Biosensing applications of all-dielectric SiO<sub>2</sub>-PDMS meta-stadium grating nanocombs

M. Ghasemi; M. Ghasemi; N. Roostaei; F. Sohrabi; S. M. Hamidi; S. M. Hamidi; P. K. Choudhury; P. K. Choudhury

doi:10.1364/OME.389361

1. Introduction

In the context of metal-dielectric or dielectric-dielectric interface(s), the existence of surface waves (SWs) depends on the complexity of the physical and material properties of the patterned mediums grown over a dielectric platform [1–3]. Among the recognized SWs, Tamm SW relates to the situation wherein at least one of the two partnering mediums is periodically nonhomogeneous normal to the interface guiding the SWs. Furthermore, both the partnering mediums are isotropic dielectrics [4,5]. The existence of Tamm waves has been verified experimentally for natural and artificially designed periodic partnering mediums [6–8].

Photonic crystals (PCs) have been proved to be prudent for localization and confinement of light [9–12]. Further, in layered structures, the existence of SWs corresponds to the presence of at least one negative refractive index (RI) partnering medium [13]. As such, the combination of PC and positive RI medium remains essential to alter the negative permittivity for the SW polarization [14–16]. The negative index mediums can be engineered to provide the on-demand kinds of spectral characteristics, which may be harnessed for varieties of technology oriented applications. Many such forms of complex-structured metadevices have been reported in the literature for operations in different spectral frequencies [17–20].

The irradiation of sub-wavelength sized periodic metasurface [21–24] by the incident light within the band-gap would be analogous to the crystalline atomic lattice [25,26]. For instance, the defects in solid crystals result in the localization of SWs in a similar way as in the case of artificial defects in PCs [27,28]. As such, crystal can be assumed as a kind of prefect optical guide in which its confinement property forms around the sharp bends and cavities of the wavelength-scale dimensions.

In the present work, we aim at investigating the effect of Tamm SWs exploiting the method of spectroscopic ellipsometry at the micron-scale roughness. For this purpose, we consider the homogenous and non-homogenous partnering materials to be polydimethylsiloxane (PDMS) and engineered symmetric meta-stadium silica (SiO₂) grating nanocombs, respectively. The biological and chemical affinity of PDMS and its inherent properties of chemical stability, optical transparency (from the UV to IR), mechanical compliance, good permeability to gasses, thermal stability, and bio-compatibility allow the use of PDMS as the isotropic partnering material [29,30]. We also use SiO₂ owing to the low cost, long-term mechanical stability and its strong adhesion with the PDMS [31,32]. Apart from these, researchers have reported the bio-compatibility of SiO₂ metasurface in sensing applications [33–36].

It is noteworthy that the SiO₂ metasurface in the form of stadium-nanocomb is analogous to PC, and plays the role of exhibiting forbidden electron state on a crystal surface [37]. Due to the possible existence of Tamm state on immensely flat surface with the roughness of an atomic scale, the experimental verification of Tamm SWs becomes extremely cumbersome [38]. While investigating the effect of Tamm SWs, here we exploit the outcome of the results of using the aqueous solutions of glucose having different concentrations. In the experiment, the solutions were sieved to the fabricated silica-based meta-stadium grating nanocombs.

Within the context, glucose monitoring has been highly demanding in medical diagnostics, particularly for the diabetic patients. The involved processes may be invasive or noninvasive. The optical route to measure the level of glucose in the human body essentially exploits varieties of spectroscopic techniques that rely on the alterations of light intensity when a light beam of certain wavelength impinges on skin tissue [39,40]. The study of the relevant scattering characteristics would yield the glucose content [41]. Some other forms of non-invasive optical sensors for glucose monitoring exploit the interference techniques [42]. The present work is, however, aimed to demonstrate the usefulness of the proposed PDMS meta-stadium grating nanocomb structure in the monitoring of glucose concentration exploiting the method of ellipsometry.

In the following sections, we will discuss the patterning process of silica over the PDMS substrate, theory and experimental technique of the applied spectroscopic ellipsometry, and the obtained results in respect of the sensitivity of the proposed structure.

2. Fabrication process

Figure 1 demonstrates the fabrication steps followed for the micro-projection imprinting of grating nanocombs on silicon (Si) mold. In the imprinting lithography process [43,44], we use the Si mold having the dimensional features, as shown in Fig. 2(b), as the template. Figure 2(b) exhibits the schematic of the array of nanocombs in the pool [as shown in Fig. 1(a)].

Fig. 1. Fabrication process flow incorporating (a) the design of Si-mold, (b) treating the mold with cured PDMS, (c) baking, imprinting and separation processes, and finally (d) ending up with the silica coating.

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Fig. 2. (a) Dimensional features of the unit cell of meta-stadium nanocomb, and (b) front-view of the unit-cell array of Si-mold.

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The PDMS, SYLGARD 184 Silicone Elastomer Kit, has two parts including the main part and the curing agent. These two components were mixed in a ratio of 10:1. After being homogenized using a mixer, the mixture was poured on the mold [Fig. 1(a)], and degassed using the desiccator over several minutes. When all bubbles were eliminated, the mold including the uncured PDMS was put over the heater [Fig. 1(b)]. The upright posture of PDMS nanocombs took place after several steps of baking (the first step: 30 mins at 50 °C, the second step: 15 mins at 70 °C, and the last step: 15 mins at 100 °C). Following the baking process, the layer of PDMS nanocombs [Fig. 1(c)] was separated from the mold after cooling down the whole structure for over 24 hours. The final phase of fabricating the 2D grating silica-PDMS nanocombs involved the sputtering of 100 nm thick SiO₂-layer on the top surface of PDMS nanocombs [Fig. 1(d)].

Figure 3 exhibits the scanning electron micrograph (SEM) of the developed meta-stadium grating nanocomb structure; Fig. 3(a) shows the image itself, whereas Fig. 3(b) exhibits the magnified image of the same, in order to mention the dimensional features more explicitly. As shown in Fig. 3(b), the distance between the two neighboring straight sides and the arch edges of meta-stadium nanocombs is 139 nm and 417 nm, respectively. Apart from these, the width of each comb is 2 µm from either side, and the height of the same is 5 µm [as shown in Fig. 2(a)].

Fig. 3. (a) SEM of the grating PDMS nanocombs, and (b) a magnified image showing the dimensional features.

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3. Spectroscopic ellipsometry measurements

Spectroscopic ellipsometry remains a prudent technique to characterize the optical properties of varieties of mediums with high precision and low latency. It involves the polarization (${s}$ and ${p}$) of obliquely incident light (on a medium) for both the reflected and transmitted radiations by the medium. In the schematic of Fig. 4(a), we assume that the incident light is initially polarized into the ${s}$- and ${p}$-waves using the Glan-Taylor calcite polarizer [Fig. 4(b)]; the orthogonal combination of both waves is irradiated on a sample with specific values of RI ${n}$ and extinction coefficient ${k}$. Assuming the ellipsometry parameters ${\Psi }$ and ${\Delta }$ to be the amplitude ratio and variation in polarization states, respectively, of the ${s}$- and ${p}$-polarized waves [45], the variables ${\Psi }$, ${\Delta }$, ${{E}_{{is}}}$, ${{E}_{{ip}}}$, ${{E}_{{rs}}}$ and ${{E}_{{rp}}}$ can be defined in terms of a unique variable ${\Lambda }$ by the equations

(1)$${\Lambda }({\omega } )= {\tan} [{{\varPsi }({\omega } )} ]{\exp} [{{i}{\Delta }({\omega } )} ]$$

(2)$$\textrm{and } \quad {\Lambda }({\omega } )\equiv \frac{{{{r}_{{p}}}({\omega } )}}{{{{r}_{{s}}}({\omega } )}} \equiv \frac{{{{E}_{{rp}}}({\omega } ).{{E}_{{is}}}({\omega } )}}{{{{E}_{{ip}}}({\omega } ).\; {{E}_{{rs}}}({\omega } )}}$$

Here ${E}$ represents in the electric field, ${i}$, ${r}$ in the subscript indicate the cases of incident and reflected radiations, respectively, and the subscripts ${s}$, ${p}$ correspond to the respective polarization states. Also, ${\omega }$ is the angular frequency of wave in unbounded medium.

Fig. 4. (a) Schematic representation of ellipsometry, and (b) beam polarization using the Glan-Taylor calcite polarizer.

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Equations (1) and (2) determine the roles of incident and reflected electric fields in evaluating the ratio of ${s}$- and ${p}$-polarized waves. The reflectivity ${r}({\omega } )$ at the interface [46,47] of sample and the other medium (e.g., here it is considered as vacuum) can be expressed in terms of ${n}({\omega } )$ and ${k}({\omega } )$ as

(3)$${r}({\omega } )= \frac{{{n}({\omega } )- {1} + {ik}({\omega } )}}{{{n}({\omega } )+ {1} + {ik}({\omega } )}}$$

Equations (2) and (3) manifest the continuation of reflectivity from the real axis into the rectifiable path of the disk-shaped boundary in the upper-half of the complex angular frequency ${\omega }$-plane (holomorphicity domain) in the situation where the sample being dielectric [48,49]. By assuming the linearly polarized light and applying the symmetry relation on the measured complex reflectivity, the conjugation conversion is written as

(4)$${r}({ - {\omega }} )= {[{{r}({\omega } )} ]^\ast }$$

In the case of circular or elliptical polarization, the reflectivity measurements remind the realty of the combination of the ${s}$- and ${p}$-polarized lights, which would affect the symmetry of complex reflectivity [50]. As such, the reflectance ${R}({\omega } )$ is generally the square of the modulus of the amplitude of complex reflectivity, i.e.,

(5)$${R}({\omega } )= {|{{r}({\omega } )} |^{2}} = {r}({\omega } ).{r}{({\omega } )^\ast }$$

Rewriting Eq. (5) in polar coordinates, we get Eq. (6), which is a logarithmic function; the divergence of its integration at infinite frequency never allows deriving the dispersion relation for complex reflectivity [51,52].

(6)$${i\theta } = {\ln}\,{r}({\omega } )- {\ln} |{{r}({\omega } )} |$$

Thus, the existence of zeros for ${\Lambda }({\omega } )$ is not predicated for finite values of ${\omega }$ in the upper-half of the complex plane or on the real axis. Therefore, a fundamental key function is required to enhance the zero approaching to infinity, and for the applicability of Cuachy-theorem. Such a function (say ${\Upsilon }$) might solve the problem by expressing it as [53]

(7)$${\Upsilon }({{\omega^{\prime}}} )= \frac{{|{{\ln}\,{r}({{\omega^{\prime}}} )} |}}{{{{{\omega ^{\prime}}}^{2}} - {{\omega }^{2}}}}$$

where ${\omega ^{\prime}}$ is real even when ${\omega }$ is infinitely extended. The solution satisfying the general conditions of square integrability, after being substituted in the dispersion relation for phase, could be given as [54]

(8)$${\theta }({\omega } )={-} \frac{{{2}{\omega }}}{{\pi }}{P}\mathop \smallint \nolimits_{{0}}^\infty {\Upsilon }({{\omega^{\prime}}} ){d\omega ^{\prime}}$$

Now, the dispersion relation to express the complex amplitude of reflectivity can be stated as the subtraction of two amplitudes at different frequencies, i.e.,

(9)$${\ln} |{{r}({{{\omega}_{{1}}}} )} |- {\ln} |{r}({{\omega }_{{2}}}) |= \frac{{2}}{{\pi }}{P}\mathop \smallint \nolimits_{{0}}^\infty {\omega ^{\prime}\theta }({{\omega^{\prime}}} )\left[ {\frac{{1}}{{{{{\omega^{\prime}}}^{2}} - {\omega }_{{1}}^{2}}} - \frac{{1}}{{{{{\omega^{\prime}}}^{2}} - {\omega }_{{2}}^{2}}}} \right] {d}{\omega} ^{\prime}$$

The problem of divergence of each of the expressions in the right-hand side of Eq. (9) still remains. Despite the divergence, the whole expression under subtraction is convergent [54].

The complete retrieval of phase values through the Kramer-Kronig relation [Eq. (9)] may be feasible after considering some facts during the real experiment. First, the reflection recording may be required to perform through the transparent window [55]. Second, the obtained reflection is reasonable when the target sample is opaque medium/liquids. Here, the broad wavelength range is in contradiction with the complexity imposed by the ellipsometer (a simple reflectometer, however, would satisfy this range), and also, the data extraction within the limited spectral range diminishes the efficacy of data inversion while applying the Kramer-Kronig relation. Equation (10) corresponds to the solution, presented by Modine et al. [56], to overcome this problem. It defines the upper limit (${{\omega }_{{m}}})$ of the reflectance data and assumes the extrapolation of data even at zero frequency.

(10)$${\Delta }{\theta }({\omega } )={-} \frac{{\omega }}{{\pi }}{P}\mathop \smallint \nolimits_{{{\omega }_{{m}}}}^\infty {\Upsilon }({{\omega^{\prime}}} ){d\omega ^{\prime}}$$

4. Experimental steps

Figure 5 illustrates the schematic of the experimental set-up constructed to conduct the ellipsometry measurements [57]. It exploits the usage of suitable light source, collimator, polarizer, converging lenses, graduated rotary sample; the spectrometer measures the values of ${\Psi }$ and ${\Delta }$, as defined before. In our experiment, the unpolarized light impinges the lower arm of the set-up, as shown in Fig. 5. As the light source, we use a halogen fiber optic illuminator (from THORLABS) with the output power of 150W and wideband spectral response within the range of 300–900 nm. Figure 6 exhibits the nature of light source used in the experiment.

Fig. 5. Schematic of the experimental set-up for ellipsometry measurements.

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Fig. 6. Spectral response of white light used for the ellipsometry measurements.

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The collimator was built exploiting two curved lenses located at a distance twice of their confocal lengths inside a cylindrical tube. The aligned beams from the collimator enter the Glan-Taylor calcite (birefringent crystal) polarizer (GT10-A from THORLABS) with the supporting wavelength range of 300 nm to 2.3 µm. The polarizer was structurally formed by the combination of two triangular prisms with narrow air-space in between, and has the optical property of depolarization (at the ratio of 100,000:1) of the incident beam into two (ordinary and extraordinary) components. Assuming the reflection of the ${p}$-polarized component, it then exits the polarizer at 68° angle from one end to another of the two uncoated side ports; this allowed the bidirectional usage of polarizer [Fig. 4(b)]. It must be reminded that the polarizer would not fully polarize the beam, and only some portion of the transmitted extraordinary ray could be used for measurements [58].

The micro-sized airy-disk thereafter cleans up the polarized beam from possible diffraction, and allows it to impinge on the curved lens [59], as shown in Fig. 5. The role of this lens is to enhance the optimized interaction of light with the sample placed behind the halved-prism over the sample rotary. The reflection angle from the sample could be varied by rotating the graduated disk. This way the ellipsometry parameters ${\Psi }$ and ${\Delta }$ of the reflected beam, which passes through the second curved lens in the upper arm (Fig. 5), could be changed proportionally. The spectrometer records these values as the input data to the mathematical model, as discussed in the previous section. Figure 7 exhibits the experimental set-up used in this work, in order to run the ellipsometry measurements.

Fig. 7. Experimental set-up used to measure the light polarization parameters (${\Psi },{\Delta }$).

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In the experimental set-up (Fig. 7), the broadband light, after passing through the different optical components, such as collimator, Glan-Taylor polarizer, pin-hole and converging lens, reach the sample mounted over the rotary graduated holder. The components were adjusted vertically for transferring the maximum power to the sample at certain angles. Replacing the Glan-Taylor polarizer on the side other than the previous side allows the user to select the preferred beam polarization (i.e. switching between the ${s}$- or ${p}$-waves in the transmission line [Fig. 4(b)]. The sample and liquid holder are put in a tiny box having one side open for light treatment, and the rest of the parts allow the liquid to infiltrate the developed meta-stadium grating structure.

5. Results and discussion

Figure 8 illustrates the cross-sectional view of the unit cell of the developed PDMS meta-stadium grating nanocombs in this investigation. It shows the parametric symbols to construct the schematic. However, the curve edges of combs (as can be viewed in Fig. 3) are not shown in this figure. As the unit cell depicts, the substrate and comb(s) are made of the same PDMS material, which is mounted with the homogeneously sputtered 100 nm thick SiO₂ layer. It is clear that the SiO₂ layer exists over the PDMS combs and the blank spaces between neighboring unit cells. Table 1 exhibits the used parametric values to feature the finally developed grating nanocombs.

Fig. 8. Schematic of the cross-sectional view of the unit cell.

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Table 1. Parametric values of the developed PDMS meta-stadium grating nanocombs.

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While attempting to observe the effect of metasurface in sensing applications, it remains important to evaluate the effective permittivity (or the effective RI) of metasurface. Figure 9 depicts the wavelength ${\lambda }$-dependence of RI of the SiO₂ and PDMS mediums in the range of 250–1750 nm. This plot is shown in the context of the usage of mediums in forming the metasurface. In obtaining the effective RI, the incorporation of measurand will also play the role, and therefore, we introduce the fill-factor ${\zeta }$ parameter, defined as

(11)$${\zeta} = \frac{{{{t}_{{\textrm{Si}}{{\textrm{O}}_{{2}}}}}}}{{{{t}_{{\textrm{Si}}{{\textrm{O}}_{{2}}}}} + {{t}_{{\textrm{Water}}/{\textrm{Glucose}}}}}}$$

where ${t}$ represents the thickness. The effective permittivity ${{\varepsilon }_{{eff}}}$ is determined as [60]

(12)$${{\varepsilon }_{{eff}}} = {{\varepsilon }_{{\textrm{Si}}{{\textrm{O}}_{{2}}}}}\frac{{{2}({{1} - {\zeta }} ){{\varepsilon }_{{\textrm{Si}}{{\textrm{O}}_2}}} + ({{1} + {2}{\zeta }} ){{\varepsilon }_{{\textrm{Water}}/{\textrm{Glucose}}}}}}{{({{2} + {\zeta }} ){{\varepsilon }_{{\textrm{Si}}{{\textrm{O}}_{{2}}}}} + ({{1} - {\zeta }} ){{\varepsilon }_{{\textrm{Water}}/{\textrm{Glucose}}}}}}$$

where ${\varepsilon }$ represents the permittivity.

Fig. 9. Broadband RI variation of SiO₂ and PDMS mediums with wavelength.

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The permittivity of SiO₂ in the visible range [61] is given as

(13)$${{\varepsilon }_{{\textrm{Si}}{{\textrm{O}}_{{2}}}}} = \frac{{{0.69617}{{\lambda }^{2}}}}{{{{\lambda }^{2}} - {{{0.0684043}}^{2}}}} + \frac{{{0.4079426}{{\lambda }^{2}}}}{{{{\lambda }^{2}} - {{{0.1162414}}^{2}}}} + \frac{{{0.8974794}{{\lambda }^{2}}}}{{{{\lambda }^{2}} - {{{9.896161}}^{2}}}} + {1}$$

Also, we evaluate the permittivity of water and the aqueous solutions of different glucose concentrations using the ellipsometry measurements. Figure 10 illustrates the obtained results; the plot incorporates the determination of ${\Psi }$ and ${\Delta }$. It can be observed from this figure that the permittivity of water (${{\varepsilon }_{{\textrm{Water}}}}$), and that corresponding to the aqueous solutions of different glucose concentrations (viz. 50 mg/l, 75 mg/l and 100 mg/l) attain the values as ${{\varepsilon }_{{\textrm{Water}}}} = {1.776809020}$, ${{\varepsilon }_{{\textrm{Gl}}{{\textrm{u}}_{{50}}}}} = 1.7881305841$, ${\varepsilon}_{{\textrm{Glu}}_{75}} = {1.7939387844}$, and ${{\varepsilon }_{{\textrm{Gl}}{{\textrm{u}}_{{100}}}}} = {1.80123241}$.

Fig. 10. Plots of ${\Psi }$ and ${\Delta }$ to determine the permittivity values.

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As stated before, the used measurand over the top metasurface will have the impact on ${{\varepsilon }_{{eff}}}$. Keeping this in mind, we illustrate the ${\lambda }$-dependence of effective permittivity, taking into account different values of measurand thickness, namely 25 nm [ Fig. 11(a)], 50 nm [Fig. 11(b)] and 100 nm [Fig. 11(c)]; the SiO₂ layer thickness ${{t}_{{\textrm{Si}}{{\textrm{O}}_{{2}}}}}$ is kept fixed to 100 nm.

Fig. 11. Wavelength dependence of effective permittivity corresponding to measurand thickness (a) 25 nm, (b) 50 nm and (c) 100 nm.

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It is clear from Fig. 11 that the increase in measurand thickness causes two-fold – (i) decrease in ${{\varepsilon }_{{eff}}}$, and also, (ii) decrease in dispersive characteristic. As such, the role of metasurface becomes more prominent corresponding to the case of less measurand thickness. We also observe that the ${\lambda }$-dependence of ${{\varepsilon }_{{eff}}}$ remains stronger in the low wavelength regime. Figure 11 also indicates that ${{\varepsilon }_{{eff}}}$ increases with the increase in glucose concentration, which is truly justified from the physical point of view.

We now attempt to observe the reflection spectra of the fabricated 2D-grating nanocomb sample upon infiltrating the void regions of the same with the aqueous solutions of different glucose concentrations, namely 50 mg/l, 75 mg/l and 100 mg/l. While experimenting, we vary the oblique incidence angle ${\theta }$ from 30° to 70° in a step of 5°. Figure 12 exhibits the obtained reflection spectra for the ${s}$- [Figs. 12(a), 12(b)] and ${p}$-polarized [Figs. 12(c), 12(d)] waves. It was found that the incidence angles of 38° [Figs. 12(a), 12(c)] and 48° [Figs. 12(b), 12(d)] show strong reflection peaks in the visible range, and therefore, we consider the observations corresponding to these two particular values of incidence angle ${\theta }$ upon varying the measurand concentration. Table 2 gives the details of the observations from Fig. 12. Though the shifts in peak reflectance are not significant enough upon changing the measurand concentration, the trends corresponding to the type of polarization and the angle of incidence are almost similar.

Fig. 12. Reflection spectra of the 2D-grating nanocombs infiltrated with water and aqueous solutions of different glucose concentrations corresponding to the ${s}$- (a, b) and ${p}$-polarized (c, d) waves. The used values of ${\theta }$ are 38° (a, c) and 48° (b, d).

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Table 2. The observation details of Fig. 12 corresponding to 38° and 48° angles of incidence.

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It is clear from Fig. 12 that, though strong reflection peaks are observed corresponding to the chosen incidence angles, shifts in the positions of peaks are too small to measure low variations in measurand concentration (viz. 50 mg/l, 75 mg/l). It is noteworthy that the lock-in and signal amplification techniques might be the feasible solutions to improve the quality of optical response [62]. However, the present work exploits the method of optical ellipsometry to characterize the reflection of light from the measurand sample.

Within the context, the extraction of ellipsometry parameters ${\Psi }$ and ${\Delta }$, which represent the amplitude ratio and phase difference between the ${s}$- and ${p}$-polarized waves, respectively, for enhancing the resolution of the obtained spectra and distinguishing the features may be useful to evaluate the sensitivity of the adopted sensor configuration. Figure 13 illustrates the relation between the resonant wavelengths of ellipsometry parameters and the RI values of measurands having different glucose concentrations. These results are obtained corresponding to 48° angle of incidence. We observe that the increase in RI shifts the resonant wavelengths to the lower values, which becomes more prominent in the case of ${p}$-polarized waves; such blue-shifts in reflection peaks can be noticed in Fig. 12 as well.

Fig. 13. Dependence of ${\Psi }$ and ${\Delta}$ on the measurand RI corresponding to ${\theta}$ as 48°.

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The main aim of this communication is to demonstrate the capability of the used ellipsometry model to enhance the resolution of sensitivity for sensing application. Within the context, as mentioned before, the parameter ${\Psi}$ is the amplitude ratio between the ${s}$- and ${p}$-polarizations, and can take the values between 0° and 90°, whereas the phase difference ${\Delta }$ (between these two polarizations) can be defined in two ranges, i.e., –180° to 180° and 0° to 360°. It has been found that the measured RI at 632 nm wavelength for water is 1.33297. Also, the same upon utilizing the other measurands, i.e., the aqueous solutions of different sugar concentrations, namely 50 mg/l, 75 mg/l and 100 mg/l, are 1.33721, 1.33938 and 1.34210, respectively. As such, the use of water as the measurand exhibits the lowest RI, and can be considered as the reference sample in the analysis of the obtained ellipsometry spectra.

Figure 14 exhibits the ellipsometry responses corresponding to two particular values of ${\theta }$, viz. 38° and 48°, while using the measurands as water (as the reference medium) and aqueous solutions of glucose having different concentrations over the fabricated 2D-grating nanocombs sample.

Fig. 14. Spectral response of the 2D-grating nanocombs infiltrated with water and aqueous solutions of different glucose concentrations corresponding to 38° (a, b) and 48° (c, d) values of ${\theta }$; measurements of wavelength-dependence of ${\Psi }$ (a, b) and (c, d).

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The sensitivity coefficient of ${\Psi }$ and ${\Delta }$ can be expressed in the forms of

(14)$${({{{\Psi }_{{s}}}} )_{{\textrm{Conc}}.}} = {\left|{\frac{{{{\Psi }_{{\textrm{Water}}}} - {{\Psi }_{{\textrm{Glucose}}}}}}{{{{\lambda }_{{\textrm{Water}}}} - {{\lambda }_{{\textrm{Glucose}}}}}}} \right|_{{{\textrm{Conc}}}.}}$$

(15)$${({{{\Delta }_{{s}}}} )_{{\textrm{Conc}}.}} = {\left|{\frac{{{{\Delta }_{{\textrm{Water}}}} - {{\Delta }_{{\textrm{Glucose}}}}}}{{{{\lambda }_{{\textrm{Water}}}} - {{\lambda }_{{\textrm{Glucose}}}}}}} \right|_{{\textrm{Conc}}.}}$$

Using these equations, Table 3 shows the obtained results of ellipsometry measurements corresponding to the ${\theta }$-values as 38° and 48°. The table incorporates the values of ${\Psi }$ and ${\Delta }$, and their respective positions of dips in wavelengths in the spectral characteristics, as obtained in Fig. 14. These results are utilized to determine the sensitivity in the unit of degree/nm (i.e., °/nm).

Table 3. Ellipsometry parameters ${\boldsymbol{\Psi}}$ and $\boldsymbol{\Delta }$ corresponding to the incidence angles 38° and 48°, as obtained in Fig. 14, toward determining the sensitivity.

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Looking at Fig. 14, we observe corresponding to the spectral characteristic of ${\Psi }$ that the incidence angle of 38° results in blue-shifts of dips from 400 nm to above 500 nm upon increase in glucose concentration. This figure exhibits nonlinear grow in sensitivity at very small slopes. However, raising the value of ${\theta }$ to 48° results in red-shifts in the dips. We clearly notice from Fig. 14 that the parameter ${\Psi }$ exhibits small sensitivity in the form of nonlinear manner in the visible range corresponding to the ${\theta }$-values as 38° and 48° upon altering the glucose concentration. The use of ${\theta }$ as 38° is not promising enough owing to the small sensitivity in detecting glucose concentration above 50 mg/l.

Figure 14 also exhibits that the amplitude variations of dips in ${\Delta }$ spectra shift up in the order of low to high concentration of glucose. Besides narrow spectral shifts, the best sensitivity among all the results in Fig. 14, and following the observations shown in Table 3, is noticed corresponding to the ${\theta }$-value of 48° and the variations in ${\Delta }$ over the visible range.

We discussed so far the ellipsometry spectra in the presence of measurand samples of different concentrations, and also, water (Fig. 14). However, it would be interesting to observe the spectral characteristics in the absence of any measurand. With this viewpoint in mind, Fig. 15 illustrates the plots of ${\lambda }$-dependence of the ellipsometry parameters ${\Psi }$ [Fig. 15(a)] and ${\Delta }$ [Fig. 15(b)] in the case when the void region of 2D-grating nanocombs is simply the free-space, and the oblique incidence happens at an angle of 48°. We notice in this figure that the spectral dips corresponding to ${\Psi }$ and ${\Delta }$ exist at the wavelengths 485.66 nm and 381.27 nm, respectively, along with their respective values as 34.5 and –75.5. Comparing these results with those in Table 3 for 48° incidence angle, the shifts in the positions of spectral dips upon replacing the free-space with measurands become evident.

Fig. 15. Spectral response of the 2D-grating nanocombs having free-space void region corresponding to 48° incidence angle.

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In the context of sensing, one may have thoughts on the effect of temperature on the ellipsometry measurements performed in this experiment. In this stream, the temperature ${T}$ dependence of RI ${n}$ of SiO₂ films can be written as [63,64]

(16)$$\frac{{\partial n}}{{\partial T}} = R\frac{{\partial D}}{{\partial T}} + d\frac{{\partial R}}{{\partial T}}$$

In this equation, $D$ is the coefficient of thermal expansion and $R$ represents the molecular refraction of SiO₂. At high temperatures, R remains as a slowly varying function of T. The term $\partial n/\partial T$ depends on $\partial R/\partial T$ and the RI increases with increasing T. At low values of temperature, the term $\partial D/\partial T$ plays the determining role, and decreases the RI. The effect of T on the RI of SiO₂ film has been investigated experimentally in Ref. [65]. In the present work, however, the effect of temperature on the sensing performance is not considered; this may be taken up in future communication.

6. Conclusion

From the aforementioned discussions, it can be inferred that the PDMS and SiO₂ mediums can be used to form an arrayed structure having 2D-grating PDMS stadium-nanocombs – the configuration that can be exploited for optical sensing. In this communication, we consider the monitoring of the concentration of glucose in its aqueous solution. For this purpose, the spectroscopic method of ellipsometry was applied to the artificially engineered all-dielectric device, and the sensitivity of the structure is determined. The investigations demonstrate the existence of Tamm waves that correspond to at least one of the ellipsometric components to be highly sensitive to the variation of glucose concentration in the visible wavelength span. Furthermore, it can be expected that such 2D-grating PDMS stadium-nanocombs can be promising for sensing other bio-samples as well.

Funding

Ministry of Higher Education, Malaysia (AKU254); Shahid Beheshti University (2018-600-3012).

Disclosures

The authors declare no conflict of interest.

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Unit cell parameters	Parametric values
$a$	2000 nm
$b$	2080 nm
$f$	69.5 nm
$p$	2169 nm
$h_{1}$	1000 nm
$h_{2}$	250 nm
$h_{3}$	100 nm
$h_{4}$	350 nm

Incidence angle ( $θ$ )	Measurand	Position of peak reflectance (nm)	Reflectance $R_{s}$ , $R_{p}$
38°	Water	617.7	$R_{s}$ = 0.9930
	Glucose (50 mg/l)	619.4	$R_{s}$ = 1.0000
	Glucose (75 mg/l)	620.67	$R_{s}$ = 0.9979
	Glucose (100 mg/l)	621.94	$R_{s}$ = 0.9957
	Water	619.4	$R_{p}$ = 0.999
	Glucose (50 mg/l)	619.4	$R_{p}$ = 0.998
	Glucose (75 mg/l)	620.67	$R_{p}$ = 0.999
	Glucose (100 mg/l)	675.28	$R_{p}$ = 0.999
48°	Water	619.4	$R_{s}$ = 0.999
	Glucose (50 mg/l)	621.94	$R_{s}$ = 0.998
	Glucose (75 mg/l)	621.94	$R_{s}$ = 0.998
	Glucose (100 mg/l)	621.94	$R_{s}$ = 0.995
	Water	678.20	$R_{p}$ = 0.999
	Glucose (50 mg/l)	675.28	$R_{p}$ = 0.999
	Glucose (75 mg/l)	619.4	$R_{p}$ = 0.997
	Glucose (100 mg/l)	619.4	$R_{p}$ = 0.998

$θ$ $Ψ$ & $λ$	$Ψ_{Water}$ (deg)	$λ_{Water}$ (nm)	$Ψ_{Gl_50}$ (deg)	$λ_{Gl_50}$ (nm)	$Ψ_{GL_75}$ (deg)	$λ_{Gl_75}$ (nm)	$Ψ_{Gl_100}$ (deg)	$λ_{Gl_100}$ (nm)
38°	38	418	42.1	525	42.3	494	33.5	475
48°	36.2	503	37.2	478	42.8	456	33	413
$θ$			Sensitivity $S$ (°/nm) $Ψ_{Gl_50}$		Sensitivity $S$ (°/nm) $Ψ_{GL_75}$		Sensitivity $S$ (°/nm) $Ψ_{Gl_100}$
38°			0.038		0.056		0.078
48°			0.04		0.14		0.035
$θ$ Δ & λ	$Δ_{Water}$	$λ_{Water}$ (nm)	$Δ_{Gl_50}$	$λ_{Gl_50}$ (nm)	$Δ_{Gl_75}$	$λ_{Gl_75}$ (nm)	$Δ_{Gl_100}$	$λ_{Gl_100}$ (nm)
38°	–15.2	377	–62.5	379	–17.1	413	–10.9	389
48°	–62.8	384	–35.3	383	–19.1	381	–5	377
$θ$			Sensitivity $S$ $Δ_{g l_50_{m g}}$		Sensitivity $S$ $Δ_{g l_75_{m g}}$		Sensitivity $S$ $Δ_{g l_100_{m g}}$
38°			23.65		0.052		0.358
48°			27.5		14.56		8.25

Unit cell parameters	Parametric values
$a$	2000 nm
$b$	2080 nm
$f$	69.5 nm
$p$	2169 nm
$h_{1}$	1000 nm
$h_{2}$	250 nm
$h_{3}$	100 nm
$h_{4}$	350 nm

Incidence angle ( $θ$ )	Measurand	Position of peak reflectance (nm)	Reflectance $R_{s}$ , $R_{p}$
38°	Water	617.7	$R_{s}$ = 0.9930
	Glucose (50 mg/l)	619.4	$R_{s}$ = 1.0000
	Glucose (75 mg/l)	620.67	$R_{s}$ = 0.9979
	Glucose (100 mg/l)	621.94	$R_{s}$ = 0.9957
	Water	619.4	$R_{p}$ = 0.999
	Glucose (50 mg/l)	619.4	$R_{p}$ = 0.998
	Glucose (75 mg/l)	620.67	$R_{p}$ = 0.999
	Glucose (100 mg/l)	675.28	$R_{p}$ = 0.999
48°	Water	619.4	$R_{s}$ = 0.999
	Glucose (50 mg/l)	621.94	$R_{s}$ = 0.998
	Glucose (75 mg/l)	621.94	$R_{s}$ = 0.998
	Glucose (100 mg/l)	621.94	$R_{s}$ = 0.995
	Water	678.20	$R_{p}$ = 0.999
	Glucose (50 mg/l)	675.28	$R_{p}$ = 0.999
	Glucose (75 mg/l)	619.4	$R_{p}$ = 0.997
	Glucose (100 mg/l)	619.4	$R_{p}$ = 0.998

Biosensing applications of all-dielectric SiO₂-PDMS meta-stadium grating nanocombs

Abstract

1. Introduction

2. Fabrication process

3. Spectroscopic ellipsometry measurements

4. Experimental steps

5. Results and discussion

6. Conclusion

Funding

Disclosures

References

Cited By

Figures (15)

Tables (3)

Equations (16)

Optical Materials Express