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Abstract
We describe the optical transmission properties of a surface plasmon polariton waveguide structure consisting of a metal-insulator-metal (MIM) waveguide and a semicircular resonant cavity coupled with a key-shaped resonant cavity. Finite element algorithm simulated the optical response of a MIM waveguide structure. The influence of coupling length, geometrical size, and asymmetry of the key-shaped cavity and the radius of the semicircular resonant cavity on the Fano resonance line was investigated. Results demonstrate that variation of the key-shaped cavity asymmetry leads to the appearance of dual Fano resonances. When materials with different refractive index fill in the key-shaped cavity, the MIM waveguide structure achieves a sensitivity of 1261.67 nm/RIU. This performance allows the waveguide to be used for nanoscale biosensor applications such as measuring glucose concentrations. We simulated various spiked glucose concentrations by calculating the frequency shift as the second Fano resonance line moves towards longer wavelength. Glucose concentrations were calculated from variations of the Fano resonant wavelength. The waveguide structure proposed in this paper shows impressive practical prospects for many applications in the chemical sensing and biomedical fields.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Surface plasmon polaritons (SPPs) are electromagnetic modes that originate from coupling the oscillations of incident photons and electrons on a layered metal on dielectric waveguide surface. SPPs propagate along metal-dielectric interfaces and the electromagnetic field intensity decays exponentially along the direction normal to the interface [1–4]. SPPs are able to exceed the diffraction limit of light and substantially enhance the propagation of electromagnetic field energy [5,6]. Among all possible waveguide structures, the metal-insulator-metal (MIM) waveguide is the most promising one to build the nanophotonic circuit due to its advantages including: strong confinement of SPPs, simple structure, low band loss, long propagation distance, easiness to build, and the ability to effectively reduce interferences [7–9]. Fano resonance [10,11] is a type of resonant phenomenon that gives rise to localized energy storage characterized by an asymmetric, narrow line-shape. It originates from the coupling and interference between two different EM modes: a discrete state (narrow discrete resonant state) and a continuum state (resonant continuum state). Fano resonances have significant practical prospects given that their asymmetric and narrow characteristics can enhance the sensitivity of such devices as filters and sensors. Additionally, the Fano resonance occurring in MIM waveguides [12] is especially sensitive to variations of refractive index in the near environment, as well as the structural features inherent in its design and the polarization state of incident light [13]. Hence, Fano resonance-based MIM waveguide structures accommodate the advantages of Fano resonance coupling and MIM waveguide designs to enable broad applications as photoswitches, sensors, filters, lasers, non-linear, and slow light devices in a small package [14].
Over the years, Fano resonance-based sensor structures have become a topic of continuous interest for researchers in nanophotonics. Rakhshani et al. proposed a symmetrical metal–insulator-metal (MIM) waveguides coupled to the square resonator for nano-sensing applications, especially for water glucose sensing, the plasmonic device produces a sensitivity about 6400 nm/RIU [15–19]. Zhou et al. presented a MIM waveguide-coupled trapezoid cavity and analyzed its transmission properties using finite element method. The maximum refractive index sensitivity of the MIM waveguide-coupled trapezoid cavity structure was evaluated at approximately 750 nm/RIU [20]. Zhang et al. introduced a Fano resonance-based MIM waveguide structure composed of asymmetric double elliptic cylinders (ADEC). The asymmetric metal nanostructure led to somewhat lower refractive index sensitivity (∼503 nm/RIU) [21]. Wen et al. proposed a plamonic nanosensor utilizing Fano resonances in a MIM waveguide structure that consisted of two identical slot cavities configured as two symmetric grooves in a MIM bus waveguide. The sensitivity of this nanosensor was measured to be 903 nm/RIU [22]. Yun et al. developed a coupled plasmonic waveguide resonator configuration that produced two Fano resonances, resulting from interactions between excitations of narrow discrete whispering gallery modes and the broad spectrum excitations of the MIM stub resonator. Variations of the system structural parameters led to a maximum linear refractive index sensitivity of 938 nm/RIU [23]. Tang et al. proposed a surface plasmon polariton refractive index sensor based on Fano resonances in MIM waveguides. It was demonstrated that with an increase in the refractive index of the dielectric materials in the slot waveguide, the Fano resonance peak achieved a remarkable red shift. The maximum sensitivity was 1125 nm/RIU [24].
In this paper we describe and construct a MIM waveguide structure consisting of a semicircular resonant cavity coupled with a key-shaped resonant cavity. Finite element method (FEM) is used to systematically simulate the Fano resonance conditions when the nanophotonic device is used as an optical filter. We analyze the influence of its structural characteristics on the optical transmission properties and electromagnetic field distributions that are characteristic of the waveguide. In the FEM simulations, the perfect matching layer (PML) restriction was used as the adsorbing boundary condition. Variations of coupling distance, geometrical size, and asymmetry of the key-shaped and semicircular cavities were all investigated. Refractive index sensitivity was also calculated. Our results demonstrate that the waveguide structure proposed in this work overcomes disadvantages of traditional refractive index sensors, and makes possible their use as practical nanophotonic devices that functionally perform as chemical sensors and biosensors. The waveguide nanostructure we developed was used to measure glucose concentration. A linear relationship was obtained between glucose concentration and refractive index that was used to calculate the glucose concentration straightforwardly.
2. Models and simulation methods
MIM waveguide structure consisting of a semicircular resonant cavity coupled to a key-shaped resonant cavity. SiO2 was used as the substrate. Silver was used as the conducting metal, which is denoted by the grey area. To ensure that only TM modes are allowed to propagate in the cavity, the thickness of the dielectric layers were all maintained at 50 nm. The length, width, and height of the key-shaped cavity is denoted by L, w, and d, respectively. The semicircular ring consists of two semicircles with radii of R1 and R2. The shift of the horizontal center of the key-shaped resonant cavity relative to its vertical center is denoted by q. The radius of the semicircular cavity is denoted by R, and the coupling distance between the semicircular cavity and the key-shaped cavity is denoted by g. To describe the transmission properties of the waveguide structure, the transmittance was defined as the ratio of power output, Pout, to the power input, Pin and was calculated as follows: $\textrm{T} = {P_{out}}/{P_{in}},{\; }{P_{in}} = \smallint {P_{oavx}}d{S_1},{\; }{P_{out}} = \smallint {P_{oavx}}d{S_2}$, where ${P_{oavx}}$ is the x-component of the time-averaged power in the waveguide.
The dispersion relationship of the surface plasmon polaritons (SPPs) on the TM surface in MIM waveguide structure can be described as [25]:
3. Parameter characteristics analysis
Typical transmission spectra of the MIM waveguide consisting of a semicircular resonant cavity coupled to a key-shaped resonant cavity are shown in Fig. 1. For purposes of comparison, Fig. 1(a) and (b) present both the transmission spectra vs optical wavelength and spatial distributions of magnetic field in the single key-shaped resonant cavity and the semicircular resonant cavity, respectively. An ultra-sharp stop band is observed for the key-shaped resonant cavity, which is a result of the weak coupling between the key-shaped cavity and the straight waveguide. The narrow band is regarded as a narrow discrete state. Figure 1(b) presents the transmission spectrum (magnetic field component) into the single semicircular resonant cavity, which is regarded as a broad continuous state. The transmission spectrum into the coupling structure consisting of a semicircular resonant cavity and a key-shaped cavity is presented in Fig. 2(a). An asymmetric Fano-type transmission spectrum is observed as a result of the coherent superposition between the two states. The transmittance decreased dramatically from the peak value at $\lambda = 813nm$ to the dip value at $\lambda = \textrm{834}nm$. This result demonstrates significant and practical prospects of the dual cavity structure for use as a nano plasmon sensor and other slow light effect applications. In Fig. 2(a), the left transmission peak is marked as Peak I and the right dip is marked as Dip I. Figure 2(b) presents the magnetic field spatial distributions corresponding to Fig. 2(a).
Fig. 1. The transmittance spectra and magnetic field distribution in the designed cavity structures. (a) The transmittance spectra and magnetic field distribution of the key-shaped cavity. (b) The transmittance spectra and magnetic field distribution of the semicircular cavity.
Fig. 2. (a) The transmittance spectra of the key-shaped resonant cavity when coupled directly to the waveguide through the semicircular cavity. (b) The magnetic field distribution of the key-shaped resonant cavity coupled to the waveguide through the semicircular cavity.
The influence of geometrical parameters on Fano resonance line was also investigated. Figure 3 presents the transmission spectrum of magnetic field component from the semicircular cavity to the key cavity when the coupling distance between the two cavities increases from 9 nm to 15 nm. Here other parameters are fixed at w = 50 nm, L = 300 nm, d = 100 nm, R = 90 nm, R1 = 50 nm, R2 = 25 nm, q = 0 nm and n = 1, where n is the refractive index of both cavities. It is seen in Fig. 3 that as the coupling distance g increases, the Fano resonance line exhibits an increasing blue shift. The transmittance of the left peak I decreases from 0.80 to 0.66, and the right Dip I increases slightly from 0.01 to 0.04. Based on the transmission spectra in Fig. 3(a) coupling distance g of 9 nm was chosen for further study. Figure 4 shows the transmission spectra when the radius of the semicircular resonant cavity, R, increases from 80 nm to 110 nm. Here other parameters were fixed as w = 50 nm, L = 300 nm, d = 100 nm, g = 9 nm, q = 0 nm, and n = 1. As R increases, the position of the left peak I shows a red shift, and the transmittance decreases from 0.83 to 0.76. Variations of the position and transmittance of the right Dip I are almost negligible. Based on the transmission spectra in Fig. 4, we choose to use a radius R of 80 nm.
Fig. 3. The transmittance spectra of the semicircular resonant cavity coupled to the key-shaped resonant cavity with different coupling distance values g.
Fig. 4. The transmittance spectra of the semicircular resonant cavity as its radius, R, increases from 80 nm to 110 nm.
The influence of the key-shaped resonant cavity length (L), width (w), and height (d), together with the semicircle radius (R) on Fano resonance lines was then examined. Figure 5 shows the transmission spectral changes as the width, w, increases from 50 nm to 80 nm. Here other parameters are fixed as L = 300 nm, d = 100 nm, R = 80 nm, g = 9 nm, q = 0 nm and n = 1. As is shown, when w increases, the Fano resonance lines exhibit a blue shift. The transmittance of the left Peak I decreases from 0.83 to 0.79, while the transmittance of the right Dip I remains almost unchanged. Based on the transmission trend in Fig. 5, we chose to use a width w of 50 nm. Figure 6 presents the transmission spectra when the key-shaped resonance cavity length, L, increases from 260 nm to 320 nm. Here, other parameters were fixed as w = 50 nm, d = 100 nm, R = 80 nm, g = 9 nm, q = 0 nm and n = 1. As shown in Fig. 6, the Fano resonance lines exhibit a red shift as L increases. The transmittance of the left Peak I increases from 0.80 to 0.84. The transmittance of right Dip I is below 0.01 and remains almost unchanged. Based on the transmission spectra in Fig. 6, we chose to use an L of 320 nm. Figure 7 shows the transmission spectra when the key-shaped resonance cavity height, d, increases from 80 nm to 110 nm. Here other parameters are fixed as w = 50 nm, L = 320 nm, R = 80 nm, g = 9 nm, q = 0 nm and n=1. As shown in Fig. 7, the Fano resonance lines manifest a red shift with increasing d and the transmittance improves with increasing d. Variation of the structural parameter d was shown to result in a significant red shift and dramatically increases the transmittance peak value. The transmittance of Peak I increases from 0.76 to 0.88 and the transmittance of Dip I increases from 0.01 to 0.02. Based on transmission spectra in Fig. 7, we choose to incorporate a d value of 110 nm in our nanocavity prototype.
Fig. 5. The transmittance spectra of the key-shaped resonant cavity as its width, w, increases from 50 nm to 80 nm.
Fig. 6. The transmittance spectra of the key-shaped cavity as its resonant length, L, increases from 260 nm to 320 nm.
Fig. 7. The transmittance spectra of the key-shaped cavity as its resonant height, d, increases from 80 nm to 110 nm.
The next structural parameter we investigated is the ring radius. Here, other parameters are fixed as w = 50 nm, L = 320 nm, R = 80 nm, g = 9 nm, d = 110 nm, q = 0 nm and n=1, while R1 is varied. As shown in Fig. 8, spectra with different key cavity R1 values almost overlap. Therefore, the value of R1 appears to have little influence on transmittance. Based on these results, we chose to use an R1 of 50 nm to build the prototype structure.
Fig. 8. The transmittance spectra of the key-shaped cavity as its resonant ring radius, R1, increases from 45 nm to 60 nm.
Another geometrical parameter that influences the transmission properties of the cavity coupling in this work is the vertical offset, q, of the T shaped cavity. Its influence was studied when other parameters were fixed, to wit: w = 50 nm, L = 320 nm, R = 80 nm, g = 9 nm, d = 110 nm and n=1. The results are presented in Fig. 9. As shown in Figs. 9(a) and 9(b), as the vertical shift, q, increases from q=0, a second Fano resonance line appears. As the q value increases, the original Fano resonance line red shifts slightly from its original wavelength, while the second Fano resonance line shifts markedly down frequency. In addition to their location on the wavelength scale, the two Fano resonances also display markedly different magnitudes in their transmittance peaks. Based on fabrication cost, the feasibility of fabricating the identified design feature, and the measured transmittance spectra, we chose to use an offset q of 100 nm as the design specification for the prototype biosensor. In this paper, a large number of transmission spectra of structural parameters did have been simulated. The main reason is that the most intuitive way to evaluate the performance of a sensor is through the transmissivity of the sensor. In other words, the higher the light transmittance, the less energy lost by the light source excited by the light, which also means that the device performance is better.
Fig. 9. The transmittance spectra of the key-shaped resonant cavity as the vertical shift, q, increases (a) from 0 nm to 150 nm, (b) from 80 nm to 120 nm.
4. Detection of glucose concentration and sensitivity analysis
4.1 Detection of glucose concentration
To simulate the practical condition where the biosensor can be applied, the refractive index of the glucose solution is described as [27]:
where C is the glucose concentration (g/L) and n is the refractive index of the glucose concentration. Equation (3) specifies the linear relationship between the glucose concentration and refractive index. Given that the transmittance spectra from the FEM results relate refractive index to Fano resonance wavelength and the glucose concentration is related to refractive index, a relationship can be established between glucose concentration and wavelength. Figure 10 presents the transmittance and wavelength of the solution when the glucose concentration, C, increases from 0 g/L to 200 g/L.Fig. 10. (a) The transmittance spectra of the key-shaped cavity as the glucose concentration, C, increases from 0 g/L to 200 g/L. (b) The wavelength changes associated with each of the three Fano resonant line structure features with changes in C.
Equation (3) serves as a foundation to analyze the glucose concentration based on transmittance spectra when a solution with a glucose concentration between 0 to 200 g/L is tested. Within this concentration range, the sample refractive index typically varies within the range from 1.3323 to 1.3561. Variation of glucose solution refractive index also changes the resonant wavelength of the spectrums. Our results provide relevant information to critique the performance of the biosensor in analyzing the concentration of glucose in solution.
In Eq. (3), we can know that the relationship between refractive index and glucose concentration is linear. Theoretically, when the concentration of glucose changes, the value of refractive index will also change, and the change of refractive index will directly affect the wavelength of the transmission spectrum. Using the finite element algorithm, when the glucose concentration changes, the simulated transmission spectrum is shown in Fig. 10(a). We can intuitively see that when the glucose concentration changes, the wavelength of the Fano resonance shifts red. Through its offset, we can fit its line graph as shown in Fig. 10(b).
4.2 Sensitivity analysis
The refractive index sensitivity was also studied based on the above structural specifications. The refractive index sensitivity is defined as:
Sensitivity is one of the most appropriate parameter to evaluate the performance of sensors. Figure 10 presents a comprehensive sensitivity analysis. When the glucose concentration is 0 g/L, the second dip in the Fano resonance lines, Dip II, locates at 1729nm and corresponds to the smallest transmittance. When the glucose concentration was set to 50 g/L, 100 g/L, 150 g/L and 200 g/L, the corresponding wavelength was 1735nm, 1744nm, 1750nm and 1759nm, respectively. The sensitivity of this structure was calculated to be 1261.67 nm/RIU according to Eqs. (3) and (4).
The structure developed in this work shows high sensitivity to refractive index changes, indicating great refractive index sensing characteristics. Our research provides a new opportunity to design and optimize refractive index sensors on the nanoscale and test their performance before committing to expensive and time-consuming circuit construction.
Finally, the results from this work were compared with previous results from other workers within this field. A detailed comparison is shown in Table 1. Overall, compared with previous efforts [28–30], where the refractive index sensitivity was reported to be 825, 1131 and 1280 nm/RIU, we achieved a refractive index sensitivity that was higher. In addition, compared with previous Fano system [31–32], the sensitivity of our waveguide which manufacturing technology is simpler is very close.
Table 1. Sensitivity reported in references.
5. Conclusions
This study proposes a new design for a biosensor comprising an MIM surface plasmon polariton waveguide that consists of a semicircular resonant cavity coupled to a key-shaped resonant cavity. The simulated SPPs transmission spectra for this structure was shown to correspond to asymmetric Fano line resonances at optical frequencies. Utilizing the finite element method was used to simulate the influence of the geometrical parameters of the cavities on the fine structure (details) of transmittance spectra. Variation of the asymmetry parameter q led to the appearance of double Fano resonances as well as a frequency shift of Fano resonance lines towards longer wavelength. When the final stage cavity was modeled as filled with glucose solution, different glucose concentrations produced different frequency shifts associated with their respective refractive index values. The wavelength shifts of the Fano resonances were used to determne the glucose concentrations in the cavity. Detection sensitivity was as high as 1261.57 nm/RIU. In addition, the MIM waveguide structure in this work could also be used to simulate other liquids besides glucose solution or measure the refractive index of liquids within a refractive index range of 1–2. This waveguide and resonance cavity structures offer wide berth as a foundation for undertaking many practical measurements. This study provides the theoretical foundation for comparing designs for guided microwave structures that enable measurement of a wide variety of analytes.
Funding
Natural Science Foundation of Guangxi Zhuang Autonomous Region (2017GXNSFAA198313, 2018GXNSFAA294003); One thousand Young and Middle-Aged College and University Backbone Teachers Cultivation Program of Guangxi (2019); National Natural Science Foundation of China (51965007).
Acknowledgments
Written informed consent was obtained from all the authors for publication of their individual details and accompanying images in this manuscript. All authors read and approved the final manuscript.
Disclosures
No conflict of interest exits in the submission of this manuscript
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