~2.5x10⁻⁴ RIU. This is about one order of magnitude lower than published result under the same detectible ability [10].

 

Fig. 4 (a) Transmission spectra for the proposed tiny SPR sensor integrated on a Si waveguide in which L_FP=250 nm, t_a=50 nm, and t_m=50 nm when the refractive index of the analyte is changed from 1.33 to 1.35 RIU. (b) Resonant wavelength as a function of the refractive index of the analyte. (c) Schematic of the tiny SPR sensor integrated on a Si waveguide with a micro/nano fluidic channel. (d) Transmission spectra for the left inset of Fig. 4(d) which is the cross section in the micro/nano fluidic region of Fig. 4(c), in which L_FP=250 nm, t_a=50 nm, and t_m=50 nm when the refractive index of the analyte is changed from 1.33 to 1.35 RIU. The right inset shows the resonant wavelength shift as a function of the refractive index of the analyte.

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Figure 4(c) shows the schematic of the tiny SPR sensor integrated on Si waveguide with a micro/nano fluidic channel, which can be fabricated by patterning nanoscale structures as the sacrificial material using E-beam lithography [16] and removing the sacrificial material in a subsequent process. Figure 4(d) shows the transmission spectra for the inset of Fig. 4(d), which is the cross section in the micro/nano fluidic region of Fig. 4(c). Under the same structure parameters as in Fig. 4(a), with L_FP=250 nm and t_a=t_m=50 nm, the resonances occur around 1.59 μm, as compared to 1.55 μm in Fig. 4(a), and the sensitivity was calculated to be ~460 nm/RIU, as compared to ~635 nm/RIU in Fig. 4(b).

5. Conclusions

In conclusion, we demonstrated a tiny SPR sensor integrated on a Si waveguide based on vertical coupling into a f-MIM plasmonic waveguide that can be monolithically incorporated into CMOS fabrication processes. A sensitivity of ~635 nm/RIU was achieved at a 1.55 μm transmission wavelength with a footprint of ~0.0375 μm². This sensor can be applied to the integration of SPR sensing with nanophotonic structures and devices. The next step is to realize a SPR sensor with higher sensitivity, and we are planning to add improvements to the proposed structure.