Introduction

Surface plasmon polaritons (SPPs) are transverse magnetic (TM) surface modes, which are generated at the interface between metal and dielectric due to the coupling between the photons and free electron density fluctuation on the metal surface. The SPPs modes show several fascinating features such as the ability to be guided beyond the diffraction limit, a strong enhancement of the local fields, and highly sensitive to interaction with the surrounding environment [1]. In the last decade, various SPPs waveguides have been proposed and designed. Among them, dielectric loaded surface plasmon polariton waveguides (DLSPPWs) [2, 3] have several unique advantages, including technological simplification, compatible with different dielectrics, and easy to fabrication by using large-scale UV lithography. In addition, because of the strong guiding property, the DLSPPWs allow for bend elements with negligible bend loss. Thus, it can be applied to dense integrated photonic circuits. Until now, the DLSPPWs have been extensively investigated to realize the directional couplers [4], polarization converter [5], Mach-Zehnder interferometer [6, 7], electro-optic switch [8], thermo-optic modulation components [9], and refractive index (RI) sensor [10].

The optical devices based on microring resonators (MRRs) have attracted great interest, especially for highly sensitive sensing. Because the performance of micrometer-scale ring resonator highly depends on the bending loss, the strong mode confinement and low propagation loss should be satisfied simultaneously. The SPPs waveguide is a good candidate as it supports SPPs modes, which is propagated around the sharp bends with subwavelength confinement [11]. The two-layer dielectric loaded surface plasmon polariton waveguide (TDLSPPW)-based MRRs have also been widely studied [12–14]. Unfortunately, for sensing application, the TDLSPPW-based MRRs have a key disadvantage due to its high propagation loss. When the RIs of analytes detected are close to that of the DLSPPs waveguides, the optical field confinement evidently decreases, and the propagation length sharply reduces. So it is necessary to increase the propagation length for high performance of the proposed TDLSPPW-based MRR. The influence of propagation losses can be reduced by integration of short DLSPPWs with long dielectric waveguides [15]. A design of a very thin metallic film in a dielectric core is used to increase the propagation length [16]. Some hybrid SPPs waveguides are also demonstrated to increase the propagation length [17, 18]. Recently, a TDLSPPW has preliminarily been proposed to increase the propagation length [19]. However, to the best of our knowledge, there are no relevant reports on the TDLSPPW-based MRRs for sensing application.

In this paper, we propose and design a biochemical sensor made of the MoO3-MgF2 TDLSPPW-based MRR. The propagation properties of the TDLSPPW are investigated by boundary mode analysis of the 3D finite element method (3D-FEM). The dependences of effective index n eff, propagation length L prop, and waveguide sensitivity S wg on the structure parameters of the TDLSPPW are studied. Then, the frequency domain analysis is used to show the transmission characteristic and the sensing performance of the proposed TDLSPPW-based MRR. Quality factor (Q) and extinction ratio (ER) are also investigated. The effects of the waveguide shape deviations on the characteristics of the TDLSPPW-based MRR are also discussed. Finally, the sensing sensitivity (S) and detection limit (DL) of the TDLSPPW-based MRR based biochemical sensor for glucose concentration in urine and chemical gases are demonstrated.

TDLSPPW-Based MRR Structure

Figure 1 shows the structure of the proposed TDLSPPW-based MRR. Both the bus and ring waveguide are made of two-layer dielectric with different RIs deposited on a 70-nm thick gold film, as shown in Fig. 2a. Specifically, for wavelengths from 1500 to 1600 nm, the thickness of 70 nm is adequate for the exponentially decaying tail of the fundamental SPPs mode in metallic film [13]. The single-mode propagation of the DLSPP ridge waveguide can be realized for the thickness smaller than 630 nm and width below 655 nm [3]. In order to investigate the single-mode condition in the wavelength range from 1500 to 1600 nm, the width of the ridge waveguide w is chosen as 500 nm. The cross-section profile of the TDLSPPW is shown in Fig. 2a. The two different RI dielectric layers of the TDLSPPW are MoO3 and MgF2, respectively. The upper layer is MoO3 with high RI of n 1 and a thickness t 1, and the low-index part has a refractive index n 2 (MgF2) and a thickness t 2. The total thickness t of the TDLSPPW is also labeled in Fig. 2a. The t and t 2 are the parameters used for the boundary mode analysis in “Performance of the Proposed Device.” The refractive index of gold, n 3, is obtained from Ref 20. The microring radius R is chosen as 5 μm because the bending loss of the SPPs waveguide is reduced to 1 dB when the radius R is 5 μm [21]. The gap W gap between the bus waveguide and the microring is also chosen as a parameter for the TDLSPPW-based MRR in the following simulation.

Fig. 1
figure 1

Schematic of a TDLSPPW-based MRR

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Fig. 2
figure 2

a Cross-section profile of the proposed TDLSPPW, b the hybrid mode, and c the photonic-like mode

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The FEM is widely used to simulate the electro-magnetic behavior in photonic devices [22] due to its accurate and fast simulation on the light interaction with the nanostructure [23]. The propagation properties of the TDLSPPWs can be investigated by boundary mode analysis of the 3D FEM simulation, which is also used to simulate the guided modes of the input and output ports in the TDLSPPs waveguide. Subsequently, the frequency domain analysis of 3D FEM is employed to simulate the performance of the TDLSPPs MRR. The transmission response can be calculated by using S 21

$$ {S}_{21}\;\left(\mathrm{dB}\right)=10 \lg \left({P}_o/{P}_i\right) $$
(1)

where P i and P o are the powers at the input and output port, respectively.

The TDLSPPW-based MRR can be fabricated [19]. The gold film is coated on SiO2 insulator layer by an electron gun evaporator. After coating the gold film, the MRR patterns are defined by electron beam exposure to a 700-nm thick polymethylmethacrylate (PMMA) layer which spin coating on the substrate. The MgF2 layer (n 2 = 1.35) and MoO3 layer (n 1 = 2.06) are deposited in sequence by a thermal evaporator. Then, the TDLSPPW-based MRR can be formed after removing the PMMA by acetone.

Performance of the Proposed Device

A. Propagation Characteristics

The TDLSPPW with top cladding of air (n c = 1) supports a hybrid plasmonic/photonic-like mode and a low-loss photonic-like mode, as shown in Fig. 2b, c, respectively. The properties of these modes have been discussed [21]. The hybrid mode is a combination of a SPPs mode in low-RI layer and a guided-mode in high-RI layer. The electromagnetic energy of the hybrid mode is mainly distributed over the adjacent metal–dielectric interface inside low-index layer, which can effectively decrease the ohmic loss from the metal film and provide a better mode confinement. However, the photonic-like mode, which is similar to the guided-mode of rectangular dielectric waveguide, is not a SPPs mode.

The guided-mode propagation in the TDLSPPW greatly depends on its geometrical dimensions, especially the thickness [14]. Hence, the propagation properties of the TDLSPPW at 1.55 μm are discussed with different t 2 and t. The propagation property of a plasmonic waveguide can be characterized through the effective index n eff and propagation length L prop. The n eff of the TDLSPPW can be calculated by boundary mode analysis of the 3D FEM simulation, and L prop can be calculated as following [24]

$$ {L}_{\mathrm{prop}}=\frac{\lambda }{4\pi \times Im\left[{n}_{\mathrm{eff}}\right]}, $$
(2)

where λ is the wavelength in vacuum.

The mode RI and L prop of the TDLSPPW as functions of t 2 and t are shown in Fig. 3a, b, respectively. From Fig. 3a, b, the real component of RI monotonically decreases with the increasing of t 2 for the same t and increases with the increasing of t for the same t 2 for both the hybrid and photonic-like modes. It can be seen from Fig. 3a that only the hybrid mode can exist in the gray areas. L prop monotonically increases with the increasing of t 2 when t is less than 600 nm. However, L prop firstly increases to the maximum value and then decreases when t is larger than 500 nm. In Fig. 3b, all curves end at the points of the hybrid mode cut-off. The single-mode operation can be achieved for t 2 = 270 ~ 510 nm with different t 2 when t = 700 nm. In order to achieve the longer L prop, t and t 2 should be chosen as 700 and 280 nm, respectively. In this case, L prop of the TDLSPPW is ~126 μm, which is about 3 times of that of polymer DLSPPW (~42 μm) [13].

Fig. 3
figure 3

a Real component of mode effective index of hybrid mode and photonic-like mode and b L prop of the hybrid mode with different h and t 2 at the wavelength of 1550 nm

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For sensing application, the sensitivity S is a crucial parameter that defines the ability of a sensor to transduce an input signal to an output one. Specifically, it can be defined as the amount of change in the optical parameters (e.g., wavelength, intensity, phase) induced by the surrounding analytes for optical sensing. For the resonant wave length shift detection scheme, S is defined as the magnitude in shift of resonant wavelength (Δλ res) versus the RI change (Δn c) of the analytes detected which is induced by biological material and/or chemical concentration change. S of the RI sensor is given as following [25]

$$ S=\frac{\Delta {\lambda}_{res}}{\Delta {n}_{\mathrm{c}}}=\frac{\Delta {\lambda}_{res}}{\Delta {n}_{\mathrm{eff}}}\cdot \frac{\Delta {n}_{\mathrm{eff}}}{\Delta {n}_{\mathrm{c}}}={S}_{dev}{S}_{wg}, $$
(3)

where Δn eff is the change of n eff, S dev and S wg are the device sensitivity and waveguide sensitivity, respectively. S dev and S wg can be given by [25]

$$ {S}_{dev}=\frac{\Delta {\lambda}_{res}}{\Delta {n}_{\mathrm{eff}}}=\frac{L}{m}, $$
(4)
$$ {S}_{wg}=\frac{\Delta {n}_{\mathrm{eff}}}{\Delta {n}_{\mathrm{c}}}\approx {\left.\frac{\mathrm{d}{n}_{\mathrm{eff}}}{\mathrm{d}{n}_{\mathrm{c}}}\right|}_{n_{\mathrm{c}}}, $$
(5)

where L and m stand for the circumference of the microring and resonance order, respectively. S dev only depends on the device properties while S wg depends on the waveguide structure. The design strategy is to optimize the S dev and S wg to improve S. At a fixed wavelength, the ratio L/m is a constant because the m varies linearly with L for the MRR detection scheme. Thus, S of the TDLSPPs MRR sensor depends mainly on S wg. The relationship between S wg and n c and t 2 is shown in Fig. 4a. S wg increases with the increasing of n c and t 2 . L prop of the TDLSPPs waveguide as a function of n c is also shown in Fig. 4b. With the increase of n c, L prop firstly increases to the maximum value and then decreases. Thus, t = 700 nm and t 2 = 280 nm are reasonable for the propagation more than 90 μm. S wg varies from 0.31 to 0.69 as n c is changed from 1 to 1.6.

Fig. 4
figure 4

a S wg and b L prop of the TDLSPPW as functions of n c with different t 2 at the wavelength of 1550 nm and h = 700 nm

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To understand the effects of n c on S wg and L prop, the distributions of electric energy density are simulated by boundary mode analysis. The x and y axes are labeled in Fig. 5a, and the distributions of electric energy density along the y axis with different n c are shown in Fig. 5b. The energy in MoO3 layer increases with the increase of the RI of analyte from 1 to 1.6, which increases the energy of evanescent field. Therefore, the interaction with the analytes detected can be enhanced. Thus, S wg increases with the increase of n c, agreeing well with the results in Fig. 4a. However, higher n c will induce the radiation losses, which can reduce L prop, as shown in Fig. 4b. On the contrary, the electric energy in MgF2 layer is comparative with that in MoO3 layer at smaller n c. The interaction between the evanescent field and the analytes becomes weaker, which will induce the decrease of S wg. Meanwhile, the ohmic losses increase due to the enhancement of the electric energy at the interface between Au and MgF2 layers, which results in the decrease of L prop at small n c as shown in Fig. 4b.

Fig. 5
figure 5

a Cross-section profile of the TDLSPPW covered with analytes and b electric energy density along the y axis (x = 0)

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B. Transmission Responses

In order to fully describe the performance of the proposed sensor, the detection limit (DL) needs to be presented. For the spectral shift method, the DL characterizes the smallest RI change, which can be accurately measured and expressed as following [26]

$$ DL=\frac{R_{\sigma }}{S} $$
(6)

where R σ is the sensor resolution which describes the measurable smallest spectral shift. Q factor plays an important role in the DL of the sensor because high Q factor can reduce the spectral noise. In order to enhance the Q factor, it is crucial to reduce the losses of the resonator, especially the coupling loss [27]. Therefore, the Q factor and ER are optimized as a function of W gap, as shown in Fig. 6a. Q factor monotonically increases with the increase of W gap from 100 to 500 nm. However, the ER first increases to the maximum value at W gap = 320 nm and then decreases. A larger W gap can achieve higher Q factor but smaller ER, as seen from Fig. 6a. Therefore, W gap of 400 nm is chosen for the tradeoff between Q factor and ER. In this case, the MRR is in the under-coupling state. Q factor of 541.2 and ER of 12.2 dB can be obtained. The transmission spectrum of the TDLSPPW-based MRR at W gap of 400 nm is shown in Fig. 6b. The free spectral range (FSR) of the TDLSPPW-based MRR is also shown in Fig. 6b. Moreover, the measurement range of the wavelength shift-dependent MRR sensing is greatly limited by the FSR. The FSR of the proposed TDLSPPW-based MRR is more than 41 nm, which is beneficial to achieving larger measurement range.

Fig. 6
figure 6

a The dependence of Q factor and ER of the TDLSPPW-based MRR on W gap at the resonance wavelength (around 1566.2 nm) and b transmission spectrum of the TDLSPPW-based MRR at under-coupling (W gap = 400)

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C. Effect of Dimensional Deviations

One important practical issue of high-integrated plasmonic circuits is high sensitivity to dimensional deviations in the fabrication process. Hence, it is necessary to discuss the effects of the dimensional deviations on the performance of the TDLSPPW and TDLSPPW-based MRR to ensure the accuracy and stability of the manufactured devices. The deviations of several structure parameters, such as w, t, t 2 , and W gap, are selected to evaluate the effect on n eff, L prop, Q, and ER of the TDLSPPW and TDLSPPW-based MRR. With the optimized structural parameters t of 700 nm, w of 500 nm, t 2 of 280, and W gap of 400 nm, the nominal values of Re(n eff), L prop, ER, and Q are calculated to approximately 1.361, 125.5 μm, 12.21 dB, and 541.21, respectively. The simulation results for the change of the real component of effective RI ΔRe(n eff) and the change of propagation length ΔL prop as well as the relative deviation from the nominal values in % are presented in Figs. 7a, b, respectively. Δw, Δt, Δt 2, and ΔW gap are the dimensional deviations.

Fig. 7
figure 7

a The ΔRe(n eff) and deviation from the calculated nominal value of 1.361 in % and b the ΔL prop and deviation from the calculated nominal value of 125.5 μm in %. Both graphs are plotted over the tolerances Δw, Δt, and Δt 2

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As seen from Figs. 7a, b, Re(n eff ) and L prop of the TDLSPPW-based MRR are very stable in regards to Δw compared to the other tolerances. The increase of Δw leads to an increase of Re(n eff ) and L prop for less than 0.8 and 1.3 %, respectively. However, Δt and Δt 2 have notable influences on L prop and Re(n eff), respectively.

The deviations ΔQ and ΔER of the TDLSPPW-based MRR induced by the tolerances Δw, Δt, Δt 2, and ΔW gap are also shown in Figs. 8a, b, respectively. From Fig. 8a, ΔQ is influenced greatly by the changes of t and W gap. The effect of Δt 2 on ΔQ is less than 2.8 %. Positive changes of Δw have almost no effect on the ΔQ (less than 0.83 %). However, negative changes of Δw lead to a great increase of Q for a maximum of 11.8 % due to the strong mode confinement in the waveguide core. It can be seen from Fig. 8b that the changes of Δt and Δt 2 cause a slight change of ER, and the maximum changes of ER are 0.87 and 0.33 dB, respectively. However, the Δw and ΔW gap show a remarkable influence on the change of ER. For different Δw and ΔW gap, the maximum changes of ER are 2.03 and 2.92 dB, respectively.

Fig. 8
figure 8

a The ΔQ and deviation from the calculated nominal value of 541 in % and b the ΔER and deviation from the calculated nominal value of 12.2 dB in %. Both graphs are plotted over the tolerances Δw, Δt, Δt 2, and ΔW gap

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From the simulation results, the Q and ER are sensitive to w, t, and W gap but insensitive to t 2. In order to achieve the accuracy and stability of the TDLSPPW-based MRR-based biochemical sensor, w, t, and W gap should be optimized in the fabrication process. The simulation results for deviations in Re(n eff), L prop, Q, and ER indicate that the different tolerances could compensate each other [28].

Biochemical RI Sensing

Detection of glucose concentration in urine is an important mean to monitor diabetes. The proposed TDLSPPW-based MRR sensor can be used for biochemical detection of glucose concentration in urine since the biological molecules have larger permittivity than those of the air and water. The RI of urine is highly sensitive to the change in glucose concentration. The refractive index n c of urine with different concentrations of glucose varies from 1.335 to 1.347 when the concentration of glucose changes from 0.015 to 10 mg/dl [29]. In order to simulate the sensing characteristics, the proposed sensor is covered by the urine with different concentrations of glucose instead of the air. The transmission characteristics of the TDLSPPW-based MRR in response to n c are shown in Fig. 9a. The resonance wavelength of the transmission spectrum shifts toward the longer waveguide side with the increases of the RI of urine. The resonance wavelength shift as a function of n c and its linear fit are shown in Fig. 9b. The slope of the fitted line is 408.7 nm/RIU, which is the sensitivity of the proposed TDLSPPW-based MRR sensor. The sensitivity is ~6 times of that obtained by the conventional Si-based MRR (70 nm/RIU [30]). Following the convention of three standard deviations (3σ) of the total system noise as a measure of the sensor resolution R σ, the RI detection limit of the proposed sensor can be calculated as following

$$ DL=\frac{R_{\sigma }}{S}=\frac{3\sigma }{S}=\frac{0.087\; nm}{408.7\; nm/RIU}=2.13\times {10}^{-4}RIU $$
(7)
Fig. 9
figure 9

a Transmission spectrum of the TDLSPPW-based MRR with different urine RI n c from 1.335 to 1.347 with a step of 0.001 and b the wavelength shift as a function of urine RI n c

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The proposed structure can be also applied for detections of chemical gases due to the good gas-sensing property of MoO3 thin film, such as CO, H2, NO2, and TMA (Trimethylamine) vapor sensing [31]. Here, n c varies from 1.00 to 1.03 which includes most of the chemical gases. The transmission spectra for the different n c are shown in Fig. 10a. The change of the central wavelength shift with respect to the change of n c is given in Fig. 10b. It can be seen that the linearity between the central wavelength shift and n c is very good, and the determination coefficient of linear fit can be up to 0.99991. S is 276.4 nm/RIU, corresponding to the slope of the fitted line. Meanwhile, the DL of 6.97 × 10−5 RIU can be also calculated by Eq. (6).

Fig. 10
figure 10

a Transmission spectrum of the TDLSPPs MRR with different chemical gases RI (n c) from 1.00 to 1.03 with a step of 0.002 and b the wavelength shift as a function of chemical gases RI (n c)

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Conclusions

In summary, a highly sensitive biochemical sensor made of the TDLSPPW-based MRR is proposed. The propagation properties of the TDLSPPs waveguide and MRR are improved by optimizing the structure parameters. The propagation length of the proposed waveguide is ~126 μm, and the Q of 541.2 and ER of 12.2 dB are achieved. The effects of dimension deviations of the TDLSPPW-based MRR on L prop, Q and ER have been studied. The Q and ER are sensitivity to the w, t, and W gap but insensitivity to t 2. The TDLSPPW-based MRR-based biochemical sensor shows the sensitivity of 408 nm/RIU and detection limit of 2.13 × 10−4RIU for detection of glucose concentration in urine and the sensitivity of 260 nm/RIU and detection limit of 6.97 × 10−5RIU for detection of chemical gases.