Sensors are essential in our daily lives, and we can encounter various types in our daily activities and surroundings. These sensors contribute to making our lives more comfortable, safe, and sophisticated. A sensor is a device that receives signals or responds to stimuli, and it can be defined by its measurements, properties, and various factors such as input signal, characteristics, cost, accuracy, range, applications, materials used, production technologies, and other parameters play crucial roles in the sensor industry.

Therefore, many types of sensors depend on various signals, including physical, chemical, biological signals, etc. Additionally, sensors are categorized based on applications such as thermal, electrical, magnetic, optical, chemical, vibrational, pressure, moisture, speed sensors, etc. Among these, optical sensors are of particular interest for this research. Optical sensors are highly advanced and sensitive devices capable of monitoring parameters such as intensity, polarization, phase, or spectroscopic changes of a given light source. Optical phenomena of interest include mechanisms such as Raman scattering, reflection and transmission, as well as laser-Doppler methods.

In this study, we investigated three systems: Surface Plasmon Resonance (SPR), Fano-line shape resonance, and Bloch Surface Wave (BSW). We conducted a quantitative comparison of experimental data with two numerical simulations: i) Fresnel equations (FE) and matrix transfer (MT) formalism, and ii) Finite-Difference Time-Domain (FDTD), for achieving sub-monolayer precision.

Both optical simulation models are employed to study the optical response of these sensors. The optical properties of materials are determined by measuring the ellipsometric angles Ψ (°) and Δ (°). As a first step, we qualitatively compare the far-field projection simulations of FE and FDTD results with experimental data, aiming for lower mean square error (MSE) values to ensure good agreement. Ellipsometry measures the complex ratio of the p- and s- Fresnel reflection coefficients as the ellipsometric angles (Ψ,Δ ) given by tan⁡(ψ) e^iΔ=r ̃_p/r ̃_s, where r ̃_p and r ̃_s are the complex Fresnel reflection coefficients of p- and s- polarized plane waves, which relate with reflectance as: R_p =|r ̃_p |² and R_s =|r ̃_s |², where R_p and Rs are the power, or intensity, reflection coefficients for the p- and s- polarizations, respectively.

Our approach involved two main numerical modeling strategies: i) FE and MT formalism, and ii) FDTD method. First, the FE simulation model is used to analyze the experimental data by least squares regression analysis of an optical model to obtain the best fit parameters (such as the thickness and optical properties (n, k) of each layer in the sample). After achieving good agreement between the Experiment (Ψ, Δ)Exp and the FE simulation (Ψ, Δ)FE, the parameters of the optical model (such as wavelength, AoI, pol, thickness and optical properties (n, k) are used in the FDTD simulation to obtain the NF response of the sample. In turn, the NF response is used to obtain the far-field projection of the resulting NF which enables calculation of the ellipsometric angles derived from the FDTD model (Ψ, Δ)FDTD. Finally, a comparison between the ellipsometric angles from both numerical simulations (Ψ, Δ)FDTD and (Ψ, Δ)FE with the experimental values confirms that the FDTD simulations are validated. As a next step, near field investigations are addressed in the FDTD simulation to achieve better understanding and additional insights of the sample for future applications. By using the accepted results from the FE model as a comparison standard, the FDTD model can be demonstrated to achieve sub-monolayer precision in the determination of the optical properties and thickness of ideal layers in a multilayer sample. Accordingly, the corresponding sub-monolayer precision between these two methods confirms that FDTD is well matched to the precision and accuracy of spectroscopic ellipsometry (SE) measurements. Importantly however, FDTD simulations provide much additional information as it can enable: i) visualization of the, spectrally resolved, electric field distribution around metamaterials and other non-planar systems, and ii) visualization of the time-resolved evolution of the electric field and resonances arising in these systems. Such information can in turn, help to confirm or identify the nature of near-field (NF) enhancements as SPR, SPP, and Localized Surface Plasmon Resonance (LSPR). Furthermore, time profiles, enable visualization of the different aspects of NF light propagation along with energy transfer and decay. These FDTD NF simulations thus provide additional insights, deeper understanding, and valuable knowledge that can motivate technical improvements and novel designs in photonic and plasmonic materials and devices.

For the SPR system, the sensing resonance Ψ (°) is achieved in p- polarization with the glass and Ag layer prism configurations. Ψ and Δ values are in good agreement with the Angle of Incidence (AoI) of 45° at 501 nm for both FE and FDTD simulations. The original electric field enhancement of the SPR system is ~17. However, the electric field intensity for the SPR system is enhanced by up to six orders of magnitude by using gold metallic particles with optimized diameters and AoIs.

In the Fano-line shape system, fabricated using a three-layer Metal-Dielectric-Metal (MDM) structure of Silver (Ag)-Aluminum Nitride (AlN)-Silver (Ag), the reflection response of SE measurements was determined in the AoI range from 55° to 75° and in the spectral range from 400 nm to 1600 nm. The Fano-line shape resonances were excited at two AoIs: 70° and 61°, with corresponding resonances occurring at 591.94 nm and 1241.40 nm, respectively, by overlapping the two polarization points R_p and R_s. A detailed investigation of the electric field distribution was conducted for Rp when Ψ approaches 0, while Ψ approaches 90°, bringing R_s resonance at wavelengths of 591.94 nm and 1241.40 nm with AoI of 70° and 61°, respectively. The excitation of Surface Plasmon Polariton (SPP) and Plasmonic Waveguide (PWG) were visualized and confirmed in the MDM sample to excite the Fano-line shape resonances. For the electric field intensity, a 40 nm AuNP was used, considering three percentages of Effective Medium Approximation (EMA) in water sensing medium. This resulted in enhanced in the NF region at the hot spot, demonstrating LSPR with a six-orders-of-magnitude factor compared to the original Fano-line shape resonance enhancement, ~5 for 1241.40 nm with 61° and ~25 for 591.94 nm with 70°.

In the third case study, a BSW structure formed with 16 layers of dielectric materials (Ta₂O₅ and SiO₂) was investigated for its application as an excitation source for SERS. This used a HeNe laser (633 nm, REO Optical Solutions), as the excitation source for the BSW resonance. The BSW resonance, in turn, becomes the excitation source, driving the SERS Raman enhancement effect. The ellipsometric angle Ψ value of ~88° under the s- polarization was achieved in FE simulation and was quantitatively compared with the FDTD simulation. The electric field distributions, for wavelengths on- and off- resonances, were obtained from the FDTD model to highlight the nature of the photonic resonance and sensitive dependence on the excitation conditions such as AoI, polarization (pol), etc. The substantial electric field enhancement expected from BSW sensor, was also achieved with three orders of magnitude. This was accomplished by maintaining the energy at the SiO2 material layer operating as an absorption layer in the second to last layer of the BSW stack. The FDTD simulations provided further insight into the nature of the energy storage in the BSW, by providing visualization of the long decaying time, ~ 50,000 fs, of the BSW wave packet. It was further confirmed that the BSW photonic wave packet can efficiently transfer energy to the AuNP to excite strong NF localized plasmonic enhancement (LSP) at the hotspot region defined by the AuNP and multilayer. The effective, efficient, strong NF enhancement at the hot spot of the AuNP was enhanced by up to eight orders of magnitude. This makes it applicable for strong NF Raman signals, useful for chemical identifications and quantification over a large (mm2) area. The strong optical resonance and long decaying energy in the BSW multilayer, as along with the efficient optical antennae effects of the AuNPs, can be used to future sensing applications. These include the development of cross-propagating BSW (cp-BSW) systems that can be used to develop photonic systems akin to Nano CT scan devices.