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. 2024 Feb 12;9(8):9625–9632. doi: 10.1021/acsomega.3c09589

One-Dimensional Defect Layer Photonic Crystal Sensor for Purity Assessment of Organic Solvents

Divya Sampath 1,*, Venkateswaran Narasimhan 1
PMCID: PMC10905966  PMID: 38434907

Abstract

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This paper presents the design and analysis of a one-dimensional defect layer photonic crystal (1D-DLPC) sensor for the assessment of the purity of chemical solvents with enhanced accuracy. Chemical solvents are frequently used in chemical processes as reaction mediums. It is essential to ascertain its purity since impurities can significantly affect the outcome of the reaction. The structure of the proposed one-dimensional defect layer photonic crystal sensor consists of a defect layer sandwiched between alternate layers of ZnO and SiO2 organized with a certain periodicity. It has been shown that the localized defect modes inside the structure can detect minute refractive index changes based on the degree of impurity of chemical solvents. Simulation studies have been performed through the transfer matrix method (TMM) and the performance of the design is evaluated using several metrics such as sensitivity, full width at half-maximum, figure of merit, quality factor, and dynamic range. Results indicate that the designed one-dimensional defect layer photonic crystal sensor has a significantly high efficiency and is suitable for detecting impure solvents.

1. Introduction

Since the emergence of photonic crystals in the early 1990s, various exciting applications have been researched across different fields. These crystals manipulate light flow like semiconductors controlling electron flow engineered at light wavelength scales. Photonic crystals consist of a periodic structure of materials, creating a band gap that prevents certain frequencies of light from propagating through the material. It finds numerous applications in both science and technology, such as optics, photonic integrated devices, light-emitting diodes (LEDs), lasers, biosensors, and chemical sensors, etc. In Photonic crystals, reflectance, transmittance, band structure, group velocity, and the rate of spontaneous emission are a few features that are considerably altered by the periodic modification of the refractive index.1

This paper presents a one-dimensional defect layer photonic crystal crafted specifically to track the displacement of the defect mode within the photonic band gap. The primary objective is to assess the purity of chemical solvents through this innovative design. We investigated a one-dimensional defect layer photonic crystal (1D-DLPC) with a defect layer positioned between alternating ZnO and SiO2 layers.2,3 Using physical vapor deposition (PVD) or chemical vapor deposition (CVD) techniques, the layers of the photonic crystal can be fabricated. During the fabrication process, the defect layer can be introduced as a cavity, where the solvent can be used. This cavity can be created by omitting the deposition of material in that specific region or etching away material. This photonic crystal structure can further be optimized to identify minute variations in the refractive index brought about by introducing contaminants in the acetone–water mixture through the localized fault modes.4

Traditional methods for assessing the purity of organic substances, such as solvate chromic fluorescence probes, electronic noses, quartz crystal microbalances, solvent-response materials, and chromatography–mass spectrometry, often involve complex setups, are challenging to use, expensive, and time-consuming.5,6 In response to these challenges, there is growing interest in alternative detection technologies. One promising approach is photonic crystal (PC) based detection, leveraging the powerful sensing and detection capabilities of photonic crystals. These periodic optical nanostructures possess an exceptional capability of sensing organic compounds by selectively capturing alterations in the refractive index. One-dimensional defective photonic crystals, among other photonic crystal structures, present a standout advantage due to their simpler, cost-effective fabrication compared to higher-dimensional models. This characteristic renders them highly compelling for pioneering efficient detection technologies.7 The inclusion of a defect layer within the one-dimensional photonic crystal structure leverages the distinct optical characteristics of acetone and water to discern the purity of a mixture. The Transfer Matrix Method (TMM) is a widely used technique for the investigation of complicated multilayer structures, including photonic crystals.8 The method is well suited to layered structures with varying properties. Compared to the Finite Difference Time Domain (FDTD) and Finite Element Method, TMM is simple when the entire structure interacts only with adjacent layers with a repeating pattern.

The structure of the proposed work is as follows: The design and optimization of the 1D defect layer photonic crystal (1D-DLPC) structure are presented in Section 2. The measurement of the refractive index of the acetone–water mixture is covered in Section 4. The many performance measures used to assess the organic sensor are covered in Section 5. The simulation results are shown in Section 6, and the conclusions are shown in Section 7.

2. Design and Optimization of the One-Dimensional Defect Layer Photonic Crystal (1D-DLPC)

To assess solvent purity, we explored the application of a conventional one-dimensional defect layer photonic crystal structure. This structure comprises alternating layers of two dielectric types, each with distinct thickness and dielectric constant values while maintaining a constant spatial period. We assume uniformity and an infinite extension of each layer along the length and width dimensions. The term “one-dimensional” describes the variation of the dielectric function solely along a single dimension. Photonic crystals, periodic or quasiperiodic, possess lattice dimensions comparable to light wavelengths. Interaction with these structures leads to the formation of bandgaps for distinct light wavelengths.9 Fabricating cavity-based photonic chemical sensors of this nature is achievable using commonly available thin-film methods such as spin-coating and dip-coating.10

The design parameter of the defect layer between two symmetric one-dimensional sub-PCs has alternating layers of ZnO and SiO2 with refractive indices of nA = 2.003 and nB = 1.45, respectively. For, small values of Inline graphic, many works of literature present more general design equations that maximize the band gap.11 From Figure 1, it was shown that for the two materials with refractive indices (nA and nB) and thicknesses dA and dB respectively, for the normal incidence, the band gap is maximized when dAnA = dBnB or, equivalently, Inline graphic, where a = dA + dB and nc = effective refractive index. In this case, it can be shown that the midband frequency ωm is Inline graphic where c = velocity of light in free space. Thus, the ZnO and SiO2 layers have thicknesses of dA = 52 nm and dB = 72 nm, respectively. The choice of periodicity is optimized to obtain deep transmission minima.

Figure 1.

Figure 1

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Design of the chemical sensor based on the one-dimensional defect layer photonic crystal structure.

Localized states emerge within the band gap of a photonic crystal upon introduction of a discontinuity in its periodic arrangement, akin to electronic bandgaps in semiconductors. The thickness of the defect layer governs the resonance wavelength, confining light within the flaw. Altering this thickness impacts the initial band gap and, consequently, the range of wavelengths the crystal can transmit or reflect.12,13 It may also influence guided light’s group velocity and dispersion. Simulation helps identify the optimal defect layer thickness to achieve the desired performance.

3. Theoretical Formulation of the Transfer Matrix Method (TMM)

The transfer matrix method is a robust mathematical technique employed to analyze the transmission of light through a photonic crystal containing multiple layers with distinct optical properties.14,15 This method operates under the assumption that the optical properties remain constant and are known within each layer. Additionally, it presupposes that the light wave can be expressed as a combination of plane waves propagating within the material. For every layer, a 2 × 2 transfer matrix, also termed the propagation matrix, is constructed to characterize the optical properties specific to that layer. This transfer matrix establishes a connection between the incoming wave amplitudes and the outgoing wave amplitudes at each interface and can be expressed as follows

3. 1

where, k denotes various layers A, B, and C.

ρk is defined as

3.

where, dk, nk, and θk signify the thickness, refractive index, and angle of incidence of the kth layer, respectively. Free space wavelength is denoted as λ. ϕk is defined as ϕk = Z0nk cos θk for TE mode and Inline graphic for TM mode, where z0 is the free space impedance.

To find the overall transfer matrix for the entire structure, the transfer matrices of all the individual layers are simply multiplied together. The transfer matrix of the complete structure is

3. 2

Here, MA, MB, and MD represent the transfer matrix ZnO, SiO2, and defect layer.

The transmittance coefficient and reflectance coefficient are given by

3. 3
3. 4

where γ0 and γy signify the impedance of the incident and output medium of the proposed structure. In the case of TE polarized light, γ0 and γy is given by γ0 = Z0n0 cos θin and γy = Z0ny cos θy. Here Z0 represents the free space impedance. Once the overall transfer matrix is obtained, the reflectance (R) and transmittance (T) of the proposed one-dimensional photonic crystal can be calculated from

3. 5
3. 6

Absorption (A) of the multilayer structure can be given as

3.

where n0 is the refractive index of the input medium.

nout is the refractive index of the output medium, either air or any other substrate.

Transfer matrix method (TMM) was simulated in MATLAB R2023, to evaluate the performance. The advantage of 1D-DLPC simulations in MATLAB is that they can shorten and lower the experimental testing time.

4. Estimation of the Refractive Index of the Acetone–Water Mixture

Estimating the refractive index of acetone/water mixtures holds significance across various scientific disciplines due to the indispensability of organic solvents. These solvents play vital roles in chemistry, biology, pharmacology, and materials science, facilitating material extraction, suspension, and dissolution.16,17 They serve as crucial reaction media in chemical operations, ensuring reactant dissolution, homogeneous reactions, and controlled reaction rates. Laboratories rely on solvents for tasks like dilution, chromatography, and sample preparation, while industrial settings utilize various organic solvents like isopropyl alcohol, trichloroethylene, and perchloroethylene for effective degreasing and cleaning processes.18

In liquid–liquid mixtures, which are used in many industrial applications, the refractive index is an important tool for indirectly determining their purity. The degree of reflection and light transmission through a material are both strongly impacted by the purity of the substance.19,20 Reduced transmittance can occur from light absorption and scattering caused by contaminants. This study explores the correlation between a material’s transmittance and its refractive index, specifically examining the effects of varying acetone concentrations on these properties. Distilled water and pure acetone exhibit refractive indices of 1.333 and 1.3586, respectively. The investigation centers on acetone–water mixtures, encompassing concentrations from 20 to 80%. The mixing process induces structural reorientation attributed to differences in component shape, size, and intermolecular interactions. The purity of acetone substantially impacts its optical traits and usability.21

Many pure liquids have refractive index values that are either well-known or easily accessible in the literature. Nevertheless, interferometric or deflection methods are usually employed to ascertain the refractive indices of a binary liquid combination.20 Refractometers are used in deflection procedures to determine the refractive index using the critical angle effect. Abbe refractometers, inline process refractometers, conventional hand-held refractometers, and digital hand-held refractometers are the four basic types of refractometers.22,23 In general, an Abbe refractometer can be used to evaluate the refractive indices of water and acetone mixtures, providing an accurate measurement. As an alternative, an exact mixing rule can be used to estimate the refractive index from pure components.

The refractive indices of pure components and their mixes were determined across various temperatures and volume fractions, validating established mixing laws as outlined by Nowakowska J. et al.24 The Arago-Biot relation, based on volume additivity during mixing, stands as the simplest approximation to the true values for binary mixtures, offering a foundational perspective in this regard. It is stated as

4. 7

where, nm = refractive index of the mixture

n1, n2 = refractive index of pure components

y1, and y2 = volume fractions

The calculated estimated refractive indices using the straightforward Arago-Biot relation exhibit significant variations across different volume fractions in Table 1. This variation highlights the substantial change in refractive indices within the mixtures, as derived from eq 7. The Arago-Biot mixing rule’s advantage lies in its simplicity and extensive applicability across various scenarios, distinguishing it from other relations discussed in the literature.

Table 1. Refractive Index of Water and Acetone Mixture Concentration.

s. no concentration of impurity of acetone (%) refractive index (n)
1 0% (pure acetone) 1.3586
2 20% 1.3548
3 40% 1.3484
4 60% 1.3432
5 80% 1.3381
6 100% 1.3330
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5. Performance Metrics for the Evaluation of the Chemical Sensor

This section delves into a few crucial parameters that are necessary to assess the suggested sensor’s performance. Quantitatively assessing performance involves examining various metrics like sensitivity (S), figure of merit (FoM), quality factor (QF), and dynamic range (DR).25,26 Sensitivity (S) is determined by observing the shift in the peak position of the defect mode caused by the influence of impure acetone/water mixtures on the refractive index. The following is a way to express this sensitivity

5. 8

An additional quantitative indicator used to evaluate the performance of the suggested sensor is called the “Figure of Merit” (FoM). The ratio of the spectral width at half-maximum to the value of the peak resonant wavelength is used to calculate this statistic. The FoM is defined as

5. 9

fwhm, which stands for “Full Width at Half Maximum”, is commonly utilized to characterize the spectral resolution of a sensor. It represents the bandwidth of the sensor’s response, indicating the range over which the sensor can effectively detect signals. A narrower fwhm generally signifies a higher sensitivity and a higher Figure of Merit (FoM), enabling the sensor to detect smaller changes in the input signal.

The Quality Factor (Qf) serves as a metric for the energy stored in the photonic crystal cavity relative to the energy lost through dissipative mechanisms such as absorption and scattering. It quantifies the effectiveness of the photonic crystal in trapping and storing light within the resonator. Minimizing losses attributed to scattering, absorption, and fabrication imperfections contribute to an increased Quality factor.

A higher Quality Factor suggests that the photonic crystal cavity excels in efficiently detecting changes in the refractive index of the surrounding environment. Mathematically, the Quality Factor (Qf) can be defined as

5. 10

Where λD is the resonant frequency of the cavity mode (the frequency at which the cavity strongly interacts with light). Δω is the full width at half-maximum (fwhm) of the resonant peak in the photonic crystal’s transmission or reflection spectrum.

The dynamic range (DR) of a 1D photonic crystal refers to the difference between maximum and minimum input power levels that a photonic crystal device can operate effectively and accurately. It is calculated using the relation,

5. 11

The design is aimed at a broader dynamic range performance by optimizing the device’s structure.

6. Simulation Results and Discussion

6.1. Evaluation of the Refractive Index and Transmittance of the Acetone–Water Mixture Samples

In this section, the performance of the proposed design was evaluated concerning variations in the refractive indices of the acetone–water mixture, periodicity, and thickness of the defect layer. This evaluation was conducted by analyzing the transmittance spectra at normal incidence. A crucial physical parameter for assessing the purity of any solvent is its refractive index.27,28 The refractive indices of pure acetone and water, along with their respective proportions, determine the refractive index of the mixture. At a specific temperature of 30 °C, the refractive indices of the acetone and water mixtures were determined using the Arago-Biot relation and are presented in Table 1.

Water and acetone molecules possess distinct molecular structures and polarities. When mixed, water molecules interact with acetone molecules through dipole–dipole interactions and hydrogen bonding. These interactions cause the local electric fields around the molecules to align, resulting in an increase in the effective refractive index of the mixture compared to that of water alone. A higher refractive index in pure acetone indicates that light travels slower in the defect cavity.28,29

Further, the proposed sensor is evaluated for the transmittance spectra of the mixture of acetone–water at various compositions at normal incidence simulated using the MATLAB simulation tool. The transmittance of the (ZnO SiO2)N defect layer (ZnO SiO2)N photonic crystal sensor has been evaluated using the TMM. Initially, the thickness of d1 and d2 was arrived using the design formulas presented in Section 4, as 52 and 72 nm, respectively. The periodicity of the layers considered is N = 8. Using a water sample in the defect layer, the transmittance is depicted in Figure 2. The observed resonance within the photonic band gap reveals a distinctive feature known as the defect resonant mode, stemming from the perturbation within the structure’s periodicity. Figure 3 demonstrates a defect mode with 94% transmittance, notably centered at a wavelength of 445.5 nm. Additionally, the transmittance spectra within the photonic band gap exhibit some high-transmittance ripples, notably on the higher wavelength side. Since the cavity region is in the middle of the design, the two identical (ZnO SiO2)N sub-PCs on either side of it serve as identical Bragg mirrors. Localized defect modes are a result of light being able to bounce back and forth in the area between the two Bragg mirrors.

Figure 2.

Figure 2

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Transmittance spectra of water and acetone with refractive index at normal incidence in a (ZnO SiO2)N defect layer (ZnO SiO2)N sensor with defect layer thickness dD = 620 nm and periodicity N = 8.

Figure 3.

Figure 3

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Transmittance spectra of the different defect layer thickness at normal incidence in a (ZnO SiO2)N defect layer (ZnO SiO2)N sensor with (a) dD = 470 nm. (b) dD = 620 nm and (c) dD = 930 nm.

6.2. Evaluation of the Performance of the (ZnO SiO2)N Defect Layer (ZnO SiO2)N Sensor for different Thicknesses of the Defect Layer

The effect of change in defect layer thickness with dD = 620 nm, dD = 470 nm, and dD = 930 nm was studied on the transmission properties. Figure 3 shows the transmittance characteristics of the mixture of water and acetone with a range of refractive indexes of 1.3330–1.3586. As the thickness is increased from dD = 470 nm, the sequence of discrete modes pulls down into the gap from the upper bands for different impurity values.

Table 2 illustrates the changes in the refractive index of the mixture, peak resonant position, transmittance, and sensitivity of the resonant modes associated with three distinct defect layer thicknesses. The analysis reveals that the peak wavelength consistently decreases as the concentration shifts from pure to impure for all three defect layer thicknesses. Concurrently, an increase in defect layer thickness corresponds to a decrease in transmittance. However, it can be noted from Figure 4a,b that the relationship between refractive index vs peak wavelength and refractive index vs sensitivity seems to follow certain linearity but can vary with temperature and other factors. Better Sensitivity measure is observed for resonant modes with dD = 620 nm for N = 8.

Table 2. Peak Wavelength, Transmittance, and Sensitivity of Resonant Modes for different Defect Layer Thickness at Normal Incidence in a (ZnO SiO2)N Defect Layer (ZnO SiO2)N Sensor.

  dD = 470 nm
 dD = 620 nm
 dD = 930 nm
refractive index of the mixture wavelength (nm) transmittance (T) sensitivity nm per RIU wavelength (nm) transmittance (T) sensitivity nm per RIU wavelength (nm) transmittance (T) sensitivity nm per RIU
1.3586 456.0 0.9317 336 450.0 0.8621 331 443.5 0.6665 326
1.3548 455.5 0.9257 336 449.0 0.8208 331 443.0 0.8269 327
1.3484 455.0 0.8752 337 448.0 0.8754 332 441.5 0.9262 327
1.3432 454.0 0.9682 338 447.0 0.7720 333 440.5 0.8660 328
1.3381 453.5 0.8924 339 446.5 0.8300 334 439.5 0.7814 328
1.3330 452.5 0.9364 340 445.5 0.9403 334 438.5 0.7659 329
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Figure 4.

Figure 4

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(a) Peak wavelength and (b) sensitivity of resonant modes associated with defect layer thickness at normal incidence in a (ZnO SiO2)N defect layer (ZnO SiO2)N sensor has different defect layer thickness dD = 470 nm, dD = 620 nm, and dD = 930 nm for N = 8.

6.3. Performance of the Proposed (ZnO SiO2)N Defect Layer (ZnO SiO2)N Sensor for different Period Number (N)

Investigations have been performed to study the transmission characteristics of the proposed multilayer sensor. change as the number of periods changes from N = 4 to N = 10 in steps of two.

Figure 5 shows the transmittance spectra and peak wavelength of resonant modes at normal incidence in a (ZnO SiO2)N Defect layer (ZnO SiO2)N sensor associated with N = 4, N = 6, and N = 8 for defect layer thickness equal to 620 nm. Table 3 distinctly illustrates the resonant mode wavelength shifting toward the lower band with increased periodicity, consequently leading to reduced transmittance. Furthermore, the sensitivity measure of resonant modes indicates the sensor’s capability to uniformly detect and respond to changes in the periodicity parameter N.

Figure 5.

Figure 5

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Transmittance spectra and resonant wavelength at normal incidence in a (ZnO SiO2)N Defect layer (ZnO SiO2)N sensor for various periodicities (a) N = 4, (b) N = 6 and (c) N = 8.

Table 3. Wavelength and Sensitivity of Resonant Modes at Normal Incidence in a (ZnO SiO2)N Defect Layer (ZnO SiO2)N Sensor for Various Periodicity N = 4, N = 6, and N = 8.

  N = 4
 N = 6
 N = 8
refractive index of the mixture wavelength (nm) transmittance (T) sensitivity nm per RIU wavelength (nm) transmittance (T) sensitivity nm per RIU wavelength (nm) transmittance (T) sensitivity nm per RIU
1.3586 453.0 0.9517 333 450.5 0.9378 332 450.0 0.8621 331
1.3548 452.5 0.9524 334 450.0 0.9563 332 449.0 0.8208 331
1.3484 451.0 0.9506 334 449.0 0.9516 333 448.0 0.8754 332
1.3432 450.0 0.9507 335 448.0 0.9533 334 447.0 0.7720 333
1.3381 449.0 0.9504 336 447.0 0.9538 334 446.5 0.8300 334
1.3330 448.0 0.9492 336 446.0 0.9463 335 445.5 0.9403 334
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Figure 6a,b shows the correlation between the refractive index and peak wavelength, as well as the refractive index and sensitivity. This appears to exhibit a degree of linearity. However, it is noteworthy that this relationship may exhibit variations influenced by factors such as temperature and others. A higher sensitivity measure is observed for resonant modes with a defect layer thickness (dD) of 620 nm when the number of layers (N) is equal to 8.

Figure 6.

Figure 6

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(a) Peak wavelength and (b) Sensitivity of resonant modes at normal incidence in a (ZnO SiO2)N Defect layer (ZnO SiO2)N sensor for various associated with defect layer thickness dD = 470 nm, dD = 620 nm, and dD = 930 nm for N = 8.

6.4. Performance Analysis of the Proposed (ZnO SiO2)N Defect Layer (ZnO SiO2)N Sensor

The performance of the proposed sensor has been assessed using several standard metrics, including Full Width at Half Maximum (fwhm), figure of merit (FoM), quality factor (QF), and dynamic range (DL) for two distinct values of the periodicity parameter.29 The results are summarized in Table 4. It is evident that a narrower fwhm is achieved for N = 8. Additionally, higher FoM values for N = 8 suggest that the designed sensor exhibits increased sensitivity, enabling the detection of smaller changes in the input signal.

Table 4. Performance of the Proposed (ZnO SiO2)N Defect Layer (ZnO SiO2)N Sensor with Defect Layer Thickness 620 nm.

  fwhm (nm)
 FoM (nm per RIU)
 quality factor (Qf)
 dynamic range (DR)
refractive Index of the mixture N = 4 N = 6 N = 8 N = 4 N = 6 N = 8 N = 4 N = 6 N = 8 N = 4 N = 6 N = 8
1.3586 0.0615 0.0505 0.0486 5415 6574 6815 7366 8920 9259 1827 2005 2041
1.3548 0.0645 0.0598 0.0476 5178 5552 6962 7016 7525 8804 1781 1840 1988
1.3484 0.0635 0.0615 0.0496 5259 5415 6694 7102 7300 9032 1790 1811 2012
1.3432 0.0625 0.0589 0.0485 5360 5660 6866 7200 7606 8994 1800 1846 2005
1.3381 0.0618 0.0628 0.0483 5437 5321 6907 7265 7118 8842 1806 1784 1986
1.3330 0.0632 0.0565 0.0500 5316 5929 6680 7088 7893 8910 1782 1876 1992
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The Quality factor quantifies the sharpness of the resonance peak. As depicted in Table 4, a higher Quality factor for N = 8 indicates heightened sharpness and selectivity in the sensor’s response near its resonant wavelength. This denotes an increased efficacy in detecting impurity levels with minimal changes in the refractive index. Moreover, at N = 8, a higher dynamic range is evident, suggesting the sensor’s ability to function across a wide range of signal levels and detect weak signals, even amid substantial variations in the input signal.

7. Conclusions

In this paper, the design and analysis of a one-dimensional photonic crystal sensor (ZnO SiO2)N Defect layer (ZnO SiO2)N are aimed to detect impurities in acetone–water mixtures by monitoring minute refractive index variations. Employing the transfer matrix method, the investigation delves into transmittance concerning impurity levels, considering fluctuations in defect layer thickness, periodicity, and impurity concentrations. Simulation outcomes validate the efficacy of the proposed sensor design, showcasing optimized parameters: ZnO and SiO2 layer thicknesses of 52 and 72 nm, defect layer thickness of 620 nm, and N = 8. This configuration exhibits exceptional quality and efficacy in discerning the purity levels of acetone–water mixtures. The research findings bear substantial implications for propelling advancements in photonic sensors, particularly within the chemical industry and various related applications.

Acknowledgments

Authors acknowledge the management, Department of ECE, and Department BME of Sri Sivasubramaniya Nadar College of Engineering (Autonomous), OMR, Kalavakkam, Chennai 603110, Tamil Nadu, India for their support.

The authors declare no competing financial interest.

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