1. Introduction

Guided-mode resonance (GMR) has gained research interest since the early 1990s [1–4], which is also known as resonant grating waveguides [5], resonant waveguide gratings [6], photonic crystals [7], and photonic crystal slabs [8]. The GMR effect has been demonstrated theoretically and experimentally [1–4]; various designs and experimental setups for obtaining this effect have been applied to different fields and applications, such as optical communications [9], displays [10], pressure sensors [11], strain sensors [12], photovoltaics [13], lasers [14,15], bioimaging [16], and fluorescence detection [17]. GMR-based label-free biosensors were one of the most studied devices due to their various applications. These devices were also commercialized by several companies as desktop-sized systems.

Typically, GMR devices comprise a substrate, waveguide, and subwavelength grating. The grating can be placed on top of the waveguide, can be embedded in the waveguide, or can be combined with the waveguide in other configurations as long as the waveguide modes overlap the grating structure. For a broadband light source at normal incidence, a specific wavelength of light (resonant wavelength, $\lambda_{R}$) reflects back and the remaining light transmits through a GMR when suitable dimensions and materials are selected. A transmission dip or reflection peak can be observed through experimentation with the dip or peak wavelength corresponding to $\lambda_{R}$. Moreover, $\lambda_{R}$ can be calculated based on the second-order Bragg condition [18]:

Here, n_eff represents the effective refractive index (RI), and L denotes the grating period. Note that n_eff is the weighted RI of the overall structure that supports the waveguide modes and is related to the low RI of the substrate, high RI of the dielectric waveguide layer and cover (sample) layers, and thickness of the waveguide layer. The explicit formula to calculate the value of n_eff was published previously [19].

Changes of the RI of cover layers due to different sample concentrations or different quantities of surface bound biomolecules cause variation in the values of n_eff and $\lambda_{R}$. This variation was identified to be a change in the wavelength shift through a high-resolution spectrometer with a broadband light source [20,21] or a tunable light source and photodetector [22,23]. Other methods that are based on the change in the incident angle [24], reflected intensity [25], and phase variation [26] are also demonstrated.

Different designs and fabrication techniques have been demonstrated to realize a tunable GMR filters for various applications [27–31]. In 2017, Triggs et al. [32] proposed a chirped GMR-based biosensor based on graded duty cycles, instead of using the GMR effect with a fixed grating period. Our group also demonstrated RI sensors based on two types of gradient GMRs—gradient grating period (GGP) GMR (GGP-GMR) [33] and gradient waveguide thickness (GWT) GMR (GWT-GMR) [34]. The basic mechanisms for gradient GMRs is as follows: light resonates at a specific duty cycle [32], grating period [33], or waveguide thickness [34] such that the light is reflected back at this particular location and transmitted to other locations at a fixed incident wavelength and a given sample concentration (with a particular RI). Therefore, charge-coupled devices (CCDs) in these types of gradient-GMR-based sensors exhibit a dip-like intensity distribution and the minimum intensity corresponding pixel (MICP) can be recorded. According to Eq. (1), an incident wavelength must resonate at a different grating period, waveguide thickness, or duty cycle when a change occurs in the sample solution or RI. Subsequently, the dip-like intensity distribution and the MICP of the CCD varies accordingly. Here, the amount of shift can be correlated to the amount of change in the sample concentration or RI [33,34].

Compared with a regular GMR-based sensor with a fixed grating period, the use of gradient-GMR-based RI sensors presents several advantages as follows. First, compared to uniform GMRs using wavelength modulation technique, the use of an expensive spectrometer can be avoided by directly converting spectral information into spatial information. Second, the sensor can use any suitable, inexpensive, readily available light-source, such as an LED, LD, or vertical-cavity surface-emitting laser. Third, the spectral shift in pixels is converted to spatial shift at the CCD. This measurement is self-referencing and could be more accurate than that obtained by conducting a typical intensity modulation measurement [32]. Fourth, the light source is illuminated normally at the sensor without sophisticated optical alignment and the transmitted intensity can be directly measured from the CCD, so gradient GMR is suitable for integration with a smartphone or handheld device. This could have great potential for a future Internet of Medical Things.

For a gradient GMR, sensitivity can be defined as the ratio of the shift in MICP to the change in sample RI. A gradient can be flattened to increase its sensitivity (and thus to produce a larger shift in MICP). Typically, this increases the size of the sensor used for the same detection range and can complicate the optical setup and increase the overall system size because the beam size must be expanded to cover the entire sensor. The detection results for solutions with 0%–60% sucrose solution in mixtures from studies using GGP-GMR [33] and GWT-GMR [34] are summarized in Table 1. That table indicates that GWT-GMR exhibits higher sensitivity and a lower detection limit, but GGP-GMR provides a much more compact sensor size for the same detection range.

Table 1. Comparison between GGP-GMR and GWT-GMR

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Two-dimensional arrays of CCDs or CMOSs are mature products that can easily be purchased commercially; thus, in this work, we introduced a 2D gradient in a single GMR sensor, which is termed as our 2D gradient GMR (TDG-GMR). A TDG-GMR is demarcated in terms of the GGP in one direction and gradient waveguide thickness in another direction to simultaneously maintain optimal sensitivity and limit of detection (LOD) and to achieve a broad detection range with a compact sensor chip. For presenting the detection principle, an analogy can be drawn between a TDG-GMR and a ruler. In the GGP direction, each pixel can be thought of analogous to one centimeter. In the GWT direction, a single pixel is used to resolve variations smaller than those in the GGP direction; this can be compared to a ruler marked with millimeters providing better resolution than a ruler marked with centimeters. The calibration details of both GGP-GMR and GWT-GMR are discussed in a later section.

2. Method

The overall experimental setup, a TDG-GMR sensor design, and the working principle of the sensor are illustrated in the Fig. 1. Each part is discussed in the following sections.

 

Fig. 1. (a) Sketch of a TDG-GMR and the intensity distribution on a CCD exhibiting a slanted dark band. (b) Illustration of the overall experimental setup. (c) Illustration of the shift in the dark bands for samples with large variation, and (d) the intensity distribution along the yellow line, which is in the GGP direction. (e) Illustration of the shift in the dark bands of two samples with a small difference in their RIs, and (f) intensity distribution along the yellow dashed line, which is in the GWT direction.

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2.1 Design and fabrication of TDG-GMR

The TDG-GMR comprises the GGP in one direction and the GWT in another direction (Fig. 1(a)). The grating period varies from 250 to 550 nm with increments of 2 nm with each period, thus comprising 100 repeated cycles. The waveguide thickness varied from 79 to 124 nm in the orthogonal direction with a gradient value of approximately 4.5 nm/mm. The overall chip dimension was 6 × 10 mm². However, in this study, a very small portion (approximately 150 × 130 µm²) of the sensor was used to demonstrate the RI and biomolecule measurement.

Three main processes were used to fabricate the TDG-GMR—electron beam lithography (EBL), replica molding, and sputtering deposition. The fabrication process was initiated using EBL and reactive ion etching (RIE) to fabricate a GGP on a Si master. Then, replica molding was used to replicate the structure on an ultraviolet-curable polymer (Norland 68, NOA68) placed on a flexible plastic sheet comprising a polyethylene terephthalate layer. Finally, the replicated sample was placed in a self-made fixture, and sputtering deposition was employed to deposit a gradient TiO₂ layer to complete the process. The detailed fabrication processes can be found in our previous studies [34,35].

2.2 Design and fabrication of a microfluidic channel

A microfluidic channel was fabricated and was attached to the TDG-GMR for providing various sample solutions. The microfluidic channel was fabricated using a polydimethylsiloxane polymer (PDMS) (Sylgard 184 Elastomer Kit, Dow Corning Corporation, USA) and poly-methyl methacrylate (PMMA) mold. First, a PMMA mold with a height of 3 mm and central width of 10 mm was manufactured using micromilling (EGX-400 engraving machine, Roland, USA). Second, the mold was covered with a layer of Sylgard 184 silicone elastomer (or PDMS) with a resin and curing agent ratio of 8:1. Subsequently, the PDMS–PMMA structure was cured at 90 °C for 60 min in an oven. In contrast to the commonly used resin:curing agent ratio of 10:1, a higher proportion of curing agent was used in this experiment to increase the PDMS channel stiffness. The high stiffness prevented channel deformation during sample delivery. Subsequently, the PDMS was separated from the PMMA mold, and inlet and outlet holes were punched using a biopsy punch (Ted Pella Inc., USA).

The TDG-GMR sensor was first bonded with a glass slide through NOA68 to integrate the TDG-GMR sensor with the microfluidic channel. Subsequently, the PDMS microfluidic channel was irreversibly bonded with the glass slide after both devices were treated with oxygen plasma (Zepto plasma, Diener, DE) under 5-N oxygen pressure of 1 mbar (0.5 L/h⁻¹) at 60 W for 60 s. Finally, the tube was connected to the access hole; this enabled subsequent sucrose measurement to compare the sensor performance in terms of sensitivity and LOD in the GGP and GWT directions. The device was also used for albumin detection to demonstrate its usefulness for practical biosensing applications.

2.3 Working principle

A specific wavelength of light resonates at the appropriate combinations of grating period and waveguide thickness when a narrowband of light is used to illuminate a TDG-GMR. In this case, the light is reflected back from particular locations. When a CCD is used under the TDG-GMR, a minimum intensity is obtained. This intensity is observed as a dark band in Fig. 1(a). The measurement principle in the GGP and GWT directions is displayed in Fig. 1(c)–1(f). Figure 1(c) represents three dark bands on the CCD that correspond to three different samples. The intensity distributions along the GGP direction represented by the yellow line in Fig. 1(c) are illustrated in Fig. 1(d). The shift in the MICP can be used to correlate the changes in the sample concentration. The dark bands measured on the CCD are represented by black- and red curves in Fig. 1(e) when the difference between the sample concentrations is small. In this case, the intensity distributions along the yellow line in the GGP direction exhibit the same MICP value due to the limited LOD in the GGP direction. However, the intensity distribution along the GWT direction (yellow dashed line) exhibited by these two dark bands have different MICPs (Fig. 1(f)) due to the higher resolution provided by GWT-GMR. In this manner, the approximate concentration can be estimated in the GGP direction first. Then, an accurate concentration may be obtained in the GWT direction.

3. Experimental results and discussion

3.1 Measurement of the gradient resonant wavelength

The transmission spectra at different spatial locations were obtained to verify the gradient resonance of the fabricated TDG-GMR. To obtain the spectra, the TDG-GMR was mounted on a 2D translational stage with a resolution of 10 µm. A 50-µm optical fiber connected to a broadband light source was in close proximity to illuminate the TDG-GMR at normal incidence. The transmitted light passing through a polarizer was collected using another fiber connected to a spectrometer. Transverse magnetic (TM) polarization was conducted throughout this study due to the narrower linewidth of this method for obtaining a higher detection resolution.

We first measured the transmission spectra at different grating periods but with the same TiO₂ thickness, as illustrated by the white dashed line in Fig. 1(a). The results are summarized in Fig. 2(a). The spectra was measured from the smallest grating period of 0 mm. The translational stage was gradually moved such that the incident light illuminated at the GMR at a larger grating period. The resonant wavelengths gradually increased toward the longer wavelengths, as predicted in Eq. (1). The resonant wavelength varied from 455 to 839 nm for a length of 5.5 mm along the GGP direction, which provides a gradient resonance value of approximately 69.8 nm/mm. The transmission efficiency at a resonant wavelength value between 455 and 754 nm (corresponding to the position from 0 to 4 mm) was between 22% and 33% with linewidth between 6.9 and 12.6 nm. The transmission efficiency increases slightly with the resonant wavelength when the resonant wavelength is greater than 782 nm (corresponding to the position of 4.5 mm and the estimated grating period of 490 nm), thus indicating decrease in the coupling efficiency. Moreover, two resonant peaks were observed as shown at locations of 4.5, 5, and 5.5 mm at larger periods. One of the reasons for these double peaks was possibly because of a slightly off normal incidence resulting from the bonding of a large TDG-GMR on a glass slide. A more detailed discussion on transmission spectra measurement can be found in our previous study [35].

 

Fig. 2. Transmission spectra along the (a) GGP direction at a constant TiO₂ thickness and (b) GWT direction at a constant grating period. (c) Resonance map for a 1.1 × 1.4 mm² region.

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Regarding the variation of the resonant wavelength along the GWT direction with the same grating period, we measured the transmission represented by the blue dashed line in Fig. 1(a). The results are displayed in Fig. 2(b). Moreover, n_eff increases with the TiO₂ thickness. Thus, the resonant wavelength gradually increases from 599 to 634 nm. The thickness of TiO₂ increased while gradually moving the translational stage with an increment of 1 mm, thus resulting in a resonance gradient of 3.5 nm/mm. The resonant wavelength exhibits a 20-times flatter gradient in the GWT direction than the GGP direction (3.5 vs. 69.8 nm/mm). This implies that the detection range is smaller in the GWT direction but with a much higher resolution at the same length in both directions. The reflection efficiency was between 23.6% and 30.5% and the linewidth was between 9.11 and 13.96 nm at a position beyond 4 mm (the estimated TiO₂ thickness of 90 nm) and a resonant wavelength of 606.8 nm. The device had slightly higher transmission efficiency (35%–37.4%) at a position between 0 and 3 mm. This result indicates a poor coupling efficiency, which was probably due to insufficient TiO₂ thickness.

The broader linewidths compared to that obtained in simulation (not shown here) or in other literatures on the traditional GMRs with a fixed grating period and nonuniform waveguide thickness are possibly due to the following reasons. First of all, the illumination spot in the transmission measurement actually comprises more than one period and varying TiO₂ thicknesses due to the nature of the gradients in both direction in our TDG-GMR sensor. Additionally, the replicated grating structure on the NOA68 and the subsequent deposition TiO₂ exhibited slightly rounded edges and corners [34], which could also cause deteriorating resonance resulting broaden linewidth. Nonetheless, the resonant wavelength map generated by moving the translational stage with 0.1-mm increments in both GWT and GGP directions in a 1.1 × 1.4 mm² region (red rectangle in Fig. 1(a)) was presented in Fig. 2(c). This confirms that the TDG-GMR was successfully fabricated with the gradient resonant wavelengths in both directions. This region will be used in the following sample measurement.

3.2 Measurement of sucrose solution

Sucrose solutions were used to verify the proposed TDG-GMR sensor and investigate the sensitivity and LOD of the fabricated TDG-GMR. The calibration procedure for the measurements is explained in this section. The vertical experiment setup is displayed in Fig. 1(b). A narrow band of light with a wavelength of 625 nm that was generated from a monochromator (DK242, Spectral Products) was coupled into a fiber (QP600-2-UV-VIS, Ocean Optics) with a 600-µm-diameter core that has a collimator at its exit. The light was TM polarized before it was incident on the sample and interacted with the TDG-GMR sensor. The transmitted light was then recorded using a CCD (SMN-B050-U, Mightex) with a total pixel count of 2560 × 1920; each pixel has a size of 2.2 × 2.2 µm². The calibration procedure is described in the following section.

3.2.1 Calibration in the GGP direction

First, the approximate interval of the concentration (or RI) was determined in the GGP direction. The experiment was conducted for solutions with 0% (water only)–60% sucrose content with an increment of 5%. Each sample solution was aspirated out before applying the next sample solution. The experiment was conducted for total of three runs, and the TDG-GMR was rinsed with water between each runs.

Two intensity distribution examples on the CCD for 0% and 60% sucrose content are presented in Fig. 3(a) and 3(b), where the gradient period and waveguide thickness are in the horizontal and vertical directions, respectively. As aforementioned, the light is reflected back and causes dark bands (the slanted dark line) in the CCD when the appropriate combination of grating period and TiO₂ thickness is used. The pixels in the middle row of the CCD (blue line) indicate that the same TiO₂ thickness was selected to determine where the MICPs were for each concentration along the GGP direction. Figure 3(c) displays the intensity distributions for solutions with 0 and 60% sucrose content along the blue line presented in Fig. 3(a) and 3(b), which clearly exhibits a shift. The shift values in the MICPs of different sucrose solution concentrations with respect to that of the 0% solution are summarized in Fig. 3(d), which exhibits a linear response. The total shift value in the MICP was approximately 64 pixels for 0%–60% sucrose solutions.

 

Fig. 3. The CCD image for (a) 0% and (b) 60% sucrose solution. (c) Intensity distribution along the blue line. (d) Shift in MICP as a function of the sucrose concentration. The corresponding refractive indices for different concentrations were based on the literature results [36].

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The sensitivity value indicated the amount of shift in the MICP relative to the amount of change in the RI of the sample and can be defined as the slope of the linear fitted curve (Fig. 3(d); 1291.3 µm/RIU or approximately 1 pixel/%). The definition of sensitivity used in gradient GMRs differs from the commonly used definition in relevant studies of spectrometer measurements, which is the ratio of the amount of peak wavelength shift to the change in RI variation. In this study, the LOD value was calculated as three times the average standard deviation (0.624 pixels or 1.3728 µm) obtained from all measurements divided by the sensitivity value, which is 3.19 × 10⁻³ RIU (∼1% in sucrose concentration).

3.2.2 Establish a pixel reference line in the GGP direction

Experiments were conducted for solutions with sucrose content between 0% and 5% with a 0.5% increment to further investigate the detection limit. Due to both electronic noise and random noise from the CCD and light source, the MICP fluctuated but gradually shifted with increases in sample concentration. Moreover, the total MICP shift was approximately 4–5 pixels (Fig. 4). The average MICP at pixel 184 for 2.5% can then be selected as a reference column for the 0%–5% measurement. One can use the same procedure for other concentration ranges.

 

Fig. 4. Pixel shift of 0% to 5% with an increment of 0.5%

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3.2.3 Calibration in the GWT direction

Once the reference column of pixels (i.e., column no. 184, which indicates the same grating period) is decided for solutions with sucrose content between 0% and 5%, the MICP shift within a 5% interval is calibrated at these columns in the GWT direction. Thus, the experiment is initiated from 0% (water only) to 5% with an increment of 0.5%.

Figure 5(a) and 5(b) display the CCD images for solutions with 0% and 5% sucrose content, respectively. The intensity distributions along the reference column indicated by the green line were presented in Fig. 5(c). Raw data was fitted using a mathematical model to define the MICP appropriately. Figure 5(d) displays the fitted intensity distribution for all sucrose concentrations and indicates that the GWT direction can appropriately resolve the 0.5% difference in the sucrose solutions. The relationship between the shift value in the MICPs of different concentration solutions with respect to the MICP of the solution with 0% sucrose concentration is presented in Fig. 5(e).

 

Fig. 5. CCD images for solutions with sucrose content of (a) 0% and (b) 5%. (c) Raw and fitted intensity distributions along the reference column (green line). (d) Fitted intensity distribution along the reference column for the 0% to 5% solutions with an increment of 0.5%. (e) Shift in MICP as a function of the sucrose concentration in the GWT direction.

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The total shift in MICP was approximately 57 pixels for a 5% difference in the sucrose concentration, which was a much higher shift than that obtained in the GGP direction (∼5 pixels). This implies that higher sensitivity and better LOD values were obtained in the GWT direction, as explained in the previous section. The sensitivity was determined as the slope of the linear fitted curve and was 17129 µm/RIU, which was approximately 13 times the slope obtained in the GGP direction. The standard deviation for all the measurements was 3.21 µm (or 1.46 pixels). Thus, the resulting LOD was 5.62 × 10⁻⁴ RIU, which was approximately one order smaller than the value (3.19 × 10⁻³ RIU) in the GGP direction.

3.2.4 Establish a reference plane

The same procedure can be applied to other concentration intervals, such as 5%–10% and 10%–15%. For example, in 5%–10%, a reference column can be found for 7.5%. Then, the experiment can be conducted for 5%–10% to determine the MICP shift in the GWT direction in this column. Eventually, one can establish a reference plane for the interested concentration range.

3.2.5 Unknown sample measurement

To determine the concentration of an unknown sample, the approximate concentration range can be first determined based on the MICP value by referring to the intensity distribution in the GGP direction (Step 1). Then, the corresponding reference column can be used to obtain the intensity distribution and the MICP in the GWT direction. The concentration can then be determined on the basis of the calibration plane.

3.3 Biomolecule detection

Albumin was used as a test model to demonstrate the use of the TDG-GMR for biomolecule detection. Thus, the TDG-GMR surface was first silanized by applying epoxy sliane (1% 3-Glycidoxypropyl dimethoxysilane in toluene) on the top of the TDG-GMR sensor surface after oxygen plasma treatment. After incubation for 60 min at room temperature, the GGP-GMR sensor was rinsed with acetone, ethanol, and then deionized (DI) water; finally it was blown dry with N₂ gas. After the aforementioned bonding with the microfluidic chip, phosphate buffered saline (PBS) was injected into the channel to stabilize the sensor. The PBS was aspirated; 100 µg/mL of anti-albumin antibodies (CSB-PA00060E1Rb, Cusabio) were mixed in PBS and the mixture was injected; the system incubated for 30 min. The sample was then aspirated and the sensor was rinsed with PBS.

During the experiment, the intensities on the CCD were recorded after every 10 s and the corresponding MICP values were determined in both GGP and GWT directions (Fig. 6(a)). The resulting MICP shift was approximately 50 µm in the GWT direction, which indicates an approximate enhancement of 14.7 times relative to that in the GGP direction (∼3.4 µm). The results are comparable to those obtained from sucrose measurement, where the sensitivity in the GWT direction was 13 times higher than that in the GGP direction.

 

Fig. 6. (a) Shifts in the MICP with time for antibody immobilization in the GGP and GWT directions. (b) Shifts in the MICP with time for the different albumin binding concentrations in the GGP and GWT directions. (c) and (d) Dose-response curves for the GGP and GWT directions.

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Three different albumin concentrations were tested. The experiment was initiated with an injection of 20 µg/mL of albumin and incubation of the sample for 30 min, followed by rinsing of the sample with PBS. The procedures were repeated for 100 and 500 µg/mL of albumin. The relative shift in the MICP against time is displayed in Fig. 6(b). The binding with albumin caused a much larger shift in the GWT direction for all three concentrations due to the small resonance gradient that provided high sensitivity. The MICP shifts as functions of the albumin concentrations in the GGP and GWT directions are presented in Fig. 6(c) and 6(d), respectively.

A concentration variation between 100 and 500 µg/mL of albumin could be identified based on the MICP shift in the GGP direction. However, the concentration variation could not be identified between 20 and 100 µg/mL. Conversely, 20 and 100 µg/mL can still be distinguished through the MICP shift in the GWT direction. These phenomena are in agreement with our notion that GWT-GMR has higher-than-usual sensitivity due to its flatter-than-usual gradient.

3.4 Discussion

3.4.1 Compact sensor size

As mentioned in the Introduction, this type of sensor has a tradeoff between detection range and LOD for a given gradient GMR sensor size. A sensor with only a single gradient, such as a GGP-GMR system, can achieve a detection range of 0.109 RIU with a size of ∼150 µm but can deliver an LOD only on the order of approximately 10⁻² to 10⁻³ RIU. By contrast, a GWT-GMR with a thickness gradient of 7.14 nm/mm [34] can achieve an LOD of 7.39×10⁻⁴ RIU, but to have a detection range of 0.109 RIU, it must have a GWT-GMR that is 1.26 mm in length.

With the proposed TDG-GMR, the total shift was approximately 64 pixels for solutions with sucrose content of 0% to 60% in the GGP direction. The MICP shifted by approximately 57 pixels in the GWT direction for solutions with sucrose levels of 0%–5%. The CCD used in this study had a pixel size of 2.2 × 2.2 µm², which means for a sensor size of 140.8 × 125.4 µm², we simultaneouly achieved a detection range of 0.109 RIU provided by GGP-GMR with an LOD of 5.62 × 10⁻⁴ RIU provided by the GWT-GMR; this performance cannot be achieved with a single-gradient GMR. The comparison between three types of gradient GMRs are listed in Table 1.

3.4.2 Sensitivity and LOD

Sensitivity is the ability of the MICP to shift in response to some change in RI. If one improves on an existing design for a gradient GMR by a new design with a flatter gradient, the new design will be more sensitive than the old design. By contrast, LOD is related to system noise. The LOD defines the smallest detectable signal, which can be calculated as 3s divided by the sensitivity. Here, s represents the standard deviation of measurements. For the optical resonator sensor types, s is related to the resonance linewidth and the light source and CCD stability. The average linewidth in the GGP direction for the 0%–60% sucrose measurement was 13 pixels (10–17 pixels). Conversely, the average linewidth was 172 pixels for the 0%–5% sucrose measurement in the GWT direction (Fig. 5(d)). The linewidth is inversely proportional to the resonance gradient. A broader linewidth results in a greater variation in determining the MICP. Figures 3(d) and 5(e) reveal that the average overall standard deviations were 0.62 and 1.459 pixels (1.37 and 3.21 µm) in the GGP and GWT directions, respectively. To reduce the linewidth, two approaches can be taken in the near future. First, as discussed previously, the rounded edges and corners of grating structure from replica molding deteriorate resonance and broaden linewidth. To overcome this, EBL and RIE can be used to pattern GGP grating structure on a quartz or glass substrate and followed by gradient TiO₂ deposition to fabricate the devices. We believe such devices can achieve better grating structure and narrower linewidth. Secondly, an incident light source with narrower linewidth can be used to have narrower linewidth in CCD measurement, which could result in smaller variation during measurement to further reduce the s and improve LOD.

A system with a notably flat gradient can achieve notably high sensitivity, but its linewidth as measured in pixels must be notably broad, which results in a high standard deviation in the MICP shift. Nonetheless, GWT can still provide excellent LOD based on the results presented for sucrose measurement and albumin detection (Fig. 6). Here, the MICP shift in the GWT direction can detect concentration up to a value of 20 µg/mL, which is 100 µg/mL in the GGP direction.

Light was directly transmitted through the TDG-GMR and recorded by a CCD in this study. Further improvement in sensitivity could be achieved using a flatter gradient or optimizing the optical path design, such as the incorporation of magnification components between the gradient GMR and CCD. Conversely, the LOD is associated with measurement noise, which could be addressed by optimizing the assay protocol or by using a more stable light sources or CCDs.

3.4.3 Comparison to current GMR and gradient GMR sensor

For uniform GMRs, four common readout techniques have been demonstrated to track the resonance upon adsorption of biomolecules. The most straight forward technique is to track the wavelength shift using a broadband light source and high resolution spectrometer [37,38], which achieves LOD on the order of 10⁻⁵ RIU [37]. The need of a bulky spectrometer can be challenging for miniaturization. Secondly, the angular modulation based on a diode laser and a photodetector [24] or photomultiplier [39] with LOD of 10⁻⁴ [24] or 10⁻⁵ RIU [39] have also been demonstrated. However, a high resolution rotational stage is required to rotate the sensor to obtain the correct coupling angle, which can be time consuming and difficult to integrate with handheld devices. Thirdly, through the characteristic of rapid variation of the phase near the resonant wavelength, Sahoo [26] and Wen [40] were able to achieve LOD of 10⁻⁷ RIU. However, the experimental setup and the data analysis are much more complicated than other techniques, which is not practical to miniaturize for portable devices. Lastly, a simple LED and photodetector have been applied to measure intensity variation upon biomolecule adsorption and achieved LOD on the order of 10⁻⁴ [8] and 10⁻⁵ RIU [25]. Although the intensity measurement can be suitable for integration, the signal can fluctuate with environmental conditions. Sophisticated sign amplification or filtration are required to overcome these issues [25].

Although the LOD of current TDG-GMR is not optimal compared to uniform GMRs, we believe this can be further improved as discussed previously. The advantage of TDG-GMR is to convert spectral information into spatial information and to be read out directly with a CCD without a bulky spectometer, rotational stage or complicated optical setup. The simple optical design can be beneficial for miniaturization. Additionally, the sensing information is obtained as a relative shift in the pixel location, which provides self-referencing and can be more accurate than intensity-based measurement where only a single intensity value is measured [32].

To the best of our knowledge, Triggs et al. [32] was the first group to use gradient GMR for biosensing applications where the gradient duty cycle was employed. Our sensor exhibits approximately 5x enhancement in sensitivity (17129 µm/RIU versus 3469 µm/RIU). By contrast, the LOD (5.62 × 10⁻⁴ RIU) achieved with our system is slightly inferior to that obtained by Triggs (2.37× 10⁻⁴ RIU). The reason can be attributed to larger standard deviation possibly resulting from different definitions on LOD and the instrument used.

The LOD is defined as 3s/sensitivity where the s was measured from the same sample (0% glucose) over 35 min in [32]; however, the average standard deviation of all measurement was used in this work.

The incident narrowband light source from broadband laser has linewidth of 0.6 nm [32]. By contrast, we used halogen lamp coupled with monochromator to generate narrowband light source with linewidth of 2.65 nm. The broader incident light source results in broader linewidth in CCD measurement, which causes larger standard deviation during measurement. Additionally, compared to our regular CCD (about 1250 USD), a high-end cooled CCD camera was used in Triggs’ paper, which could have more stable intensity distribution resulting a more consistent MICP measurement.

4. Conclusion

A unique RI sensor and biosensor that employs TDG-GMR was demonstrated in this study. The sensor combines two different GWT and GGP gradients into a single GMR device. The resonance in the GGP direction allows a broader-than-usual detection range in a small footprint, whereas resonance in the GWT direction provides high sensitivity and excellent LOD. With a sensor size of 140.8 × 125.4 µm², the The proposed TDG-GMR can achieve a detection range of 0.109 RIU with an LOD value of 5.62 × 10⁻⁴ at a sensor size of 140.8 × 125.4 µm².

In our proposed design, the gradient GMR converted spectral information into spatial information with a CCD, thus avoiding the use of a relatively expensive and bulky spectrometer typically used in common GMR devices. The detection of a test model of anti-albumin and albumin binding pairs was also successfully demonstrated. This finding proves that the TDG-GMR can be applied for practical biomolecule detection with appropriate surface functionalization and has a broad detection range and high resolution with a compact sensor size. The monochromator was used as the narrowband light source to prove the concept of TDG-GMR sensor, which in practice can be replaced by an LED with a narrowband filter. If combined with a simple optical readout design the TDG-GMR is suitable for use in a portable device or for integration with smartphones for numerous biosensing applications.