Innovative MIM diplexer with neural network enhanced refractive index detection for advanced photonic applications | Scientific Reports

Scientific Reports volume 14, Article number: 31473 (2024) Cite this article

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This study introduces a high-performance 4-channel Metal-Insulator-Metal (MIM) diplexer, employing silver and Teflon, optimized for advanced photonic applications. The proposed diplexer, configured with two novel band-pass filters (BPFs), operates across four distinct wavelength bands (843 nm, 1090 nm, 1452 nm, 1675 nm) by precisely manipulating the passband dimensions. Utilizing Finite-Difference Time-Domain (FDTD) simulations, the designed diplexer achieves exceptional sensitivity values of 3500 nm/RIU, 4250 nm/RIU, 3375 nm/RIU, and 4003 nm/RIU, along with high figures of merit (FOM) ranging from 113.4 to 124.7 1/RIU. Also, the compact design (400 nm × 830 nm) underscores its suitability for integrated photonic circuits and advanced sensing applications. Furthermore, to further enhance accuracy in detecting refractive index (RI) changes, a multilayer perceptron (MLP) neural network was employed, ensuring the highest sensor accuracy. The accuracy of the MIM diplexer’s RI measurements was statistically validated through a one-sample t-test, confirming the sensor’s reliability. Comparative analysis with existing sensors highlights the diplexer’s superior sensitivity and efficiency, setting a new benchmark in optical communication and photonic sensing technologies. This work paves the way for future advancements in miniaturized, high-sensitivity optical devices, offering robust solutions for next-generation communication and sensing systems.

The rapid advancement in optical and plasmonic technologies has led to the development of various MIM structures that play a crucial role in enhancing the performance of a wide range of optical devices. Among these, MIM diplexers have emerged as significant components due to their ability to manage light at nanoscale dimensions, making them highly suitable for applications in sensing, communication, and information processing1,2.

MIM structures consist of a thin insulating layer sandwiched between two metal layers. These arrangements make use of electromagnetic waves called surface plasmon polaritons (SPPs), which travel along the boundary between a dielectric and a metal. The unique properties of SPPs, such as their confinement to subwavelength scales and their sensitivity to changes in the surrounding environment, make MIM structures highly effective for a variety of applications3,4.

Diplexers are devices that can combine or separate signals of different wavelengths. MIM diplexers utilize the properties of MIM structures to manage optical signals at different wavelengths efficiently. Their ability to handle multiple signals simultaneously makes them invaluable in complex optical communication networks. Despite their potential, designing MIM diplexers involves several challenges that need to be addressed to optimize their performance. The choice of materials for the metal and insulator layers significantly impacts the performance of MIM diplexers. Metals such as gold and silver are commonly used due to their excellent plasmonic properties, but they also introduce losses that can degrade performance. Insulator materials must be carefully selected to provide the desired dielectric properties while maintaining compatibility with the metals used5,6,7.

Generally, the design process involves complex simulations and optimizations to achieve the desired performance characteristics. Advanced computational tools and methods are required to model the behavior of MIM diplexers accurately.

In8, the authors propose a silicon-on-insulator wavelength diplexer design that incorporates an adiabatic bent taper and an innovative multimode waveguide. They optimize the device’s geometry using particle swarm optimization. Despite having a new design, this structure suffers from inappropriate insertion losses and small pass-bands.

In9, a diplexer and a triplexer using three optical filters - implemented by internal cavities placed in the waveguides - as well as two PhC waveguides with a line defect are presented. The resonance behavior of any optical filter is adjusted by tuning the size or defect index of the center point of the cavity to divide the three wavelength signals. Three distinct micropillars form the resonant ring, which makes tuning the resonant wavelength easier and improves power coupling effectiveness.

In10, the authors propose a broadband diplexer based on spoof surface plasmon polaritons. They analyze the dispersion properties of the spoof SPP unit cell, demonstrating that the high/low cutoff frequency and bandwidth of the channel filter can be flexibly controlled. Building on the proposed structure-based BPF, they develop a WR-4 wideband diplexer using a space mapping technique, which enhances both computational efficiency and design accuracy. However the presented structure is complicated and has relatively large dimensions. An ultra-compact wavelength diplexer that was designed and built using THz spoof SPP waveguiding devices is detailed in Ref11. The coupling length can be adjusted by engineering the RI of the odd modes that are anti-symmetrically dispersed by adding a certain number of periodic pillars to the coupling component of the directional coupler. The device can couple the SPP modes at two target frequencies an odd or even number of times by modifying the periodic pillar parameters correctly. This allows the modes at these frequencies to be coupled out from distinct ports.

A new metamaterial-based terahertz demultiplexer was suggested in12. A rectangular wire and two U-shaped components make up its surface metal structure. Low insertion losses and excellent isolations allow the demultiplexer to distinguish 0.225 THz and 0.41 THz.

Dividing the available spectrum into non-overlapping multicarrier frequency sub-bands remains a challenge in the design of frequency-selective time-invariant channels. In13, an on-chip topological diplexer is reported that exhibits terahertz bandpass filtering through Klein tunneling in topological edge modes. In14, the authors introduce a novel wideband diplexer for microwave frequencies. This diplexer combines spoof SPP structures with substrate-integrated waveguide designs. The low cutoff frequency of the filters is determined by the dimensions of the substrate-integrated waveguide. Additionally, two filters are fed using a T-junction microstrip with stepped impedance conversion. By optimizing the feed lines, the electromagnetic waves are directed efficiently within each operational band.

Efficient light injection from a broadband source into MIM waveguides is crucial for achieving optimal performance in photonic devices. Various coupling strategies have been developed to enhance the compatibility of MIM structures with broadband light sources, thereby increasing light transfer efficiency into the waveguide. Recent studies have presented several promising methods, including orthogonal mode couplers and tapered waveguide mode converters.

Ref15. introduced an orthogonal mode coupler specifically designed for MIM-based plasmonic devices used in temperature sensing applications. This coupling approach aligns well with the waveguide’s mode structure, enabling efficient light transfer with minimal losses, which is advantageous in broadband sensing environments. Meanwhile, Ref16. presented a tapered waveguide mode converter that gradually adjusts the waveguide’s dimensions to facilitate mode matching and improve light coupling efficiency into MIM structures. This tapered structure supports effective light coupling while maintaining high transmission, which is essential for applications that demand high sensitivity.

Additionally, Ref17. highlighted the importance of optimizing light injection techniques in MIM-based sensors for biological applications, where precise light coupling is critical for achieving high sensitivity. In their dual-mode optical sensor, efficient coupling techniques were shown to be essential for detecting cancer cells with significant sensitivity. These studies underscore the potential of both orthogonal mode couplers and tapered waveguide converters to improve the performance of MIM-based sensors across various applications.

Despite the promising applications of MIM diplexers, particularly in THz band applications, limited research has been conducted in this specific domain. The terahertz frequency range poses unique challenges due to the stringent requirements for precise control over waveguide dimensions and material properties. Designing efficient and compact THz band diplexers requires overcoming significant obstacles such as high propagation losses and integration complexities with existing THz systems.

In this article, an innovative MIM structure is presented, utilizing silver as the metal and Teflon as the insulator, and configured with two band-pass filters to form a highly efficient diplexer. This diplexer operates across four distinct wavelength bands by precisely adjusting the passband dimensions. Also, the new Drude and critical point model have been utilized for material analysis. The performance analysis, conducted through FDTD simulations, demonstrates a high transmission rate of 0.87, compact dimensions (400 nm by 830 nm), and exceptional sensitivity. These results underscore the MIM structure’s capability for high-efficiency operation across multiple wavelength bands, highlighting its significant potential for advanced applications in sensing and communication technologies.

Recent advancements in MIM waveguide-based plasmonic sensors have demonstrated that innovative cavity designs can significantly enhance device sensitivity, particularly in applications such as RI and gas sensing. These studies illustrate that tailored cavity geometries, including various resonant structures, facilitate improved light-matter interactions within the MIM framework, thus achieving higher sensitivity by increasing electromagnetic field confinement and boosting coupling efficiency. Such configurations enable more precise detection capabilities by allowing narrower linewidths and heightened responsiveness to small environmental changes, which are essential in high-performance sensing applications. Integrating these insights into cavity design with the current MIM diplexer structure underscores the potential for achieving both compactness and high sensitivity, further validating the effectiveness of MIM architectures in next-generation photonic sensing technologies18,19,20.

The 4-band MIM diplexer designed in this article comprises two novel separate BPFs, each contributing two passbands. These filters have been meticulously engineered to achieve the desired wavelength response, ensuring optimal performance for the 4-channel diplexer. In the sections that follow, a detailed explanation of the design, structure, and operational principles of these low-pass filters will be provided, highlighting their role in achieving the overall functionality of the diplexer. Through this innovative design approach, the diplexer effectively accommodates the required four passbands, enhancing its application in the RI detection of materials.

Figure 1(a) to 1(c) illustrate the design of the initial proposed plasmonic BPF and its corresponding transmission spectrum. The layout demonstrates that the primary filter comprises an input waveguide, an output waveguide, and three diagonal stubs positioned between them. The substrate is depicted in grey in Fig. 1(a) and is composed of silver. Teflon (the relative permittivity of Teflon is εr = 1.37), represented in yellow in Fig. 1(a), is used as the dielectric material for both the waveguides and the stubs.

(a) The layout of the first BPF, filter transmission rate for (b) different A2’s, and (c) different A3’s.

Figure 1(b) and 1(c) present the simulation results for the transmission rate of the designed structure with varying stub lengths and widths. According to the results, the optimal response occurs when the stub width is 65 nm and the length is 230 nm. Under these conditions, the filter exhibits two pass bands: one from 920 nm to 984 nm and another from 1486 nm to 1540 nm. The maximum transmission rates within these bands are 0.96 and 0.94, respectively. These results demonstrate that the passbands shift when the dimensions of the stubs are altered, indicating that the designed filter is adjustable. This tunability allows for precise control over the filter’s wavelength response, making it highly adaptable for various applications. The most optimal dimensions of this filter are: A1 = 85 nm, A2 = 65 nm, A3 = A4 = 230 nm, g1 = 18 nm, and ϴ=120º.

The critical point model is used to describe transmission at high wavelengths near-ultraviolet light, providing benefits such as Kramers-Kronig compatibility and precise reproduction of silver dispersion. In this study, we combine the critical point model with the Drude model, as detailed in references3,21.

The Drude model and the critical point model are combined in this study to create a comprehensive dielectric function for silver, which is necessary to account for both free electron response and interband transitions across a broad range of frequencies, particularly at high wavelengths approaching the ultraviolet region. Each model contributes distinct aspects of the material’s electromagnetic behavior3.

The Drude model is primarily used to describe the free electron response within metals, where the dielectric function is affected by electron oscillations without significant interband transitions. The Drude dielectric function, \(\:{\epsilon\:}_{D}\left(\omega\:\right)\), is given by:

This model is effective at lower frequencies, where free electrons dominate the response. However, the critical point model is essential to capture the effects of interband transitions at higher frequencies, where electron transitions between energy bands significantly impact the dielectric behavior. The critical point model, \(\:{\epsilon\:}_{cp}\left(\omega\:\right)\), describes these transitions through a series of critical points, each representing a specific frequency where these transitions occur:

This model enables accurate characterization of the high-frequency dielectric response. The combined dielectric function, \(\:\epsilon\:\left({\upomega\:}\right)\), incorporates the Drude and critical point contributions to form a unified expression that accurately represents the dielectric properties of silver over a wide spectral range:

This total dielectric function, \(\:\epsilon\:\left({\upomega\:}\right)\), allows for precise modeling of silver’s response to electromagnetic waves, addressing both free electron behavior at lower frequencies and interband transitions at higher frequencies. This combination is crucial for accurate simulation and design in photonic applications, where materials must respond predictably across a broad spectrum. Consequently, the parameters for the Drude-Critical Points model for silver are summarized in Table 1.

This study combines the Drude and critical point models to thoroughly characterize the optical properties of silver. The Drude model describes the free electron response at lower frequencies, while the critical point model captures interband transitions at higher frequencies. Together, these models provide a comprehensive dielectric profile for silver across a broad wavelength range, which is essential for improving the design and sensitivity of the MIM structure. Although Teflon’s dielectric properties remain stable within the operational range, accurate modeling of silver’s behavior enables fine-tuning of the sensor to achieve optimal performance in advanced photonic applications.

Note that the Lumerical simulator is utilized in the calculation of these findings using the FDTD approach. The data points up to a wavelength of 600 nm to 1800 nm. This filter generates only two passbands, whereas our objective is to design a 4-channel diplexer. To achieve this, an additional low-pass filter is introduced below.

It is important to note that FDTD simulations are essential in the photonic design process, as they provide a detailed model of electromagnetic wave interactions within complex structures. In this study, FDTD simulations were used to refine the design parameters of the MIM diplexer, specifically optimizing the dimensions of the waveguides and stubs to achieve target wavelength responses, high transmission efficiency, and enhanced sensitivity. This simulation method allows for iterative adjustments and precise tuning of the device architecture prior to fabrication, ensuring that the final design meets the stringent performance requirements necessary for cutting-edge photonic applications.

The second designed plasmonic band-pass filter is illustrated in Fig. 2. This configuration includes two waveguides, one for input and one for output, along with five vertical stubs positioned equidistantly. The close proximity of the stubs induces a coupling effect, which facilitates the transfer of the radiated wave to the output side. This precise arrangement ensures efficient transmission and enhances the filter’s performance.

(a) The layout of the second BPF, filter transmission rate for (b) different B2’s, and (c) different B3’s.

Similar to the first filter, the simulation of the transmission rate for this filter has been conducted with varying lengths and widths of the stubs. The results of these simulations are presented in Fig. 2(b) and 2(c). The most optimal response is achieved for B2 = 190 nm, and B3 = 400 nm, where the filter exhibits two passbands: one from 1008 nm to 1060 nm and another from 1582 nm to 1630 nm. Additionally, the maximum transmission rates at wavelengths 1028 nm and 1600 nm are 0.974 and 0.982, respectively. It should be noted that in this simulation method, the cells are two-dimensional, with spatial steps set at 1 nm. The FDTD numerical approach involves sampling the continuous distribution of electromagnetic fields inside a limited spatial volume at discrete locations over a grid that is both spatial and temporal in nature. This approach allows for the detailed simulation of electromagnetic field propagation by incrementally advancing time and repeatedly solving the differential equations at each point in the spatial grid. So, the most optimal dimensions of this filter are: B1 = 85 nm, B2 = B4 = 190 nm, B3 = 400 nm, and g2 = 15 nm.

According to Fig. 3(a), the final diplexer comprises two BPFs, each with distinct passbands. The overall dimensions of the diplexer are approximately 400 nm × 830 nm. The simulation results of its transmission rate in ouput 1 and output 2 are also presented in Fig. 3(b), 3(c), respectively. This diplexer features four passbands, all of which can be controlled and adjusted by altering the dimensions of the stubs. The transmission rates at the central wavelengths of 843 nm, 1090 nm, 1452 nm, and 1675 are 0.89, 0.91, 0.87, and 0.92, respectively.

(a) The structure, and the transmission rate of the proposed diplexer in (b) output 1, and (c) output 2.

The quality factor, which is described by the following equation, is one of the metrics that will be used to evaluate the performance of the proposed structure.

The calculated results indicate that the quality factors for this structure are 7.3%, 5.9%, 4.1%, and 3.5% in its four respective passbands. These values reflect the performance and efficiency of the diplexer in each passband, with higher quality factors indicating better performance in terms of narrower bandwidths and higher selectivity.

The operating mechanism of the proposed diplexer can be elucidated by presenting the field profile of the Hz​ magnitude. As shown in Fig. 4, the field profiles of Hz​ magnitude at wavelengths of 843 nm, 1090 nm, 1452 nm, and 1675 nm are depicted.

The field profile of the Hz at wavelengths (a) 843 nm, (b) 1090 nm, (c) 1452 nm, and (d) 1675 nm.

In the FDTD simulations conducted to assess the MIM diplexer, a high-resolution mesh with a 1 nm grid size was applied. This fine mesh enables detailed modeling of electromagnetic wave propagation and accurately captures the intricate structural features of the device, thereby reducing numerical dispersion and enhancing result precision.

The simulation domain was surrounded by perfectly matched layer (PML) boundary conditions on all sides. These boundaries were selected to prevent reflections at the simulation domain’s edges, thereby simulating an open-space environment that faithfully represents wave behavior within the diplexer. The PML boundaries ensure that electromagnetic waves can exit the domain without generating artificial reflections that could distort the device’s performance evaluation.

Input and output ports were placed at the waveguide interfaces to enable effective energy transfer and accurate coupling of optical signals into and out of the device. This port configuration is essential for accurately capturing the transmission characteristics and resonance response of the diplexer at its designated operating wavelengths.

In this study, RI changes were introduced by adjusting the RI of the medium surrounding the MIM waveguide, rather than altering the Teflon insulator layer itself. As the insulating material in the MIM structure, Teflon was selected for its stable dielectric properties, including a constant RI across the relevant wavelength range, similar to air. In the FDTD simulations, only the fixed RI value of Teflon was applied, ensuring consistency in the dielectric environment within the waveguide.

To simulate realistic sensing applications, RI variations were instead introduced in the surrounding medium adjacent to the MIM structure. This setup replicates scenarios in which the sensor interacts with different substances or analytes outside the waveguide. The sensor’s sensitivity was then evaluated by analyzing shifts in the resonance wavelengths due to incremental RI changes in this surrounding medium. This configuration allowed us to measure the diplexer’s response to external RI variations, demonstrating its capacity for high sensitivity in practical applications.

The flowchart in Fig. 5 provides a step-by-step representation of the methodology used to evaluate the RI sensing capabilities of the proposed MIM diplexer. The process begins with the design of the Teflon dielectric layer and the silver sections using precise geometric and material definitions within the FDTD simulation environment. The surrounding medium is then defined with adjustable RI values, allowing incremental variations to simulate practical sensing scenarios. These RI changes are introduced while maintaining the Teflon layer’s RI constant to ensure structural stability. FDTD simulations are performed with high-resolution mesh settings to analyze the interaction of electromagnetic waves within the diplexer. The resulting spectral shifts are examined to assess the sensor’s sensitivity to RI changes, followed by the evaluation of key performance metrics, including sensitivity and FOM. This systematic approach highlights the robustness and accuracy of the sensing mechanism, emphasizing the diplexer’s potential for advanced photonic applications.

Flowchart of the RI sensing process.

So, we will investigate the effect of the transmission spectrum of the presented diplexer for different refractive indexes in output 1 and 2, as this analysis facilitates the study of optical sensors. Figure 6 illustrates the transmission rates of the designed filter for refractive indexes ranging from 1.369 to 1.373, with changes in increments of 0.001. The transmission peaks, observed at four distinct wavelength bands (approximately 843 nm, 1090 nm, 1452 nm, and 1675 nm), demonstrate the precise tunability and narrow line widths characteristic of the MIM structure. The high transmission efficiency, with values exceeding 0.87, indicates minimal insertion loss across the operational bands, validating the diplexer’s high-quality factor. The variation in RI slightly shifts the resonance wavelengths, showcasing the sensitivity of the MIM diplexer to changes in the refractive index, which is crucial for sensing applications. These results underscore the diplexer’s robustness and potential for fine-tuned spectral control, making it highly suitable for advanced THz communication and photonic sensing technologies.

Simulation results of transmission rate for different RI in (a) Output 1, and (b) Output 2.

The sensing characteristics of the proposed filter structure are quantified using two parameters: sensitivity (S) and the FOM. Table 2presents the sensitivity parameter results for the four operational modes of the 4-channel MIM diplexer. The formulas of the two parameters, the sensitivity, and FOM, which reflect the sensing characteristics of the filter structure, are as follows6,22:

FWHM represents the full-width half maximum of the spectral waveguide. By integrating these values into the understanding of the diplexer’s performance, it becomes evident how effectively the proposed structure responds to changes in the RI, highlighting its potential for sensitive and precise detection in various applications.

The four wavelengths obtained in this study (843 nm, 1090 nm, 1452 nm, and 1675 nm) were chosen as the designed working wavelengths due to their significance in various photonic applications. These wavelengths fall within the near-infrared (NIR) and short-wavelength infrared (SWIR) regions, which are highly relevant for fields such as optical communication, biomedical sensing, and environmental monitoring. Specifically, the NIR range (843 nm and 1090 nm) is well-suited for low-loss transmission in fiber-optic communication and offers deep tissue penetration, making it ideal for biological and medical imaging applications. In contrast, the SWIR wavelengths (1452 nm and 1675 nm) exhibit strong sensitivity to molecular absorption features, which enhances their utility in environmental sensing, chemical detection, and remote monitoring. By targeting these specific working wavelengths, the proposed diplexer is capable of supporting a broad range of advanced photonic and sensing applications, delivering high precision in detecting RI changes across these crucial spectral regions.

A mathematical or computational model is used by an artificial neural network (ANN) to process information using a connectionist approach to computing. The network of interconnected artificial neurons accomplishes this. It is inherently an adaptive system, meaning its structure evolves based on the data that passes through the network. ANNs are capable of identifying and modeling the relationships between inputs and outputs, enabling them to approximate the appropriate outputs for new inputs. This adaptability and learning capability make ANNs powerful tools for a variety of applications, including pattern recognition, data classification, and predictive modeling23,24.

The RI detection process relies on variations in the transmission rate, including shifts in passband and quality factor, which are sensitive to changes in the surrounding environment. Since accurately interpreting these changes is critical for reliable RI detection, a neural network model is employed to automate and refine the analysis, minimizing human error in data interpretation.

As illustrated in Fig. 7, the process begins with simulation results generated through the FDTD method. These simulations yield detailed transmission rate data for the material under study—in this case, Teflon. This transmission data includes key features sensitive to RI variations, such as transmission peaks, spectral shifts, and bandwidth characteristics, which serve as input features for the neural network model. Also, an MLP neural network model is then trained using this transmission data. The MLP model is configured to learn the complex relationships between the transmission features and the RI values, effectively mapping the input transmission characteristics to corresponding RI values. Through supervised learning, the MLP network is able to generalize and accurately predict the RI for new samples once trained. This capability is particularly advantageous for detecting subtle RI changes across different materials, as the model can detect shifts automatically without manual analysis.

Finally, the trained MLP model performs RI detection on new transmission rate data, predicting the RI based on the learned patterns. This approach enhances the precision of RI detection, reduces the potential for human error, and allows for real-time monitoring of RI variations in practical applications.

Block diagram of the implementation of the presented neural network.

In this manuscript, a MLP is used, which is a feed-forward artificial neural network model designed to map sets of input data to corresponding output data. An MLP network consists of multiple layers of nodes arranged in a directed graph, with each layer being fully connected to the subsequent one. Each layer is characterized by its own weight matrix, bias, and transfer function, enabling the network to learn complex patterns and relationships within the data25,26,27. The MLP is an enhancement of the standard linear perceptron, capable of distinguishing data that is not linearly separable. This algorithm is utilized to construct learners that demonstrate strong predictive performance. The proposed structure comprises three layers: the input layer, the hidden layer, and the output layer. The block diagram of the proposed neural network is illustrated in Fig. 8. This network was designed to map extracted features from transmission rate data to corresponding RI values, leveraging the MLP’s adaptability in identifying non-linear patterns in the data.

The implemented MLP neural network.

The input layer serves to distribute the inputs to subsequent layers. The input nodes utilize linear activation functions and do not perform any mathematical calculations. The hidden layer of the MLP, consisting of a set of neurons with nonlinear activation functions, serves as the core computational component. This layer enables the model to learn complex, non-linear relationships between the input features and RI values, enhancing its ability to make accurate predictions. Finally, the output layer uses a linear activation function to generate the final predicted RI value.

To use a neural network, a set of inputs and outputs that are used for training and testing the network must be determined. Transmission rates have many components. Also, distributed data in the transmission rate can prevent the convergence of the MLP network or cause its convergence to occur with a long time delay. Therefore, transmission rate data cannot be directly considered as input to the neural network. Due to the difference in the data of different materials, 5 parameters extracted from the transmission rate were considered as the input of the neural network. It should be noted that a parameter was first considered to select the input parameters of the neural network. But the trained neural network did not get acceptable results and a significant number of predicted outputs were wrong. In this way, the number of input parameters increased and the error percentage was set to 0 for 5 parameters. The diagram of the mean relative error (MRE) percentage per number of neural network input parameters for RI is shown in Fig. 9.

A graphical representation of the MRE (%) as a function of the RI neural network’s input parameters.

As the number of input parameters increases from 1 to 5, the MRE decreases significantly, indicating an improvement in the accuracy of the MLP model. This trend suggests that incorporating more input parameters into the MLP model enhances its predictive capability, thereby reducing the relative error. The curve demonstrates a steep decline in MRE from around 17% with one input to approximately 1% with five inputs, highlighting the importance of including multiple relevant inputs to achieve a more precise and reliable neural network model. Therefore, 5 inputs are considered for the designed network.

The defined input parameters for the neural network are as follows:

Total summation of components: This parameter represents the overall summation of all components within the transmission rate data.

Local summation of components: This parameter accounts for the summation of components within a specific localized region of the transmission rate data. Here, is the summation of the first 1/4 of all components.

Total power of components: This parameter measures the total power of all components in the transmission rate data.

Local power of components: This parameter evaluates the power of components within a specific localized region of the transmission rate data.

Peak wavelength components: This parameter identifies the wavelength at which the maximum transmission rate occurs. It provides insight into the dominant wavelength component within the transmission rate data.

To determine the outputs of the proposed neural network, various materials with different refractive indices were considered.

Also, to train the neural network and test the accuracy of the predicted results, data from several measurements were required. For each reference material, measurements were performed more than 30 times. The training dataset comprised 10 samples with a RI of 1 (reference data), along with 10 samples each for refractive indices of 1.2, 1.4, and so on, up to a RI of 2. This provided a comprehensive training set to cover the range of refractive indices.

Another set of 30 samples was used as test data to evaluate the network’s performance. To determine the RI of a particular material, its transmission rate data is input into the trained neural network. The network then predicts the output, which can be used to accurately determine the material’s refractive index. This process ensures that the neural network is robust and reliable in identifying the refractive indices of different materials based on their transmission rate data.

The use of a MLP neural network in this study significantly enhances the sensor’s accuracy by enabling advanced data analysis techniques that go beyond traditional methods. Traditional RI detection methods often rely on straightforward linear relationships or threshold-based analyses, which may overlook subtle, complex patterns in the transmission data. In contrast, the MLP neural network is specifically designed to capture and learn non-linear relationships among multiple input features, such as total and localized transmission power, peak wavelength, and cumulative transmission components. This capability allows the MLP to account for intricate variations within the transmission data that are sensitive to small RI changes.

Furthermore, the adaptability of the MLP enables it to learn from large datasets and continuously refine its predictive model through iterative training. This is especially advantageous for photonic sensing applications, where the accuracy of RI measurements depends on detecting minor shifts in transmission characteristics. By processing input features collectively rather than independently, the MLP can distinguish subtle patterns that may correspond to specific RI values, thus reducing the likelihood of misclassification and improving prediction reliability.

Overall, the MLP neural network’s capacity to handle non-linearity, learn from complex data distributions, and improve through training makes it an ideal choice for enhancing sensor accuracy. This approach enables a more robust and precise RI detection system, ensuring higher performance and reliability in advanced sensing applications compared to traditional methods.

Furthermore, to verify the performance of the designed sensor, the one-sample T-test has been used, the results of which are as follows:

By taking into account the sample size (m) and sample standard deviation (SD), the one-sample T-test determines if there is a statistically significant difference between the sample mean (\(\:\stackrel{-}{x}\)) and the population mean (\(\:\mu\:\)). Here is the formula for calculating the test statistic (t)28,29:

At a selected significance level (α), usually 0.05 for a 95% confidence level, the computed t-value is contrasted with the crucial t-value from the T-distribution table. The null hypothesis, which states that the sample mean is equal to the population mean, is rejected, showing a significant difference, if the estimated t-value exceeds the critical t-value.

The provided diplexer has been measured seven times throughout the experiment to ensure its performance with this test. Assume that 2 RIU is the known RI. The RIU readings that the sensor may provide are 2.001, 1.997, 2.002, 2.089, 1.895, 2.001, and 1.991. The results of this experiment show that \(\:\stackrel{-}{x}\) is 1.9966 and SD is 0.0562. So:

The t-value of −0.16 is compared against the critical t-value from the t-distribution table for m − 1 = 6 degrees of freedom at a chosen significance level (commonly α = 0.05). The critical t-value for a two-tailed test at α = 0.05 is approximately ± 2.447. Since our calculated t-value (−0.16) is within the range of −2.447 to 2.447, we fail to reject the null hypothesis that the sample mean is equal to the population mean.

The one-sample t-test was specifically chosen to validate the accuracy and reliability of the diplexer’s RI measurements by comparing the sensor’s readings against a known reference value (2 RIU). This statistical test is particularly suitable for evaluating the precision of measurement devices, as it allows us to determine whether any observed deviations from the reference RI are due to random variation or indicate a systematic error in the sensor’s performance. By confirming that the calculated t-value falls within the non-significant range, we established that the measured RI values align closely with the reference, thereby verifying the sensor’s accuracy.

Based on the predicted outputs of the neural network, it can be concluded that using a trained neural network can accurately predict the outcomes of new measurements. This capability significantly mitigates the challenges associated with analyzing experimental data manually, offering a reliable and efficient method for determining the refractive indices of various materials. By automating the analysis process, the neural network ensures consistent and precise results, enhancing the overall accuracy and reliability of the measurements. This innovative approach of leveraging neural networks in photonic design not only enhances device performance but also paves the way for the development of advanced, high-sensitivity optical systems for next-generation communication and sensing technologies.

Table 3 provides a comparison of the performance of the diplexer presented in this article with similar sensors from previous works. The results indicate that this sensor boasts the smallest dimensions, the highest sensitivity, and employs one of the most effective techniques designed to date. Also, the FWHM values obtained for our proposed MIM diplexer are significantly lower than those reported in most comparable studies, as shown in Table 3. This reduced FWHM is advantageous in the context of photonic sensing because a narrower FWHM indicates a sharper, more defined resonance peak. Such precision enhances the sensor’s ability to detect small changes in the refractive index with higher accuracy and minimal interference, as narrower peaks are less likely to overlap with adjacent signals or channels. This comparison underscores the superior performance and compact design of the diplexer, highlighting its advancements over existing sensors in the field.

This work presents a high-performance 4-channel MIM diplexer, leveraging silver and Teflon, designed for advanced photonic applications. The diplexer, equipped with two band-pass filters, operates across four distinct wavelength bands, demonstrating exceptional sensitivity and high figures of merit. FDTD simulations validate the diplexer’s efficiency, while an MLP neural network enhances its RI detection accuracy. Furthermore, the new Drude and critical point model has been employed for material analysis. The sensor’s compact design and superior performance in optical communication and photonic sensing technologies are underscored by a one-sample t-test. Comparative analysis reveals that this diplexer surpasses existing sensors in sensitivity and efficiency. These findings highlight the diplexer’s potential for integration into next-generation photonic devices, such as medical diagnostics, environmental monitoring, and data communications, paving the way for advancements in high-sensitivity, miniaturized optical systems.

The datasets generated during the study are available from the corresponding author on reasonable request.

A Correction to this paper has been published: https://doi.org/10.1038/s41598-025-89351-z

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Electrical Engineering Department, Razi University, Kermanshah, Iran

Seyed Abed Zonouri

Faculty of Engineering, Warith Al-Anbiyaa University, Karbala, 56001, Iraq

Ali Basem

College of Education, Department of Physics, Misan University, Amarah, Iraq

Younis Mohamed Atiah Al-zahy

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S. A. Z.: Software, Validation, Formal analysis, Methodology, Conceptualization, Supervision, Project administration, A. B.: revising, Validation, and Y. M. A.: Grammar review, Validation.

Correspondence to Seyed Abed Zonouri.

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The original online version of this Article was revised: The original version of this Article contained an error in the name of the author Younis Mohamed Atiah Al-zahy, which was incorrectly given as Mohamed Atiah Younis Al-zahy.

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Zonouri, S.A., Basem, A. & Al-zahy, Y.M.A. Innovative MIM diplexer with neural network enhanced refractive index detection for advanced photonic applications. Sci Rep 14, 31473 (2024). https://doi.org/10.1038/s41598-024-83066-3

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Received: 24 September 2024

Accepted: 11 December 2024

Published: 28 December 2024

DOI: https://doi.org/10.1038/s41598-024-83066-3

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