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Abstract
This article presents a refractive index (RI) nanosensor utilizing gold as the plasmonic material. The layout of the sensor includes metal-insulator-metal (MIM) waveguides coupled with a cog-shaped resonator studded with gold nanorods. At the mid-infrared (MIR) spectrum, the spectral characteristics of the sensor are numerically analyzed employing the finite element method (FEM). Moreover, the refractive index sensing property is thoroughly explored by varying the key parameters, establishing a linear correlation with the transmittance profile. After extensive simulations, the most optimum structure displays the highest sensitivity of 6227.6 nm/RIU. Furthermore, the capability of the proposed device as a temperature sensor is investigated with five different liquids (ethanol, polydimethylsiloxane, toluene, chloroform, and the mixture of toluene and chloroform); among these, chloroform exhibits maximum temperature sensitivity of 6.66 nm/°C. Due to being chemically stable and demonstrating satisfactory performance in RI and temperature sensing, the suggested schematic can be a suitable replacement for silver-based sensors.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
In recent times, nanometallic structures have a profound influence on the efficacy of optical properties due to surface plasmon polaritons (SPPs), which led to the development in the field of nanophotonics. SPPs are transverse electromagnetic (EM) waves that propagate along and decay exponentially away from the metal-dielectric juncture [1,2]. SPPs cause confinement and enhancement of light, enabling independent subwavelength sensors to be established in nanometer-sized arrays [3–7]. Moreover, these EM waves can overcome the standard diffraction limit of light, magnify and tune light-metal interactions, making them sensitive to any minute changes in the ambient medium [8–11]. The improved spatial properties of SPPs open up new possibilities in RI sensing applications [12–15]. Furthermore, the mid-infrared (MIR) wavelength range (2.5 $\mu$m to 10 $\mu$m) embodies a strategically significant spectral regime for RI sensing applications, as absorption fingerprints of most biological and chemical materials in their gaseous or liquid forms are found here [16–19].
SPPs in RI sensors are guided by various waveguide structures, among which MIM is the most prominent one. MIM structures are more widely employed due to their ability to direct light with precise confinement, quick response and label-free detection [20–22]. Nevertheless, MIM nanosensors relatively have lower sensitivity (characterized in Table 4) than traditional $\mu$m-sized fiber sensors and need to be enhanced to develop efficacious lab-on-chip systems.
Multiprocessor systems-on-chip (MPSoCs) have attracted considerable attention in recent years for their superior performance in applications. Temperature sensitivity, which is an essential attribute of optical devices due to the thermo-optic phenomenon, becomes one of the possible concerns impacting the performance of MPSoCs [23]. Therefore, it is imperative to monitor processor temperatures to analyze and safeguard MPSoCs. SPP-based RI sensors can be a notable solution for this purpose as RI changes with temperature.
This research proposes a temperature-sensing ultrasensitive MIM refractive index sensor. It comprises a cog-shaped resonator studded with an array of gold nanorods to enhance the sensing capability of the device. A maximum sensitivity of 6227.6 nm/RIU for an ambient RI range of 1.5 to 1.6 is attained. Furthermore, the proposed model is scrutinized with various temperature-sensitive liquids, making it pertinent for commercial applications.
2. Sensor schematic and theoretical analysis
The two-dimensional schematic of the proposed structure is illustrated in Fig. 1(a), where the golden and white zones represent gold and the material under sensing (MUS), respectively. Gold is preferred due to its strong oxidation resistance and stability compared to other conventional plasmonic materials, such as copper and silver [24]. The structure consists of input and output waveguides coupled with a cog-shaped resonator. Two consecutive gratings of the cog like resonator are kept at an angular distance of 90$^{\circ }$, and one gold nanorod is placed in each grating.
The nano-filling technique based on capillarity attraction can be implemented to fill the resonator and waveguide cavities with the MUS [25]. Fig. 1(b) illustrates the transmittance profile of the device at a refractive index (n) of 1.5. At resonant wavelengths of 1679 nm and 3918 nm, two asymmetric peaks are observed. Since the proposed sensor is evaluated in the MIR region, only mode 2 is considered for assessment. The $\left | H_ {z}\right | ^{2}$ component of the magnetic field for the resonant wavelength of 3918 nm is shown in Fig. 1(c). The initial simulation parameters are tabulated in Table 1.
Fig. 1. (a) Topology of the proposed nanosensor. (b) Transmittance profile at n = 1.5. (c) The magnetic field distribution ($\left | H_ {z}\right | ^{2}$-field) at the resonant wavelength of 3918 nm.
Table 1. Initial 2D simulation parameters.
The proposed work is simulated employing COMSOL Multiphysics 5.3a software. Initially, the physics interface is chosen as EM-wave frequency domain (ewfd), incorporated with 2D-Finite Element Method (FEM). Boundary mode analysis is integrated into the study, and extra-fine triangular meshing is employed for discretization. Moreover, scattering boundary conditions are applied to absorb evasive EM-field energy with minimal reflection. A plane wave at the input port excites the TM mode of the MIM waveguide. Thus, the transmittance of power is calculated as T = output power (Po) / input power (Pi).
At high frequency, the complex permittivity of gold is wavelength dependent, which is characterized through the Lorentz-Drude model and the equation can be derived as [26],
Table 2. Lorentz-Drude parameters for Au [26].
As $\textit {w}_{1}\ll$ $\lambda _{incident}$, the dispersion relation of the fundamental transverse magnetic (TM0) mode can be characterized through an equation defined as [27],
Furthermore, $p={{\varepsilon }_{MUS}}/{{\varepsilon }_{Au}}$, and ${{\alpha }_{c}}=\sqrt {k_{0}^{2}\left ( {{\varepsilon }_{MUS}}-{{\varepsilon }_{Au}} \right )+k}$, where, $\varepsilon _{MUS}$ and $\varepsilon _{Au}$ are the permittivity of the MUS and gold, respectively. In addition, $k_{0}$ is the wave vector in free space.
The real part of the effective refractive index $Re(n_{eff})$, can be determined through an equation described as [28],
As per the standing wave theory, the resonant wavelength is proportional to the effective refractive index and the perimeter ($L$) of the resonator, which can be defined as [29,30],
In practical setup, quantum cascade lasers are used as light source for their coverage over the MIR region, which encompasses $\lambda _{res}$. A single-mode fiber (SMF) carries the light to the input side of the sensor [31]. The output side of the nanosensor is linked to an optical spectrum analyzer (OSA) through another SMF to detect variations in resonant wavelength. To experimentally verify the correctness of this proposed work, simulated and practical values of the resonant wavelength can be compared.
3. Computation and results evaluation
The sensing performance of the proposed nanosensor can be evaluated by the sensitivity value ($S$), which can be expressed as,
where $\Delta \lambda$ is the change in the resonance wavelength and $\Delta n$ is the change in the RI. The transmission characteristics of the schematic are studied, exploiting the primary structural specifications, as mentioned in Table 1.The refractive index of the MUS is varied from n = 1.5 to n = 1.6, with a step size of 0.025, by filling the cavities with different concentrations of glucose for testing purpose [32]. Biomaterials such as albumin, DNA, fibrinogen, and hemoglobin concentrations and various polymers and organic materials, for example, aluminium oxides, and polycarbonates also have refractive indices between 1.5 to 1.6 [27,33,34]. The corresponding transmittance spectra are illustrated in Fig. 2. As per Eq. (5), the inset of Fig. 2 exhibits a linear correlation between the refractive index and resonant wavelength, where the positive slope denotes an initial sensitivity of 4474 nm/RIU.
The spectral properties of the sensor are highly susceptible to its structural parameters. Hence, optimization is performed to acquire the most sensitive parameters. To initiate the optimization, r2, d, r3, g, l, and w2 are altered without affecting the initial values of the remaining parameters. At first, the outer radius of the cog-shaped resonator r2 is varied from 200 nm to 240 nm with a step of 10 nm, as illustrated in Fig. 3(a). According to Eq. (5), when the radius is increased, $\lambda _{res}$ increases. It is well noted that the resonant wavelength undergoes a redshift of 31.1 nm for a small change of 1 nm in radius. Secondly, the number of nanorods d in the ring is added periodically from 4 to 24, with a step size of 4. The positive slope exhibited in the inset of Fig. 3(b) implies that increasing d advances the resonant wavelength by 28.5 nm to the right of the wavelength domain. The effective coupling of light within the gaps between the neighboring nanorods escalates the total electric field energy of the resonating SPPs. This phenomenon is known as gap plasmon resonance (GPR) [35,36]. Thus, the transmittance value increases with the increase of d. Both the parameters act as a crucial tuning factor during the fabrication of the sensor. A slight fabrication error can cause a large variation in the resonant wavelength.
Fig. 3. (a) Transmittance spectra of the nanosensor with changing outer radius (r2) of the resonator, and (b) with changing number of nanorods (d).
The radius of the nanorods r3 is then varied from 6.5 nm to 8.5 nm, with an increment of 0.5 nm. The transmittance peak displays a significant blueshift. The linear relationship between the resonant wavelength and the radius of the nanorods is plotted in the inset of Fig. 4(a), where a 20.2 nm change in resonant wavelength for per unit change in radius is observed. Correspondingly, the number of gratings g is varied from 1 to 4, with a unit step size. The resonant peak undergoes a substantial redshift as depicted in Fig. 4(b), which emerges to be a highly sensitive parameter for the modeled sensor.
Fig. 4. (a) Transmittance spectra of the nanosensor at varying nanorod radius (r3), and (b) at varying number of gratings (g).
The effects of the length of the grating are studied next. The grating length l is increased from 60 nm to 100 nm, with an interval of 10 nm. Figure 5(a) demonstrates the transmittance profile, where a minute redshift is observed. As l increases, the transmittance value reduces due to higher propagation loss. Finally, the gap width w2 of the straight waveguide is varied from 20 nm to 40 nm, with a step size of 5 nm, and the resulting graph is shown in Fig. 5(b). It is perceived that the resonant peak experiences redshift and results in a linear correlation between the resonant wavelength and w2.
Fig. 5. (a) Transmittance spectra of the nanosensor at varying grating length (l), and (b) at varying gap width (w2).
After numerous simulations, the corresponding values of the structural parameters resulting in the maximum sensitivity are summarized in Table 3. The transmittance spectra for the optimized 3D schematic (Fig. 6(a)) are depicted in Fig. 6(a). For an ambient RI range of 1.5 to 1.6, the resonant peak endures an ample redshift and exhibits a maximum sensitivity of 6227.6 nm/RIU. Additionally, the Figure of Merit (FOM) = S/FWHM of the presented schematic is 6.52, where FWHM is full width at half maximum. Table 4 presents a comparison with prevailing literature, demonstrating that the suggested nanosensor surpasses the recent devices in terms of sensing performance and oxidation adversities.
Fig. 6. (a) Optimized 3D schematic of the proposed nanosensor. (b) Transmittance spectra of the optimised structure.
Table 3. Summary of the most sensitive structural parameters values.
Table 4. Comparison of sensitivity with recent literature.
The proposed nanosensor can be fabricated using the Electron-Beam Lithography (EBL) technique. The key benefit of EBL is its ability to engrave unique patterns with sub-10 nm precision [42]. On a silica substrate, a thin layer of gold is deposited, preceded by the intended pattern. To eradicate the surplus of gold, wet chemical etching can be employed. For high etch selectivity, dilute nitric acid and water are used [51,52].
4. Potential as a temperature sensor
Due to compactness, immunity to EM interference, wide sensing range, dependability, and high sensitivity, plasmonic temperature sensors are rapidly displacing traditional temperature measurement devices [53]. Therefore, in this section, the performance of the proposed RI device as a temperature sensor with different filling media is explored. The refractive index of a medium fluctuates with temperature owing to the thermo-optic effect. During simulation, the temperature-sensitive liquids are filled inside the cavities and corresponding sensitivity is achieved. The temperature sensitivity can be calculated as [54],
where, $\Delta \lambda$ = change in resonant wavelength, and $\Delta T$ = corresponding change in temperature.4.1 Ethanol
The refractive index of ethanol can be expressed as [54],
where, $\textit {T}_{0}$ is the typical room temperature (20$^{\circ }$C) and T is the temperature of the liquid (in $^{\circ }$C).Figure 7(a) plots the transmittance profile for T = -100$^{\circ }$C to T = 60$^{\circ }$C, with a step size of 40$^{\circ }$C, for ethanol. As T increases, the resonant wavelength experiences a blueshift. Using Eq. (7), the proposed nanosensor attains a sensitivity of 2.36 nm/$^{\circ }$C for ethanol. The sensitivity is plotted as a steep negative slope (due to blueshift) in Fig. 7(b). Moreover, a linear association is established between the resonant wavelength and T. The melting and boiling points of ethanol are -114.3$^{\circ }$C and 78.4$^{\circ }$C, respectively. Thus, the designed sensor is suitable for sensing low temperatures.
Fig. 7. (a) Transmittance spectra for different values of temperature in ethanol. (b) Resonant wavelength against the corresponding temperature range.
4.2 Polydimethylsiloxane (PDMS)
Polydimethylsiloxane (PDMS) has a high thermo-optic coefficient and is non-flammable [55]. Thus, PDMS can be an excellent choice as a filling medium for temperature sensing. The refractive index of PDMS is calculated as [55],
With increasing T (20$^{\circ }$C to 70$^{\circ }$C, with an interval of 10$^{\circ }$C), the resonant peak moves to a shorter wavelength region (Fig. 8(a)). Furthermore, the modeled sensor achieves maximum sensitivity of 3.35 nm/$^{\circ }$C, as displayed in Fig. 8(b).
Fig. 8. (a) Transmittance spectra for different values of temperature in PDMS. (b) Resonant wavelength against the corresponding temperature range.
4.3 Chloroform
The refractive index of chloroform at $T_{0}$ = 20$^{\circ }$C is given as [56],
Figure 9(a) plots the transmittance spectra for T = 30$^{\circ }$C to T = 34$^{\circ }$C, with a unit step size. The resonant wavelength experiences a blueshift. Figure 9(b) demonstrates the linear association between the resonant wavelength and temperature. Due to chloroform, the illustrated layout achieves the highest sensitivity of 6.66 nm/$^{\circ }$C.
Fig. 9. (a) Transmittance spectra for different values of temperature in chloroform. (b) Resonant wavelength against the corresponding temperature range.
4.4 Toluene
The relationship between temperature and RI of toluene can be shown as [57],
T is varied from 0$^{\circ }$C to 80$^{\circ }$C, with a step size of 20$^{\circ }$C for toluene. The transmittance profile exhibits a significant blueshift (Fig. 10). The inset of Fig. 10 plots the resonant wavelength vs. temperature graph. For toluene, a sensitivity of 3.42 nm/$^{\circ }$C is reported.
4.5 Mixture of chloroform and toluene
Finally, the proposed nanosensor is simulated with a mixture of chloroform and toluene. The mixture has the following relationship between n and T [58],
The $\rho$ values are chosen as 30%, 37.5% and 45% [58]. Afterward, for T = 20$^{\circ }$C to T = 60$^{\circ }$C, with an interval of 10$^{\circ }$C, transmittance profiles for different concentrations of toluene are plotted in Fig. 11(a) to Fig. 11(c). The resonant peak shifts from right to left in all three cases. Figure 11(d) plots the resonant wavelength versus temperature graphs for different values of $\rho$. For $\rho$ = 30%, 37.5% and 45%, the suggested setup exhibits maximum sensitivity of 4.21 nm/$^{\circ }$C, 4.23 nm/$^{\circ }$C and 3.92 nm/$^{\circ }$C, respectively.
Fig. 11. (a) Transmittance spectra for different values of temperature at $\rho$ = 30%, (b) $\rho$ = 37.5%, and (c) $\rho$ = 45%. (d) Resonant wavelength vs temperature graph for different values of $\rho$.
According to the literature review, the modeled nanosensor has higher temperature sensitivity than the sensors presented in Table 5.
Table 5. Comparison of temperature sensitivity with recent literature.
5. Conclusion
In this article, an RI nanosensor comprising of a cog-shaped resonator coupled with MIM waveguides is investigated in the MIR region. The 2D layout of the proposed sensor is simulated in COMSOL Multiphysics 5.3a software, utilizing gold as the plasmonic material. The structural parameters are numerically evaluated employing the FEM. After extensive simulations, a maximum sensitivity of 6227.6 nm/RIU is achieved. Moreover, the proposed schematic is analyzed as a temperature sensor by filling the cavities with different temperature-sensitive chemicals, for example, ethanol, PDMS, chloroform, and toluene. The highest temperature sensitivity of 6.66 nm/$^{\circ }$C is attained. The simple architecture and coherent performance of the nanosensor make it useful in advanced temperature sensing platforms.
Acknowledgment
We acknowledge the fruitful discussion of all the authors who contributed to this paper. K. S. Rashid conceived the structure and performed simulations. I. Tathfif explored and developed the temperature sensing methods. A. A. Yaseer handled illustrations and revised the article. M. F. Hassan performed the formal analysis of the simulations and revised the article. R. H. Sagor revised the article and supervised the project.
Disclosures
The authors declare no conflicts of interest.
Data availability
No data were generated or analyzed in the presented research.
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