Plasmonic Refractive Index Sensor Optimized for Color Detection

In this paper, a six cavity-based metal-insulator-metal plasmonic sensor is proposed. The designed sensor can detect six primary colors in the visible wavelength. Moreover, the proposed sensor can also sense the change in the refractive index. An initial sensitivity of 648.41 nm/RIU and ﬁgure of merit of (FOM) 141.29 are found based on the transmittance proﬁle extracted through the two-dimensional (2D) ﬁnite element method (FEM). The structural parameters are optimized to maximize the performance of the modeled de-vice both as a color ﬁlter and a refractive index sensor. The optimized FOM, FOM* and sensitivity are recorded as 218.80, 4.771 × 10 4 , and 865.31 nm/RIU, respectively. Due to high FOM and FOM*, this sensor is expected to be utilized as a color ﬁlter in various sectors, such as medical, industrial, and forensic, where the light of a particular wavelength is mandatory.


Introduction
In recent times, color filters have become one of the vital elements in organic light-emitting diodes, digital projectors, digital photography, and display units of computerized systems. Color filters can deal with specific wavelengths of interest or filter white light into individual colors. Researchers are continuously searching for a method to produce low-cost, compact, and transmissionefficient color filters comparing to traditional pigment-based printing [1][2][3][4][5].
Color filters based on SPPs are researched through different Metal-Insulator-Metal (MIM) schematics. Diest et al. [20] placed two slits into the waveguide and distinguished three colors -red, green, and blue. Incorporating six unequal square cavities, Butt et al. [22] filtered white colors into six colors and reported a maximum sensitivity of 700 nm/RIU. Zhang et al. [21] demonstrated a multiband four-mode color filter possessing an ellipse resonator and recorded the highest sensitivity of 608 nm/RIU and figure of merit (FOM) of 105.02.
In this work, a new schematic of the MIM color filter is proposed using six rectangular cavities. This structure is found to filter out six basic colors with 2 a maximum sensitivity of 865. 31  Ag Air x y z D1 Figure 1: Two-dimensional schematic design of the proposed sensor.
The schematic design of the proposed sensor is presented in Figure 1, where the orange color represents silver, and the white color denotes air. The sug- from the waveguide, where the distance between each cavity is D2. The value of the structural parameters are stated in Table 1. In this paper, silver is chosen as the plasmonic material to provide an electromagnetic response within the near-infrared range due to possessing the smallest imaginary part of relative permittivity [22]. This permittivity is frequencydependent and is characterized by Lorentz-Drude Model through an equation defined as [23],ε where,ε(ω) denotes the complex relative permittivity. ω p , and ω n designate the plasma frequency, and the resonant frequency, respectively. Furthermore, Γ 0 , Γ n , and f n denote the collision frequency, the damping frequency, and the oscillator strength, respectively.
Furthermore, parts of incident waves are coupled into cavities to reach the 4 output port due to the excitation of fundamental mode at the input port. This dispersion relation is expressed as [24], where, k c1 , and k c2 are momentum conservations defined as, where, the dielectric constant of silver and air are represented as ε silver , and ε air , respectively. Furthermore, the resonance wavelength, λ res is derived as [24], where, L is the effective resonance length, M is the mode integer, ψ r is the phase shift of the beam caused by reflection at one end of the cavity and η ef f is the effective refractive index. The real part of η ef f can be calculated from, where, k 0 is the wavenumber. Therefore, the proposed sensor contains six different-length cavities to detect six basic colors -violet, blue, green, yellow, orange, and red. Different resonance wavelengths confine in the specific cavity. The E-field confinement of those resonance wavelengths has been depicted in Figure 2. The transmittance curve (shown in Figure 3) exhibits six sharp resonance dips at six different resonance wavelengths at refractive index, η = 1. Table 2 provides a comparison between these resonance wavelengths of six colors and their typical wavelength range [22]. Therefore, the detection of those specific colors is established.   The performance of a RI sensor can be measured through two significant factors -sensitivity and figure of merit which are determined as, and, .  To calculate the sensitivity of the proposed structure, the refractive index is varied from 1 to 1.01, with an interval of .005, and redshift is observed at resonance dips (Figure 4a). Furthermore, the sensitivity and FOM have been calculated, and the existence of positive slopes in Figure 4b substantiates the redshift. The highest sensitivity and FOM are found as 648.41 nm/RIU and 141.29 at η = 1. The proposed structure is optimized in terms of FOM in the later section to obtain superior filter performance.

Optimization of Parameter D2 and D1
The optimization of the proposed sensor starts by varying D2 from 200 nm to 350 nm, with an interval of 50 nm, while keeping D1 constant at 40 nm.
The parametric value of D2 more than 300 nm shifts the resonance dip from desired visible color range and distorts the transmittance curve (Figure 5a).  000 1.001 1.002 1.003 1.004 1  is prioritized in this particular scenario as recent works explored the use of the 9 violet light in various cases such as fungal study [25], dental bleaching [26], forensic science [27], surgical management [28].     (Table 2). Furthermore, when D1 ≥ 60 nm, the resonance dips are not so sharp and almost diminishing. Hence, D1 = 30 nm and D1 = 60 nm cannot be taken as optimized values. Figure 6b and Figure 6c   Finally, Figure 7 displays the transmittance vs. wavelength curve for the optimized parameters, where the legend indicates the resonance wavelengths. Furthermore, Figure 8 portrays the E-field confinement in the cavities for those resonance wavelengths. Moreover, Table 3 epitomizes the change of sensitivity and FOM before and after the optimization process. Therefore, the highest sensitivity and FOM offered by the proposed sensor are 865.31 nm/RIU and 218.80, respectively. In different literature, another performance metric FOM* is measured at a defined wavelength as [29], where, ∆R stands for variation in reflection intensity caused by variation in refractive index (∆η) and R is the reflection rate in the sensor.
The measured FOM* is plotted in the Figure 9, where three FOM* peaks are observed. The highest FOM* is found as 4.771 × 10 4 . Therefore, the proposed sensor surpasses recent plasmonic-based RI sensors in terms of FOM and FOM* (Table 4). 16.7 - [21] 105.02 - [34] 159.6 -Proposed sensor 218. rication process [35]. The whole procedure is illustrated in Figure 10, where the silicon wafer is considered as the substrate. The first step is imprinting the blueprint of the sensor over the resin using a stamp (Figure 10a). The undesired resin is then removed from the compressed area through O 2 plasma etching ( Figure 10b). Subsequently, electron beam evaporation (Figure 10c) deposits the silver on the substrate, followed by eliminating residual resin through the lift-off technique (Figure 10d).

Conclusion
In summary, the transmission spectra of the proposed structure consisting of six rectangular cavities are scrutinized through the finite element method. The resonance dips achieved through simulation can detect six basic colors used in various medical, photonics, industrial applications. Alternatively, this color detection-focused optimized structure can also be used as an RI sensor with maximum sensitivity, FOM, and FOM* of 865.31 nm/RIU, 218.80, and 4.771 × 10 4 , respectively. Due to the implementation of a low-cost and high throughput fabrication process along with satisfactory performance, the proposed struc-14 ture will be a perfect choice both as a color detector and a RI sensor.

Declarations Funding
The manuscript did not receive any grant support or funding.

Conflict of Interest
All authors certify that they have no affiliations with or involvement in any organization or entity with any financial interest or non-financial interest in the subject matter or materials discussed in this manuscript.

Availability of Data and Material
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Code Availability
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Ethics approval
This is an observational and simulation-based study. No ethical approval is required. 15