Lossy Mode Resonance Sensors Based on Planar Waveguides: Theoretical and Experimental Comparison

Lossy mode resonance (LMR) has garnered significant attention in sensor applications. LMR was primarily explored in fiber-based systems, however, there has been a recent upsurge in its application within planar waveguides. This article compares the LMR phenomenon in planar waveguides with the most employed coatings in the field, specifically SnO2, TiO2, and ITO. Additionally, the experimental findings are compared with simulations conducted using the finite element method (FEM) within the COMSOL Multiphysics environment. The novelty of this research lies in the integration of both experimental results and theoretical calculations, utilizing strong FEM simulation tools, in a single study.

LMR presents several advantages of other fiber and waveguide-based sensing techniques.Unlike widely used methods such as surface plasmon resonance (SPR), LMR has the ability to generate multiple resonances.Moreover, LMR can be observed using both TE and TM polarized light, whereas SPR is limited to TM polarization [11].Furthermore, LMR proves to be a more versatile approach as it can be observed with various cladding materials, including polymer [5], semiconductor [12] and dielectric [13] materials.This characteristic offers flexibility and cost-effectiveness in the fabrication of sensing devices.
More recently, generation of LMR through lateral light incidence in nanocoated planar waveguides has been demonstrated [14].There are several advantages in using a planar structure as opposed to an optical fiber.Firstly, planar waveguide offers a more robust platform than optical fibers, eliminating the need for splices and making the setup easier to handle.Another important benefit of the planar waveguide is its ability to operate in a wide spectrum with either the TE or the TM resonance separately.Moreover, thin films can be deposited on both sides, enabling the creation of a two-parameter sensor.Lastly, the diverse range of available coverslip geometries enables seamless integration of LMR sensors of this configuration into more complex systems [11].Considering its simplicity, robustness, and other advantages, the transfer of planar waveguide technology to the industry appears more straightforward than its fiber optic counterpart.
Subsequent to the demonstration of LMR generation in planar waveguides [14], this scientific discipline has undergone significant advancement.Over the recent years, applications such as measuring voltage [15], monitoring breath [16], biosensing [17], gas detection [18], and temperature measurements [19] have been conducted utilizing the LMR phenomenon within planar waveguides.Nevertheless, it is crucial to underscore that the existing literature in this field predominantly focuses on engineering aspects, resulting in a notable lack of theoretical background and comprehension of the fundamental processes intrinsic to the LMR phenomenon.
This paper conducts a comparison of the LMR phenomenon in planar waveguides with the most common coatings used in the LMR field, including SnO 2 [20], TiO 2 [21], and ITO [22].Furthermore, the experimental results obtained will be compared with simulations performed using the finite element method (FEM) in COMSOL Multiphysics.The solid novelty of this research lies in the integration of both experimental results and theoretical calculations, utilizing strong FEM simulation tools, in a single study.

A. Sample Fabrication
The deposition of SnO 2 , TiO 2 , and ITO coatings on microscope coverslips (12 × 12 × 0.15 mm) was carried out using the Sidrabe G500M DC magnetron sputtering system.For the SnO 2 coating, a reactive sputtering process was employed in an Ar/O 2 plasma with a flow ratio of 1:1.The process utilized a Sn 100 × 200 × 9 mm target and operated at a pressure of 4.5 mTorr and a power of 200 W. Similarly, the TiO 2 coating was produced through a reactive sputtering process in an Ar/O 2 plasma with a flow ratio of 10:1 due to the intensive oxidation of the target during the process.The TiO 2 coating process employed a Ti 100 × 200 × 9 mm target at a pressure of 4.5 mTorr and a power of 500 W. The ITO coating process employed an ITO (In 2 O/SnO 2 with a weight ratio 9:1) 100 × 200 × 9 mm target at a pressure of 5 mTorr and a power of 200 W. Compared to TiO 2 and SnO 2 deposition, ITO deposition involved a non-reactive sputtering process that exclusively used Ar plasma.Prior to deposition, the microscope coverslips underwent a cleaning process using acetone and isopropanol.To achieve selective area deposition, the coverslip was masked with Kapton tape, resulting in the fabrication of the device illustrated in Fig. 1.

B. Sample Characterization
Spectral ellipsometry was employed, using the Woollam RC2-XL equipment and CompleteEASE software, to assess the optical properties of both the microscope coverslip and the deposited thin films.The measurements were conducted within the visible and near-infrared ranges, covering angles of incidence from 45°to 80°.The dispersion of the microscope coverslip was characterized using the Cauchy equation [23]: where λ represents the wavelength in µm, while A and B are coefficients obtained through fitting.Since the deposited thin films are absorbing layers, the optical properties were determined using the Lorentz oscillator model.The permittivities of SnO 2 , TiO 2 , and ITO were calculated using the equation provided in the CompleteEASE software manual: where all parameters except photon energy E are fitted parameters.
To investigate the LMR phenomenon in fabricated samples, a specific experimental setup was utilized (see Fig. 1).The light source used was an Ocean Insight DH-2000, which was coupled into an optical fiber (Thorlabs M29L) and directed into the rectangular edge of the sample, which had dimensions of 15 × 0.15 mm, transforming it into a planar waveguide with a thickness of 150 μm.The outgoing light from the sample was collected using another optical fiber (Thorlabs M29L) and then subjected to analysis using an Ocean Optics HR4000 spectrometer.To establish a reference spectrum, an initial measurement was conducted through the uncoated sector of the sample.This reference spectrum served as a baseline for subsequent measurements.A linear polarizer was employed between the sample and the input fiber to investigate LMR shifts related to various light polarizations.Additionally, LMR shifts induced by solvents by dispensing it on the covered part of the sample were investigated.

C. Sample Simulations
The behavior of the designed device was simulated using COMSOL Multiphysics based on FEM.Initially, a twodimensional cross-sectional geometry was defined to analyze electromagnetic distribution of the guided modes (see Fig. 2).This simplified approach characterizes the behavior of the guided mode in an infinite homogeneous planar waveguide, disregarding certain parameters that are relevant at this stage.Next, materials were defined for five different environments, Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.including glass coverslip, SnO 2 TiO 2 , ITO, and the sensing media.The optical parameters of these materials were determined experimentally through spectral ellipsometry.To establish an infinite planar waveguide, materials were assigned not only within domains but also at boundaries.The "Electromagnetic Waves, Frequency Domain" physics module was employed to solve the posed problems.The geometry was meshed with physics-controlled element size less than the coating thickness in its domain, while other domains were meshed with element sizes comparable to the wavelength.The grid comprised 88000 triangular elements with maximum element size of 100 nm, covering an overall area of 4•10 -8 m 2 , with the majority of elements situated in the thin film structure.A parametric sweep was conducted to explore various coating thicknesses and materials.To analyze the distribution of the electromagnetic field in the planar waveguide, mode analysis was performed, allowing for the evaluation of the effective refractive index n ef f .This parameter was subsequently utilized to simulate transmittance spectra using equation [24]: where T represents the transmittance, λ denotes the wavelength, and L corresponds to the length of the sensing region of 1 cm.

III. RESULTS AND DISCUSSIONS
Fig. 3 displays dispersion curves obtained from ellipsometry measurements for both the glass coverslip and the thin films that were deposited.These curves have been generated using the fitted parameters extracted from ( 1) and ( 2), which are outlined in Table I.The curves depicted in Fig. 3 and the parameters fitted from Table I are then utilized to characterize the optical properties of materials in simulations conducted through the finite element method.
The most effective method for comparing simulations and experimental outcomes involves employing color plots that cover a range of cladding thicknesses.This strategy will offer a comprehensive overview of whether the theoretical model effectively explains the physics of LMR phenomenon in fabricated devices.Theoretical calculations of extinction ratios corresponding to various TiO 2 thicknesses are presented as a function of wavelength in Fig. 4, while the experimentally   obtained LMRs are displayed in Fig. 5.A comparison was made between the theoretical and experimental results specifically for TE-polarized light.
A similar assessment between theoretical predictions and experimental data was conducted for SnO 2 (Figs. 6 and 7) and ITO coatings (Figs. 8 and 9).For every cladding material a specific thickness was chosen as an example in order to display the spectra across different polarizations and enable a direct comparison with theoretical predictions.These example thicknesses for TiO 2 , SnO 2 , and ITO are indicated in Figs. 5, 7, and Fig. 9, respectively.We chose these thicknesses as an example because they allow us to observe the largest number of LMRs simultaneously, making it easier to compare with theoretical calculations.Figs. 10, 11, and Fig. 12 depict the transmittance spectra that have been theoretically calculated and experimentally measured for TiO 2 , SnO 2 and ITO coatings at selected thicknesses, respectively.The resonance wavelength of the theoretical and experimental spectra exhibits a minor inconsistency, which can be attributed to slight variations in coating thickness between the experimental and theoretical outcomes.Even a variance of a few nanometers in the film thickness can result in a noticeable divergence in the  LMR wavelength.This is further supported by the observation that lower order LMRs exhibit a greater degree of sensitivity to changes in coating thickness, resulting in a more pronounced resonance wavelength divergence compared to higher order LMRs.It is worth observing that there are variations in the shapes of the LMR peaks between theoretical and experimental spectra, which can be attributed to the inhomogeneity of the deposited coating.Nonetheless, the differences in FWHM are relatively minor.It is important to note that in devices coated with TiO 2 and SnO 2 , the LMR effect became less noticeable with increasing wavelength.This effect was so significant that some peaks simply ceased to be observed at wavelengths over 600 nm, although theoretical calculations predicted their presence.In Fig. 5, within the wavelength range of approximately 700 nm, for a TiO 2 coating with a thickness of 420 nm, theoretical calculations indicated the possibility of an additional peak, but this peak was not observed in the actual experiments.This Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.behavior aligns with what was observed in [14] study for similar coverslips.
In the case of ITO, the LMR effect did not disappear with increasing wavelength.In [19] was shown that increased O 2 flow during the reactive magnetron sputtering results in increased surface roughness and the formation of crystalline grains.This phenomenon provides an explanation of the LMR behavior observed in coatings produced through both reactive and nonreactive magnetron sputtering.The weakening of the LMR effect at longer wavelengths in TiO 2 and SnO 2 coatings can be attributed to the creation of crystalline grains whose sizes  are comparable to the operational wavelength.An alternative explanation for the observed phenomenon may be associated with the dispersion of the extinction coefficient.It is widely known that having a non-zero extinction coefficient is a fundamental requirement for observing the LMR phenomenon [4].As depicted in Fig. 3, the extinction coefficient shows a decreasing trend with increasing wavelength for TiO 2 and SnO 2 coatings.In contrast, when considering ITO coating, extinction coefficient rises at wavelengths above 500 nm, leading to more pronounced LMRs at longer wavelengths.
Sensing performance assessment, involving both theoretical simulations and experimental measurements (Figs. 13 and 14, respectively), was exclusively conducted for the ITO coated sample.This was explained by the fact that the first order LMR shift could not be observed due to the disappearance of the LMR effect at longer wavelengths described above for TiO 2 and SnO 2 coatings.Figs. 13 and 14 clearly illustrate that the LMR wavelengths and sensitivities obtained from both theoretical simulations and experimental data closely align with each other.Small variations in LMR wavelengths can be attributed  to the potential inhomogeneity of the applied coating and minor discrepancies of a few nanometers in thickness between the theoretical and actual measurements.This fact is further supported by ellipsometry mapping, wherein the thickness of the ITO coating on one of the fabricated samples was assessed at different points to determine the approximate thickness variation in the samples.Results from ellipsometry mapping revealed variations in thickness of around 2% in the designated area.As depicted in Fig. 15, subsequent simulations illustrated that considering this 2% thickness variability situates the experimental LMR peaks between the theoretical LMR peaks in the boundary cases.
The spectra given in Figs. 13 and 14 can be utilized to assess the sensing capabilities of the fabricated device.The relationship between LMR wavelength and the refractive index of the surrounding environment is depicted in Fig. 16.The sensitivity characteristics obtained experimentally and calculated theoretically have some differences.The sensitivity characteristics obtained experimentally and calculated theoretically have some differences: for TM polarized light experimentally obtained sensitivity is 98.5% of calculated theoretically, for TE polarized light experimentally obtained sensitivity is 73.6% of calculated theoretically.The disparities, again, can be attributed to a slight variation of a few nanometers in thickness between the theoretical and experimental values.The shape of the LMR peak and its associated sensitivity can be employed to compute the Q-factor [9] for an ITO coated device and subsequently compare it with theoretical values: where S represents the sensitivity, and F W HM LM R is the full width at half minimum of the LMR peak.These calculated Q-factor values are summarized in Table II and calculated from spectra given in Figs. 13 and 14.The results clearly demonstrate that there is a discrepancy between theoretical and experimental results, which is explained by the wider FWHM expected due to the fact that this parameter is very sensitive to the quality and homogeneity of thin film.It is worth noting that both theoretical and experimental data indicate a superior Q-factor for TM-polarized light in comparison to TE-polarized light, corroborating findings from prior literature [25].The Q-factor and sensitivity values achieved are lower compared to those obtained with silica optical fibers using the same coating [22], as can be straightforwardly accounted for by the higher refractive index of the planar waveguide, as detailed in reference [26].

IV. CONCLUSION
In this study, the LMR effect was studied on planar waveguides with TiO 2 , SnO 2 , and ITO coatings.Comparing the experimental data obtained with each other, a noteworthy finding emerged: the ITO coating demonstrated the best suitability for LMR-based sensor applications.This is likely attributable to the deposition technique employed, wherein ITO was deposited using non-reactive magnetron sputtering, while the other oxides underwent deposition via a reactive process, leading to the formation of crystalline grains that exhibited limited interaction with long-wavelength light.An alternative explanation for this observation may be attributed to the differences in the dispersion of extinction coefficients for ITO and other oxide coatings.
Through a comprehensive comparison between theoretical simulations and experimental observations, it was deduced that the finite element method's mode analysis effectively captures the underlying physics of the LMR phenomenon within planar waveguides.The theoretical color plots demonstrated a sufficient level of agreement with the experimentally derived results across the entire range of coating thicknesses.However, it is important to note certain distinctions in Q-factors obtained theoretically and experimentally, which can be attributed to inhomogeneity of thin films and the possibility of less precise theoretical input data regarding the optical properties of the analyzed medium and coating thickness.
The sensitivities and Q-factors obtained do not reach a level where they can rivel fiber-based LMR sensors.However, it is important to note that this study did not aim to achieve that goal, Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.
primarily because planar waveguides come with their inherent drawbacks, such as significant light losses and a high refractive index.It is worth emprasizing that despite these limitations, planar waveguides offer unique advantages over optical fibers, including ease of handling, the ability to deposit thin films on both sides, and straightforward integration into more complex systems.

Fig. 2 .
Fig. 2. Two-dimensional cross-sectional geometry of the simulated problem and an example of the resulting electromagnetic distribution in the waveguide.

TABLE I MATERIALS
FITTED PARAMETERS

TABLE II THEORETICAL
AND EXPERIMENTAL Q-FACTOR CALCULATIONS