Theoretical modeling and investigations of lossy mode resonance prism sensor based on TiO<sub>2</sub> film

Yizhuo Zhang; Yizhuo Zhang; Yizhuo Zhang; Pengyu Zhang; Pengyu Zhang; Pengyu Zhang; Maolin Zhao; Maolin Zhao; Zhiqi Li; Zhiqi Li; Danping Xu; Danping Xu; Chenghao Tong; Chenghao Tong; Jian Shen; Jian Shen; Chaoyang Li; Chaoyang Li; Chaoyang Li

doi:10.1364/OE.466170

1. Introduction

Lossy mode resonance (LMR) is a unique optical effect which initially arises from the periodic coupling between the lossy modes (a guided mode with a complex effective index) supported by the semiconductor cladding layer and the lossless modes of dielectric waveguide [1,2]. It was originally used in the design of highly efficient polarizers [3]. Del Villar et al. successfully used LMR in the design of optical sensors and proposed a wavelength-sensitive LMR optical fiber sensor in 2010 [4], and since then the optical sensors based on LMR have been widely studied [5–8]. The generation condition of LMR is a function of permittivity [9]: $\mathrm{\varepsilon }_\textrm{2}^\mathrm{\prime}\mathrm{\ > 0\;\ \&\ }\; |{\mathrm{\varepsilon }_\textrm{2}^\mathrm{\prime}} |\mathrm{\ > }|{\mathrm{\varepsilon }_\textrm{2}^{\mathrm{\prime\prime}}} |\; \& \; |{\mathrm{\varepsilon }_\textrm{2}^\mathrm{\prime}} |\mathrm{\ > }|{\mathrm{\varepsilon }_\textrm{3}^\mathrm{\prime}} |$. $\mathrm{\varepsilon }_\textrm{2}^\mathrm{\prime}$ and $\mathrm{\varepsilon }_\textrm{2}^{\mathrm{\prime\prime}}$ are the real and imaginary parts of the permittivity of the lossy materials used to excite LMR. $\mathrm{\varepsilon }_\textrm{3}^\mathrm{\prime}$ is the real part of the permittivity of the surrounding medium.

The LMR sensors differ from traditional surface plasmon resonance (SPR) sensors in the following two points. Firstly, SPR can only be excited by TM polarized light, whereas LMR can operate under both TE and TM polarization. Secondly, the excitation materials are different. The common excitation materials for SPR are gold (Au) and silver (Ag), both of which are very expensive [10,11]. Sodium (Na) can also be used as the excitation material for SPR. Due to its high chemical reactivity, Na can be easily oxidized when exposed to air and resulting in the formation of an external transition layer which will affects the sensor performance. Fabrication of Na films using traditional metal deposition techniques has also been challenging [12,13]. Materials used to excite LMR are typically lossy mediums with a complex refractive index. LMR can be generated by using polymers, transparent conducting oxides (TCOs) and dielectrics [14–16], making LMR sensors cheaper to fabricate and more stable in performance than SPR. In addition, data shows that optical sensors based on LMR can overcome the limitations of traditional SPR sensors and provide higher sensitivity [17]. As a result, LMR sensors have been widely researched and applied in the fields of refractive index detection [18], biomonitoring [19], breathing monitoring [20], pH measurement [21], chemical examination [17] and voltage detection [22].

Titanium dioxide (TiO₂) has been one of the most attractive oxide semiconductor materials over the past decades due to its low cost and long-term photostability [23,24]. TiO₂ is non-toxic, but if the particle size of TiO₂ reaches nanoscale, the particles may enter the blood circulation directly through the lungs. High concentrations of TiO₂ particles is harmful to human body [25]. Therefore, the inhalation of particles should be avoided during the preparation of TiO₂-based devices. The preparation techniques of TiO₂ are well established, various chemical and physical methods have been used to prepare TiO₂ thin films deposited on different substrates. For example, the sol-gel method [26–28], chemical vapor deposition (CVD) [29,30], spray pyrolysis technique (SPT) [31], radio frequency (RF) magnetron sputtering [32–34] and layer-by-layer (LbL) method [35]. In addition, TiO₂ has been theoretically and experimentally demonstrated to be a lossy material for LMR optical fiber sensors. M. Hernaez et al. proposed an optical fiber LMR sensor based on TiO₂ with a sensitivity of 1987nm/RIU when the refractive index (RI) of the surrounding medium varies between 1.32 and 1.40 [36]. Then C. R. Zamarreño et al. presented the fabrication of TiO₂ and PSS resonance supporting coatings onto optical fibers [37]. Del Villar et al. summarised the design rules for LMR optical fiber sensors based on TiO₂/PSS coating [38]. Nidhi Paliwal and Joseph John put forward theoretical modelling of tapered LMR optical fiber sensors and enhanced the sensitivity using a TiO₂ layer [39].

It can be seen from the available studies that TiO₂ is mainly used in the design of optical fiber LMR sensors. This is because the prism-based sensors generally operate under angular interrogation, unlike optical fiber sensors which operate under wavelength interrogation. The LMR dips excited by monolayer lossy material film are around 85° in the visible wavelength region, which is challenging for sensing detection under angle interrogation [5]. However, optical fiber-based LMR sensors are brittle and not suitable for mass production or applications. D-shaped optical fibers are commonly used to improve the sensitivity, but the coating, cleaning and surface modification processes for the detection of specific analytes are difficult to handle. The prism-based LMR sensor is more stable. The sensor structure can be changed by depositing the films of different thicknesses on substrates and the substrate can be connected to the prism by refractive index matching fluid. In addition, the optical prism-based LMR sensor can operate under angle interrogation. The sensing detection can be carried out by using a single frequency laser source and optical power meter without requiring a broadband light source, spectrometer or other expensive equipment. There have been no model investigations about the prism LMR sensors based on TiO₂ so far. Therefore, it is necessary to conduct a practical theoretical model of the TiO₂-based LMR prism sensor which can operate under angle interrogation. Research on the characteristic of this model can guide the design and application of LMR prism sensors.

In this paper, we provide a detailed four-layer LMR sensor theoretical model based on the configuration of prism/matching layer/lossy layer/sensing layer, with a TiO₂ film as the lossy layer and a LiF film as the matching layer, effectively improving the resonance signal under angle interrogation and making the sensor cost effective. The proposed sensor is based on the principle of attenuated total reflection (ATR) and is less complex for fabrication. Incident light at 633 nm is used to excite the LMR signal which is stable under both TE and TM polarized light. Based on the electric field distribution at resonance and the coupled mode theory, the structural parameters (film thickness, refractive index of matching layer and sensing layer) affecting the LMR signal have been analyzed. Data shows that the detection range of the proposed sensor varies dynamically with the refractive index of the matching layer being the midpoint. There is a trade-off between the detection range and detection accuracy of the proposed LMR sensor, which can be improved by adjusting the thickness ratio of the matching and lossy layers. In addition, all suitable combinations of film thicknesses are given as a reference for the design of LMR prism sensor based on TiO₂ film. Under proper thickness combination, the proposed sensor is capable of detecting the medium with refractive index ranging from 1.32 ∼ 1.47, with a sensitivity range of 34 ∼ 148 °/RIU under angle interrogation and a maximum value of 192 RIU⁻¹ for FOM under TM polarization. We hope these theoretical studies can demonstrate the advantages of LMR prism sensors and provide guidance for future experimental implementations of LMR prism sensors.

2. Model structure and theoretical analysis

2.1 Model structure

The LMR prism sensor proposed in this paper is based on the improved Kretschmann-Reather (KR) structure. The common helium-neon gas laser (λ = 633 nm) is used as the light source due to the incident light being generally transmitted in free space under angular interrogation. As shown in Fig. 1(a), θ is the angle between the incident light and the normal line to the prism/matching layer interface. The LMR is strongly excited when the phase matching condition is satisfied at a specific incident angle, which will guide the energy transfer to the lossy layer and form the lossy mode. This will reduce the reflected light intensity and the variation of reflectance with incident angle can be recorded by an optical power meter for sensing detection.

Fig. 1. (a) Schematic diagram of the four-layer LMR sensor based on the improved KR structure. (b) The proposed LMR sensor is based on BK7/LiF/TiO₂/sensing medium configuration.

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The common BK7 prism is used as a coupling prism to balance angular sensitivity and detection range. The refractive index of the BK7 is n_p = 1.5151 at 633 nm, which is calculated by Eq. (1) [40].

(1)$${n_\textrm{p}} = {\left( {\frac{{1.03961212{\lambda^2}}}{{{\lambda^2} - 0.0060069867}} + \frac{{0.231792344{\lambda^2}}}{{{\lambda^2} - 0.0200179144}} + \frac{{1.01046945{\lambda^2}}}{{{\lambda^2} - 103.560653}} + 1} \right)^{\frac{1}{2}}}$$

λ is in units of µm and Eq. (1) is effective for wavelengths in the range of 0.30 to 2.50 µm.

From Fig. 1(a-b), it can be clearly seen that the proposed prism-based LMR sensor structure is composed of four layers, in the order of prism, matching layer, lossy layer and sensing layer. The matching layer (L₁) is the first thin film coated on the prism to adjust the resonance dips at 633 nm. The proposed LMR sensor is based on the principle of attenuated total reflection so the refractive index of the matching layer film should be lower than the refractive index of the prism. Furthermore, our data show that the detection range of the sensor varies dynamically with the RI of the matching layer being the midpoint. Considering that lossy layer films (TiO₂) mostly require a high-temperature environment during the deposition process, Lithium Fluoride (LiF) is chosen as the matching layer material. The common melting point of LiF is 848 °C, which allows it to withstand high temperatures during the deposition of lossy layer films. In addition, LiF is transparent from 0.12-9.0 µm and practically insoluble. It can be deposited on different substrates (glass, fused silica and amorphous metal) by a variety of physical vapour deposition (PVD) techniques [41,42]. Equation (2) is the dispersion equation of LiF in the wavelength region 0.10-11.0 µm [43]. The RI of LiF at λ = 633 nm is calculated to be 1.391 which ensures the modes coupling can be satisfied when the refractive index n_s of the sensing medium changes.

(2)$${n^2} = 1 + \frac{{0.92549{\lambda ^2}}}{{{\lambda ^2} - {{(0.07376)}^2}}} + \frac{{6.96747{\lambda ^2}}}{{{\lambda ^2} - {{(32.79)}^2}}}$$

The lossy layer (L₂) consists of TiO₂ thin film. If the thickness of the lossy layer is suitable, the radiation field will be trapped in the lossy layer and the LMR will be strongly excited. For TiO₂, the dispersion relation is defined by the Lorentz model. E is the photon energy, defined as E = hc/λ where h and c are the Planck’s constant and speed of light in a vacuum respectively. The following parameters are used in this paper: amplitude A_k = 101 eV², center energy B_k = 1.2 eV, high frequency dielectric constant ε_∞ = 1 and E_k= 6.2 eV [44].

(3)$${n^2} = {\varepsilon _\infty } + \sum\limits_k {\frac{{{A_k}}}{{E_k^2 - {E^2} - i{B_k}E}}}$$

The refractive index of the sensing layer (L₃) is defined as n_s. The sensing layer can be a sensing medium or an analyte. It can also be liquid as both the lossy layer and matching layer materials are practically insoluble. LMR dip is very sensitive to the variation of n_s. The value of n_s will change if the concentration of the solution changes or biochemical reactions occurs. Then there will be a corresponding movement of the resonance angle θ_R. Therefore, the angular sensitivity is defined as Eq. (4) and the unit is deg/RIU.

(4)$$S = \frac{{\Delta {\theta _R}}}{{\Delta {n_\textrm{s}}}}$$

The figure of merit (FOM) is a comprehensive evaluation index of sensor performance, which is defined as Eq. (5).

(5)$$FOM = \frac{S}{{FWHM}}$$

The unit of FOM is RIU⁻¹. The full width at half maximum (FWHM) is used to describe the width of the resonance dip, which reflects the dissipation of energy caused by the imaginary part of the lossy material.

2.2 N-layer reflection matrix model

The dip in reflectance can be explained by using the coupling mode theory. Lossy mode is a special mode with a complex effective index and the resonance dip is a result of lossy mode formations in the structure. For the structure proposed in this paper, the N-layer reflectance matrix model can be used for a preliminary analysis of the factors affecting reflectance variation [45]. The layers are arranged along the Z-axis as shown in Fig. 2. The boundaries of two adjacent layers are denoted by Z_j in turn and set Z₁ = 0. Then the thickness d of each layer can be expressed as d_j = Z_j - Z_j-1.

Fig. 2. N-layer reflection matrix model

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In this model, the relation between the tangential field at each boundary is given by Eq. (6).

(6)$$\left[ \begin{array}{l} {U_1}\\ {V_1} \end{array} \right] = M\left[ \begin{array}{l} {U_{N - 1}}\\ {V_{N - 1}} \end{array} \right]$$

where M is the characteristic matrix of the N-layer model. U and V are the tangential components of electric and magnetic fields at the corresponding boundaries. M is defined as

(7)$$M = \prod\limits_{j = 2}^{N - 1} {{M_j}} = \left[ {\begin{array}{cc} {{M_{11}}}&{{M_{12}}}\\ {{M_{21}}}&{{M_{22}}} \end{array}} \right]$$

with

(8)$${M_j} = \left[ {\begin{array}{cc} {\cos {\beta_j}}&{ - \frac{i}{{{q_j}}}\sin {\beta_j}}\\ { - i{q_j}\sin {\beta_j}}&{\cos {\beta_j}} \end{array}} \right]$$

Under TE polarization

(9)$${q_\textrm{j}} = \sqrt {{\varepsilon _j} - n_1^2{{\sin }^2}\theta }$$

Under TM polarization

(10)$${q_\textrm{j}} = \sqrt {\frac{{{\mu _j}}}{{{\varepsilon _j}}}} \cos \theta = \frac{{\sqrt {{\varepsilon _j} - n_1^2{{\sin }^2}\theta } }}{{{\varepsilon _j}}}$$

The phase thickness β_j is defined as

(11)$${\beta _\textrm{j}} = \frac{{2\pi }}{\lambda }{n_j}\cos \theta ({Z_j} - {Z_{j - 1}}) = \frac{{2\pi {d_j}}}{\lambda }\sqrt {{\varepsilon _j} - n_1^2{{\sin }^2}\theta }$$

The total reflection coefficient is given by Eq. (12).

(12)$$r = \frac{{({{M_{11}} + {M_{12}}{q_N}} ){q_1} - ({{M_{21}} + {M_{22}}{q_N}} )}}{{({{M_{11}} + {M_{12}}{q_N}} ){q_1} + ({{M_{21}} + {M_{22}}{q_N}} )}}$$

and reflectance of the structure can be calculated by Eq. (13).

(13)$$R = {|r |^2}$$

It can be seen from the model that the excitation conditions for LMR under TE and TM polarization are different. The wavelength λ of the incident light is constant under angular interrogation. The mode coupling is mainly influenced by the incident angle θ, the layer thickness d, the dielectric constant ε and the refractive index n. In fact, we can choose different lossy films as the lossy layer according to requirements. The change of the lossy layer film brings about the change in the complex refractive index, so the parameter of each layer needs to be adjusted accordingly to keep the eigenvalue equation to be 0. For the proposed LMR sensor based on BK7/LiF/TiO₂/sensing medium structure, the prism and the sensing medium can be regarded as semi-infinite. LMR is generated when there is an effective coupling of light between the evanescent wave and the lossy mode in the TiO₂ film. This coupling can only occur if the phase matching conditions are satisfied, which can be adjusted by changing incident angle θ. The thickness of the matching layer will also affect the coupling efficiency of evanescent wave. In addition, the radiation field will be trapped in the TiO₂ layer when LMR is excited. The lossy mode can only be sustained when the mode cut-off condition is satisfied, which can be adjusted by changing the thickness of the lossy layer or the RI of the sensing layer. As the LMR sensor is able to operate under both TE and TM polarization, the mode coupling can also be adjusted by changing the polarization.

3. Results and discussion

3.1 Effect of the matching layer

The modelling and theoretical simulations are carried out by using Comsol Multiphysics Software in this paper. Floquet periodic boundary condition (PBC) is used and the excitation is added from the surface of the prism by using a periodic input port. The prism and the sensing layer can be regarded as semi-infinite and the thickness is set to 1000 nm in the model, which does not affect the reflectance results. For the structure proposed in this paper, we recommend using the physics-controlled mesh and setting the maximum mesh element size to λ/M. This is because the approximate solutions obtained are based on the finite element method (FEM) and the mesh size will affect the results. By changing the value of M, the mesh element density can be easily adjusted to balance the speed and accuracy of the calculation. In general, we recommend setting this value to λ/10. The value of M can be increased when calculating the field distribution at the layer interface to obtain more stable results.

Figure 3(a-b) shows the LMR signals based on the BK7/TiO₂/sensing medium structure without a matching layer. The thickness of the lossy layer is 40 nm and 60 nm under TE and TM polarization respectively. The resonance angle varies in the range of 83.5° ∼ 88.6° when the refractive index n_s of the sensing medium is changed from 1.33 to 1.45, and the resonance dips are not sensitive to the changes in n_s. This limits the sensing detection under angular interrogation and further improvements in sensor structure are necessary. Here we use R_min (the minimum reflectance of the resonance dip) to describe the LMR signal. If the thickness of the matching layer and lossy layer is proper, the energy will be absorbed by the lossy layer and R_min will be less than 0.01. The LMR is then considered to be strongly excited.

Fig. 3. Variation of reflectance with incident angle based on the BK7/TiO₂/sensing medium structure when n_s changes from 1.33 to 1.45. (a) The thickness of TiO₂ is 40 nm under TE polarization. (b) The thickness of TiO₂ is 60 nm TM polarization.

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The excitation conditions for LMR signal under TE and TM polarization are different. To obtain high quality LMR signal, we designed different sensor structures for TE and TM polarization. Figure 4(a) shows the improved LMR signals under TE polarization when thickness of the matching layer is L₁ = 300 nm. As the n_s changes from 1.33 to 1.45, the resonance dip shifts towards a larger angle, but is limited in the range of 62°–80°. When the LiF thickness is L₁ = 500 nm and the TiO₂ thickness is L₂ = 60 nm, the reflectance curves under TM polarization are plotted in Fig. 4(b). By comparing Fig. 4(a) and Fig. 4(b), it can be seen that the FWHM of the resonance dips under TM polarization are narrower, which can provide better detection accuracy. In addition, the resonance dips under TM polarization are shallower (Larger value of R_min) than TE polarization when n_s is 1.33 or 1.45. This indicates that the LMR signal decays more rapidly under TM polarization, which may affect the detection range of the sensor.

Fig. 4. Variation of reflectance curves for the proposed BK7/LiF/TiO₂/sensing medium structure when n_s changes from 1.33 to 1.45. (a) Under TE polarization, the thickness of LiF is L₁ = 300 nm and the thickness of TiO₂ is L₂ = 40 nm. (b) Under TM polarization, the thickness of LiF is L₁ = 500 nm and the thickness of TiO₂ is L₂ = 60 nm.

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3.2 Electric field distribution at resonance

The intensity of the LMR signal is related to the distribution of the radiation field in the proposed structure. Figure 5(a) shows the y-component of the electric field under TE polarization. The layers in this structure are arranged along the z-direction and the thickness of each layer is the same as in Fig. 4(a). For TE polarization, the electric field vibrates in the y-direction. The phase matching condition is satisfied when the incident angle θ is 71.65° and the energy is concentrated in the lossy layer. This in turn reduces the intensity of reflected light, then the LMR is strongly excited and resonance dips can be observed. The electric field intensity is normalized in Fig. 5(b), where |E₀| is the electric field norm (amplitude of the electric field) at the BK7/LiF layer interface. The average energy flow density of the light is proportional to the square of the electric field norm, so |E|²/|E₀|² is used to study the electric field distribution in this structure. From Fig. 5(b), the enhancement of the electric field by the matching layer can be observed with a maximum enhancement of 7.02 times when n_s = 1.39. The electric field reaches its maximum value in the TiO₂ layer at resonance and decays exponentially with the distance to the analyte interface (TiO₂ layer/sensing medium interface). This makes the LMR signal very sensitive to changes in the sensing medium. For different n_s values, the electric field distribution in Fig. 5(b) shows a good correspondence with the minimum value of R_min in Fig. 4(a). This indicates that the prerequisite for generating a sharp LMR dip is to ensure the maximum transfer of energy from the evanescent wave to the lossy mode.

Fig. 5. (a) The 2D plot of the y-component of the electric field under TE polarization at resonance when n_s = 1.39. (b) The electric field distribution with different n_s values at resonance.

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The electric field under TM polarization can be decomposed into two components, x-component and z-component. According to the electromagnetic field boundary conditions, the x-component of the electric field on both sides of the interface should be continuous, while the z-component is discontinuous. Therefore, the distribution of the x-component of the electric field when n_s = 1.39 was studied and the results are shown in Fig. 6(a) and Fig. 6(b). Similarly, |E_0x| is the electric field norm of x-component at the interface between the prism and the LiF layer. The resonance angle under this structure is about 69.6°. It can be observed that the maximum value of the electric field intensity of the x-component is at the surface of the TiO₂ layer, while it tends to zero at the center of the TiO₂ layer, which is significantly different from the electric field distribution of conventional single interface SPR sensors [46]. This results in a significant enhancement of the field at the surface of the lossy layer. The electric field distribution on the upper and lower surface of the lossy layer can be adjusted by changing the incident angle, but the value at the resonance angle is the largest compared with other incident angles with a maximum enhancement of 5.35 times.

Fig. 6. (a) The 2D plot of the x-component of the electric field under TM polarization at resonance when n_s = 1.39. (b) The distribution of x-component of the electric field at different incident angle when n_s = 1.39.

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3.3 LMR signal parameters for different n_s

The changes in the refractive index n_s of sensing medium will lead to variations in the LMR signal, which may be caused by the changes in concentration, or by biological, physical and chemical reactions. Then sensing detection can be achieved by monitoring the change in resonance angle. Optical prism sensors for biochemical detection typically use 1.33 as the operating starting point (the refractive index of water at room temperature). As the concentration of the liquid increases, the value of the refractive index gradually increases. Figure 7 and Fig. 8 show the variation of LMR signal parameters (resonance angle, R_min, sensitivity and FWHM) with different n_s under TE and TM polarization, with the selected n_s value ranging from 1.32 to 1.47.

Fig. 7. The variation of LMR signal with different n_s under TE polarization when L₁ = 300 nm, L₂ = 40 nm. (a) The variation of resonance angle θ_R and minimum reflectance R_min. (b) The variation of sensitivity and FWHM.

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Fig. 8. The variation of LMR signal with different n_s under TM polarization when L₁ = 500 nm, L₂ = 60 nm. (a) The variation of resonance angle θ_R and minimum reflectance R_min. (b) The variation of sensitivity and FWHM.

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By comparing Fig. 7(a) and Fig. 8(a), it can be seen that the resonance angle increases gradually when n_s changes from 1.32 to 1.47 but remains in the range of 60°–80° which can facilitate the experimental manipulation under angular interrogation. The resonance dip has the minimum R_min value when n_s = 1.39. It can be noted that this refractive index value is close to that of LiF at 633 nm. That indicates that the refractive index n_s of the sensing layer also affects the transfer of energy to the lossy mode. The sensitivity and FWHM of the LMR signal are presented in Fig. 7(b) and Fig. 8(b) to demonstrate the sensing detection potential of the device. As n_s increases from 1.32 to 1.47, the sensitivity of the resonance signal gradually increases while the FWHM becomes progressively narrower, both under TE and TM polarization. The value of the FOM can be calculated by Eq. (5) and is positively correlated with n_s. The highest sensitivity (148 °/RIU) and the narrowest FWHM (0.77 °) values were both obtained at n_s = 1.47 under TM polarization, and the FOM is calculated as 192 RIU⁻¹. Table 1 shows the performance comparison of the proposed LMR structure and Au/Ag based sensors. Compared with the SPR prism coupling structure based on KR configuration, the LMR sensor proposed in this paper has better FOM value. [47,48]. Achieving higher angular sensitivity (above 500 °/RIU) with a traditional KR configuration is challenging. Some works improve the angular sensitivity of the prism sensor by using grating and two-dimensional materials, which also increases the cost and fabrication difficulty of the device. Therefore, it can be seen that the proposed LMR sensor structure in this paper also has the advantage of low cost, wide detection range and the ability to operate under TE and TM polarization.

Table 1. Performance comparison of various sensor structures

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The detection range of the device is not limited to the refractive index range of 1.32 - 1.47. The theoretical upper limit of the detectable refractive index value is n_p (the refractive index of the prism), the lower limit depends on the critical angle. From the data, the polarization of light has a limited effect on sensitivity. The device would perform better if n_s was closer to n_p. This is the characteristic of sensors based on KR structures. Therefore, the sensitivity under angular interrogation can also be improved by adjusting the refractive index of the coupling prism [49]. The wide detection range of the device is suitable for concentration measurement of high refractive index solutions. For example, the refractive index of the sucrose solution changes from 1.334 to 1.465 as the concentration increases from 1% to 70% [50]. Dynamic monitoring of concentrations can be achieved by detecting the variations in LMR signals and the whole process is non-destructive and rapid.

3.4 Adjustment of the detection range

From the above discussion, it can be found that the LMR signal decays more rapidly under TM polarization. The R_min of the resonance dip is close to 0.6 when n_s is 1.45, and the LMR signal will attenuate further as the n_s increases. It is more challenging to detect the resonance dip if it is too shallow, which requires the detection equipment with higher accuracy. In a sense, R_min reflects the quality of the resonance signal and influences the detection range of the sensor. Figure 9(a-b) provide the electric field distribution under TM polarization when n_s is 1.39 and 1.45 respectively. The results show that when n_s is close to the refractive index n₁ of the matching layer, the entire radiation field is concentrated on the lossy layer at resonance. This can be explained by the coupling mode theory. The mode can only be guided in the lossy layer if the cut-off condition is satisfied. The guided wave solution in the TiO₂ film is related to the refractive index of the surrounded layer. Figure 10 shows the variation of LMR signal with different n_s under TM polarization if cytop (a fluorine-containing material with refractive index of 1.34) is used as the matching layer. It can be observed that the LMR signal has the minimum R_min value when n_s = 1.34. That means if the thickness of the structure is determined, the detection range can be adjusted by changing the matching layer film. For the structure proposed in this paper, the detection range of the sensor can be regarded as dynamically varying, with n₁ (the RI of the matching layer) as the midpoint. Therefore, when designing the LMR sensor, the appropriate matching layer film should be selected according to the required detection range.

Fig. 9. The electric field distributions at resonance under TM polarization when L₁ = 500 nm, L₂ = 60 nm. (a) The refractive index n_s of the sensing layer is 1.39. (b) The refractive index n_s of the sensing layer is 1.45.

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Fig. 10. Variation of LMR signals for different n_s when L₁ = 500 nm and L₂ = 60 nm under TM polarization, cytop is used as the matching layer.

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Here we provide another structure design idea, so that the resonance dips under TE and TM polarization can be excited simultaneously in the identical structure. In Section 3.3, we show the effect of n_s changes on R_min. We can exploit this property to adjust the detection range by switching the polarization, allowing the sensor to excite deep resonance dips at different n_s values. As shown in Fig. 11(a), when L₁ = 450 nm, L₂ = 40 nm, we can simultaneously excite two resonance dips with TE and TM polarized light, where n_s = 1.39 and R_min is about 0.26. Compared with the structure thickness we recommend in Section 3.1, the thickness of matching layer for TE polarization is increased and the thickness of lossy layer for TM polarization is decreased. The resonance dips become shallower because L₁ and L₂ are not the optimal thickness. In Fig. 11(b), by changing the value of n_s, we can observe that if the value of n_s becomes smaller, the resonance dip is deeper under TE polarization. If the value of n_s increases, the resonance dip is deeper under TM polarization. This means that the sensor can be adapted to different detection ranges by switching the TE/TM polarization under specific structural design. This is the unique advantage of LMR sensors.

Fig. 11. (a) The LMR signal of the proposed LMR sensor when L₁ = 450 nm, L₂ = 40 nm and n_s = 1.39. (b) Variations of the LMR signal of the proposed LMR sensor in the identical structure with different n_s.

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3.5 Structure design of the LMR prism sensor

It is also important to determine the proper film thickness to obtain a deep resonance signal. Mode redistribution is possible by changing the thickness of the matching layer and lossy layer. This enables adjustment of the LMR signal parameters and switching between TE and TM polarization. For the sensor structure proposed in this paper, the role of the matching layer and the lossy layer are different. Attenuated total reflection occurs at the prism/matching layer interface for evanescent wave generation. The thickness L₁ of the matching layer influences the light coupling between the evanescent wave and the lossy mode in the lossy layer, which serves to improve the curve of resonance dip and field distribution. Figure 12 shows the variation of the LMR signal with L₁ under TE and TM polarization. It can be observed that if the L₂ thickness is determined, a proper matching layer thickness L_1c can be found to obtain the strongest resonance signal. If L₁ is less than L_1c, then the FWHM of the resonant dip becomes wider. If L₁ is greater than L_1c, the resonance dip becomes narrower and the resonance signal gradually attenuates with the increase of L₁.

Fig. 12. Variations of the LMR signal of the proposed LMR sensor for different L₁ when n_s = 1.39. (a) L₂ = 40 nm under TE polarization. (b) L₂ = 60 nm under TM polarization.

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The proper thickness of matching layer for the sensor structure shown in Fig. 12 is about 300 nm under TE polarization and around 500 nm under TM polarization. The design basis of the layer thickness can be explained by using the coupling mode theory. Lossy mode is a special mode with a complex effective index and the resonance dip is a result of lossy mode formations in the structure. Due to the presence of evanescent waves, light can penetrate the matching layer and be trapped by the lossy layer under a specific structure. This requires the phase matching condition to be satisfied and eigenvalue equation to be 0. From the TMM equation in Section 2.2, it can be seen that if the thickness and refractive index of the other layers are determined, the mode coupling can be adjusted by changing the incident angle θ, wavelength λ and matching layer. Due to the penetration depth of evanescent waves, the matching layer cannot be too thick. If the matching layer is too thin, the control effect on light coupling is also limited. Hence there is a suitable L₁ range so that the LMR can be strongly excited.

The variation of the electric field distribution with L₁ is shown in Fig. 13. The E_z component of the electric field under TM polarization is discontinuous, so abrupt changes in the electric field at the film interface can be observed in Fig. 13(d-f). When L₁ is close to the optimum thickness L_1c, the energy is concentrated near the lossy layer. The LMR is strongly excited and the R_min of the resonance dip tends to be 0.

Fig. 13. The electric field distribution of the proposed sensor configuration varies with the thickness of the matching layer when n_s = 1.39. (a-c) L₂ = 40 nm under TE polarization. (d-f) L₂ = 60 nm under TM polarization.

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For the proposed LMR sensor in this paper, we recommend that L₁ should be greater than 200 nm. In general, the variation in the L₁ would have little effect on the resonance angle and mainly causes a variation in R_min, for the thickness of the matching layer, does not affect the cut-off condition of the lossy mode. However, if the thickness of the matching layer is too thin, the FWHM of the LMR signal will become very wide and the resonance angle tends to increase. The curve will become irregular and close to the shape shown in Fig. 3. Therefore, the appropriate matching layer thickness is very important for designing a practical LMR sensor.

If the LMR is excited, lossy modes are guided in the TiO₂ film and the energy will be concentrated in the lossy layer. The mode is sustained when the cut-off condition is satisfied, which is mainly related to the thickness of the lossy layer. The effect of the variation in thickness L₂ of the lossy layer on the resonance signal can be observed in Fig. 14. The resonance angle shifts substantially with different L₂, which is due to the change of mode cut-off conditions caused by the variation in phase thickness. In addition, the FWHM of the resonance dip will become wider with the increase of L₂. According to the relationship between the FWHM and L₁ and L₂, it can be concluded that the FWHM of the resonance dip is narrower if the thickness ratio L₁/L₂ is larger. It should be noted that as L₂ decreases, the resonance angle gradually approaches the critical angle. If L₂ < 20 nm, the LMR signal will disappear because of the limitation of the critical angle.

Fig. 14. Variations of the LMR signal of the proposed LMR sensor for different L₂ when n_s = 1.39. (a) L₁ = 300 nm under TE polarization. (b) L₁ = 500 nm under TM polarization.

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As the thickness of the lossy layer increases, an appropriate reduction in the thickness of the matching layer can maintain the maximum transfer of energy to the lossy mode. In the above discussion, we have studied the lower limits of the thicknesses of the matching and lossy layers, from which we can determine the practicable L₁ and L₂ ranges. The variation of R_min with L₁ and L₂ is shown in Fig. 15 as a reference for the structural design of the TiO₂-based LMR sensor proposed in this paper. The red image corresponds to the LMR configuration with the strongest LMR signal. From the data, it can be concluded that the LMR can be converted between TE and TM polarization by varying the thickness of the matching layer and lossy layer. Compared to TE polarization, the value of L₁/L₂ needs to be larger under TM polarization for the same lossy layer thickness to obtain a stronger resonance signal. This is also the reason for the narrower FWHM under TM polarization. The narrower FWHM of the resonance dips can bring a higher FOM value to the sensor, which can be achieved by adjusting the layer thickness. However, it should also be noted that higher L₁/L₂ values bring the resonance angle close to the critical angle, which limits the detection range of the sensor in such a configuration.

Fig. 15. Variation of R_min with the thickness change of matching layer and lossy layer when n_s = 1.39 for (a) under TE polarization and (b) under TM polarization.

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4. Conclusion

In this work, a four-layer LMR sensor model based on the configuration of prism/matching layer/lossy layer/sensing layer is proposed and theoretically investigated. Different from the SPR sensor, the proposed LMR sensor is able to operate under TE and TM polarization. LiF is used as the matching layer, effectively improving the resonance signals under angular interrogation of the TiO₂-based LMR sensor, and making the sensor cost effective. Based on the coupling modes theory and electric field distribution at resonance, the sensing principle of the LMR sensor and the structural parameters affecting the resonance signal is analyzed. The characteristics of the model under angle interrogation are summarized, which are applicable to other LMR sensors with such a configuration. One of the major advantages of the proposed sensor is that the detection range is dynamically adjustable. It was theoretically demonstrated in Section 3.3 and Section 3.4 that the detection range of the LMR sensor can be changed by switching the polarization light or selecting proper matching layer. In addition, there is a trade-off between the detection range and the FOM of the LMR device, which can be improved by adjusting the thickness ratio of the matching and lossy layers. We give a range of structure combinations for LMR sensors based on TiO₂ thin films. In an appropriate combination, the sensor can detect the medium with a refractive index range from 1.32 to 1.47, with a sensitivity range under angular interrogation of 34-148 °/RIU and a maximum value of 192 RIU⁻¹ for FOM under TM polarization. We hope that these theoretical studies will demonstrate the inherent advantages of the LMR prism sensor and provide a reference for researchers to experimentally realize LMR prism sensors in the future.

Funding

Finance Science and Technology Project of Hainan Province (ZDKJ2020009); Natural Science Foundation of Hainan Province (2019RC054).

Disclosures

The authors declare no conflicts of interest.

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

References

1. R. F. Carson and T. E. Batchman, “Coupling and absorption phenomena in semiconductor-clad dielectric optical waveguides,” in Integrated Optical Circuit Engineering V, (International Society for Optics and Photonics, 1988), 18–22.

2. R. F. Carson and T. E. Batchman, “Multimode phenomena in semiconductor-clad dielectric optical waveguide structures,” Appl. Opt. 29(18), 2769–2780 (1990). [CrossRef]

3. M. Marciniak, J. Grzegorzewski, and M. Szustakowski, “Analysis of lossy mode cut-off conditions in planar waveguides with semiconductor guiding layer,” IEE Proc.-J: Optoelectron. 140(4), 247–252 (1993). [CrossRef]

4. I. Del Villar, C. R. Zamarreno, M. Hernaez, F. J. Arregui, and I. R. Matias, “Lossy Mode Resonance Generation With Indium-Tin-Oxide-Coated Optical Fibers for Sensing Applications,” J. Lightwave Technol. 28(1), 111–117 (2010). [CrossRef]

5. I. Del Villar, V. Torres, and M. Beruete, “Experimental demonstration of lossy mode and surface plasmon resonance generation with Kretschmann configuration,” Opt. Lett. 40(20), 4739–4742 (2015). [CrossRef]

6. O. Fuentes, I. Del Villar, J. M. Corres, and I. R. Matias, “Lossy mode resonance sensors based on lateral light incidence in nanocoated planar waveguides,” Sci. Rep. 9(1), 8882 (2019). [CrossRef]

7. Y.-C. Lin and L.-Y. Chen, “Development of a Temperature-Controlled Optical Planar Waveguide Sensor with Lossy Mode Resonance for Refractive Index Measurement,” Photonics 8(6), 199 (2021). [CrossRef]

8. Q. Wang, X. Li, W.-M. Zhao, and S. Jin, “Lossy mode resonance-based fiber optic sensor using layer-by-layer SnO₂ thin film and SnO₂ nanoparticles,” Appl. Surf. Sci. 492, 374–381 (2019). [CrossRef]

9. I. Del Villar, F. J. Arregui, C. R. Zamarreño, J. M. Corres, C. Bariain, J. Goicoechea, C. Elosua, M. Hernaez, P. J. Rivero, A. B. Socorro, A. Urrutia, P. Sanchez, P. Zubiate, D. Lopez, N. De Acha, J. Ascorbe, and I. R. Matias, “Optical sensors based on lossy-mode resonances,” Sens. Actuators, B 240, 174–185 (2017). [CrossRef]

10. F. Xiao, D. Michel, G. Li, A. Xu, and K. Alameh, “Simultaneous Measurement of Refractive Index and Temperature Based on Surface Plasmon Resonance Sensors,” J. Lightwave Technol. 32(21), 4169–4173 (2014). [CrossRef]

11. J. Zhu and N. Li, “Novel high sensitivity SPR sensor based on surface plasmon resonance technology and IMI waveguide structure,” Results Phys. 17, 103049 (2020). [CrossRef]

12. M. Zhao, J. Wang, Y. Zhang, M. Ge, P. Zhang, J. Shen, and C. Li, “Self-referenced refractive index sensor based on double-dips method with bimetal-dielectric and double-groove grating,” Opt. Express 30(5), 8376–8390 (2022). [CrossRef]

13. Y. Wang, J. Yu, Y. F. Mao, J. Chen, S. Wang, H. Z. Chen, Y. Zhang, S. Y. Wang, X. Chen, T. Li, L. Zhou, R. M. Ma, S. Zhu, W. Cai, and J. Zhu, “Stable, high-performance sodium-based plasmonic devices in the near infrared,” Nature 581(7809), 401–405 (2020). [CrossRef]

14. A. B. Socorro, I. Del Villar, J. M. Corres, F. J. Arregui, and I. R. Matias, “Influence of Waist Length in Lossy Mode Resonances Generated With Coated Tapered Single-Mode Optical Fibers,” IEEE Photonics Technol. Lett. 23(21), 1579–1581 (2011). [CrossRef]

15. C. R. Zamarreño, M. Hernáez, I. Del Villar, I. R. Matías, and F. J. Arregui, “Optical fiber pH sensor based on lossy-mode resonances by means of thin polymeric coatings,” Sens. Actuators, B 155(1), 290–297 (2011). [CrossRef]

16. P. Sanchez, C. R. Zamarreno, M. Hernaez, I. D. Villar, I. R. Matias, and F. J. Arregui, “Considerations for Lossy-Mode Resonance-Based Optical Fiber Sensor,” IEEE Sens. J. 13(4), 1167–1171 (2013). [CrossRef]

17. S. P. Usha, S. K. Mishra, and B. D. Gupta, “Fiber optic hydrogen sulfide gas sensors utilizing ZnO thin film/ZnO nanoparticles: A comparison of surface plasmon resonance and lossy mode resonance,” Sens. Actuators, B 218, 196–204 (2015). [CrossRef]

18. A. Ozcariz, M. Dominik, M. Smietana, C. Zamarreño, I. D. Villar, and F. J. Arregui, “Lossy mode resonance optical sensors based on indium-gallium-zinc oxide thin film,” Sens. Actuators, A 290, 20–27 (2019). [CrossRef]

19. F. Chiavaioli, P. Zubiate, I. del Villar, C. R. Zamarreño, A. Giannetti, S. Tombelli, C. Trono, I. R. Matias, F. J. Arregui, and F. Baldini, “Lossy Mode Resonance Fiber-Optic Biosensing Allowing Ultra-Low Detection Limit,” in The European Conference on Lasers and Electro-Optics, (Optical Society of America, 2019), 50019.

20. D. Bohorquez, I. Del Villar, J. M. Corres, and I. R. Matias, “Wavelength and intensity based lossy mode resonance breathing sensor,” Opt. Laser Technol. 140, 107063 (2021). [CrossRef]

21. P. Zubiate, C. R. Zamarreno, I. D. Villar, I. R. Matias, and F. J. Arregui, “Tunable optical fiber pH sensors based on TE and TM Lossy Mode Resonances (LMRs),” Sens. Actuators, B 231, 484–490 (2016). [CrossRef]

22. J. M. Corres, J. Ascorbe, F. J. Arregui, and I. R. Matias, “Tunable electro-optic wavelength filter based on lossy-guided mode resonances,” Opt. Express 21(25), 31668–31677 (2013). [CrossRef]

23. D. Grosso, G. J. d, A. Soler-Illia, E. L. Crepaldi, F. Cagnol, C. Sinturel, A. Bourgeois, A. Brunet-Bruneau, H. Amenitsch, P. A. Albouy, and C. Sanchez, “Highly porous TiO₂ anatase optical thin films with cubic mesostructure stabilized at 700 C,” Chem. Mater. 15(24), 4562–4570 (2003). [CrossRef]

24. T. Tolenis, L. Grineviciute, L. Mažule, A. Selskis, and R. Drazdys, “Low-stress phase plates produced by serial bideposition of TiO₂thin films,” J. Nanophotonics 10(3), 036003 (2016). [CrossRef]

25. M. Shakeel, F. Jabeen, S. Shabbir, M. S. Asghar, M. S. Khan, and A. S. Chaudhry, “Toxicity of Nano-Titanium Dioxide (TiO₂-NP) Through Various Routes of Exposure: a Review,” Biol. Trace Elem. Res. 172(1), 1–36 (2016). [CrossRef]

26. Z. N. Kayani, M. Saleem, S. Riaz, S. Naseem, and F. Saleemi, “Structure and Optical Properties of TiO₂ Thin Films Prepared by a Sol-Gel Processing,” Zeitschrift für Naturforschung A 74(7), 635–642 (2019). [CrossRef]

27. Y. Liang, S. Sun, T. Deng, H. Ding, W. Chen, and Y. Chen, “The Preparation of TiO₍₂₎ Film by the Sol-Gel Method and Evaluation of Its Self-Cleaning Property,” Materials 11(3), 450 (2018). [CrossRef]

28. S. H. Nam, S. J. Cho, C. K. Jung, J. H. Boo, J. Šícha, D. Heřman, J. Musil, and J. Vlček, “Comparison of hydrophilic properties of TiO₂ thin films prepared by sol–gel method and reactive magnetron sputtering system,” Thin Solid Films 519(20), 6944–6950 (2011). [CrossRef]

29. P. Evans, T. English, D. Hammond, M. E. Pemble, and D. W. Sheel, “The role of SiO₂ barrier layers in determining the structure and photocatalytic activity of TiO₂ films deposited on stainless steel,” Appl. Catal., A 321(2), 140–146 (2007). [CrossRef]

30. Y. Masuda, Y. Jinbo, and K. Koumoto, “Room Temperature CVD of TiO₂ Thin Films and Their Electronic Properties,” Sci. Adv. Mater. 1(2), 138–143 (2009). [CrossRef]

31. B. Y. Fugare and B. J. Lokhande, “The influence of concentration on the morphology of TiO₂ thin films prepared by spray pyrolysis for electrochemical study,” Appl. Phys. A 123(6), 394 (2017). [CrossRef]

32. A. Kozlovskiy, I. Shlimas, K. Dukenbayev, and M. Zdorovets, “Structure and corrosion properties of thin TiO₂ films obtained by magnetron sputtering,” Vacuum 164, 224–232 (2019). [CrossRef]

33. J. Singh, S. A. Khan, J. Shah, R. K. Kotnala, and S. Mohapatra, “Nanostructured TiO₂ thin films prepared by RF magnetron sputtering for photocatalytic applications,” Appl. Surf. Sci. 422, 953–961 (2017). [CrossRef]

34. V. S. S. Sobrinho, J. Q. M. Neto, L. L. F. Lima, I. A. Souza, M. S. Libório, J. C. A. Queiroz, R. R. M. Sousa, E. O. Almeida, M. C. Feitor, and T. H. C. Costa, “Optical-Electrical Properties and Thickness Analysis of TiO₂ Thin Films Obtained by Magnetron Sputtering,” Braz. J. Phys. 50(6), 771–779 (2020). [CrossRef]

35. M. Hernáez, I. Del Villar, C. R. Zamarreño, F. J. Arregui, and I. R. Matias, “Optical fiber refractometers based on lossy mode resonances supported by TiO₂ coatings,” Appl. Opt. 49(20), 3980–3985 (2010). [CrossRef]

36. M. Hernaez, C. R. Zamarreño, I. Del Villar, I. R. Matias, and F. J. Arregui, “Lossy mode resonances supported by TiO₂ -coated optical fibers,” Procedia Eng. 5, 1099–1102 (2010). [CrossRef]

37. C. R. Zamarreño, M. Hernaez, P. Sanchez, I. Del Villar, I. R. Matias, and F. J. Arregui, “Optical Fiber Humidity Sensor Based on Lossy Mode Resonances Supported by TiO₂/PSS Coatings,” Procedia Eng. 25, 1385–1388 (2011). [CrossRef]

38. I. Del Villar, M. Hernaez, C. R. Zamarreño, P. Sánchez, C. Fernández-Valdivielso, F. J. Arregui, and I. R. Matias, “Design rules for lossy mode resonance based sensors,” Appl. Opt. 51(19), 4298–4307 (2012). [CrossRef]

39. N. Paliwal and J. John, “Theoretical modeling of lossy mode resonance based refractive index sensors with ITO/TiO(2) bilayers,” Appl. Opt. 53(15), 3241–3246 (2014). [CrossRef]

40. S. Zeng, S. Hu, J. Xia, T. Anderson, X.-Q. Dinh, X.-M. Meng, P. Coquet, and K.-T. Yong, “Graphene–MoS₂ hybrid nanostructures enhanced surface plasmon resonance biosensors,” Sens. Actuators, B 207, 801–810 (2015). [CrossRef]

41. R. M. Montereali, G. Baldacchini, S. Martelli, and L. S. Do Carmo, “LiF films: production and characterization,” Thin Solid Films 196(1), 75–83 (1991). [CrossRef]

42. A. Perea, J. Gonzalo, C. N. Afonso, S. Martelli, and R. Montereali, “On the growth of LiF films by Pulsed Laser Deposition,” Appl. Surf. Sci. 138-139, 533–537 (1999). [CrossRef]

43. H. H. Li, “Refractive index of alkali halides and its wavelength and temperature derivatives,” J. Phys. Chem. Ref. Data 5(2), 329–528 (1976). [CrossRef]

44. N. Paliwal and J. John, “Theoretical modeling and investigations of AZO coated LMR based fiber optic tapered tip sensor utilizing an additional TiO₂ layer for sensitivity enhancement,” Sens. Actuators, B 238, 1–8 (2017). [CrossRef]

45. N. Paliwal and J. John, “Lossy Mode Resonance (LMR) Based Fiber Optic Sensors: A Review,” IEEE Sens. J. 15(10), 5361–5371 (2015). [CrossRef]

46. A. Shalabney and I. Abdulhalim, “Electromagnetic fields distribution in multilayer thin film structures and the origin of sensitivity enhancement in surface plasmon resonance sensors,” Sens. Actuators, A 159(1), 24–32 (2010). [CrossRef]

47. P. Zhang, J. Wang, G. Chen, J. Shen, C. Li, and T. Tang, “A High-Sensitivity SPR Sensor with Bimetal/Silicon/Two-Dimensional Material Structure: A Theoretical Analysis,” Photonics 8(7), 270 (2021). [CrossRef]

48. D. T. Nurrohman and N.-F. Chiu, “Surface Plasmon Resonance Biosensor Performance Analysis on 2D Material Based on Graphene and Transition Metal Dichalcogenides,” ECS J. Solid State Sci. Technol. 9(11), 115023 (2020). [CrossRef]

49. D. Kaur, V. K. Sharma, and A. Kapoor, “Effect of prism index on sensitivity of lossy mode resonance sensors operating in visible region,” J. Nanophotonics 9(1), 093042 (2015). [CrossRef]

50. R. Saini, A. Kumar, G. Bhatt, A. Kapoor, A. Paliwal, M. Tomar, and V. Gupta, “Lossy Mode Resonance-Based Refractive Index Sensor for Sucrose Concentration Measurement,” IEEE Sens. J. 20(3), 1217–1222 (2020). [CrossRef]

51. M. Pandaram, S. Santhanakumar, R. Veeran, R. K. Balasundaram, R. Jha, and Z. Jaroszewicz, “Platinum Layers Sandwiched Between Black Phosphorous and Graphene for Enhanced SPR Sensor Performance,” Plasmonics 17(1), 213–222 (2022). [CrossRef]

52. L. Chen, J. Li, J. Liu, and H. Yang, “A Ag-Au bimetallic nanograting surface plasmon resonance sensor based on a prism structure,” Opt. Commun. 461, 125105 (2020). [CrossRef]

Wave-length (nm)	Structure	Maximum sensitivity (deg/RIU)	Maximum FOM (RIU⁻¹)	Detection range (RIU)	Ref.
632.8	BK7/Ag/Au	133.8	47.2	-	[47]
632.8	BK7/Au/Ag/Si/MXene	274	36.88	-	[47]
633	BK7/Au	33	14.65	1.30-1.38	[48]
632.8	BK7/Au/MoS₂	174.15	27.86	1.30-1.38	[48]
633	BK7/Ag/BP/Pt/graphene	412	71.88	1.33-1.35	[51]
694.3	ZF6/Ag/Au/Au Grating	342	125.3	1.335-1.373	[52]
1190	LaSF35/MgF₂ Grating/Na	690	329.4	1.33-1.347	[12]
	Grating/Na/Au/Au
	Grating/ZnS Grating
633	BK7/LiF/TiO₂	148	192	1.32-1.47	Our work

Theoretical modeling and investigations of lossy mode resonance prism sensor based on TiO₂ film

Abstract

1. Introduction