A High-Quality Optical Sensor with High Resolution Based on Coin-like Resonator

: A nanoscale plasmonic temperature sensor via a metal-insulator-metal (MIM) structure is proposed in this paper, and the waveguide structure is composed of a coin-like resonator. The ﬁnite element method (FEM) is used to study the structure’s transmission characteristics and electromagnetic ﬁeld distributions. The calculated maximum temperature sensitivity is about 0.38 nm/ ◦ C, and the ﬁgure of (FOM) merit can be as high as 30,158, higher than most of the published MIM structure research. Compared to the structure without a square resonator, the FOM is enhanced by about 479%. We believe the proposed sensor can be a promising platform for future sensing applications such as ﬁlters, absorbers, and splitters.


Introduction
Surface plasmon polaritons (SPPS) are transverse electromagnetic (TM) waves propagating along the metal-dielectric surface and decay exponentially away from the meta-dielectric interface. Spps have unique properties that make them suitable for research in areas such as photonic integrated circuits [1,2], filters [3][4][5], splitters [6,7], modulators [8], switchers [9], and plasmonic sensors [10][11][12]. One structure that stands out is the metal-insulator-metal (MIM) structure, which has solid optical confinement and a long propagation distance. Compared to other sensors, such as Bragg grating with a dielectric solution or hybrid ones [13,14], whose sensitivity usually reaches about 500 nm/RIU, the MIM structure has a more prominent and straightforward structure. However, maintaining relatively high sensitivities with a high figure of merit (FOM) is difficult in the MIM structure. Therefore, there is a need for novel MIM structures with high sensitivity and high quality. For example, Zhang et al. [15] proposed a refractive index sensor based on a MIM waveguide coupled with dual rectangular cavities, which achieved a sensitivity of 596 nm/RIU. Li [16] reported a cascaded optical device with double cavities with a 701 nm/RIU sensitivity. However, the sensitivities and FOM of these proposed structures still need to be higher [17][18][19] compared to what can be achieved with improved MIM structures. In summary, apps offer a promising avenue for exploring novel photonic devices. Improving the sensitivity and FOM of MIM structures will lead to better performance in various applications, including plasmonic sensors.
Optical signals possess properties such as transmission flexibility, anti-interference abilities, and high sensitivity, which make them excellent carriers for detecting changes in the background. MIM structures [20,21] are preferred because they have a compact structure of only a nano-meter scale and can easily be integrated into optoelectronic chips [22][23][24]. For example, a temperature sensor based on the MIM structure can transfer ambient temperature signals to the optical transmission spectrum [25,26]. Analyzing the correlation between temperature and optical spectral lines enables the successful design of a highresolution optical sensor.
In this article, we present a temperature sensor that resembles a coin in shape and has high resolution and a high figure of merit (FOM). The sensor is based on a MIM structure and includes a square resonator embedded with a ring resonator. Additionally, two vertical rectangular channels are utilized to connect the two resonators. The waveguide features two silver walls that induce a broad mode and couple it to resonance modes in the resonator. For optimization of the structural parameter, we employed the finite element method (FEM, COMSOL 5.6). Our calculations demonstrate that this structure has superior sensitivity of 0.38 nm/ • C and a high FOM of 30,158.4, higher than most proposed MIM sensors. Our proposed structure has a significant advantage over other MIM optical sensors and may inspire other broadband passers, filters, absorbers, and switchers that incorporate a similar structural design.

Schematic and Theoretical Analysis
Figure 1a displays a two-dimensional schematic of the proposed structure. The grey and white portions indicate silver and dielectric materials. A material under sensing (MUS) that responds to the surroundings can replace the dielectric region. Silver has been chosen due to its minimal loss in the near-infrared spectrum. The ring resonator's inner radius measures 300 nm while its width is 50 nm, with the stubs measuring 10 nm in thickness and 20 nm in distance apart. The waveguide width is also fixed at 50 nm, ensuring only the fundamental transverse magnetic mode (TM0) exists [27]. Table 1 provides further details on the proposed structure. bient temperature signals to the optical transmission spectrum [25,26]. Analyzing the correlation between temperature and optical spectral lines enables the successful design of a high-resolution optical sensor.
In this article, we present a temperature sensor that resembles a coin in shape and has high resolution and a high figure of merit (FOM). The sensor is based on a MIM structure and includes a square resonator embedded with a ring resonator. Additionally, two vertical rectangular channels are utilized to connect the two resonators. The waveguide features two silver walls that induce a broad mode and couple it to resonance modes in the resonator. For optimization of the structural parameter, we employed the finite element method (FEM, COMSOL 5.6). Our calculations demonstrate that this structure has superior sensitivity of 0.38 nm/°C and a high FOM of 30,158.4, higher than most proposed MIM sensors. Our proposed structure has a significant advantage over other MIM optical sensors and may inspire other broadband passers, filters, absorbers, and switchers that incorporate a similar structural design. Figure 1a displays a two-dimensional schematic of the proposed structure. The grey and white portions indicate silver and dielectric materials. A material under sensing (MUS) that responds to the surroundings can replace the dielectric region. Silver has been chosen due to its minimal loss in the near-infrared spectrum. The ring resonator's inner radius measures 300 nm while its width is 50 nm, with the stubs measuring 10 nm in thickness and 20 nm in distance apart. The waveguide width is also fixed at 50 nm, ensuring only the fundamental transverse magnetic mode (TM0) exists [27]. Table 1 provides further details on the proposed structure.    Regarding the material parameter, the dielectric's relative permittivity is set as ε d = 1. For silver, the Drude model [11,28] can be utilized to characterize it in the NIR region. The Drude model is expressed as follows:

Schematic and Theoretical Analysis
Here, ω represents the angular frequency of incident light while ω p is the plasma frequency. Additionally, γ p is the damping frequency, and ε ∞ is the relative permittivity at infinite frequency. The detail of the parameter is presented in Table 2. The dispersion equation [29,30] of the TM0 mode in the MIM structure can be represented by are the propagated mode in dielectric and silver, respectively, β = k 0 n e f f is the propagation constant, k 0 = 2π λ is the wavevector in vacuum. According to standing wave theory, the resonant wavelength is proportional to the effective refractive index and the length of the resonator, which can be represented as where m and ϕ represented the mode integer and the phase shift due to reflection from the resonator, respectively. L e f f is the effective length of the cavity and Re n e f f is the real part of the effective refractive index.

Ring Resonator with High Sensitivity
In Figure 1b, three fano resonances originate from the interface of resonance modes in waveguide and ring resonator of different orders. The detail of the broad continuous mode in the waveguide and the narrow linewidth mode in the ring resonator are plotted in Figure 1b. The study investigates the relationship between structural parameters and the peak of different orders' modes in transmission patterns, such as the stub distance d in the waveguide, the radius r of the ring resonator, and the coupling distance g. Figure 2 demonstrates that decreasing the coupling distance g and the stub distance d heightens the significance of the peak of these fano modes while the center of these modes remains stable. This is because the coupling process loses less energy, strengthening the coupling amplitude between the two modes. Another observation is that the location of the maximum transmission of different fano resonances experiences a red shift when the radius of the ring resonator is larger. This may be explained by the standing wave theory when the length of the resonator corresponds to a longer resonance wavelength. the ring resonator is larger. This may be explained by the standing wave theory when the length of the resonator corresponds to a longer resonance wavelength. Transmittance spectrum for ring resonator radius from r2 = 250 nm to r2 = 400 nm. The red, yellow, blue, and green lines represent radii from 250nm to 400nm at intervals of 50nm, and the dots of the circle, triangle, diamond, and pentagonal represent the second, third, fourth, and fifth order annular cavity mode field resonance wavelengths, respectively. (c) Transmittance spectrum for coupling distance from g = 5 nm to g = 20 nm.
The plasmonic sensor based on the MIM structure is suitable for sensing due to its compactness, immunity to an electromagnetic interface, wide sensing range, and high sensitivity. For example, ethanol has a melting point of −114.3 °C and a boiling point of 78.4 °C, which covers the most possible temperature on earth, making it a suitable dielectric for sensing. The refractive index of ethanol can be expressed as [28] = 1.36048 − 3.94 × 10 − where T0 is room temperature (20 °C), and T is the ambient temperature. Figure 3a illustrates the transmittance profile from T = −60 °C to T = 60 °C with a step of 40 °C. Sensitivity is defined as = ∆ ∆ ⁄ , where ∆ is the change is resonance wavelength and ∆ represent the temperature change. In addition, FOM is defined as where ∆ ′ represent the transmission rate change and T' representing the transmission rate in the spectrum [31]. The results show that the location of the peak increases linearly with temperature increase, and our sensor has a sensitivity of 0.365 nm/°C and a FOM of 5208.5. Additionally, Figure 3d-i. Display the magnetic field distribution of different orders at the peaks and valleys of Fano resonance. Transmittance spectrum for ring resonator radius from r 2 = 250 nm to r 2 = 400 nm. The red, yellow, blue, and green lines represent radii from 250nm to 400nm at intervals of 50nm, and the dots of the circle, triangle, diamond, and pentagonal represent the second, third, fourth, and fifth order annular cavity mode field resonance wavelengths, respectively. (c) Transmittance spectrum for coupling distance from g = 5 nm to g = 20 nm.
The plasmonic sensor based on the MIM structure is suitable for sensing due to its compactness, immunity to an electromagnetic interface, wide sensing range, and high sensitivity. For example, ethanol has a melting point of −114.3 • C and a boiling point of 78.4 • C, which covers the most possible temperature on earth, making it a suitable dielectric for sensing. The refractive index of ethanol can be expressed as [28] n Ethanol (T) where T 0 is room temperature (20 • C), and T is the ambient temperature. Figure 3a illustrates the transmittance profile from T = −60 • C to T = 60 • C with a step of 40 • C. Sensitivity is defined as S = ∆λ/∆T, where ∆λ is the change is resonance wavelength and ∆T represent the temperature change. In addition, FOM is defined as FOM = ∆T /(∆n * T ), where ∆T represent the transmission rate change and T' representing the transmission rate in the spectrum [31]. The results show that the location of the peak increases linearly with temperature increase, and our sensor has a sensitivity of 0.365 nm/ • C and a FOM of 5208.5. Additionally, Figure 3d-i. Display the magnetic field distribution of different orders at the peaks and valleys of Fano resonance.

Coin-like Resonator
Studies have indicated that adding grooves and baffles in a cavity can enhance sensitivity. However, the FOM for such high-sensitivity MIM structures is typically around 10. Because the multiple Fano resonances originate from different mechanisms, they can be turned semi-independently by changing the cavity's parameters around the ring resonator. Structure with high sensitivity and high FOM has potential in sensing, slow light, and other nonlinear devices in highly integrated devices. Here, we propose a resonator resembling a coin, which has been successful in increasing sensitivity to 0.38 nm/ • C as well as its FOM to over 30,158. Figure 4a illustrates the schematic, from which we can observe that two additional fano modes are generated due to the square resonator and the rectangle channel connecting two resonators. This relationship is further supported by the linear relationship between the square resonator length and the fano peak wavelength shown in Figure 4b,c. As the temperature decrease, peaks of different order modes also exhibit a redshift, as seen in Figure 4d. The FOM of this coin-like resonator is plotted in Figure 4d. Compared to the ring resonator MIM structure, our sensor has an increased sensitivity of approximately 5% and a FOM increase of about 479%. Results from Table 3 comparing the sensitivity and FOM of our sensor with those published in the relevant literature demonstrate its significant advantages over other sensors.

Coin-Like Resonator
Studies have indicated that adding grooves and baffles in a cavity can enhance sensitivity. However, the FOM for such high-sensitivity MIM structures is typically around 10. Because the multiple Fano resonances originate from different mechanisms, they can be turned semi-independently by changing the cavity's parameters around the ring resonator. Structure with high sensitivity and high FOM has potential in sensing, slow light, and other nonlinear devices in highly integrated devices. Here, we propose a resonator resembling a coin, which has been successful in increasing sensitivity to 0.38 nm/°C as well as its FOM to over 30,158. Figure 4a illustrates the schematic, from which we can observe that two additional fano modes are generated due to the square resonator and the rectangle channel connecting two resonators. This relationship is further supported by the linear relationship between the square resonator length and the fano peak wavelength shown in Figure 4b,c. As the temperature decrease, peaks of different order modes also exhibit a redshift, as seen in Figure 4d. The FOM of this coin-like resonator is plotted in Figure 4d. Compared to the ring resonator MIM structure, our sensor has an increased sensitivity of approximately 5% and a FOM increase of about 479%. Results from Table 3 comparing the sensitivity and FOM of our sensor with those published in the relevant literature demonstrate its significant advantages over other sensors.

Conclusions
In this manuscript, we have presented a high-sensitivity sensor in the shape of a coin, utilizing the MIM structure. The coin-like resonant cavity and waveguide obtain Fano resonances by interacting with the narrowband discrete and broad-band contiguous states. By analyzing the device's geometrical parameters, we could tune the transmittance peaks

Conclusions
In this manuscript, we have presented a high-sensitivity sensor in the shape of a coin, utilizing the MIM structure. The coin-like resonant cavity and waveguide obtain Fano resonances by interacting with the narrowband discrete and broad-band contiguous states. By analyzing the device's geometrical parameters, we could tune the transmittance peaks and resonance modes. Our findings demonstrate that the coin-like cavity achieved a sensitivity of 0.38 nm/ • C and a figure of merit (FOM) of 30,158. Compared to the cavity without a square resonator, the sensitivity increased marginally while the FOM increased to over 479%. The quality can be further enhanced when combined with other structures, such as photonic crystals, reaching as high as 109 [36,37]. We believe the proposed structure can be applied to the on-chip plasmonic nano-sensor and may inspire other future integrated optical systems on chips.