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Abstract
Sensing abilities of a one-dimensional photonic crystal (1DPhC) represented by a multilayer dielectric structure are analyzed theoretically and experimentally, using a new wavelength interrogation interference method. The structure comprising a glass substrate and six bilayers of TiO2/SiO2 with a termination layer of TiO2 is employed in both gas sensing based on the Bloch surface wave (BSW) resonance and liquid analyte sensing based on a self-referenced guide-mode resonance (GMR). We model the spectral interference reflectance responses in the Kretschmann configuration with a coupling prism made of BK7 glass and show that a sharp dip with maximum depth associated with the BSW excitation is red-shifted as the refractive index (RI) changes in a range of 1–1.005. Thus, a sensitivity of 1456 nm per RI unit (RIU) and figure of merit (FOM) of 91 RIU−1 are reached. Similarly, we model the responses for aqueous solutions of ethanol to show that dips of maximum depth are associated with the GMRs, and the highest sensitivity and FOM reached are 751 nm/RIU and 25 RIU−1, respectively. Moreover, we show that one of the dips is with the smallest shift as the RI changes, and hence it can be used as a reference. The theoretical results are confirmed by the experimental ones when the BSW resonance is used in sensing of humid air with a sensitivity of 0.027 nm/%relative humidity (RH) and FOM of 1.4×10−3 %RH−1. Similarly, the GMR is used in sensing of aqueous solutions of ethanol, and the highest sensitivity and FOM reached 682 nm/RIU and 23 RIU−1, respectively. The reference dip is also resolved and this self-reference makes the measurement more accurate and repeatable, and less sensitive to optomechanical drifts.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Bragg mirrors or one-dimensional photonic crystals (1DPhCs), as realizations of complex dielectric structures [1], have a huge impact on research of numerous topics and applications, such as omnidirectional reflectors [2], polarization selectors [3], narrowband optical filters using omnidirectional photonic band gaps (OPBGs) [4], and especially sensors utilizing Bloch surface waves (BSWs) [5–16]. BSWs exist at the interfaces of truncated 1DPhCs [17] that exhibit PBGs, and enable the study of surface interactions with the external media [18–20] in controlled manner with several possible advantages compared to surface plasmon polaritons (SPPs) [20,21]. BSWs can be excited by both $s$- and $p$-polarized waves [22] at any wavelength, including also near- and mid-infrared region [16,23], by suitably changing the geometry and materials of the photonic crystal. BSW-based sensors exhibit sharper resonances than conventional surface plasmon resonance (SPR) sensors [24] because they do not rely on the use of metals. Most importantly, with an appropriate choice of the dielectric materials of the PhC, sensors based on BSWs are mechanically and chemically robust, offering the possibility of operation in aggressive environments.
The optical field in the multilayer structure is enhanced and decays on both sides of the boundary so that the BSW resonance, similarly as SPR, is attractive to sensing in various fields of interest [5–10,12,25,26]. In addition, fiber optic sensors with multilayer structures have been proposed and realized [27–31], including configurations in which a multilayer structure has been deposited on a tapered fiber [27], on the outer surface of optical fiber [28], at the tip of a single-mode fiber [29], and inside of a photonic crystal fiber [30,31]. As a new alternative, Tamm plasmon (TP) based sensors utilizing a type of surface waves at the interface between a metal and a 1DPhCs have been studied [32], and a direct excitation from free space and excitation by both $s$- and $p$-polarized waves have been utilized [33–35].
However, one of possible advantages of SP-based sensors represents a regime of two plasmons [36–38] when one responds to changes in analyte refractive index (RI) while the other, a reference one, is sensitive to the RI of the substrate [36]. Similar effect show sensors based on hybrid-Tamm-plasmon-polariton modes [39].
In this paper, a multilayer dielectric structure employed in both gas and liquid analyte sensing is analyzed theoretically and experimentally. A new wavelength interrogation interference method is used to reveal either the BSW resonance in the gas sensing or a self-referenced guide-mode resonance (GMR) in liquid analyte sensing. The spectral interference reflectance responses in the Kretschmann configuration are modeled for the structure consisting of a glass substrate and six bilayers of TiO$_2$/SiO$_{2}$ with a termination layer of TiO$_2$, provided that the structure layers are characterized by a method of spectral ellipsometry. The responses show that both the BSW excitation and the GMR are accompanied by sharp dips with maximum depth. We revealed that in the gas analyte sensing the highest sensitivity and figure of merit (FOM) reached 1456 nm/RIU and 91 RIU$^{-1}$, respectively. Similarly, in liquid analyte sensing, the corresponding sensitivity and FOM are up to 751 nm/RIU and 25 RIU$^{-1}$, respectively. In addition, in liquid analyte sensing we revealed that one of the dips is with the smallest shift as the RI changes so that a self-referencing mode can be employed. The theoretical results are confirmed by experimental ones when the BSW resonances are resolved for humid air, and the GMRs with the reference dip are resolved for aqueous solutions of ethanol. Thus, the gas and liquid analyte sensors employing dielectric multilayers represent an effective alternative to available sensors, with advantages such better mechanical and chemical stability, and self-referencing for liquid analytes.
2. Material characterization
The multilayer structure under study, whose normal incidence reflection spectrum is characterized by a band gap approximately 270 nm wide (from 730 to 1000 nm), was prepared by a sputtering thin film deposition technique. Parameters such as layer thicknesses and dispersions were not provided by the manufacturer (Meopta, Czech Republic) so that different techniques were utilized for material characterization. In the first step, the structure was inspected by a destructive technique employing a scanning electron microscope (FEI Quanta 650 FEG, USA). It was revealed that the structure is represented by a system of six bilayers of TiO$_2$/SiO$_{2}$ and a termination layer of TiO$_2$, as evident from SEM images shown in Fig. 1(a).
Fig. 1. SEM images of a multilayer structure (a), and the geometric representation of the structure (b).
In the next step, the structure was inspected by a method of spectral ellipsometry, and the variable angle spectroscopic ellipsometric (VASE) data obtained by ellipsometer RC2 (J. A. Woollam Co., Inc., USA) were analyzed to determine the thicknesses and refractive index dispersions of the layers employing software CompleteEASE (J. A. Woollam Co., Inc., USA). Thus, it was found that six bilayers of TiO$_2$/SiO$_{2}$ ($i=j=$1,..,6) are with thicknesses $t_{0i}=124.9, 87.6, 90.8, 132.9, 107.7$ and 119.2 nm, and $t_{1j}=141.7, 127.9, 125.8, 108.9, 132.6$ and 106 nm, respectively, and the TiO$_2$ termination layer of thickness $t_{07}=91.1$ nm is with a rough layer of thickness $t_{08}=13.3$ nm as schematically shown in Fig. 1(b). The ellipsometric data have also enabled to obtain the RI dispersions of the structure materials. The RI dispersion of a glass substrate was described by a Cauchy formula
where $\lambda$ is the wavelength in $\mu \mathrm {m}$ and the values of coefficients $A$, $B$ and $C$ obtained by the VASE were as follows: $A=1.446$, $B=5.184\times 10^{-3}~{\mu \mathrm {m}}^2$ and $C=-2.514\times 10^{-4}~{\mu \mathrm {m}}^4$.Similarly, TiO$_{2}$ and SiO$_{2}$ layers were described by a modified one-oscillator Sellmeier formula
where $\lambda$ is the wavelength in $\mu \mathrm {m}$ and $A$, $B$, $C$ and $D$ are coefficients with the values for the TiO$_{2}$ layers obtained by the VASE: $A=0$, $B=4.672$, $C=0.22935~{\mu \mathrm {m}}$ and $D=0~{\mu \mathrm {m}}^{-2}$. Similarly, for SiO$_{2}$ layers the values obtained were: $A=1.348$, $B=0.756$, $C=0.10683~{\mu \mathrm {m}}$ and $D=0.00975~{\mu \mathrm {m}}^{-2}$. In addition, the extinction coefficients for TiO$_2$ and SiO$_2$ obtained were $\kappa _{\textrm {TiO}_{2}}=\kappa _{\textrm {SiO}_{2}}\approx 0$. For the dispersion of a coupling prism made of BK7 glass, a three-oscillator Sellmeier formula [40] was employed.3. Theoretical model
3.1 Transfer matrix method
A powerful tool in the analysis of light propagation through multilayer dielectric structures is the transfer matrix method (TMM) [41,42]. The method enables to express the optical response of the structures using the fact that electric or magnetic fields in one position can be related to those in other positions through a transfer matrix. For the case of $N$ dielectric layers, the total transfer matrix $\boldsymbol {\mathrm M}$ can be obtained by transmission matrices across different interfaces and propagation matrices in different homogeneous dielectric media:
Similarly, the propagation matrices are given by
The reflection coefficient $r$ is expressed using the total transfer matrix elements
and the spectral reflectances $R_{s,p}(\lambda )$ can be calculated for both $s$ and $p$ polarizations as3.2 Band structure
It is well know that waves localized near the boundary between a semi-infinite or finite multilayer structure and surrounding medium, referred to as Bloch surface waves, are related to the band structure. The band structure can be obtained from the dispersion relation of the infinite periodic system of bilayers, which for the case of TM-polarized waves is in Ref. [21], and for TE-polarized waves has a similar form [42]:
In Fig. 2 is shown the computed band diagram of the infinite 1DPhC consisting of $\mathrm {TiO}_2/\mathrm {SiO}_2$ bilayers with thicknesses $a=111\,\mathrm {nm}$ and $b=124\,\mathrm {nm}$ ($\Lambda =235\,\mathrm {nm}$), including both TE- and TM-polarized waves. The thicknesses $a$ and $b$ have been chosen as the average ones from the ellipsometry measurements presented in section 2. Instead of frequency and propagation constant, the reduced (dimensionless) variables $\overline {\omega }=\frac {\omega }{c}\frac {\Lambda }{2\pi }=\Lambda /\lambda$ and $\overline {\beta }=\beta \frac {\Lambda }{2\pi }$ are used. The band structure was obtained using Eq. (10). The upper limit for the computation was chosen as $\lambda =0.4~\mu \mathrm {m}$ ($\overline {\beta }=0.59$, for given $\Lambda$) and the dispersion properties of all media were taken into account.
Fig. 2. Computed band diagram of an infinite PhC for TE (left) and TM (right) polarizations. The Bloch states for a semi-infinite 1DPhC and the analyte with $n=1$ are depicted as dots.
Appropriate part of the band diagram related to our experimental conditions is shown in Fig. 2, where the light lines for air ($n=1$), together with the points corresponding to BSWs are depicted. Their positions were derived from the reflectance spectra computed using the TMM for a finite multilayer structure comprising 100 $\mathrm {TiO}_2/\mathrm {SiO}_2$ bilayers. The TM-polarized wave is considered to be incident from the glass substrate and the surrounding medium is with $n=1$. The positions of the dip in one spectral region are traced as the angle incidence is changed. When plotted in the right part of the band diagram, the corresponding points are located in the mentioned band gap near its edge, thus confirming the possibility to excite the BSW. Respecting diversity in film thicknesses of the real 1DPhC, different thicknesses, such as $a=130\,\mathrm {nm}$ and $b=105\,\mathrm {nm}$ can be chosen, for which both the band diagram and Bloch states are changed so that the corresponding points are located far from the edge between bands. The excitation of the BSW is manifested by the spectral response of the multilayer structure at the angle of incidence $\theta =42^\circ$ when the surrounding medium (analyte) is with $n=1$. Taking into account the dispersion of materials of the structure specified above, and assuming that the extinction coefficients for TiO$_2$ and SiO$_2$ layers are $\kappa _{\textrm {TiO}_2}=1.6\times 10^{-3}$ and $\kappa _{\textrm {SiO}_2}=3.4\times 10^{-4}$ [6], respectively, Fig. 3(a) shows the theoretical spectral reflectances for both $s$- and $p$-polarized waves. As it is apparent from Fig. 3(a), a wide band gap for $s$-polarized and a narrower one for $p$-polarized wave are resolved in the considered wavelength range. Moreover, the $p$-polarized wave excites the BSW and this is accompanied by a shallow dip near a wavelength of 685.5 nm in the reflection spectrum. To confirm the BSW excitation, the normalized optical field intensity $\left |H_x\right |^2/\left |H_{x0}\right |^2$ in the structure at a wavelength of 685.5 nm is shown in Fig. 3(b). The computation was performed using the matrix method [44] and $H_{x0}$ is $x$ component of the incident magnetic field that is perpendicular to the plane of incidence as evident from Fig. 1(b). This figure clearly demonstrates that the enhanced optical field, characterized by more than a thirty-fold enhancement of the optical intensity with respect to the incident beam, is confined to the surface of the 1DPhC. In addition, the results can also be confirmed by a finite element method (FEM) using commercial software COMSOL Multiphysics. In Fig. 3(b), an exponential tail in the analyte (air) is apparent, illustrating the potential of the multilayer structure to be used in sensing applications.
Fig. 3. Theoretical spectral reflectances $R_s(\lambda )$ and $R_p(\lambda )$ for the analyte with $n=1$ and the angle of incidence $\theta =42^\circ$(a). The normalized optical field intensity distribution for the $p$-polarized wave at a wavelength of 685.5 nm (b).
However, some limitations in measuring the spectral response of a multilayer structure characterized by the BSW resonances (for both $s$- and $p$-polarized waves) can occur. These include, for example, too shallow resonance reflectance dips. Fortunately, a new approach was proposed and verified [15] that utilizes the spectral interference of the polarized waves reflected from the multilayer structure and enables the BSW resonance dip to be resolved with maximum depth. Extending this approach, the interference is attained when the polarizer at the input is oriented $+45^\circ$ with respect to the plane of incidence, and the analyzer at the output is oriented either $+45^\circ$ or $-45^\circ$, and the corresponding reflectances $R_{\pm {\rm 45}}(\lambda )$ are expressed as
Fig. 4. Theoretical spectral reflectance $R_{+{\rm 45}}(\lambda )$ for analytes with RIs in a range of 1.000–1.005 and two angles of incidence: $\theta =43.5^\circ$ (a), $\theta =42^\circ$(b).
In Fig. 5(a), the resonance wavelength as a function of the RI is shown together with fitting functions (second-order polynomials). Such non-linear response means that the sensitivity to the refractive index $S_n$, defined as
where $\delta \lambda _r$ is the change in the position of the dip with respect to the refractive index change $\delta n$ of the analyte, is linearly RIU-dependent, as shown Fig. 5(b). The sensitivity $S_n$ ranges from 371 nm/RIU to 415 nm/RIU for $\theta =43.5^\circ$, and for $\theta =42^\circ$ it is enhanced and changes in a range of 1036–1456 nm/RIU. Thus, it is comparable to that of a simple SPR sensor with Au layer (1050–2110 nm/RIU [45]), but is higher as compared to a TP sensor with mesoporous multilayers (55 nm/RIU [34]). In any case, the sensor with the 1DPhC has advantages in better mechanical and chemical stability, offering the possibility of operation in aggressive environments. The performance of the BSW-based sensor is evaluated also in terms of figure of merit (FOM), defined as the sensitivity $S_n$ divided by the FWHM of the dip which demands that the dip should be as narrow as possible. Actually, for $\theta =43.5^\circ$ and the constant FWHM (16 nm), the FOM is up to 26 RIU$^{-1}$. For $\theta =42^\circ$ the FWHM reaches 16.2 nm and the FOM is as high as 91 RIU$^{-1}$ due to the sensitivity enhancement.Fig. 5. Resonance wavelength as a function of the analyte RI for two angles of incidence $\theta$ with solid lines as fits (a). The corresponding sensitivity functions (b).
The potential of the multilayer dielectric structure to be used in sensing of liquid analytes is huge owing to mechanical and chemical stability, so we consider aqueous solutions of ethanol, whose dispersion is specified elsewhere [13]. In this case, the new interference approach is very effective as illustrated in Fig. 6(a), showing the theoretical spectral reflectances $R_{-{\rm 45}}(\lambda )$ for angle of incidence $\theta =70^\circ$ and different RIs of the analyte. As it is evident from Fig. 6(a), three dips are resolved: two in the wavelength range 580–660 nm and one in the wavelength range 750–760 nm. The dips do not correspond to the BSW excitation because the optical field distributions in the multilayer structure are with no exponential envelope such as that shown in Fig. 3(b). This is illustrated in Fig. 7(a), showing the normalized optical field intensity $\left |H_x\right |^2/\left |H_{x0}\right |^2$ at the wavelengths 593.5 nm and 651.6 nm, respectively. Thus, the two dips are related to GMR of the $p$-polarized modes (GMR1 and GMR2) and have maximum depth and different widths. These resonances are comparable in magnitude with ones commonly exhibited by SPR [45], but are narrower. As an example, an FWHM of 17.5 nm at $\theta =70^\circ$ for the long-wavelength dip (GMR2) is more than three times smaller than an FWHM of 60 nm for the SPR dip [21]. The GMR dips are also with greater red shifts as the RI increases, what is simply justified by an increase in penetration depth of mode fields in the analyte when $\theta$ decreases, as evident from Fig. 7(a).
Fig. 6. Theoretical spectral reflectance $R_{-{\rm 45}}(\lambda )$ for different RIs of aqueous solutions of ethanol and angles of incidence: $\theta =70^\circ$ (a) and $\theta =64.3^\circ$ (b). The dashed curves correspond to the analyte with $n=1$.
Fig. 7. Normalized optical field intensity distribution for guided modes at wavelengths of 593.6 nm (blue), 651.6 nm (red) and 701.9 nm (dashed) for the $p$-polarized mode (a), at wavelengths of 753 nm and 777.8 nm for the $s$-polarized mode (b). The analyte is water, $\theta =70^\circ$ and $\theta =64.3^\circ$ (dashed).
A very narrow dip resolved in the wavelength range 750–760 nm is related to GMR of the $s$-polarized mode as illustrated in Fig. 7(b), showing the normalized optical field intensity $\left |E_x\right |^2/\left |E_{x0}\right |^2$ at a wavelength of 593.5 nm. The smallest resonance wavelength shift is due to the smallest penetration depth of mode field in the analyte. The depth of the corresponding dip is affected by interference with the $p$-polarized mode. This is illustrated in Figs. 6(a) and 6(b) and performance of the sensor is the result of the measurement method to be employed. The width of the resonances and their depth change with the angle of incidence. Two shifts of these GMR dips, that can be simply explained by change of the guided mode line and its intersection with the light line, can be enlarged as it is evident from Fig. 6(b), showing the same dependence for $\theta =64.3^\circ$. Importantly, the third, the longest-wavelength dip is with the smallest shift, and hence it can be used as a reference. In Figs. 6(a) and 6(b) are also shown the dashed curves illustrating how a dip is shifted when the analyte is changed from air to water.
In addition, in Fig. 8(a), the resonance wavelength as a function of the RI is shown together with the fitting functions (second-order polynomials), and the non-linear response means that the sensitivity $S_n$ is linearly RIU-dependent, as shown Fig. 8(b). The sensitivity $S_n$ ranges from 203 nm/RIU to 243 nm/RIU for the angle of incidence $\theta =70^\circ$, while for $\theta =64.3^\circ$ it is enhanced to a range of 234-751 nm/RIU. The FWHMs of the most sensitive dips, respecting variable depth of the dip for $\theta =64.3^\circ$, are 17.5 nm and 29.7 nm, so that the FOMs are up to 13 RIU$^{-1}$ and 25 RIU$^{-1}$, respectively. To quickly compare sensing abilities of the GMRs, we evaluated an average sensitivity $S^\textrm {a}_n$ from a linear approximation of the resonance wavelength function on the refractive index. Values of 223 nm/RIU and 498 nm/RIU, respectively, and a value of 1.4 nm/RIU corresponding to the reference dip, are also depicted in Figs. 6(a) and 6(b). It should be stressed that when a shift of the dip in the spectral reflectance $R_s$ is analyzed as corresponds to a standard approach, a sensitivity of 11.9 nm/RIU is obtained. Thus, nearly nine times reduced sensitivity obtained in this case is due to interference of $s$- and $p$-polarized modes and their opposite effect on the GMR as the analyte RI changes. Most importantly, this is a substantially different approach than that used in sensors utilizing two plasmons with a reference one sensitive to the RI of the substrate [36]. Moreover, even if the sensitivity of the GMR-based sensors applied to liquid analytes is much lower compared to available optical sensors [46], they have advantages such better mechanical and chemical stability, and self-referencing.
Fig. 8. Resonance wavelength as a function of the RI of the aqueous solution of ethanol for the GMR2 and two angles of incidence $\theta$ with solid lines as fits (a), and the corresponding sensitivity functions (b).
4. Experimental setup
The response of a 1DPhC (multilayer structure) to different surrounding media (analytes) was measured in two experimental setups, with one of them shown in Fig. 9 and employed to liquid analytes. It represents the Kretschmann configuration and enables to measure the spectral reflectance of both $s$- and $p$-polarized waves, $R_s(\lambda )$ and $R_p(\lambda )$, and the cross spectral reflectances $R_{\pm {\rm 45}}(\lambda )$. The setup comprises white-light source WLS (halogen lamp HL-2000, Ocean Optics, USA) with launching optics and a part including an input optical fiber and collimating lens CL to generate a collimated beam of 1 mm diameter. The light beam passes through linear polarizer P (LPVIS050, Thorlabs, USA) oriented $45^\circ$ with respect to the plane of incidence (both $s$- and $p$-polarized components are present) and then is coupled to the multilayer structure under test employing equilateral BK7 prism (Ealing, Inc., USA) and a thin layer of index-matching fluid (Cargille, USA, $n_D$=1.516). The reflected light passes through linear analyzer A (LPVIS050, Thorlabs, USA) and its perpendicular or parallel orientation to the plane of incidence, and also $+45^\circ$ or $-45^\circ$ orientation can be adjusted. Thus, the spectral reflectances $R_s(\lambda )$ or $R_p(\lambda )$, and also $R_{+{\rm 45}}(\lambda )$ or $R_{-{\rm 45}}(\lambda )$ are measured when the light is launched via microscope objective MO into a read optical fiber (M15L02, Thorlabs, USA) of a spectrometer (USB4000, Ocean Optics, USA).
Fig. 9. Experimental setup for measuring the reflectance responses of a multilayer structure in the Kretschmann configuration.
In RH measurements, the CL was attached to the rotary stage [47], so that the external angle of incidence $\alpha$ and thus the corresponding internal angle $\theta$, as shown in Fig. 1(b), can be adjusted, and these angles are governed by a simple relation [13]. As analytes, in the first step a humid air, and in the next step aqueous solutions of ethanol were prepared. A part of the setup for the adjustment of the relative humidity of air, which was described in detail in a previous paper [48], consists of a humidifier [49] and a two-line peristaltic pump (BT100M, 2xYZ1515x, Baoding Chuang Rui Precision Pump Co., Ltd.). Aqueous solutions of ethanol were characterized by the RIs, measured at a wavelength of 589.3 nm by refractometer Abbemat MW (Anton Paar GmbH, Austria). Six sample solutions were prepared, including a pure water, with RIs of 1.3334, 1.3352, 1.3355, 1.3450, 1.3502, and 1.3584 measured at a temperature of $22^\circ$C.
5. Experimental results and discussion
In the first step, the spectral response of the multilayer structure under test was measured for humid air, and in Fig. 10(a), the measured spectral reflectance ratio $R_{+{\rm 45}}(\lambda )/R_s(\lambda )$ is shown for the external angle of incidence $\alpha =27.7^\circ$ ($\theta \approx 42.1^\circ$) when the relative humidity of air is changed in a range of 33.7–78.9 %RH. This figure illustrates, in accordance with the theory, that the BSW excitation shows up as a dip with maximum depth near a wavelength of 678 nm, which differs from the theoretical one, as shown in Fig. 5(a), due to a different angle of incidence $\theta$. The resonance wavelength, determined with a precision of 0.01 nm using a zero-crossing in the first derivative of the reflectance ratio, is shown in Fig. 10(b) as a function of the RH of air and this dependence is well approximated by a linear function. Moreover, a hysteresis-free response and repeatability of the measurement were revealed.
Fig. 10. Spectral reflectance ratio $R_{+{\rm 45}}(\lambda )/R_s(\lambda )$ for different values of the RH of air measured at angle of incidence $\alpha =27.7^\circ$ (a). Resonance wavelength as a function of the RH of air for two angles of incidence $\alpha$ with solid lines as fits (b).
The resonance wavelength shift can be attributed to adsorption of water molecules on the surface of the 1DPhC resulting in the change in the effective thickness of water condensation as RH increases [50]. One of important parameters in this case is the sensitivity $S_\textrm {RH}$ to the RH, defined as the change in the position of the dip $\delta \lambda _r$ with respect to the change $\delta \textrm {RH}$ in the RH of humid air
with a value of 0.027 nm/%RH. In Fig. 10(b) is also shown the resonance wavelength as a function of the RH of air for $\alpha =23.2^\circ$ ($\theta \approx 44.9^\circ$), well approximated by a linear function that gives the sensitivity $S_\textrm {RH}=0.026$ nm/%RH.Another important parameter in this case is the FOM$_\textrm {RH}$ of the RH measurement given by a similar relation to the FOM of the RI measurement:
The FWHM of the dip in the first case is 19.6 nm and the FOM reaches 1.4$\times 10^{-3}$ %RH$^{-1}$. In the second case, the FWHM is 21 nm and the FOM is slightly lowered to 1.2$\times 10^{-3}$ %RH$^{-1}$. It is interesting to note that even if the sensitivity is lower as compared to that for the 1DPhC comprising four bilayers [21], the FOM is nearly the same because of the smaller FWHM for the 1DPhC comprising six bilayers. Moreover, the results confirm that due to narrow resonance dip the BSW resonance based sensor is comparable or outperforms some optical RH sensors in the FOM [21,51], including the SPR-based sensors [21] and the GMR-based sensors employing a polymer thin film [51]. The analyzed sensor and other BSW resonance based sensors outperform a number of optical RH sensors in terms of sensitivity, such as RH sensors based on the GMR and employing an agarose gel [52], sensors based on PhC mode resonances [53], and sensors utilizing lossy mode resonances in planar waveguides [54].The measurement of the spectral responses of the multilayer structure under test was extended to liquid analytes represented by aqueous solutions of ethanol. In Fig. 11(a), the measured spectral reflectances $R_{-{\rm 45}}(\lambda )$ for different RIs of liquid analytes are shown when the external angle of incidence $\alpha =-8.4^\circ$ ($\theta \approx 65.5^\circ$). It is clearly seen that three dips are resolved in a wavelength range of 570–810 nm. In accordance with the theory, two of them are with maximum depth and with a resonance wavelength shift toward longer wavelengths as the RI of liquid analyte increases. Third, the narrowest dip is with the smallest shift, hence it can be used as a reference. Different shifts of the GMRs are manifested by the dashed curve, illustrating how a dip is shifted when the surrounding medium is changed from air to liquid analyte. Moreover, a hysteresis-free response and repeatability of the measurement were revealed.
Fig. 11. Spectral reflectance ratio $R_{-{\rm 45}}(\lambda )/R_s(\lambda )$ for the RI of the aqueous solutions of ethanol measured at two angles of incidence: $\alpha =-8.4^\circ$ (a), $\alpha =-6.3^\circ$ (b).
The shift of the dips can be magnified by changing the angle of incidence to $\alpha =-6.3^\circ$ ($\theta \approx 64.2^\circ$) as illustrated in Fig. 11(b), showing the measured spectral reflectances $R_{-{\rm 45}}(\lambda )$ for different RIs of liquid analytes and air. These results, including those shown in Fig. 11(a), are in agreement with the theoretical ones presented in Figs. 6(a) and 6(b). In addition, Fig. 12(a) shows the resonance wavelength as a function of the RI of analyte for the dip with the greatest shift (GMR2) and both angles $\alpha$, together with fitting functions (first- and second-order polynomials). Figure 12(a) indicates that the resonance wavelength has a greater shift for a higher RI. In addition, for the greater $\theta$ the function is linear and the sensitivity $S_n$ has a constant value of 349 nm/RIU, while for the smaller $\theta$ the sensitivity $S_n$ increases in the considered range from 234 nm/RIU to 682 nm/RIU, as shown in Fig. 12(b) for the GMR2. Respecting variable depth of the dip, the FWHM is 30 nm and it gives the FOM up to 23 RIU$^{-1}$. Values of the sensitivity and FOM are in good agreement with the theoretical ones ($S_n=$234–751 nm/RIU, FOM=25 RIU$^{-1}$). In the same figure is also shown the sensitivity function for the short-wavelength dip (GMR1) with the constant FWHM (35 nm), and the sensitivity is increasing from 124 nm/RIU to 334 nm/RIU, and the FOM is up to 10 RIU$^{-1}$. The narrowest dip has the smallest shift and this is illustrated in Figs. 11(a) and 11(b) by values of the average sensitivity $S^a_n$ for all the dips. Moreover, the average sensitivity $S^a_n$ for the reference dip changes from 0.4 nm/RIU to $-3.3$ nm/RIU, when $\alpha$ changes from $-8.4^\circ$ to $-6.3^\circ$, and this indicates that the reference dip may be totally non-sensitive by properly adjusting the angle of incidence $\theta$.
Fig. 12. Resonance wavelength as a function of the RI of the aqueous solution of ethanol for the GMR2 and two angles of incidence $\alpha$ with solid lines as fits (a). Sensitivity as a function of the RI of the analyte for two GMRs at angle of incidence $\alpha =-6.3^\circ$ (b).
6. Conclusions
In this paper, sensing abilities of a 1DPhC represented by a multilayer dielectric structure have been analyzed theoretically and experimentally. A new wavelength interrogation interference method has been used and the reflectance responses in the Kretschmann configuration with a coupling prism made of BK7 glass have been modeled using the results obtained from material characterization of the structure by spectral ellipsometry. For a 1DPhC comprising a glass substrate and six bilayers of TiO$_2$/SiO$_{2}$ with a termination layer of TiO$_2$ gas sensing ability based on the BSW resonance has been revealed. The highest sensitivity and FOM deduced from the theory reached 1456 nm/RIU and 91 RIU$^{-1}$, respectively. Experimental results for humid air gave a sensitivity of 0.027 nm/%RH and FOM of 1.4$\times 10^{-3}$ %RH$^{-1}$, respectively.
Liquid analyte sensing ability based on a self-referenced GMR has also been revealed, and the highest sensitivity and FOM reached 751 nm/RIU and 25 RIU$^{-1}$, respectively. Experimentally resolved GMRs in sensing of aqueous solutions of ethanol were with the highest sensitivity and FOM 682 nm/RIU and 23 RIU$^{-1}$, respectively. In addition, it was experimentally confirmed that one of the GMR dips has the smallest shift as the RI changes, and hence it can be used as a reference.
The proposed concept, based on the use of the multilayer dielectric structures that are mechanically and chemically robust, offering the possibility of operation in aggressive environments, is applicable for a wide variety of both gaseous and liquid analytes. Moreover, it has advantages in resonance dips with maximum depth and in a reference dip making the measurement more accurate and repeatable, and less sensitive to optomechanical drifts.
Funding
Science and Research in the Moravia-Silesia Region 2019 (RRC/10/2019); Student Grant System (SP2021/64).
Acknowledgments
The authors would like to thank P. Koleják and D. Vala for the ellipsometric characterization of the thin-film structures.
Disclosures
The authors declare no conflicts of interest.
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