3.2.1. Thin-Film Sensing: Thickness Detection
Figure 4 illustrates the spectral variation of a 249 μm
W MCWM for nine different PAA membranes; the corresponding transmittance values at the first-order peaks were normalized to focus on their spectral shift effect. The various weight densities of the PAA membranes (
ρ) in the figure represent different physical thicknesses deposited on the MCWM. The measured results indicated that the spectral shifts increased with the PAA densities for the first-order dip and peak frequencies, but the frequency shift range of the second-order dip was comparatively small for sensing the same PAA membranes. Furthermore, the spectral positions of the second-order peak frequencies were almost stationary as the PAA membrane densities increased. This finding revealed that the traditional EOT resonance, associated with the second-order peak, did not show sensitivity to the dielectric environment through spectral shifts, and only the transmitted intensity of the EOT was modified due to the sample material loss. A sensing mechanism based on the intensity interrogation of the EOT resonance has been demonstrated in various sensing applications [
22,
24]. In this study, we merely investigated the spectral-shift characteristics of MCWMs at the first-order dip and peak frequencies to identify sample molecular quantities and categories.
Figure 5a shows the measured transmission spectra of the 90 μm
W MCWM loaded with nine different weight densities of PAA membranes compared with that under blank conditions (i.e., orange curve). The dip and peak frequencies of the blank 90 μm
W MCWM were obviously higher than those of the 249 μm
W MCWM (
Figure 2) due to the smaller structural dimensions (
Table 1). In terms of the spectral response for thickness sensing, the first-order transmission dip and peak were gradually redshifted in the spectral range of 0.2–0.9 THz as the densities of the PAA membrane increased. For the curves under blank and low-density conditions (
ρ = 0, 2.59 and 5.71 μg/mm
2), a fluctuating dip in the normalized
Tsample, resulting from the discrepancy in the power measurement for the
Psample+Al+PET mesh and
PPET mesh values, was exhibited at around 0.55 THz, which is an absorption-line frequency of ambient water vapor [
39]. Furthermore, considering the spectral resolution of 14 GHz, in
Figure 5a, the fluctuating spectral range of the three
Tsample curves was exactly 0.549 ± 0.014 THz. Compared to the other water vapor absorption line at 0.75 THz [
39], the fluctuating dip did not occur due to sufficiently high power transmission through the 90 μm
W MCWM, whose transmittance was above 0.1. The normalized
Tsample values at the first dip obviously rose as the PAA density increased. However, the resulting Q factors of the first dip of the 90 μm
W MCWM for sensing each PAA density were certainly sustained without obvious degradation.
The corresponding transmission spectra of the 90 μm
W MCWM simulated using the FEM method are illustrated in
Figure 5b, which shows the first-order dip and peak frequencies for the infiltration of different analyte quantities on the sensing chip. The target PAA membranes are individually presented with different PAA filling ratios (20–100%), which represent various dielectric ratios for the uniform occupation of the 128 μm structural depth of a 90 μm
W aperture (
Table 1). The dielectric membrane thickness in the FEM calculation was determined from the filling ratio of a pore depth, corresponding to the weight density of a PPA membrane in the experiment (
Figure 5a). The spectral shifts of the measured (
Figure 5a) and simulated (
Figure 5b) transmission spectra had the same trend for sensing different thicknesses of PAA membranes. The comparison demonstrated that the infiltration of a dielectric analyte inside the MCWM apertures, i.e., the
W wide pores in
Figure 1, caused an evident spectral shift. A greater sample filling depth within the MCWM pores, representing a greater membrane thickness, resulted in an increased optical path length (OPL) and, thus, a more pronounced spectral shift relative to the spectral dip and peak of the blank MCWM. The experiments also proved that the planar attachment of a 25 μm thick PE film on the 249 μm
W MCWM prevented any spectral shift of the first-order dip and peak. The sensing feasibility and mechanism of using an MCWM to recognize various membrane thicknesses were experimentally and numerically verified. The infiltration of the dielectric material inside the pores was the criterion for successful identification.
Figure 5c shows the measured frequency shifts ∆
f of the first-order spectral dip and peak, relative to the individual spectral positions of the blank 249 and 90 μm
W MCWMs, for the deposition of different quantities of PAA membranes. While the quantity of PAA molecules gradually increased in the pores of the 249 μm
W MCWM, the ∆
f values of the peak and dip slowly increased. That is, the dip and peak ∆
f values were linearly proportional to the PAA membrane density
ρ. The ∆
f values of the peak were larger than those of the dip for
ρ values above 10 μg/mm
2; conversely, the dip and peak frequency waves had comparable ∆
f values for
ρ values lower than 10 μg/mm
2. For the 90 μm
W MCWM, the ∆
f values of the dip and peak both rapidly increased and were linearly proportional to the sample densities before saturation. The MCWM sensitivity for detecting PAA membrane thicknesses could be characterized by the slopes of the linear fitting curves, which are shown in
Figure 5c. The dip frequency wave of the 90 μm
W MCWM had the highest slope value, denoted as
Sd,90. The slope of the 90 μm
W MCWM peak wave, denoted as
Sp,90, was obviously higher than the slope values of the 249 μm
W MCWM dip and peak waves, respectively denoted as
Sd,249 and
Sp,249, but slightly lower than the
Sd,90 value. That is, the sequence order of membrane thickness sensitivity was
Sd,90 ≳
Sp,90 >
Sp,249 >
Sd,249. The THz surface EM mode of the first-order resonance, corresponding to the 90 μm
W MCWM dip wave, had the best thickness sensitivity because it had the greatest field–analyte interaction strength based on the most confined modal profile and the highest
Epeak within a near-field range, as shown by the red curve in
Figure 3e.
Figure 5d illustrates the simulated ∆
f values of the first dip frequencies for the 249 and 90 μm
W MCWMs under a series of PAA membrane filling ratios. The dip ∆
f values of the 90 μm
W MCWM were obviously greater than those of the 249 μm
W MCWM for all the PAA membrane filling ratios. That is, the THz surface EM mode of the first-order dip wave for the small
Aunit size (90 μm
W MCWM) had a larger spectral shift Δ
f than for the large
Aunit size (249 μm
W MCWM). The former device had a denser surface field energy concentration within a shorter near-field range, achieving a larger field–analyte interactive strength compared with the latter device (
Figure 3e,f). The simulated dip Δ
f values increased with the sample amounts, which reasonably agreed with the measured results in
Figure 5c. The theoretical spectral responses were gradually saturated with the increased membrane filling ratios and were well-fitted by the exponential curves with a coefficient of determination above 0.98 (R
2 > 0.98). However, each filling ratio for the two different aperture sizes of the MCWMs did not represent the same PAA quantity inside the apertures of the two MCWMs. Therefore, the saturation behavior of the simulated curves in
Figure 5d was not exactly consistent with that of the measurements presented in
Figure 5c.
For the same PAA membrane infiltration quantity in the 90 and 249 μm
W MCWMs (
Figure 5c), the small apertures of the 90 μm
W MCWM reached the saturated spectral shift first due to the highly confined modal profiles at both the dip and peak frequencies (
Figure 3e). For the 249 μm
W MCWM, the distinctly large modal profiles at the corresponding dip and peak frequencies (
Figure 3f) were still not fully covered by the maximum PAA density at around 80 μg/mm
2 because of the large apertures and, therefore, it did not reach the saturation of the spectral shift in the experiment, as shown in
Figure 5c. The Δ
f values of the 90 μm
W MCWM were greater than those of the 249 μm
W MCWM for all the PAA membrane densities because of two factors. The first factor was the high filling ratio under the same PAA infiltration quantity, which meant that the refractive index of air, 1.0, was replaced by that of a PAA membrane, >1.0, so that the 90 μm
W MCWM had a greater OPL. Second factor was the sharp modal profile with a high peak intensity (
Figure 3e) that effectively interacted with the loaded PAA membranes. However, for the same filling ratio in the FEM calculation, the dip Δ
f values of the 90 μm
W MCWM were still higher than those of the 249 μm
W MCWM, as presented in
Figure 5d. This finding showed that the experimental results of the spectral responses in
Figure 5c were mostly determined by the second factor, which achieved a strong field–analyte interaction.
On the basis of the E-field distributions in
Figure 3e,f, the integral of the 1D E-field profile with respect to the
Z-axial position is illustrated in
Figure 6, where the integrating ranges are 150–290 and 350–690 μm for the 90 and 249 μm
W MCWMs, respectively.
Figure 6 depicts the accumulated electric field intensity along the Z-direction while the membrane thickness increasingly infiltrated the pores, corresponding to the thickness increase in the
Z-axial position. For the 249 μm
W MCWM, the E-field integral of the peak frequency was much greater than that of the dip frequency when the membrane thickness was large enough for
Z > 419 μm (cyan and green curves, respectively, in
Figure 6). The results of the 1D E-field integral for sensing thick membranes thus demonstrated that the peak Δ
f values were larger than the dip Δ
f values for sensing PAA membranes with the 249 μm
W MCWM (
Figure 5c). However, the curve trend was inverted as the membrane thickness became thinner than 419 μm (
Z < 419 μm). The measured dip Δ
f values approximate to the peak Δ
f values for a PAA density lower than 10 μg/mm
2 cannot be interpreted from
Figure 5c, because the 1D integral of the E-field was calculated at only one specific
X-axial position, which was insufficient for reflecting the overall field–analyte interaction strength. To evaluate the interactive strength on a thin membrane of less than 419 μm, the 2D integral of the electric field on the
XY plane should be considered for each
Z-axial position.
For the 90 μm
W MCWM, the measured Δ
f values of the dip and peak in
Figure 5c were similar and rapidly increased below the sample density of 10 μg/mm
2. The dip and peak Δ
f values were then saturated at 10 and 25 μg/mm
2, respectively, to terminate their linearly proportional relation with the PAA membrane density (
ρ) (
Figure 5c). The saturation of the spectral shift was due to the almost complete coverage of the
Z-axial E-field profile with the PAA membrane thickness (
Figure 3e,f). This also meant that the OPLs of the dip and peak frequency waves for the 90 μm
W MCWM did not change obviously at saturation. The measured results presented in
Figure 5c showed that the peak Δ
f values were obviously greater than the dip Δ
f values when the PAA membrane density increased above 25 μg/mm
2. These spectral responses of the 90 μm
W MCWM could be explained by the 1D E-field integrals, as shown in
Figure 6. For the thin membrane thickness with a membrane–air interface at the
Z-axial position of around 150 μm (
Figure 6), the E-field integral of the dip frequency was obviously larger than that of the peak frequency, which agreed with the trend observed between the dip and peak Δ
f values of the 90 μm
W MCWM for sensing PAA densities lower than 10 μg/mm
2 (
Figure 5c). As the membrane densities (i.e., thicknesses) gradually increased, the dip Δ
f value reached saturation first due to the more confined E-field profile of the dip frequency wave (
Figure 3a) compared with that of the peak frequency wave (
Figure 3c). This means that the integral E-field value in
Figure 6 for the dip wave, denoted by a black curve, was much greater than that of the peak wave, denoted by the red and blue curves, at the same
Z-axial position. When the membrane thickness further increased (
ρ >10 μg/mm
2), the dip Δ
f value could not increase further because the
Z-axial modal profile range was smaller than the PAA membrane thickness. In contrast, the peak Δ
f values increased for
ρ > 10 μg/mm
2 because of the broadened electric field distribution along the
Z-axis, where the E-field range extended from the metal surface input side to the PET substrate output side, as shown in
Figure 3c. This experimental result, presented as green squares and red triangles in
Figure 5c, reveals that thickness sensing should be conducted in the near-field range of the apparently confined E-field profile to gain a sufficiently overlapped integral of field and matter, leading to a high-sensitivity performance.
3.2.2. Thin-Film Sensing: Refractive Index Detection
Figure 7 shows the experimental sensing results of the refractive index using the 90 μm
W MCWM. To produce a series of membranes with different refractive indices, various weight concentrations of lactose powders were dissolved in the 1 wt% PAA aqueous solution and deposited on the MCWMs via the drop-and-dry process to form lactose-doped PAA membranes. As shown in
Figure 7a, the spectral position of the first-order spectral dip was significantly redshifted with increasing lactose dosages. On the basis of the resonance principle of a surface EM mode, this redshift in
Figure 7a resulted not only from the increment in the refractive index but also from the increment in the thickness for one lactose-doped PAA membrane. The frequency shift responses to various thicknesses and refractive indices of lactose-doped PAA membranes are respectively illustrated in
Figure 7b,c.
Figure 7b summarizes the dip Δ
f of the 90 μm
W MCWM in response to various thicknesses (Δ
Z in
Figure 3a–d) of PAA membranes with and without lactose doping, which were respectively obtained from the transmitted spectra in
Figure 5a and
Figure 7a. The physical thicknesses of the pure and lactose-doped PAA membranes in
Figure 7b were measured by an α-step profiler. The doped and undoped pure PAA membranes demonstrated a similar trend in spectral response, with an initially linear proportional relation followed by saturation between the Δ
f and Δ
Z parameters. These lactose-doped and pure PAA membrane trends were fit with exponential functions that are illustrated in
Figure 7b by the green and cyan curves, respectively. Within the same thickness range of 15–20 μm (
Figure 7b), the measured dip Δ
f values of the lactose-doped PAA membranes exhibited a proportional response and were obviously larger than those of the pure PAA membranes, whose Δ
f–Δ
Z relation curve in the 15–20 μm Δ
Z range reached saturation inversely. Additionally, the measured dip Δ
f of the 0% lactose membrane was located on the cyan curve of the pure PAA membrane, which represents the thickness sensing results for the pure PAA membranes (
Figure 5a). For lactose concentrations above 0%, the corresponding dip Δ
f values were larger than those of pure PAA membranes above 15 μm. The dip Δ
f values of the lactose-doped PAA membranes were thus larger than those of the pure PAA membranes even though they had the same physical thicknesses above 15 μm. This finding reveals that the linear response of the Δ
f–Δ
Z relation and the high measured Δ
f values for the doped PAA membranes predominantly originated from the refractive index change induced by the various lactose doping ratios (
Figure 7b). According to the slope of the linear fitting curve (the blue line in
Figure 7b) and the minimum spectral resolution of 7.32 GHz for our THz-TDS system, the sensitivity and LOD of the thickness sensing could thus be estimated as 8.26 GHz/μm and 886 nm (λ/531), respectively, for pure PAA membrane detection. The minimum thickness measured in the experiment was 5.36 μm, corresponding to λ/88. This also reflects that the scale at which the PAA membrane surface roughness influences the measurement or thickness sensing uncertainty is approximately the micrometer level.
Figure 7c displays the measured and calculated dip Δ
f values versus various effective refractive indices (
nmix) of lactose-doped PAA membranes, whose dip Δ
f values were obtained from those of the green circular points in
Figure 7b with a thickness range of 15–35 μm. The corresponding
nmix values were estimated as described below. The
nmix of the lactose-doped membranes in the measurement experiments was calculated based on the effective medium theory [
40], as shown in Equation (2):
where
nPAA,
nlactose, and
ρlactose are the refractive indices of PAA, lactose, and the volume ratio of lactose for one lactose-doped PAA membrane, respectively. The refractive indices of the lactose and PAA used to calculate the
nmix value in Equation (2) were 1.64 and 1.3, respectively, as measured from lactose tablets and thick PAA films in a THz-TDS system. The simulated dip Δ
f of the lactose-doped PAA membrane in
Figure 7c could be acquired from the FEM and iterative method based on the initial
nmix and depth filling ratios that were obtained from the measured membrane thicknesses in
Figure 7b. The measured and calculated results in
Figure 7c show that the proportional response between the dip Δ
f and
nmix occurred in both the experiment and the numerical simulation with a high degree of agreement. For lactose concentrations of 0–37.5% (
Figure 7a) or measured thicknesses of 15–20 μm (green circles in
Figure 7b), the proportional relation between Δ
f and
nmix was further linearly fitted, and a coefficient of determination greater than 0.99 (
R2 > 0.99) was found (
Figure 7c). The other measured
nmix data (i.e.,
nmix = 1.437 and 1.457) for lactose concentrations above 37.5% or measured thicknesses larger than 20 μm were not considered in this linear fitting process. According to the slope of the linear regression for the detection of small amounts of lactose (i.e.,
nmix of 1.315–1.425 in
Figure 7c) and the measured Δ
f inaccuracy, the sensitivity and the LOD of the 90 μm
W MCWM refractive index sensing were 547 GHz/RIU and 0.0134 RIU, respectively.
On the basis of the experimental results of thin-film sensing (
Figure 7b,c), the dip Δ
f was strongly correlated with the optical constant
nmix and the thickness Δ
Z of the membranes. The dip Δ
f of the 90 μm
W MCWM with respect to the membrane OPL, excluding the saturation region, is further summarized in
Figure 7d, where the OPL value equals the product of the
nmix and Δ
Z. That is, the data points in
Figure 7d were collected from the data points covered by the red and blue fitting lines in
Figure 7b. The dip Δ
f values proportionally increased with the OPL values, having an extremely high coefficient of determination (R
2 ~0.99) in the linear regression. On the basis of the linear fitting slopes and the measurement errors of the Δ
f in
Figure 7d, the sensitivity of thin-film sensing, represented in terms of OPL, was estimated as 5.35 THz/RIU∙mm. Based on the OPL sensitivity, the LOD of a high-refractive-index material, such as a semiconductor, could decrease lower than that of a polymeric material with a low refractive index.
3.2.3. Detection of an Inhomogeneous and a Nonuniform Analytes
The pure and lactose-doped PAA overlayers used respectively for the thickness and refractive index detections were essentially homogeneous and uniform for the MCWMs. However, when the dielectric membranes become inhomogeneous or nonuniformly distributed analytes, the sensing capability and sensitivity analysis of the MCWMs should be individually specified. In the study, the electrolyte salts and PE microspheres were considered nonuniform and inhomogeneous samples for MCWM sensing, respectively.
Figure 8a illustrates the measured transmission spectra of the 90 μm
W MCWM for sensing various amounts of salt grains, which were prepared from different concentrations of DPBS. The findings showed that the first spectral dip shifted to the low-frequency region compared to that of the blank 90 μm
W MCWM as the salt particle amount increased. The inset photo of
Figure 8a shows the salt grains, obtained from a 40
v/
v% DPBS solution and nonuniformly deposited on the 90 μm
W MCWM.
Figure 8b shows the transmission spectrum of the 90 μm
W MCWM for different concentrations of PE microparticles mixed in the PAA membrane. The thin PAA polymeric matrix could stably fix the PE sphere particles. However, the dip Δ
f values were reduced as the concentration of PE microparticles increased, which was opposite to the spectral responses for salts.
Figure 9 summarizes the experimental spectral responses of the 90 μm
W MCWM at the first spectral dip Δ
f relative to different weight densities of the four kinds of samples, namely the lactose-doped and pure (undoped) PAA membranes, PE microparticles, and salt grains. For the sensing results of the PE sphere particles, the thickness of the deposited PAA matrix was approximately 25 μm, as estimated from the dip Δ
f values of both 0 wt% PE-particle-doped and pure PAA membranes, which were measured individually in the experiments. That is, the dip Δ
f value of the first data point of the blue triangles in
Figure 9 matched that of the pure PAA membrane with a thickness of 25 μm, as detected in
Figure 7b. The 25 μm thick PAA matrix caused the dip Δ
f value to approach the saturated dip shift of the undoped PAA membrane (black squares of
Figure 9). The thickness was sufficient to firmly adhere the PE sphere particles to the metallic surface of the MCWM; however, it was obviously smaller than the PE sphere diameter (34–50 μm). The experimental results showed that the large PE sphere particles scattered the field of the THz surface EM mode on the MCWM surface without driving the THz dispersion of PAA and inevitably reduced the dip Δ
f value, which was severe at high concentrations of microspheres, as shown in the inset of
Figure 9 (blue triangles).
The experimental results of the PE sphere particles (inset of
Figure 9) showed that the measured dip Δ
f within the linear response region ranged from 0.153 to 0.072 THz, corresponding to a maximum frequency variation of 0.081 THz. This result approximated the saturated frequency variation of 60–80 GHz for sensing polystyrene microbeads using e-SRR-based metamaterials [
41]. This study demonstrated that the microbeads should be placed precisely in the microgaps of the e-SRR arrays to reach the maximum frequency variation of 80 GHz [
41]. The necessity of placing sample particles in critical locations limits the practical applications of this method. Aside from the PE sphere particles, the other three sample types showed proportional and saturated Δ
f value responses at low and high particle densities. The saturated Δ
f values for salt sensing were more than two-fold higher than the others (
Figure 9) because of the larger refractive indices of the salt grains in the THz frequency. The measured refractive index of the DPBS salt tablets was around 2, which was higher than that of the PAA slab (1.3) and the lactose tablet (1.64). This finding revealed that the sample refractive index had a substantial impact on the first spectral dip shift of the MCWMs.