Design of a multilayer photonic crystal biosensor for ocular studies enhanced with machine learning towards the evaluation of proliferative vitreoretinopathy

Abstract

Ocular studies utilizing a one-dimensional (1D) ternary photonic crystal biosensor are proposed. Incorporation of materials such as gallium nitride, aluminum nitride, and silicon in the design enhances the sensor metrics, facilitating diagnosis of diabetes and eye cancer. Multiple wavelengths are chosen in this investigation in the range of 580–1700 nm. The design analysis of this sensor is done on the basis of the transfer matrix method. Transmission characteristics exhibited by the sensor provide distinct analyte identification. The quality factor, sensitivity, and figure of merit exhibited by the sensor for the diabetes study utilizing eye tear fluids are 40,042, 783 nm RIU⁻¹, and 18,433 RIU⁻¹, respectively. The proposed photonic crystal sensor is also investigated for the study of proliferative vitreoretinopathy, and a high quality factor is exhibited by the sensor. Plane wave expansion and finite difference time domain techniques validate the band gap and field distribution analysis. Machine learning models such as random forest and extreme gradient boosting enhance the work in the prediction of transmission amplitude, considering errors during the fabrication of the photonic crystal structure.

Introduction

Photonic crystal (PC)-based sensors are widely investigated mainly due to the ease of design and better performance in a compact size. Eyes are unarguably a prime and essential part of the human body. The motivation of this work is to enhance the biosensing techniques related to visual disorders. Diabetes can be primarily detected using invasive methods such as pin pricking¹. The non-invasive techniques not only attract comfort but also ease in obtaining the results in real time. The reason for choosing an optical sensor such as a PC biosensor is based on these concepts. With respect to the choice of the analyte, human tears have been explored in the diabetic studies for a long time. The studies to prevent disorders in human vision fall in the category of sustainable development goal 3 (SDG 3), to ensure a healthy life and enhancement of well-being for mankind². The versatility of 1D PC-based sensors is underscored by the applications such as pressure sensing³, temperature sensing⁴, blood component analysis⁵, detection of cancer cells⁶, and many more.

Tears are one of the analytes that can be used for studying eye disorders such as eye melanoma⁷. For retinal studies, tears are very crucial, and they also provide a non-invasive approach⁸. In one of the recent works, tears were used in the study related to diabetic retinopathy (DR)⁸. Monitoring of glucose levels from tears utilizing contact lenses is another method that enhances the management of diabetes⁹. Human tear samples were also used in DR studies utilizing acoustic wave-based sensors¹⁰. In another study, determination of diabetes mellitus from tear fluids is demonstrated using spectroscopy methods¹¹. In a work published in 2015, a two dimensional photonic crystal sensor with a double hexagonal ring resonator was utilized to determine glucose concentration from tears¹². But the achieved sensitivity, quality factor, and related parameters were not mentioned explicitly. In 2018, a 2D PC structure highlighted the non-invasive approach to detect glucose from tears, and the performance metrics were given in terms of wavelength shifts¹³. In 2021, the quality factor achieved by a PC microstructure in the detection of diabetes is 867.97¹⁴. In 2023, a 2D PC design demonstrated a sensitivity of 688.16 nm RIU⁻¹ in the detection of diabetes utilizing human tears¹⁵. All the above works indicate the relevance and importance of research in ocular studies. The non-invasive approach is one of the techniques preferred for ocular studies and PC can play an important role in this domain. In this work, we propose the use of PC-based biosensors to detect diabetic conditions using tears with an improved quality factor.

Injuries caused in the retina can lead to proliferative vitreoretinopathy (PVR); which can further affect the vision due to separation of retina from the blood vessels¹⁶. Proliferative diabetic vitreoretinopathy (PDR) that is related to diabetes is also another disorder that affects vision¹⁷. One of the reasons for PVR is the changes in the cellular layers in the vitreous region¹⁸. Another reason for PVR is the postoperative reproliferation and the drugs to prevent this condition are under test¹⁹. The proliferation of cell membranes occurs not only on the surface of the retina but also in the intraretinal layers²⁰. The stages of PVR can progress from minimal changes to wrinkling in the retina to increasing folds in the retina and finally to extensive retinal folds¹⁸. In the situation of ocular injury, the possibility for retinal pigment epithelial cells to enter the vitreous cavity and subretinal region is high²¹. Due to the presence of abnormal growths, the vitreous cavity becomes more opaque, and this can lead to loss of transparency of the vitreous humor²². The study of protein composition of vitreous humor provides more insights into PVR and other related vitreoretinal disorders²³. The retinal disease mechanisms can be understood more clearly by investigating the details of changes in the vitreous cavity. Many strategies have been proposed by researchers to prevent the proliferation, such as daunorubicin (an antibiotic), isotretinoin (a synthetic retinoid), and decorin (a proteoglycan) that reduces the PVR²⁴. Paracentesis is done carefully to collect the aqueous humor samples from patients who are reported with PVR, and the amount of peptide substance is found to be high in the aqueous humor²⁵.

ML approaches are not limited to studies related to heart diseases²⁶, prediction of drug release²⁷, analysis of biological interactions in surface plasmon resonance sensors²⁸, sepsis diagnosis²⁹, prediction of intensity variations³⁰, and prediction of sensor sensitivity in glucose detection³¹. Thus, the primary goal of this work is to use PC structures in the detection of diabetes with enhanced sensor parameters. The second goal of this study is to differentiate normal eye tissues and cancer-affected tissues. The third goal of this work is to obtain the spectrum of healthy human aqueous humor and vitreous humor. The final goal of the work is the application of machine learning (ML) to predict the sensor parameter from the set of data with different period values.

Unlike other ocular studies using PC sensors, this work provides more in-depth analysis not only on tear fluid-based diabetic studies but also on melanoma and PVR. To the best of our knowledge, PVR studies using TPC sensors have not been reported to date. Another aspect that makes this work distinct is the use of three different materials in a specific order, optimized defect layer thickness, and highly improved QF, FOM, and WS in ocular studies. Although the majority of the PC-based sensors have performed ocular studies, incorporation of ML in this work gives an added advantage. Fabrication errors are rarely considered in PC-based simulations. Considering the fact that fabrication errors can shift the wavelength as well as introduce noise in the transmission amplitude, these ML results in this work are highly relevant and enhance the novelty.

Structural configuration and mathematical background of the ternary PC biosensor

Figure 1 shows the structure of the proposed TPC. A tunable laser light is used as the input light source. Materials are arranged in the order such that gallium nitride is placed first, followed by aluminum nitride and then silicon. These three materials form a three-layer stack. This three-material multilayer stack is repeated N times, and N denotes the period of the stack. Thus, a combination of three materials is constructed N times followed by the defect region. After the defect region, the stack is again repeated N times, and this forms the structure of the TPC. The input light signal is incident at an angle θ₀ with respect to the normal.

Fig. 1.

Structure of the 1D ternary PC

The experimental setup to obtain the transmission spectrum of the ocular analytes is shown in Fig. 2. The analyte samples are introduced into the default region. The input light initially passes through the first N stack layers of the TPC, then the analyte region, followed by the next N stack layers of the TPC. The output light signal that is detected utilizing an optical detector must be processed to obtain the required transmission plot. The wavelength of the light used in this TPC sensor ranges from 1500 to 1600 nm for the tear fluid-based diabetic studies.

Fig. 2.

Proposed ternary 1D PC biosensor system

Sellmeier equation³² is considered for the three materials in this design. RI equations^33–38 of the three materials are indicated below.

1

2

3

GaN is recommended in PC structures with multilayers because of its lattice matching, and it was recently³⁹ used in the diagnosis of malaria. Thermal stability, suitability with fabrication techniques, and non-toxicity are some of the reasons for selecting AlN in this work^40,41. High refractive index (RI), low thermo-optic coefficient, and wide acceptance in PC-based biosensors are the reasons for selecting silicon as the third material^42,43.

Implementation of the transfer matrix method

The transfer matrix method⁴⁴ (TMM) is implemented in this work using Python programming to model the multilayer photonic structure. The characteristic matrix of each layer in the structure depends on RI, thickness, and incident angle. The global transfer matrix is obtained by multiplying these matrices in a sequential order. The transmission spectrum is plotted based on these results. Thus, from TMM results, the peak wavelength, sensitivity, and other sensor parameters are calculated. TMM is selected in this investigation, as it has been applied in multiple research activities related to biosensing. The sensing areas investigated utilizing TMM is not only limited to cancer cell studies, anemia detection and dengue virus detection, but also to many other biological studies^44–46. TMM provides a link between the design variables and the desired optical output parameters. Whether it is a binary stack or ternary stack of layers, TMM supports the design and analysis of biosensors based on PCs. TMM is implemented initially utilizing MATLAB software and visualizations are enhanced utilizing Python in the Google Colab platform.

In the TMM approach, initially the RI, thickness and period of the structure is specified. The sensor is modeled in a specified order, such as N stacks, a defect layer and then the next N stacks. Each layer is defined utilizing a characteristic matrix that relates the propagating fields. The dispersion model-based equations are implemented for each material. The resultant transfer matrix obtained from the TMM provides the optical response of the entire stack. The transmission coefficient that depends on elements of the transfer matrix and phase terms is further calculated. Transmittance is obtained from the transmission coefficient and the phase contributions at the input and output interfaces.

The characteristic matrix^47,48 for each layer is denoted using C_m:

4

where δ_m represents the phase variation in each layer^47,48,

5

The optical signal wavelength is denoted by λ. The thickness of m^th layer is represented using d_m and the RI is denoted by n_m⁴⁹.

When TE polarization analysis is considered in a multilayer PC structure^47,48,

6

The relation between initial incident angle and angle of incidence into the PC structure is given by^47,48:

7

The symbol P denotes the transfer matrix of the 1D PC constructed using the three materials^47,48.

8

The elements of the transfer matrix P is denoted as P_ij and the defect layer transfer matrix is represented by P_D⁴⁷.

Based on the transfer matrix elements and phase contributions, the transmission coefficient (t)^47,48 is calculated as:

9

The transmission coefficient and the phase difference parameters are utilized in the estimation of transmittance (T)^47,48.

10

Considering a TE polarized wave, the phase contributions related with the optical signal at the input and output interfaces are represented by the terms γ_in and γ_out respectively^47,48. Tables 1 and 2 lists the simulation parameters utilized in the design of the sensor.

Table 1.

Simulation parameters for diabetes and eye cancer studies.

Parameter	Diabetes study	Eye cancer study
Wavelength range	1615–1685 nm	1525–1595 nm
Incident medium index (air)	n0 = 1.0	n0 = 1.0
Substrate index (silica)	ns = 1.44	ns = 1.44
PC material layer thicknesses	GaN = 312 nm, Si = 312 nm, AlN = 312 nm	GaN = 300 nm, Si = 300 nm, AlN = 300 nm
Defect layer thickness	9.3 µm	6.45 µm
Number of periods evaluated	5–12	5–10
Incident angle	θ0 = 0° (normal incidence)	θ0 = 0° (normal incidence)
Analyte RI	Real part (1.33, 1.35, 1.41). For imaginary part, EMT is recommended	Real part (1.33, 1.376, 1.39) For imaginary part, EMT is recommended
Dispersion models	Sellmeier equations	Sellmeier equations
Transmission normalization	Spectra normalized to maximum transmittance	Spectra normalized to maximum transmittance
Peak detection method	Maximum transmittance within 1615–1685 nm	Maximum transmittance within 1525–1595 nm

Table 2.

Simulation parameters for aqueous humor and vitreous humor study.

Parameter	Aqueous humor and vitreous humor study
Wavelength range	575–595 nm	650–665 nm	947–960 nm
Incident medium index (air)	n0 = 1.0	n0 = 1.0	n0 = 1.0
Substrate refractive index (silica)	ns = 1.44	ns = 1.44	ns = 1.44
PC material layer thicknesses	GaN = 100 nm, Si = 100 nm, AlN = 100 nm	GaN = 200 nm, Si = 200 nm, AlN = 200 nm	GaN = 300 nm, Si = 300 nm, AlN = 300 nm
Defect layer thickness	1.02 µm	1.02 µm	1.11 µm
Number of periods evaluated	5–10	5–10	5–10
Incident angle	θ0 = 0° (normal incidence)	θ0 = 0° (normal incidence)	θ0 = 0° (normal incidence)
Analyte RI	Real part (1.33, 1.348, 1.357). For imaginary part, EMT is recommended	Real part (1.33, 1.344, 1.353). For imaginary part, EMT is recommended	Real part (1.33, 1.337, 1.345). For imaginary part, EMT is recommended
Dispersion models	Sellmeier equations	Sellmeier equations	Sellmeier equations
Peak detection method	Maximum transmittance within 575–595 nm	Maximum transmittance within 650–665 nm	Maximum transmittance within 947–960 nm

Field distribution analysis utilizing finite difference time domain technique

Finite difference time domain (FDTD) facilitates the determination of field distributions of the sensor⁵⁰. To analyze the electromagnetic field components, the Opti FDTD tool is utilized. For the 1D PC design, alternating layers of GaN, AlN, and Si are arranged periodically along the propagation axis. The mesh parameters selected are mesh delta X (Δx): 0.04 µm, mesh delta Z (Δz): 0.04 µm with the number of mesh cells utilized as 336 × 336. Simulations are performed in the transverse electric (TE) mode, updating the field components E_y, H_x, and H_z. A Gaussian-modulated continuous wave source is utilized at the respective wavelength range. Anisotropic perfectly matched layer (APML) is selected as the recommended boundary condition to eliminate unintended reflections. Field monitors are positioned at the end of the structure to capture transmission spectra. Iterations were carried out for 5000–10,000 time steps, with convergence determined by the decay of electromagnetic fields. Parametric sweeps of layer thicknesses are recommended to optimize resonance sharpness and sensitivity.

Figures 3, 4 and 5 illustrate the field distribution obtained for the components E_y, H_x and H_z respectively. Analysis of field distributions is done to provide insights into the sensor’s operational mechanism. Evaluation of optical mode confinement is one mandatory requirement in the sensor design, as it exhibits the localization of the electric field in the defect region. The intensity of electric field component E_y confirms the optical confinement in the defect layer region of the PC. In electromagnetic field analysis, the contributions of H_x and H_z are inevitable because they demonstrate the magnetic coupling around the region. The electric field component analysis not only reveals that the defect layer creates a localized resonance within the photonic band gap (PBG) but also highlights the overlap between the optical field and analyte. The sensor’s sensitivity to changes in RI is dependent on the field confinement in the defect region. The FDTD technique thus validates the band gap guided confinement and field-analyte interaction.

Fig. 3.

Electric field (E_y) plot of the sensor

Fig. 4.

Magnetic field (H_x) plot of the sensor

Fig. 5.

Magnetic field (H_z) plot of the sensor

Band gap analysis utilizing plane wave expansion method

Plane wave expansion (PWE)⁵¹ technique is utilized to evaluate the photonic band gaps of the proposed sensor. To obtain the PBG diagram, the simulations are initially executed in MATLAB and subsequently verified in Python to improve visualization. The dielectric profile is expanded into Fourier components up to eleven reciprocal lattice vectors, and the Eigen value problem is solved in the first Brillouin zone⁵². The normalized frequency ωa/2πc is obtained by diagonalizing the Hermitian matrix constructed from the Fourier coefficients of the dielectric function⁵³. Band gaps are detected by comparing adjacent bands, and the first three significant gaps are considered. This approach allows accurate identification of photonic band gaps and clear visualization of the TE band diagram for the GaN–AlN–Si structure.

The three photonic band gaps obtained in the evaluation are PBG1, PBG2 and PBG3, illustrated in Fig. 6. Photonic band gap 1 (PBG1) is in the range 1.124–1.383. It has a width of 0.260 and a mid value of 1.254, The second band gap PBG2 is in the range 2.353–2.702 with a width of 0.349, and mid value of 2.527. The third band gap PBG3is in the range 3.678–3.92, with a width of 0.243 and mid value 3.8.

Fig. 6.

Photonic band diagram of the sensor

Sensor metrics of the ternary PC

To evaluate the performance of the sensor, the metrics used are wavelength sensitivity (WS), quality factor (QF), figure of merit (FOM) and detection limit (DL). The RI difference creates a proportionate change in the wavelength for each ocular analyte, and this factor, known as the sensitivity, is the prime metric of the sensor. The QF of the sensor not only depends on the period (N) but also on the resonating wavelength and full width half maximum (FWHM). The DL is related to the WS, operating wavelength and QF. The narrowness of the spectral width and the larger sensitivity enhance the FOM of the TPC.

The equations utilized for sensor evaluation are^34,47,49,54:

11

If the sensor produces a larger shift in PW, for a minute change in RI, the WS metric is considered to be superior.

12

A sharper, narrower resonance peak is one of the characteristics of a superior PC sensor and it also indicates the spectral resolution. A narrower output signal means that the QF metric achieved by the sensor is high.

13

The DL value is expected to be lower for a better PC sensor, because the lower value of DL reflects that the sensor is able to detect even fraction of changes in the analyte RI.

14

FOM is one metric that can be used to compare different sensor designs based on the spectral response and WS. Resolution of a sensor is calculated as the difference between the peak shifts in the wavelength⁵⁵.

Results and discussion on the TPC sensor

Diabetes study

The normalized transmittance plot for the diabetic studies is given in Fig. 7. The thickness of the materials chosen is 312 nm with a defect layer thickness (DLT) of 9.3 µm and a period N = 9. The peak wavelength (PW) of the normal tear fluid is observed at 1636.14 nm. For the diabetic case, the PW value is 1679.65 nm. A difference of 43.51 nm is achieved by the sensor. By selecting a period of 9 for the diabetic study, a high QF of 20,451.8 is achieved. Figures 8 and 9 represent the analysis done on QF and PW variations with respect to the refractive index changes, respectively. Figures 10, 11, 12, and 13 depict the plots for FWHM, WS, DL, and FOM with respect to the variations in RI. The RI values of human tear samples available in literature for the normal case and diabetic case are 1.35 and 1.41, respectively⁵⁶.

Fig. 7.

Transmittance plot of tear analytes (targets) for defect layer of 9.3 µm, and period N = 9.

Fig. 8.

QF versus RI schematic for defect layer of 9.3 µm and N = 9

Fig. 9.

Peak wavelength versus RI schematic for defect layer of 9.3 µm and N = 9

Fig. 10.

FWHM versus of RI schematic for defect layer of 9.3 µm and N = 9

Fig. 11.

Wavelength sensitivity versus RI schematic for defect layer of 9.3 µm and N = 9

Fig. 12.

DL versus RI schematic for defect layer of 9.3 µm and N = 9

Fig. 13.

FOM versus RI schematic for defect layer of 9.3 µm and N = 9

The TPC sensor exhibits a linear relation between PW and refractive index over the RI values from 1.32 to 1.42. The sensor achieved the smallest FWHM value of 0.08 nm for the RI value of 1.35. The WS value attained is above 700 nm RIU⁻¹ for the analytes. The DL values for the analytes are less than 0.000017 RIU. The FOM value attained is above 9000 for normal tear fluid. On increasing the period value to 10 with a defect layer thickness of 7.89 µm, the highest QF obtained is 40,104. The normalised transmittance plot for this particular DLT (7.89 µm) is given in Fig. 14. The thickness chosen for each of the three constituent materials for the results presented in Table 4 is 308 nm. Compared to sensor parameters given in Table 3, the FOM value obtained by the sensor is 18,450 RIU⁻¹ for N equal to 10 and is tabulated in Table 4.

Fig. 14.

Transmittance plot of tear analytes (targets) for defect layer of 7.89 µm, and period N = 10.

Table 4.

Sensor metrics of the 1D TPC biosensor for defect layer of 7.89 µm and period N = 10.

	RI	λpeak (nm)	Wavelength sensitivity (nm/RIU)	FWHM (nm)	QF	FOM (RIU−1)	DL (RIU)
Water (reference)	1.33	1589.41	–	0.06	26,490.2	–	–
Normal (Tear fluid)	1.35	1604.17	738.00	0.04	40,104.3	18,450.0	0.000003
Diabetic (Tear fluid)	1.41	1645.74	692.83	0.08	20,571.8	8660.4	0.000006

Table 3.

Sensor metrics of the 1D TPC biosensor for defect layer of 9.3 µm and period N = 9.

	RI	λpeak (nm)	Wavelength sensitivity (nm/RIU)	FWHM (nm)	QF	FOM (RIU−1)	DL (RIU)
Water (reference)	1.33	1620.48	–	0.09	18,005.3	–	–
Normal (Tear fluid)	1.35	1636.14	783.00	0.08	20,451.8	9787.5	0.000005
Diabetic (Tear fluid)	1.41	1679.65	725.17	0.23	7302.8	3152.9	0.000016

Eye cancer study

For the eye cancer study, the normalized transmittance plot is given in Fig. 15. The material thickness selected for each of the three materials is 300 nm. Initially the simulation was performed for a defect layer thickness of 6.5 µm, and the WS attained was 663 nm RIU⁻¹. On reducing the defect layer thickness to 6.45 µm and for a shorter period value (N = 5), the WS increased to 681 nm RIU⁻¹. The improved WS plot is illustrated in Fig. 16. A high FOM value of 13,260.9 RIU⁻¹ and a QF value of 31,507.4 are exhibited by the sensor in the eye melanoma study. From the sensor metrics for period values N = 10 and N = 5, tabulated in Table 5 and Table 6, respectively, it can be inferred that the optimum value for the defect layer thickness is 6.5 µm and the N value is 10. For the eye cancer study, the RI values for the normal case and the cancerous case available in the literature are 1.376 and 1.390, respectively⁷.

Fig. 15.

Transmittance plot of eye cells for defect layer of 6.5 µm, and period N = 10.

Fig. 16.

Transmittance plot of eye cells for defect layer of 6.45 µm, and period N = 5.

Table 5.

Sensor metrics of the 1D TPC biosensor for defect layer of 6.5 µm, and period N = 10.

	RI	λpeak (nm)	Wavelength sensitivity (nm/RIU)	FWHM (nm)	QF	FOM (RIU−1)	DL (RIU)
Water	1.330	1544.87	–	0.08	19,310.9	–	–
Normal eye cell	1.376	1575.37	663.04	0.05	31,507.4	13,260.9	0.000004
Cancer eye cell	1.390	1584.25	634.29	0.05	31,685.0	12,685.7	0.000004

Table 6.

Sensor metrics of the 1D TPC biosensor for defect layer of 6.45 µm and period N = 5.

	RI	λpeak (nm)	Wavelength sensitivity (nm/RIU)	FWHM (nm)	QF	FOM (RIU−1)	DL (RIU)
Water	1.33	1537.14	–	1.73	888.5	–	–
Normal eye cell	1.376	1568.47	681.09	1.74	901.4	391.4	0.000128
Cancer eye cell	1.39	1577.58	650.71	1.91	826.0	340.7	0.000147

Vitreous humor and aqueous humor study

From the available literature on optical properties of ocular tissues⁵⁷, the measured RI values of human aqueous humor and vitreous humor are taken as the reference to evaluate the PC sensor performance. For the wavelength range 580–590 nm, the material thickness utilized for each of the three constituent materials is 100 nm. For wavelength ranges 653–664 nm and 948–960 nm, the material thickness selected is 200 and 300 nm, respectively. The RI of aqueous humor and vitreous humor at three wavelength values of 590, 654, and 947 nm are distinct, as tabulated in Tables 7, 8, and 9. Thus, the transmission analysis at these three wavelengths is done as illustrated in Figs. 17, 18, and 19. From Tables 7, 8, and 9, it is concluded that the highest QF attained by the sensor is 29,334 with an FOM greater than 7000 RIU⁻¹ over the wavelength range 580–590 nm. As a reference, RI of water⁵⁸ is also utilized in this investigation.

Table 7.

Sensor metrics of the 1D TPC biosensor for defect layer of 1.02 µm, and period N = 10 (λ = 580–590 nm).

	RI	λpeak (nm)	Wavelength sensitivity (nm/RIU)	FWHM (nm)	QF	FOM (RIU−1)	DL (RIU)
Water (reference)	1.33	582.85	–	0.02	29,142.5	–	–
Aqueous humor	1.348	585.42	142.78	0.02	29,271.0	7138.9	0.000007
Vitreous humor	1.357	586.68	140.00	0.02	29,334.0	7000.0	0.000007

Table 8.

Sensor metrics of the 1D TPC biosensor for defect layer of 1.02 µm, and period N = 10 (λ = 652–664 nm).

	RI	λpeak (nm)	Wavelength sensitivity (nm/RIU)	FWHM (nm)	QF	FOM (RIU−1)	DL (RIU)
Water	1.33	656.33	–	0.04	16,408.3	–	–
Aqueous humor	1.344	658.14	129.29	0.03	21,938.0	4309.5	0.000012
Vitreous humor	1.353	659.30	128.89	0.03	21,976.7	4296.3	0.000012

Table 9.

Sensor metrics of the 1D TPC biosensor for defect layer of 1.11 µm, and period N = 10 (λ = 948–960 nm).

	RI	λpeak (nm)	Wavelength sensitivity (nm/RIU)	FWHM (nm)	QF	FOM (RIU−1)	DL (RIU)
Water	1.33	952.74	–	0.20	4763.7	–	–
Aqueous humor	1.337	953.62	125.71	0.18	5297.9	698.4	0.000072
Vitreous humor	1.345	954.64	127.50	0.16	5966.5	796.9	0.000063

Fig. 17.

Transmittance plot (λ = 580–590 nm) of eye cells for defect layer of 1.02 µm, and period N = 10.

Fig. 18.

Transmittance plot (λ = 652–664 nm) of eye cells for defect layer of 1.02 µm, and period N = 10.

Fig. 19.

Transmittance plot (λ = 948–960 nm) of eye cells for defect layer of 1.11 µm, and period N = 10.

EMT analysis on the studies

To study the contribution of absorption, we utilized effective medium theory (EMT), specifically the Maxwell–Garnett approximation⁵⁹. In this framework, the aqueous host medium is treated as the continuous phase, while biomolecular inclusions are incorporated at varying volume fractions. The recommended inclusion fractions in this approach are 0.05, 0.10, and 0.15. By using a complex RI for the inclusions, EMT accounts for both dispersion and absorption effects, ensuring that the effective dielectric response captures real and imaginary contributions. This approach considers the effective refractive indices, thereby providing a physically consistent basis for modeling analyte-induced optical changes in the biosensor. From the EMT analysis tabulated in Table 10, it is inferred that absorption can slightly affect the performance depending on the amount of absorption. The Drude–Lorentz model⁶⁰is another technique that can be utilized to account for absorption. The supporting transmittance spectrum plots for the three studies obtained after EMT analysis are illustrated in Figs. 20, 21, and 22. For the diabetes study, the optimal parameters of material thicknesses, DLT, and N are 308 nm, 7.89 µm, and 12, respectively. For the eye cancer study, the optimal parameters of material thicknesses, DLT, and N are 300 nm, 6.45 µm, and 5, respectively. Finally, for the PVR study, the optimal parameters of material thicknesses, DLT, and N are 100 nm, 2 µm, and 10, respectively.

Table 10.

Results obtained after performing EMT analysis.

Investigated area	Analyte	λpeak (nm)	WS (nm/RIU)	FWHM (nm)	QF	FOM (RIU−1)	DL (RIU)
Diabetic study (N = 12)	Water	1595.58	–	0.04	39,889.5	–	–
	Normal (Tear fluid)	1601.70	737.35	0.04	40,042.5	18,433.7	0.000003
	Diabetic (Tear fluid)	1613.81	725.15	0.06	26,896.8	12,085.8	0.000004
Diabetic study (N = 9)	Water	1627.03	–	0.09	18,078.1	–	–
	Normal (Tear fluid)	1633.53	783.13	0.11	14,850.3	7119.4	0.000007
	Diabetic (Tear fluid)	1646.26	762.28	0.13	12,663.5	5863.7	0.000009
Eye cancer study	Water	1542.18	–	1.67	923.5	–	–
	Normal eye cell	1550.22	687.18	1.64	945.3	419.0	0.000119
	Cancer eye cell	1553.64	684.00	1.64	947.3	417.1	0.000120
Aqueous humor and vitreous humor study	Water	568.14	–	0.03	18,938.0	–	–
	Aqueous humor	569.98	221.69	0.03	18,999.3	7389.6	0.000007
	Vitreous humor	571.80	216.67	0.02	28,590.0	10,833.3	0.000005

Fig. 20.

Transmittance plot of diabetes study after EMT analysis (N = 12)

Fig. 21.

Transmittance plot of eye cancer study after EMT analysis (N = 5)

Fig. 22.

Transmittance plot of aqueous humor and vitreous humor study after EMT analysis (N = 10)

Detection of diabetes, eye cancer and PVR

Spectroscopic studies convey that when a patient is affected with diabetes mellitus, the composition of tear fluid is altered such that it also changes the structural order of proteins present in tears⁶¹. Depending on the concentration of tear analyte, a curve can be generated that relates the tear concentration and the particular shift in the optical wavelength⁶². The excess accumulation of retinal fluids leading to diabetic macular edema (DME) also affects vision, comparable to DR (associated with diabetes mellitus type 1 and type 2)⁸. The analysis of tear fluids utilizing PC sensors facilitates diagnosis of DME and DR.

Due to eyelid cancer such as basal cell carcinoma, very minute growths formed affect the cellular composition, and PC sensors facilitate the detection alongside traditional inspection methods⁶³. In the case of retinoblastoma, the tumor cells not only proliferate into the choroid region but also to the optic nerves if not treated early⁶⁴. When eyes are affected with very minute levels of tumor due to uveal melanoma, where lesions are formed near the iris, the ocular cells are affected, and PC-based sensors can support the diagnosis⁶⁵.

Biochemical changes in the aqueous humor can affect neurogenic²⁵ and inflammatory processes, and this contributes to PVR. Thus, it is essential to understand the changes in aqueous humor composition to comprehend the depth of PVR. The growth factors in the vitreous fluid cells that increases cell proliferation include fibroblast growth factor, epidermal growth factor, insulin-like growth factor and transforming growth factor-beta⁶⁶. The subtle changes in RI of the normal vitreous humor fluid caused by these cell proliferations can be utilized in the detection of PVR.

ML for prediction of transmission amplitude of the ocular analyte

Recent studies^67–69 utilizing ML emphasize its effectiveness over other related techniques. The reasons for the selection of ML are not limited to generalization capability, ability to learn nonlinear data, high‑dimensional modeling under noisy conditions, scalability and uncertainty quantification. The implementation of ML in this work begins with the ocular dataset generated utilizing the TMM method. Google Colab is the platform utilized for implementing the Python code to perform the prediction of transmission amplitude. The ocular data must be mapped to each period value of the PC. As illustrated in Fig. 23, the next step involved is creating a data frame followed by encoding each analyte label. The ML model is evaluated for two cases. The first case is without any noise, and the second case is by considering fabrication errors. So in Fig. 23, after the noise modeling, the next step is to define the features such as analyte category, wavelength, and period. The target is to predict the amplitude under the noisy conditions.

Fig. 23.

Workflow of the ML approach in ocular study

The dataset is divided into the training and testing parts to train and evaluate the model. The remaining steps in the workflow include model training and evaluation of R²-Score, MAE and RMSE⁷⁰. Scatter plots give a visual representation of the actual value and the predicted value. K-fold cross validation⁷¹ is performed to validate the results and to avoid overfitting. The final step is concluding which model performed the best under the noisy conditions based on the regression metrics.

The libraries used in this approach are Pandas, NumPy, Matplotlib and Scikit-learn. The matplotlib library is used in this approach for visualization, and scikit-learn is implemented for partitioning the dataset, encoding of the analyte types, calculation of regression metrics, and evaluation of the models. 10 datasets are utilized for respective period values from 3 to 12. Each data set consists of 1500 samples containing the information on wavelength, analyte category, and amplitude. So the size of the sample is 45,000, as there are 10 files each containing 1500 samples for three analytes. The data frame is used to organize the spectral data into a readable format. The data frame structure consists of wavelength, analyte category, period, and amplitude. While considering the fabrication error, the data frame also includes the noisy amplitude and noisy wavelength. The feature matrix utilized in this work consists of information on wavelength, analyte category encoding, and N value. In the case of the XGB model, 500 estimators are utilized with a learning rate of 0.5, maximum depth of 8, and subsampling column sampling ratio of 0.8. In both the XGB and RF approaches, the model is trained utilizing 80% of the ocular dataset, and the remaining 20% is used for testing.

Noise modeling is done by incorporating wavelength jitter and amplitude jitter. Gaussian noise with standard deviation σ = 0.4 nm is introduced into the wavelength, and it represents the lithographic deviations in the feature geometry. Multiplicative Gaussian noise with σ equal to 20% is used in the transmittance values to represent the scattering loss due to surface roughness. Coefficient of determination ⁷⁰, mean absolute error, and root mean square error metrics are quantified utilizing respective functions in Scikit-learn. Five-fold K-fold cross-validation is applied on the ocular dataset to ensure robustness.

Results of ML models

The scatter plots for the XGB model without noise and with noise are as illustrated in Figs. 24 and 25, respectively. Figures 26 and 27 illustrate the performance of the RF model without considering the fabrication errors and with fabrication errors, respectively.

Fig. 24.

Actual amplitude vs predicted amplitude plot utilizing XGB model

Fig. 25.

Actual amplitude vs predicted amplitude plot utilizing XGB model with noise modeling

Fig. 26.

Actual amplitude vs predicted amplitude plot utilizing RF model

Fig. 27.

Actual amplitude vs predicted amplitude plot utilizing RF model with noise modeling

XGBoost Results (Predicting Amplitude without noise):

R² Score: 0.5238

MAE: 0.0447

RMSE: 0.0876

Cross-validation results:

Mean R² Score: 0.5273

Mean MAE: 0.0438

Mean RMSE: 0.0861

XGBoost results (predicting amplitude with fabrication noise):

R² Score: 0.5028

MAE: 0.0453

RMSE: 0.0917

Cross-validation results:

Mean R² Score: 0.5040

Mean MAE: 0.0444

Mean RMSE: 0.0900

Random Forest results (predicting amplitude without noise):

R² Score: 0.9890

MAE: 0.0009

RMSE: 0.0133

Cross-validation results:

Mean R² Score: 0.9915

Mean MAE: 0.0008

Mean RMSE: 0.0113

Random Forest results (predicting amplitude with fabrication noise):

R² Score: 0.9290

MAE: 0.0066

RMSE: 0.0347

Cross-validation results:

Mean R² Score: 0.9364

Mean MAE: 0.0065

Mean RMSE: 0.0321

The comparative performance analysis given in Table 11 indicates the influence of fabrication error in the prediction process across the two ML models. The RF model demonstrates exceptional accuracy (in the absence of fabrication errors) in terms of the R²-Score, indicating near‑perfect agreement between predicted amplitude data and actual amplitude data. When fabrication noise is introduced, representing realistic geometric or surface irregularities, the RF model retained strong robustness, with a decline of 5.5% in the R²-Score, reducing it to 0.936. In contrast, the XGB shows lower accuracy (R²-Score = 0.527) and a slight deterioration under noise (R²-Score = 0.504), suggesting more sensitivity to perturbations. This comparison underscores RF’s superior resilience to fabrication‑induced variability, making it a more reliable choice. Compared to the XGB model, the error values in prediction are less for the RF model. Thus, from Table 11, it is clear that the RF model performs better than the XGB model even under noisy conditions.

Table 11.

Performance of the ML models.

ML model	R2 Score	MAE	RMSE
XGB	0.527	0.0438	0.0861
XGB (with fabrication noise)	0.504	0.0444	0.0900
RF	0.991	0.0008	0.0113
RF (with fabrication noise)	0.936	0.0065	0.0321

Novelty and performance comparison of proposed PC sensor with existing PC based sensors

Table 12 lists the PC-based sensors that have been investigated for the studies related to diabetes detection, eye cancer and PVR. The works reported in 2016⁷², 2023⁷³, and 2026⁵⁶ emphasized the detection of diabetes from tears, whereas the work reported in 2024⁷ investigated eye cancer. The feature that makes our work stand out from these is that our 1D PC sensor designs not only investigated diabetes studies but also extended their scope to eye cancer. Moreover, the highlight of our work is that PVR has not been investigated by any of the listed works. The technical advantage that further extends the novelty of this work is the utilization of ML to predict the transmission amplitude by considering the possible errors that may occur during the fabrication of the sensor. Although AlN and GaN have been utilized by researchers in sensing applications, to the best of our knowledge, this combination has not been used with silicon to form a ternary PC and has not been investigated in the studies related to PVR.

Table 12.

Comparison of proposed PC with existing PC based sensors.

References	Year	Sensing approach	Investigated topic	QF	WS (nm/RIU)	FOM (RIU−1)
Ref.74	2015	PC	Diabetes studies	23,575	638	–
Ref.72	2016	PC	Disease detection from tears	1082	6.57	–
Ref.75	2020	PC	Diabetes studies	5540	500	–
Ref.14	2021	PC	Diabetes detection from tears	867	1294	699
Ref.73	2023	PC	Diabetes detection from tears	16,209	768	6300
Ref.76	2024	PC	Detection of bacteria	10,996	4073	–
Ref.77	2024	PC	Cancer detection	13,353	214	172
Ref.7	2024	PC	Eye cancer detection	1873	655	–
Ref.78	2025	PC	Diabetes studies	1400	500	–
Ref.79	2025	PC	Multiple tumor studies	10,487	355	–
Ref.56	2026	PC	Diabetes detection from tears	7719	771	995
Proposed 1D PC sensor	2026	PC	Eye cancer, diabetes, aqueous and vitreous humor studies	40,042	783	18,433

Challenges in ocular sample preparation and fabrication methods of the sensor

The two main challenges in the detection of ocular analytes for the diagnosis of cancer and PVR are the sample collection and the fabrication of the PC with absolute accuracy. To diagnose eye cancer and PVR, the samples from eyes have to be taken, and it is not as easy as collecting the tear fluids. The capillary collection method is one of the methods to collect tear samples⁸⁰. Invasive methods are usually followed to collect the eye samples to investigate cancer and PVR. Minimally invasive techniques are also available to collect the eye samples. Fine-needle aspiration biopsy (FNAB) facilitates the extraction of fluids from eyes⁸¹. For the diagnosis of choroidal plasmacytoma, a kind of a tumour that causes blurness in vision, the procedure for FNAB is crucial⁸². A plungerless intravitreal injector device is recently proposed in the sampling of aqueous humor⁸³. Pars plana vitrectomy can be utilized for collecting the vitreous sample, but the intraocular pressure of eye must be considered in the procedure⁸⁴. Introducing eye samples such as tear fluids and aqueous humor fluids into the defect region is critical, and it can be done utilizing micro-fluidic channels^85,86.

Many distinct methods have been utilized by researchers in the fabrication of 1D PC. Thin-film deposition methods such as electron beam evaporation demonstrated the fabrication of a silicon dioxide/titanium dioxide 1D PC structure, and this method facilitated the creation of a variable period PC⁸⁷. A 1D PC fabricated utilizing electron beam evaporation exhibited high sensitivity in sensing applications⁸⁸. In a PC fabrication-related article, the fabrication of aluminum oxide/titanium dioxide 1D PC structure utilizing pulsed laser deposition attained identical transmission spectrum results in both the simulation and the experiment⁸⁹. The sol-gel spin coating technique is another technique recommended for the fabrication of 1D PCs with multi layer thickness in the range from 60 to 90 nm⁹⁰. Thus, the deposition rate⁸⁷ is one factor that affects the accuracy of electron beam evaporation to create PC structures with the required period. In the case of sol-gel method, porosity⁹⁰ and roughness of layers can affect the transmission spectrum. Etching-based methods are an alternative to deposition methods. After the fabrication of the PC structure using photoelectrochemical etching, atomic force microscopy must be done to evaluate the depth of side-wall roughness⁹¹. The other techniques that can be implemented in the formation of PC structures are vapor depostion methods and molecular beam epitaxy⁹². Visible-near-IR spectroscopy is the characterization method that can be utilized in PC structures⁹⁰.

One of the main challenges in the fabrication of a ternary PC structure is to obtain the specified thickness for the materials. A small deviation in the thickness can lead to a distinct shift in the output wavelength. Selection of deposition rates and substrates must be done appropriately, or else it can lead to an unintended value of the period of the structure. Once the material is fabricated, the porosity and roughness must be checked to avoid low reflectivity. Smoothing of the side walls of the structure must be done carefully without altering the period of the PC. The substrate must be selected such that it does not affect the transmission characteristics of the PC structure. Control of the fabrication process, cost, and characterization are some factors that affect the production of the sensor at the industry level.

Limitations and future scope

We acknowledge that the work is an analytical one based on the standard techniques that are widely accepted by the research community. The experimental procedures fall in the future scope, and the lengthy process begins from fabrication, testing, collection of samples and evaluation. The contribution of absorption can exert a slight influence on the sensor’s characteristics, such as sensitivity, intensity and QF. The exact sensor metrics not only depend on the conditions such as temperature and humidity but also on factors such as the quality of the real-time samples. The full-fledged production of this sensor design can be implemented after testing the ocular samples in real-time conditions. As a part of future work, multi-state testing (tear samples from different physiological states), wavelength resolved analysis, surface functionalization, hybrid sensing (combining other complementary techniques) and ML training (multi-state samples) can be done to overcome the limitations of the RI-based sensor.

Conclusion

The ternary photonic crystal biosensor utilizing the three unique materials exhibits the relevance of optical sensors in ocular studies. The highlight of this investigation is the metrics achieved by the sensor and the optimizations exhibited in the design. The ML approach is very much relevant, as it facilitates researchers predicting the amplitude of the respective analytes even in the situation of fabrication errors. Fabrication of these unique materials across the substrate and evaluating the sensor performance in real time are the future works related to this investigation. Although the collection of eye tissues can be complicated, utilizing methods that can be critical, considering the gravity of the disorder that can affect the vision of the person, this method justifies its approach. The work provides much more than a comprehensive framework for researchers and ophthalmologists to advance the ocular studies.

Author contributions

Harikrishnan N. modeled the sensor, performed data analysis, executed machine learning algorithms and wrote the manuscript. Sangeetha A. supported the research activity, offered insightful viewpoints, and contributed to the manuscript's review.

Funding

Open access funding provided by Vellore Institute of Technology.

Data availability

The data that support the findings of this study are available upon reasonable request.

Declarations

Competing interests

The authors declare no competing interests.