Abstract

We present an investigation on the use of oblique incidence condition to enhance the sensitivity of guided-mode resonance (GMR) sensors. By adjusting the incident angle, the enhancement of GMR sensitivity in non-subwavelength regime can be obtained. The measured results show that the bulk sensitivity of the GMR sensors with period of 809 nm climbs to 177% or 292% as the incident angle increases from 15° to 25° or 35°, respectively. The same trend is also obtained for the grating period of 994 nm. Simulations based on the rigorous coupled wave analysis (RCWA) method were performed, and we also built a new slab waveguide model to describe the relationship between bulk sensitivity and the incident angle. The present investigation demonstrates a new method for enhancing the bulk sensitivity of GMR sensor. Moreover, simple fabrication techniques can be utilized since a large grating period was used.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Guided-mode resonance (GMR) effect is a peculiar optical phenomenon occurring in a subwavelength of near-wavelength waveguide grating [1]. Previous studies have shown that structures exhibiting GMR are promising candidates for use as filters and various optical modulators [24]. The narrow-band GMR wavelength is strongly dependent on the structural parameters and refractive indices of the materials. Varying the refractive index of the surrounding medium will cause the GMR wavelength shift, thus a narrow-band GMR filter can be also used as a biosensor [5]. The performance of a spectrally-resolved GMR sensor is characterized by its sensitivity, which is defined as the GMR wavelength shift divided by the change in the refractive index of the analyte [6]. A GMR sensor could facilitate real-time label-free detection that is suitable for use in mass-produced portable instruments [7]. For such biosensor, achieving more accurate detection of small molecules at low concentration requires high sensitivity. In GMR sensors, the sensitivity is proportional to the overlap between analytes and evanescent waves outside the structure [8]. In order to enhance the sensitivity of a GMR sensor, several approaches have focused on extending the span of the evanescent at the sensor surface, which is crucial for the optical sensors with high sensitivity. For example, Lin et al. proposed a metal layer-assisted GMR device that generates a strongly asymmetric resonance modal profile and doubles the span of the evanescent wave in analytes [9]. Beheiry et al. showed a free-standing structure can provide high sensitivity, in which the waveguide is not on a substrate, but is surrounded by the analyte [10]. Nazirizadeh et al. used oblique deposition to form a unique material distribution on the sidewall of the structure [11]. In addition, manipulating the geometric structure of GMR sensor offers a method for modulating the strength and distribution of evanescent wave [1214].

In order to easily exploit GMR effects and provide enough energy exchange for reflection, most research primarily focuses on GMR structures based on the sub-wavelength regime [15]. The so-called sub-wavelength regime sometimes means that the structure has a grating period that is smaller than the resonance wavelength. However, during manufacturing, smaller period structures are more susceptible to deviation, and the precise control over fill factor and grating period is challenging. In addition, expensive pattern recording equipment, for example electron-beam lithography, is often required [16,17]. Because GMR is sensitive to the changes of structure parameters, small structural deviations can induce a fluctuation in the resonance [1821]. Hence, it is desirable to fabricate a structure with larger period. Regarding GMR sensors, the challenge is to develop sensors with high sensitivity at low cost using mass manufacturing methods. Previous studies for increased sensitivity were optimized and specially designed, and these are based on a typical structure. Although this improved the detection sensitivity of the GMR sensor, the fabrication difficulty was unavoidable. We have discussed the GMR at oblique incidence in previous paper, and prove that GMR can be achieved in large gratings period [22].

In this paper, we investigate the GMR structure with enhanced bulk sensitivity under large oblique incident condition. A significant enhancement of GMR sensitivity in non-subwavelength regime can be obtained. What’s more, we propose a simple model to calculate the increased sensitivity. To our knowledge, this is the first time to study the GMR sensor’s ability in oblique incidence. Fabrication of the structure can be simplified when a grating with larger period. The present investigation demonstrates a new and simple method for enhancing the sensitivity which will also encourage the application of GMR sensors.

2. Non-subwavelength condition under oblique incidence

Typical GMR structure is shown in Fig. 1. It consists of waveguide and grating layers. The grating alternates between high and low refractive indices nh and nc (superstrate); nw and ns are the refractive indices of the waveguide layer and substrate, respectively; dg and dw are the thicknesses of the grating and waveguide layer, respectively; Λ is the grating period and f is the fill factor. During the excitation of GMR effect, it should satisfy the equation [1]:

$$\max \{{{n_c},{n_\textrm{s}}} \}\le |{{n_c}\sin \theta - i{\lambda \mathord{\left/ {\vphantom {\lambda \Lambda }} \right.} \Lambda }} |< {n_{eff}},$$
where θ is the external incident angle, i is the diffraction order, neff is the equivalent refractive index of the grating layer, as shown in Fig. 1(a). These equations can be used to estimate the resonance location with respect to the structural parameters for TM and TE modes. TE modes correspond to polarized light incident at δ = 90° and φ = 0° in Fig. 1(a), and the TM mode corresponds to δ = 90° and φ = 90° [23]. In Eq. (1), the upper limit on Λ can be increased as θ increases at a fixed GMR wavelength. We can infer that the GMR wavelength will be equal to grating period at a particularly oblique incident angle. Figure 1(b) shows the relationship between the incident angle and the value of λ/Λ, which was obtained when nh= 1.6, nw= 2.16 (These values were measured by an ellipsometer under wavelength of 800 nm, and the corresponding material is Ta2O5), nc= 1.33 (pure water), f = 0.5, ns = 1.46 (SiO2), dg = 120 nm, dw= 135 nm and the resonant wavelength λ = 800 nm. It is necessary to state that the refractive index of dielectric material varies at different wavelengths. However, the variation around 800 nm is small and the effect on the GMR wavelength can be ignored. Therefore, the above measured data were adopted in the simulation. The presented simulations are based on the rigorous coupled wave analysis (RCWA) method. At normal incidence, when Λ = 455.2 nm, the GMR wavelength is 800 nm, i.e., λ/Λ = 1.757; the corresponding spectrum is shown in Fig. 1(c). However, the GMR at non-normal incidence (θ ≠ 0) results from coupling among higher diffraction orders and leaky modes. As the incident angle increases, the grating period should increase and couple the −1st diffraction order to leaky mode, while the opposite tendency appears for the + 1st order. For the −1st order, the value of λ/Λ will decrease at larger incident angle, which means a larger Λ is needed, we assume the subwavelength regime correspond to λ/Λ ≥ 1, while λ/Λ < 1 corresponds to non-subwavelength regime when the incident angle is greater than 34.74°. The corresponding spectrum is shown in Fig. 1(d) for the angle of 34.74°, in this case the GMR wavelength value is equal to the period of grating (λ/Λ=1). In order to obtain a high efficiency GMR filter, a subwavelength pattern is always selected with Λ < λ. However, for the structure with a larger grating under oblique incidence, it is difficult to obtain a resonance efficiency of 100%, because GMR occurs due to the coupling between high evanescent diffraction and leaky modes, and not all diffraction peaks are suppressed. Figure 1(d) shows that the reflectivity at 800 nm is 79%, which means less than 100% of the energy is exchanged. It is noteworthy that when a GMR structure is used as a biosensor, changing the refractive index of the surrounding medium causes a measurable shift in the resonant wavelength. The efficiency at the GMR wavelength plays no role in determining the sensitivity, thus a structure having the reflectance peak lower than 100% can still be used as a viable sensor.

 figure: Fig. 1.

Fig. 1. (a) Schematic of a typical GMR structure. (b) Calculated relation between the incident angle and the value of λ/Λ, λ = 800 nm. (c) Calculated TE mode spectrum under normal incidence. (d) Calculated TE mode spectrum under an incident angle of 34.74°.

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3. Enhanced bulk sensitivity in larger incident angles

A rough indication of a GMR sensor performance is bulk sensitivity. Bulk sensitivity is expressed in units of nm/RIU (RIU: refractive index unit) and is usually correlated with detecting larger objects, such as cells or refractive index fluctuations in the test medium. The bulk sensitivity is

$$\textrm{S}\ =\ \Delta \lambda /\Delta {n_c},$$
where Δλ is the wavelength shift and Δnc is the change in the refractive index of the medium. In our work, in order to evaluate the bulk sensitivity, the superstrate medium refractive index was varied from 1.33 to 1.39. Figure 2 shows the GMR wavelength shifts induced by the change of the refractive index of superstrate medium.

 figure: Fig. 2.

Fig. 2. (a) Simulated transmission spectrum at normal incidence for a TE mode. Simulated transmitted spectrum at an incident angle of (b) 34.74° and (c) 0°. The grating periods are 800 nm in both panels. (d) GMR wavelength as a function of incident angle. The black and red lines were calculated for nc = 1.33 and 1.39, respectively.

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Usually, the TE mode related GMR has a lower quality-factor, hence it is more dominant in an experiment compared to the TM mode. However, the results obtained here can be also applied to TM mode. As shown in Fig. 2(a), the resonance in a structure with Λ = 455.2 nm changes from 800 nm to 802.05 nm at normal incidence when the refractive index of superstrate medium changes from 1.33 to 1.39. Hence the wavelength shift is 2.05 nm, and the bulk sensitivity is 34.17 nm/RIU. In contrast, for the refractive index nc = 1.33, when the incident angle is 34.74° and the Λ = 800 nm, GMR is also excited at 800 nm. The resonance changes to 782.35 nm as the refractive index is 1.39, as shown in Fig. 2(b). The corresponding wavelength shift and sensitivity are 17.65 nm and 294.17 nm/RIU, respectively. Compared to the GMR structure with subwavelength regime at normal incidence, the bulk sensitivity increases by 861% when incident angle is 34.74°. Previous research indicated the sensitivity will be enhanced at a larger GMR wavelength. This is easy to understand because a larger GMR wavelength usually requires a grating with larger period for excitation, which results in greater overlap between the modal field distribution and an analyte. Figure 2(a) and (b) shows two cases with different grating periods and different incident angles. In order to compare the effect of the incident angle, we consider a structure with Λ = 800 nm at normal incidence, while the other parameters are the same as the case in Fig. 2(b). For such structure, the transmitted spectrum is shown in Fig. 2(c). We can learn that the GMR wavelength is 1291.9 nm when nc= 1.33, and it shifts to 1298.7 nm when nc= 1.39, thus the change in the wavelength is 6.8 nm and the bulk sensitivity amounts to 113.33 nm/RIU. However, in the case of oblique incidence discussed above [see Fig. 2(b)], the sensitivity was 294.17 nm/RIU, which means an increment of 260% compared to the case in Fig. 2(c). It is interesting that the GMR operating in the case of oblique incidence is more sensitive to refractive index changes, even though the considered structure has same period.

Next, we investigated the relationship between the resonant wavelength and incident angle. The grating period is 800 nm, while the other structural parameters were kept unchanged. The simulation results are shown in Fig. 2(d). For a given incidence angle, the bulk sensitivity depends on the deviation between the black and red lines, where nc = 1.33 and 1.39, respectively. At normal incidence, the single GMR wavelength shift is 6.8 nm. Under oblique incidence, the +1st and −1st evanescent waves excite two GMRs at different wavelengths, thus there will be two GMR wavelengths. As the incident angle increases, the resonant wavelength corresponding to + 1st diffraction order will produce a redshift, while the −1st diffraction order corresponds to a blueshift. The non-subwavelength condition arises due to coupling between −1st evanescent waves, thus we focus on the GMR corresponding to this order. We can learn that for the blueshift resonant wavelength, the deviation caused by the refractive index change will decrease at first and subsequently increase monotonically as the incident angle increases. The GMR wavelength shift gradually increases if the incidence angle increases above 8.4°, i.e., the bulk sensitivity will increase. The shift is 6.8 nm when the incidence angle increases to 17.4°, which is equal to the case of normal incidence. The calculated bulk sensitivity will increase compared to that at normal incidence when the incidence angle is larger than 17.4°. The GMR structure operates at non-subwavelength regime when the incidence angle is 34.74°, and the wavelength shift increases to 17.65 nm.

Therefore, we demonstrated the bulk sensitivity of a GMR sensor can be increased at oblique incidence, especially when it operates in non-subwavelength regime. We can infer that the bulk sensitivity will increase if the incident angle is greater than a certain value. A larger grating period is easier to control in fabrication, thus it will be a benefit in applications. In addition, we want to state that the blueshift resonant wavelength is excited by −1st order diffraction, and the resonant wavelength which is excited by + 1st order diffraction presents redshift. These two diffraction orders inside the waveguide, i.e. the internal angle of incidence, are counter-propagating. Under oblique incidence, effective propagation constants of the waveguide layer for ± 1st order diffraction present opposite variation trend when equivalent constant of the grating layer increase [2]. Hence, we infer the counter-propagating of internal angle maybe the reason for blueshift.

4. A model for bulk sensitivity under oblique incidence

Although the numerical simulation can be used to calculate the GMR wavelength shift as a function of refractive index nc, we want to analyze structural parameters, especially the influence of incident angle on bulk sensitivity. Here we use an approximate model to analyze the relationship between incidence angle and bulk sensitivity. The dispersion equation is obtained from the approximate slab waveguide model, which is usually utilized for describing guided modes and Fabry-Perot modes. In order to excite the GMR, the phase of the wave inside the waveguide layer should change by a multiple of 2π after reflecting from the upper layer (grating layer) and lower interfaces, and propagating though the thickness of the waveguide layer, as shown in Fig. 3. This condition can be written as

$$\arg {R_1} + \arg {R_2} + 2{d_w}k_{\_z}^{} = 2\pi m.$$
Here m is an integer, R1 is the complex reflection coefficient of the grating (for the wave incident from inside the waveguide layer), R2 is the complex reflection coefficient of the lower interface of the waveguide layer, k_z is the z-component of the wave vector of the plane wave (diffraction order responsible for the mode excitation) inside the waveguide layer. k is related with the in-plane wave number of the ith diffraction order, k_x through the following relation:
$$k_{\_x}^2 + k_{\_z}^2 = k_0^2n_w^2,$$
where ${k_0} = 2\pi /\lambda$ and
$${k_{\_x}} = {k_0}{n_c}\;\textrm{sin}\theta + \frac{{2\pi }}{\Lambda }i.$$
We are focus on the bulk sensitivity of GMR structure about the refractive index nc, so we need to analyze which terms of these equations depend of nc. First, R1 depends on nc, because of the equivalent refractive index of grating layer. Moreover, both R1 and R2 depend on θ and λ. However, these dependences can be neglected and the main impact of the sensitivity gives the nc term in Eq. (5). To prove the inference, we write Eqs. (3)–(5) in the following form:
$${\left( {\frac{{2\pi m - \arg {R_1} - \arg {R_2}}}{{2{d_w}}}} \right)^2} = {\left( {\frac{{2\pi }}{\lambda }} \right)^2}n_w^2 - {\left( {\frac{{2\pi }}{\lambda }{n_c}\;\textrm{sin}\theta - \frac{{2\pi }}{\Lambda }i} \right)^2}.$$

 figure: Fig. 3.

Fig. 3. Basic slab waveguides model.

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To estimate the left-hand side, we consider the case of normal incidence (θ=0°):

$${\left( {\frac{{2\pi m - \arg {R_1} - \arg {R_2}}}{{2{d_w}}}} \right)^2} = {\left( {\frac{{2\pi }}{{{\lambda_0}}}} \right)^2}n_w^2 - {\left( {\frac{{2\pi }}{\Lambda }i} \right)^2}.$$
Here λ0 is the resonant wavelength in the case of normal incidence, i.e. θ=0°. For the considered structure, λ0=1291.8 nm. Now we can rewrite Eq. (7) as
$${\left( {\frac{{{n_c}}}{\lambda }\textrm{sin}\theta - \frac{i}{\Lambda }} \right)^2} - {\left( {\frac{i}{\Lambda }} \right)^2} = n_w^2\left( {\frac{1}{{{\lambda^2}}} - \frac{1}{{\lambda_0^2}}} \right).$$
This equation can be solved for resonant wavelength λ:
$$\lambda = \frac{{i{n_c}{{\lambda }_0}^2\textrm{sin}\theta + {{\lambda }_0}\sqrt {{\Lambda ^2}n_w^4 + n_c^2({{i^2}{\lambda }_0^2 - {\Lambda ^2}n_w^2} )\textrm{si}{\textrm{n}^2}\theta } }}{{\Lambda \,n_w^2}}.$$
Based on the parameters of Fig. 2(d), we can learn that this equation approximately describes the position of the GMR wavelength with respect to angle of incidence and refractive index of nc. If we expand it into Taylor series with respect to nc, the linear term would give us the sensitivity of the sensor:
$$\textrm{S}\ =\ \frac{{\textrm{d}\lambda }}{{\textrm{d}{n_c}}} = \frac{{{{\lambda }_0}}}{{\Lambda n_w^2}}\left( {\frac{{{n_c}({{i^2}{\lambda }_0^2 - {\Lambda ^2}n_w^2} )\textrm{si}{\textrm{n}^2}\theta }}{{\sqrt {{\Lambda ^2}n_w^4 + n_c^2({{i^2}{\lambda }_0^2 - {\Lambda ^2}n_w^2} )\textrm{si}{\textrm{n}^2}\theta } }} + i{{\lambda }_0}\sin \theta } \right).$$
In this paper we consider the structure where the GMR is excited by the −1st diffraction order. In this case, the shift of the GMR wavelength is calculated as:
$$\Delta \lambda = \frac{{{{\lambda }_0}}}{{\Lambda n_w^2}}\left( {\frac{{{n_c}({{\lambda }_0^2 - {\Lambda ^2}n_w^2} )\textrm{si}{\textrm{n}^2}\theta }}{{\sqrt {{\Lambda ^2}n_w^4 + n_c^2({{\lambda }_0^2 - {\Lambda ^2}n_w^2} )\textrm{si}{\textrm{n}^2}\theta } }} - {{\lambda }_0}\sin \theta } \right)\Delta {n_c}.$$
We can learn that the GMR shift caused by the refractive index nc, is not only related to the structure parameters, but also directly related to the incident angle θ. The shift calculated using this equation is shown in Fig. 4 with red line, where nc = 1.33, Δnc = 0.06, other parameters are the same as in Fig. 2(d). The black dotted line shows the rigorously calculated offset obtained using the RCWA method, which is also the distance between black line and red line in Fig. 2(d). The relationship between bulk sensitivity and structure parameters can be obtained using this slab waveguide model. In particular, the model predicts the increase in sensitivity when increasing the angle of incidence. This is a qualitative analysis and Eq. (11) provides a good approximation of the sensitivity, especially for the angles among 20° to 40° as shown in Table 1. It is known that the minimum difference between our model and the accurate value calculated using the RCWA method is only 0.3 nm at about 30°, and the maximum deviation is 1.1 nm at 20°. The deviation of our model from the rigorous calculation at small angle of incidence may due to the fact that a band gap opens in the dispersion relation of the mode under normal incidence. It should be mentioned that the model does not describe why the shift of the resonance is positive at small angles and negative at higher angles. To describe this effect, the dependences of R1 and R2 on θ, λ, and nc need to be taken into account.

 figure: Fig. 4.

Fig. 4. GMR wavelength shift as a function of incident angles: RCWA simulations (dashed line) and slab waveguide model (solid red line).

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Tables Icon

Table 1. GMRs shift under various angles based on the RCWA (R) and slab waveguide model (M)

5. Experimental results and discussion

In order to validate the increase of sensitivity of the GMR structure in non-subwavelength regime and compare it with subwavelength regime, three GMR samples A, B, and C with Λ = 445.2, 800, and 978.7 nm were fabricated. From Fig. 1(b), we can learn that when sample A, B, and C works at 0°, 34.74° and 45°, and the refractive index nc is 1.33, the GMR wavelength for these three samples are all 800 nm. Other parameters for these cases are the same as in Fig. 2. In experiment, the GMR chips were fabricated by depositing a 135 nm thick Ta2O5 film onto a flat SiO2 substrate. Thereafter, a 200 nm thick photoresist (AZ1500) was spin-coated on top of the Ta2O5 layer. The development process causes some photoresist to be lost, so the photoresist film is slightly thicker than the height of the grating groove in simulation. Following this, grating patterns were recorded in the photoresist using interference lithography with a He-Cd laser at 441.6 nm. The period of the holographic grating was changed by controlling the angle between two coherent beams. The interference angles were set to be 58.1°, 32.0°, and 26.1° for Λ = 455.2, 800, and 978.7 nm, respectively. Finally, the photoresist-coated samples were developed in a 5‰ sodium hydroxide solution to produce a one-dimensional surface grating. Figure 5 shows SEM images of the surface gratings fabricated on a Ta2O5 waveguide layer; the measured grating periods were 450, 809, and 994 nm. The scale bar in Fig. 5 is 5 µm, and the increased grating period is obvious. Figure 5(d) shows a photograph of the GMR chips with the same area. Since the grating period of A is much different from that of B, the dispersion cannot be seen from the same viewing angle. The diffraction effect of sample B and C are obvious, which proves that the quality of grating lines is good. It is difficult to prevent deviations in the grating period during fabrication. However, small deviations in the grating fill factor and depth should not have a large impact on the transmission spectra as the grating period is accurate. Bulk sensitivity was measured using refractive index measurements obtained via transmission experiments with TE-polarized incident beams. The TE mode GMR properties were explored by examining the transmission spectrum.

 figure: Fig. 5.

Fig. 5. SEM micrographs of the fabricated GMR samples. The measured grating periods in SEM are 450, 809, and 994 nm for (a), (b), and (c), respectively. (d) Photograph of the fabricated GMR samples.

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The transmission spectrum for TE modes were explored to evaluate the bulk sensitivities of GMR sensors and incidence conditions on sensing performance. The detection setup for the spectrum measurement is shown in Fig. 6(a). A highly stable halogen lamp emitting in the spectral range from 400 to 2400 nm was used as the light source, and the emitted light was coupled to an optical fiber. A lens was used to collimate the incident beam and was sent to an iris in order to adjust the size of the beam such that it was smaller than the sensing area of the GMR sensor. Subsequently, a linear polarizer with extinction ratio non-less than 1000 was used to control the polarization of the light beam and generate a TE-polarized beam. Finally, transmitted light was collected with a spectrometer (USB4000, Ocean Optics, wavelength range: 200 nm-1100 nm) to analyze the transmission spectrum. The bulk refractive index sensitivities were measured by pouring purified water mixed with various fractions of glycerin over the sample surface. The concentrations of glycerol in the solutions were 0, 40, 50 and 60 wt%, and the corresponding refractive indices of the mixtures (from 0 to 20% glycerin) were 1.3335, 1.3495, 1.3700, and 1.3899, respectively; these values were measured with an Abbe refractometer. After the solution was injected into the sensor and fully filled the sensing region, the transmission spectrum was recorded with the spectrometer.

 figure: Fig. 6.

Fig. 6. (a) Setup for transmission spectrum and sensitivity measurements. (b)-(d) Experimental transmission spectra for samples A, B and C, with different grating periods at incidence angles of 0°, 35°, and 45°, respectively. (e) Resonance wavelength versus the refractive index of the surrounding medium. The slopes of the fitting curves show that the refractive index sensitivities corresponding to data in (b)-(d).

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The spectra in Figs. 6(b)–6(d) were recorded at incidence angles of 0°, 35°, and 45° for the fabricated structure with Λ = 450, 809, and 994 nm, respectively. Because the wavelength shift is small (only 2.05 nm in simulation) in the GMR structure with Λ = 405 nm at normal incidence, we measured the resonant wavelengths with refractive indices of 1.3335, 1.3495, 1.3700, and 1.3899, as shown in Fig. 6(b). The measured GMR wavelength in transmission spectrum for the sample A was 794.8, 795.5, 796.2 and 796.6 nm, respectively. The GMR wavelength was redshift as nc increasing, and the GMR shift is 1.8 nm when the refractive index changed by 0.0564, and the sensitivity is 31.9 nm/RIU. The resonance efficiency is less than 100% due to absorption in the liquid and the structural imperfections, but these do not appreciably affect the analysis of the bulk sensitivity. Λ = 809 nm for sample B and GMR occurred at λ = 802.1 nm when the incident angle was 35° and the refractive index of the superstrate material was 1.3353, as shown in Fig. 6(c), which can be regarded as the mentioned non-subwavelength regimes. Other GMR wavelengths were 796, 791.4, and 785.2 nm for refractive index of 1.3495, 1.3700, and 1.3899, respectively. The GMR shift was 16.9 nm when the refractive index changed by 0.0564, thus the bulk sensitivity is 299.6 nm/RIU. Λ = 994 nm for sample C and GMR occurred at λ = 806.5 nm when the incident angle was 45° and the refractive index of the superstrate was 1.3353. The detected GMR wavelengths were 797.4, 789.2, and 781.0 nm for refractive indices of 1.3495, 1.3700, and 1.3899, respectively. The transmission spectrum is shown in Fig. 6(d). The GMR wavelength shift is 25.5 nm, and the measured bulk sensitivity is 452.12 nm/RIU. The slopes of the fitting curves in Fig. 6(e) show that the refractive index sensitivities corresponding to panels (b)-(d) were 31.9, 299.6, and 452.12 nm/RIU, respectively. Moreover, we can learn from Fig. 6 that the GMR efficiency and Q factor are reduced as the incident angle increases, this is not benefit to the enhancement of sensitivity. However, maybe because of the incident angle play a bigger role, the bulk sensitivity enhancement can be still achieved under large angle incidence [24].

For comparison, we measured the bulk sensitivity under different incident angles for sample B and C, as shown in Table 2. Four different concentrations of glycerol in the solutions were used which was mentioned above. We also present the transmission spectra for sample B and C at incident angles of 15° and 35°, respectively, as shown in Fig. 7. The blueshift of the GMR wavelength can be clearly observed. For sample B in Fig. 7(a), the GMR wavelength shift at the incident angle of 15° is significantly less than the shift at the incident angle of 35° which is shown in Fig. 6(c). The same trend can be learned from Fig. 6(d) and Fig. 7(b). As we can learn from Table 2, when the incident angle is 15° and the grating period of 809 nm, the GMR wavelength for refractive index of 1.3335 and 1.3899 are 1069.9 nm and 1065.6 nm, respectively, so the bulk sensitivity is 76.2 nm/RIU. As the incident angle increases to 25°, the wavelength shift is 11.9 nm, so the bulk sensitivity is 211.0 nm/RIU. We can learn that when the incident angle is increased by 10°, the bulk sensitivity was increased by 177%. In addition, the bulk sensitivity increases to 299.6 nm/RIU, when the incident angle is 35°. Compared with the oblique incident angle of 15°, the bulk sensitivity is increased by 292%. As we mentioned above, for larger grating period, the bulk sensitivity will be increased usually. When the incident angle is 35° and the grating period is 994 nm, the GMR wavelength for refractive index of 1.3335 and 1.3899 are 937.5 nm and 919.1 nm, so the bulk sensitivity is 326.2 nm/RIU. As the incident angle increases to 45°, the shift of GMR wavelength is 25.5 nm, so the bulk sensitivity is 452.1 nm/RIU and the enhancement is up to 138%. Hence, these two structures with different periods show the same trend. Furthermore, a comparison between the results in Figs. 6(c) and 6(d) shows that the resonance efficiency at peak wavelengths will decrease at a larger incident angle, which may be due to some higher order diffraction cannot be coupled at oblique incidence, resulting in weakened coupling efficiency. Nevertheless, significant GMR shifts can be detected. The test results are similar with those obtained from simulation, which shows that a structure operating in non-subwavelength regimes and oblique incidence has higher sensitivity compared to the structure operating under normal incidence. Finally, it should be noted that, in order to ensure the accuracy and repeatability of the experiment results, multiple chips with the same structure parameters were fabricated and tested. The results are always consistent which ensure that it is an effective method to improve the bulk sensitivity of GMR sensors under oblique incidence condition.

 figure: Fig. 7.

Fig. 7. Transmission spectra for (a) sample B at incident angle of 15° and (b) sample C at incident angle of 35°.

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Tables Icon

Table 2. Bulk sensitivity comparison for different oblique incident angles

Conclusion

In conclusion, we have demonstrated the bulk sensitivity can be enhanced when GMR sensors working under large oblique incident angles. Three samples with different grating periods were fabricated. The measured results show that the bulk sensitivity increases with the increase of incident angle. For example, when the grating period is 809 nm and the incident angle is 15°, the bulk sensitivity is 76.2 nm/RIU. As the incident angle is increased by 10° and 20°, the bulk sensitivity is increased by 177% and 292%, respectively. The same trend is obtained when the grating period is 994 nm. In addition, analysis of the slab waveguide model shows that the directed relationship between bulk sensitivity and the incident angle. This is a qualitative analysis, and the results quite accurate for the incidence angles ranging from 20° to 40°. The grating with larger period is easy to fabricate in practical. With the benefits of reduced cost and enhanced sensitivity, this method is promising for practical bio-sensing applications with more sensitive detection of samples at lower concentrations.

Funding

National Natural Science Foundation of China Foundation of Xuzhou city (KC18002); Russian Foundation for Basic Research (18-37-20038); (11704162, 61771227, 61805210); Natural Science Research of Jiangsu Higher Education Institutions of China (18KJB510048).

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5. R. Magnusson, D. Wawro, S. Zimmerman, Y. Ding, M. Shokooh-Saremi, K. J. Lee, D. Ussery, S. Kim, and S. H. Song, “Leaky-mode resonance photonics: Technology for biosensors, optical components, MEMS, and plasmonics,” Proc. SPIE 7604, 76040M (2010). [CrossRef]  

6. B. T. Cunningham, P. Li, B. Lin, and J. Pepper, “Colorimetric resonant reflection as a direct biochemical assay technique,” Sens. Actuators, B 81(2-3), 316–328 (2002). [CrossRef]  

7. B. T. Cunningham, P. Li, S. Schulz, B. Lin, C. Baird, J. Gerstenmaier, C. Genick, F. Wang, E. Fine, and L. Laing, “Label-free assays on the BIND system,” J. Biomol. Screening 9(6), 481–490 (2004). [CrossRef]  

8. I. D. Block, N. Ganesh, M. Lu, and B. T. Cunningham, “A sensitivity model for predicting photonic crystal biosensor performance,” IEEE Sens. J. 8(3), 274–280 (2008). [CrossRef]  

9. S. F. Lin, C. M. Wang, T. J. Ding, Y. L. Tsai, T. H. Yang, W. Y. Chen, and J. Y. Chang, “Sensitive metal layer assisted guided mode resonance biosensor with a spectrum inversed response and strong asymmetric resonance field distribution,” Opt. Express 20(13), 14584–14595 (2012). [CrossRef]  

10. M. El Beheiry, V. Liu, S. Fan, and O. Levi, “Sensitivity enhancement in photonic crystal slab biosensors,” Opt. Express 18(22), 22702–22714 (2010). [CrossRef]  

11. Y. Nazirizadeh, F. Oertzen, T. Karrock, J. Greve, and M. Gerken, “Enhanced sensitivity of photonic crystal slab transducers by oblique-angle layer deposition,” Opt. Express 21(16), 18661–18670 (2013). [CrossRef]  

12. W. Zhang, S. Kim, N. Ganesh, I. D. Block, P. C. Mathias, H.-Y. Wu, and B. T. Cunningham, “Deposited nanorod films for photonic crystal biosensor applications,” J. Vac. Sci. Technol. 28(4), 996–1001 (2010). [CrossRef]  

13. S. F. Lin, C. M. Wang, Y. L. Tsai, T. J. Ding, T. H. Yang, W. Y. Chen, and J. Y. Chang, “A model for fast predicting and optimizing the sensitivity of surface-relief guided mode resonance sensors,” Sens. Actuators, B 176, 1197–1203 (2013). [CrossRef]  

14. S. A. J. Moghaddas, M. Shahabadi, and M. Mohammad-Taheri, “Guided mode resonance sensor with enhanced surface sensitivity using coupled cross-stacked gratings,” IEEE Sens. J. 14(4), 1216–1222 (2014). [CrossRef]  

15. M. Niraula, J. W. Yoon, and R. Magnusson, “Concurrent spatial and spectral filtering by resonant nanogratings,” Opt. Express 23(18), 23428–23435 (2015). [CrossRef]  

16. A. Talneau, F. Lemarchand, A. L. Fehrembach, and A. Sentenac, “Impact of electron-beam lithography irregularities across millimeter-scale resonant grating filter performances,” Appl. Opt. 49(4), 658–662 (2010). [CrossRef]  

17. H. Y. Hsu, Y. H. Lan, and C. S. Huang, “A gradient grating period guided-mode resonance spectrometer,” IEEE Photonics J. 10(1), 1–9 (2018). [CrossRef]  

18. L. Y. Qian, D. W. Zhang, C. X. Tao, R. J. Hong, and S. L. Zhuang, “Tunable guided-mode resonant filter with wedged waveguide layer fabricated by masked ion beam etching,” Opt. Lett. 41(5), 982–985 (2016). [CrossRef]  

19. G. Zheng, J. Cong, L. Xu, and W. Su, “Angle-insensitive and narrow band grating filter with a gradient-index layer,” Opt. Lett. 39(20), 5929–5932 (2014). [CrossRef]  

20. H. A. Lin and C. S. Huang, “Linear variable filter based on a gradient grating period guided-mode resonance filter,” IEEE Photonics Technol. Lett. 28(9), 1042–1045 (2016). [CrossRef]  

21. L. Liu, H. A. Khan, J. Li, A. C. Hillier, and M. Lu, “A strain-tunable nanoimprint lithography for linear variable photonic crystal filters,” Nanotechnology 27(29), 295301 (2016). [CrossRef]  

22. L. Y. Qian, D. W. Zhang, Y. S. Huang, C. X. Tao, R. J. Hong, and S. L. Zhuang, “Performance of a double-layer guided mode resonance filter with non-subwavelength grating period at oblique incidence,” Opt. Laser Technol. 72, 42–47 (2015). [CrossRef]  

23. D. Lacour, G. Granet, J. P. Plumey, and A. Mure-Ravaud, “Polarization independence of a one-dimensional grating in conical mounting,” J. Opt. Soc. Am. A 20(8), 1546–1552 (2003). [CrossRef]  

24. Y. F. Ku, H. Y. Li, W. H. Hsieh, L. K. Chau, and G. E. Chang, “Enhanced sensitivity in injection-molded guided-mode-resonance sensors via low-index cavity layers,” Opt. Express 23(11), 14850–14859 (2015). [CrossRef]  

References

  • View by:

  1. S. S. Wang, R. Magnusson, J. S. Bagby, and M. G. Moharam, “Guided-mode resonances in planar dielectric-layer diffraction gratings,” J. Opt. Soc. Am. A 7(8), 1470–1474 (1990).
    [Crossref]
  2. S. S. Wang and R. Magnusson, “Theory and applications of guided-mode resonance filters,” Appl. Opt. 32(14), 2606–2613 (1993).
    [Crossref]
  3. Y. H. Ko and R. Magnusson, “Flat-top bandpass filters enabled by cascaded resonant gratings,” Opt. Lett. 41(20), 4704–4707 (2016).
    [Crossref]
  4. J. A. Weidanz, K. L. Doll, S. Mohana-Sundaram, T. Wichner, D. B. Lowe, S. Gimlin, D. Wawro Weidanz, R. Magnusson, and O. E. Hawkins, “Detection of human leukocyte antigen biomarkers in breast cancer utilizing label-free biosensor technology,” J. Visualized Exp. (97), e52159 (2015).
    [Crossref]
  5. R. Magnusson, D. Wawro, S. Zimmerman, Y. Ding, M. Shokooh-Saremi, K. J. Lee, D. Ussery, S. Kim, and S. H. Song, “Leaky-mode resonance photonics: Technology for biosensors, optical components, MEMS, and plasmonics,” Proc. SPIE 7604, 76040M (2010).
    [Crossref]
  6. B. T. Cunningham, P. Li, B. Lin, and J. Pepper, “Colorimetric resonant reflection as a direct biochemical assay technique,” Sens. Actuators, B 81(2-3), 316–328 (2002).
    [Crossref]
  7. B. T. Cunningham, P. Li, S. Schulz, B. Lin, C. Baird, J. Gerstenmaier, C. Genick, F. Wang, E. Fine, and L. Laing, “Label-free assays on the BIND system,” J. Biomol. Screening 9(6), 481–490 (2004).
    [Crossref]
  8. I. D. Block, N. Ganesh, M. Lu, and B. T. Cunningham, “A sensitivity model for predicting photonic crystal biosensor performance,” IEEE Sens. J. 8(3), 274–280 (2008).
    [Crossref]
  9. S. F. Lin, C. M. Wang, T. J. Ding, Y. L. Tsai, T. H. Yang, W. Y. Chen, and J. Y. Chang, “Sensitive metal layer assisted guided mode resonance biosensor with a spectrum inversed response and strong asymmetric resonance field distribution,” Opt. Express 20(13), 14584–14595 (2012).
    [Crossref]
  10. M. El Beheiry, V. Liu, S. Fan, and O. Levi, “Sensitivity enhancement in photonic crystal slab biosensors,” Opt. Express 18(22), 22702–22714 (2010).
    [Crossref]
  11. Y. Nazirizadeh, F. Oertzen, T. Karrock, J. Greve, and M. Gerken, “Enhanced sensitivity of photonic crystal slab transducers by oblique-angle layer deposition,” Opt. Express 21(16), 18661–18670 (2013).
    [Crossref]
  12. W. Zhang, S. Kim, N. Ganesh, I. D. Block, P. C. Mathias, H.-Y. Wu, and B. T. Cunningham, “Deposited nanorod films for photonic crystal biosensor applications,” J. Vac. Sci. Technol. 28(4), 996–1001 (2010).
    [Crossref]
  13. S. F. Lin, C. M. Wang, Y. L. Tsai, T. J. Ding, T. H. Yang, W. Y. Chen, and J. Y. Chang, “A model for fast predicting and optimizing the sensitivity of surface-relief guided mode resonance sensors,” Sens. Actuators, B 176, 1197–1203 (2013).
    [Crossref]
  14. S. A. J. Moghaddas, M. Shahabadi, and M. Mohammad-Taheri, “Guided mode resonance sensor with enhanced surface sensitivity using coupled cross-stacked gratings,” IEEE Sens. J. 14(4), 1216–1222 (2014).
    [Crossref]
  15. M. Niraula, J. W. Yoon, and R. Magnusson, “Concurrent spatial and spectral filtering by resonant nanogratings,” Opt. Express 23(18), 23428–23435 (2015).
    [Crossref]
  16. A. Talneau, F. Lemarchand, A. L. Fehrembach, and A. Sentenac, “Impact of electron-beam lithography irregularities across millimeter-scale resonant grating filter performances,” Appl. Opt. 49(4), 658–662 (2010).
    [Crossref]
  17. H. Y. Hsu, Y. H. Lan, and C. S. Huang, “A gradient grating period guided-mode resonance spectrometer,” IEEE Photonics J. 10(1), 1–9 (2018).
    [Crossref]
  18. L. Y. Qian, D. W. Zhang, C. X. Tao, R. J. Hong, and S. L. Zhuang, “Tunable guided-mode resonant filter with wedged waveguide layer fabricated by masked ion beam etching,” Opt. Lett. 41(5), 982–985 (2016).
    [Crossref]
  19. G. Zheng, J. Cong, L. Xu, and W. Su, “Angle-insensitive and narrow band grating filter with a gradient-index layer,” Opt. Lett. 39(20), 5929–5932 (2014).
    [Crossref]
  20. H. A. Lin and C. S. Huang, “Linear variable filter based on a gradient grating period guided-mode resonance filter,” IEEE Photonics Technol. Lett. 28(9), 1042–1045 (2016).
    [Crossref]
  21. L. Liu, H. A. Khan, J. Li, A. C. Hillier, and M. Lu, “A strain-tunable nanoimprint lithography for linear variable photonic crystal filters,” Nanotechnology 27(29), 295301 (2016).
    [Crossref]
  22. L. Y. Qian, D. W. Zhang, Y. S. Huang, C. X. Tao, R. J. Hong, and S. L. Zhuang, “Performance of a double-layer guided mode resonance filter with non-subwavelength grating period at oblique incidence,” Opt. Laser Technol. 72, 42–47 (2015).
    [Crossref]
  23. D. Lacour, G. Granet, J. P. Plumey, and A. Mure-Ravaud, “Polarization independence of a one-dimensional grating in conical mounting,” J. Opt. Soc. Am. A 20(8), 1546–1552 (2003).
    [Crossref]
  24. Y. F. Ku, H. Y. Li, W. H. Hsieh, L. K. Chau, and G. E. Chang, “Enhanced sensitivity in injection-molded guided-mode-resonance sensors via low-index cavity layers,” Opt. Express 23(11), 14850–14859 (2015).
    [Crossref]

2018 (1)

H. Y. Hsu, Y. H. Lan, and C. S. Huang, “A gradient grating period guided-mode resonance spectrometer,” IEEE Photonics J. 10(1), 1–9 (2018).
[Crossref]

2016 (4)

L. Y. Qian, D. W. Zhang, C. X. Tao, R. J. Hong, and S. L. Zhuang, “Tunable guided-mode resonant filter with wedged waveguide layer fabricated by masked ion beam etching,” Opt. Lett. 41(5), 982–985 (2016).
[Crossref]

Y. H. Ko and R. Magnusson, “Flat-top bandpass filters enabled by cascaded resonant gratings,” Opt. Lett. 41(20), 4704–4707 (2016).
[Crossref]

H. A. Lin and C. S. Huang, “Linear variable filter based on a gradient grating period guided-mode resonance filter,” IEEE Photonics Technol. Lett. 28(9), 1042–1045 (2016).
[Crossref]

L. Liu, H. A. Khan, J. Li, A. C. Hillier, and M. Lu, “A strain-tunable nanoimprint lithography for linear variable photonic crystal filters,” Nanotechnology 27(29), 295301 (2016).
[Crossref]

2015 (3)

2014 (2)

G. Zheng, J. Cong, L. Xu, and W. Su, “Angle-insensitive and narrow band grating filter with a gradient-index layer,” Opt. Lett. 39(20), 5929–5932 (2014).
[Crossref]

S. A. J. Moghaddas, M. Shahabadi, and M. Mohammad-Taheri, “Guided mode resonance sensor with enhanced surface sensitivity using coupled cross-stacked gratings,” IEEE Sens. J. 14(4), 1216–1222 (2014).
[Crossref]

2013 (2)

S. F. Lin, C. M. Wang, Y. L. Tsai, T. J. Ding, T. H. Yang, W. Y. Chen, and J. Y. Chang, “A model for fast predicting and optimizing the sensitivity of surface-relief guided mode resonance sensors,” Sens. Actuators, B 176, 1197–1203 (2013).
[Crossref]

Y. Nazirizadeh, F. Oertzen, T. Karrock, J. Greve, and M. Gerken, “Enhanced sensitivity of photonic crystal slab transducers by oblique-angle layer deposition,” Opt. Express 21(16), 18661–18670 (2013).
[Crossref]

2012 (1)

2010 (4)

M. El Beheiry, V. Liu, S. Fan, and O. Levi, “Sensitivity enhancement in photonic crystal slab biosensors,” Opt. Express 18(22), 22702–22714 (2010).
[Crossref]

R. Magnusson, D. Wawro, S. Zimmerman, Y. Ding, M. Shokooh-Saremi, K. J. Lee, D. Ussery, S. Kim, and S. H. Song, “Leaky-mode resonance photonics: Technology for biosensors, optical components, MEMS, and plasmonics,” Proc. SPIE 7604, 76040M (2010).
[Crossref]

W. Zhang, S. Kim, N. Ganesh, I. D. Block, P. C. Mathias, H.-Y. Wu, and B. T. Cunningham, “Deposited nanorod films for photonic crystal biosensor applications,” J. Vac. Sci. Technol. 28(4), 996–1001 (2010).
[Crossref]

A. Talneau, F. Lemarchand, A. L. Fehrembach, and A. Sentenac, “Impact of electron-beam lithography irregularities across millimeter-scale resonant grating filter performances,” Appl. Opt. 49(4), 658–662 (2010).
[Crossref]

2008 (1)

I. D. Block, N. Ganesh, M. Lu, and B. T. Cunningham, “A sensitivity model for predicting photonic crystal biosensor performance,” IEEE Sens. J. 8(3), 274–280 (2008).
[Crossref]

2004 (1)

B. T. Cunningham, P. Li, S. Schulz, B. Lin, C. Baird, J. Gerstenmaier, C. Genick, F. Wang, E. Fine, and L. Laing, “Label-free assays on the BIND system,” J. Biomol. Screening 9(6), 481–490 (2004).
[Crossref]

2003 (1)

2002 (1)

B. T. Cunningham, P. Li, B. Lin, and J. Pepper, “Colorimetric resonant reflection as a direct biochemical assay technique,” Sens. Actuators, B 81(2-3), 316–328 (2002).
[Crossref]

1993 (1)

1990 (1)

Bagby, J. S.

Baird, C.

B. T. Cunningham, P. Li, S. Schulz, B. Lin, C. Baird, J. Gerstenmaier, C. Genick, F. Wang, E. Fine, and L. Laing, “Label-free assays on the BIND system,” J. Biomol. Screening 9(6), 481–490 (2004).
[Crossref]

Block, I. D.

W. Zhang, S. Kim, N. Ganesh, I. D. Block, P. C. Mathias, H.-Y. Wu, and B. T. Cunningham, “Deposited nanorod films for photonic crystal biosensor applications,” J. Vac. Sci. Technol. 28(4), 996–1001 (2010).
[Crossref]

I. D. Block, N. Ganesh, M. Lu, and B. T. Cunningham, “A sensitivity model for predicting photonic crystal biosensor performance,” IEEE Sens. J. 8(3), 274–280 (2008).
[Crossref]

Chang, G. E.

Chang, J. Y.

S. F. Lin, C. M. Wang, Y. L. Tsai, T. J. Ding, T. H. Yang, W. Y. Chen, and J. Y. Chang, “A model for fast predicting and optimizing the sensitivity of surface-relief guided mode resonance sensors,” Sens. Actuators, B 176, 1197–1203 (2013).
[Crossref]

S. F. Lin, C. M. Wang, T. J. Ding, Y. L. Tsai, T. H. Yang, W. Y. Chen, and J. Y. Chang, “Sensitive metal layer assisted guided mode resonance biosensor with a spectrum inversed response and strong asymmetric resonance field distribution,” Opt. Express 20(13), 14584–14595 (2012).
[Crossref]

Chau, L. K.

Chen, W. Y.

S. F. Lin, C. M. Wang, Y. L. Tsai, T. J. Ding, T. H. Yang, W. Y. Chen, and J. Y. Chang, “A model for fast predicting and optimizing the sensitivity of surface-relief guided mode resonance sensors,” Sens. Actuators, B 176, 1197–1203 (2013).
[Crossref]

S. F. Lin, C. M. Wang, T. J. Ding, Y. L. Tsai, T. H. Yang, W. Y. Chen, and J. Y. Chang, “Sensitive metal layer assisted guided mode resonance biosensor with a spectrum inversed response and strong asymmetric resonance field distribution,” Opt. Express 20(13), 14584–14595 (2012).
[Crossref]

Cong, J.

Cunningham, B. T.

W. Zhang, S. Kim, N. Ganesh, I. D. Block, P. C. Mathias, H.-Y. Wu, and B. T. Cunningham, “Deposited nanorod films for photonic crystal biosensor applications,” J. Vac. Sci. Technol. 28(4), 996–1001 (2010).
[Crossref]

I. D. Block, N. Ganesh, M. Lu, and B. T. Cunningham, “A sensitivity model for predicting photonic crystal biosensor performance,” IEEE Sens. J. 8(3), 274–280 (2008).
[Crossref]

B. T. Cunningham, P. Li, S. Schulz, B. Lin, C. Baird, J. Gerstenmaier, C. Genick, F. Wang, E. Fine, and L. Laing, “Label-free assays on the BIND system,” J. Biomol. Screening 9(6), 481–490 (2004).
[Crossref]

B. T. Cunningham, P. Li, B. Lin, and J. Pepper, “Colorimetric resonant reflection as a direct biochemical assay technique,” Sens. Actuators, B 81(2-3), 316–328 (2002).
[Crossref]

Ding, T. J.

S. F. Lin, C. M. Wang, Y. L. Tsai, T. J. Ding, T. H. Yang, W. Y. Chen, and J. Y. Chang, “A model for fast predicting and optimizing the sensitivity of surface-relief guided mode resonance sensors,” Sens. Actuators, B 176, 1197–1203 (2013).
[Crossref]

S. F. Lin, C. M. Wang, T. J. Ding, Y. L. Tsai, T. H. Yang, W. Y. Chen, and J. Y. Chang, “Sensitive metal layer assisted guided mode resonance biosensor with a spectrum inversed response and strong asymmetric resonance field distribution,” Opt. Express 20(13), 14584–14595 (2012).
[Crossref]

Ding, Y.

R. Magnusson, D. Wawro, S. Zimmerman, Y. Ding, M. Shokooh-Saremi, K. J. Lee, D. Ussery, S. Kim, and S. H. Song, “Leaky-mode resonance photonics: Technology for biosensors, optical components, MEMS, and plasmonics,” Proc. SPIE 7604, 76040M (2010).
[Crossref]

Doll, K. L.

J. A. Weidanz, K. L. Doll, S. Mohana-Sundaram, T. Wichner, D. B. Lowe, S. Gimlin, D. Wawro Weidanz, R. Magnusson, and O. E. Hawkins, “Detection of human leukocyte antigen biomarkers in breast cancer utilizing label-free biosensor technology,” J. Visualized Exp. (97), e52159 (2015).
[Crossref]

El Beheiry, M.

Fan, S.

Fehrembach, A. L.

Fine, E.

B. T. Cunningham, P. Li, S. Schulz, B. Lin, C. Baird, J. Gerstenmaier, C. Genick, F. Wang, E. Fine, and L. Laing, “Label-free assays on the BIND system,” J. Biomol. Screening 9(6), 481–490 (2004).
[Crossref]

Ganesh, N.

W. Zhang, S. Kim, N. Ganesh, I. D. Block, P. C. Mathias, H.-Y. Wu, and B. T. Cunningham, “Deposited nanorod films for photonic crystal biosensor applications,” J. Vac. Sci. Technol. 28(4), 996–1001 (2010).
[Crossref]

I. D. Block, N. Ganesh, M. Lu, and B. T. Cunningham, “A sensitivity model for predicting photonic crystal biosensor performance,” IEEE Sens. J. 8(3), 274–280 (2008).
[Crossref]

Genick, C.

B. T. Cunningham, P. Li, S. Schulz, B. Lin, C. Baird, J. Gerstenmaier, C. Genick, F. Wang, E. Fine, and L. Laing, “Label-free assays on the BIND system,” J. Biomol. Screening 9(6), 481–490 (2004).
[Crossref]

Gerken, M.

Gerstenmaier, J.

B. T. Cunningham, P. Li, S. Schulz, B. Lin, C. Baird, J. Gerstenmaier, C. Genick, F. Wang, E. Fine, and L. Laing, “Label-free assays on the BIND system,” J. Biomol. Screening 9(6), 481–490 (2004).
[Crossref]

Gimlin, S.

J. A. Weidanz, K. L. Doll, S. Mohana-Sundaram, T. Wichner, D. B. Lowe, S. Gimlin, D. Wawro Weidanz, R. Magnusson, and O. E. Hawkins, “Detection of human leukocyte antigen biomarkers in breast cancer utilizing label-free biosensor technology,” J. Visualized Exp. (97), e52159 (2015).
[Crossref]

Granet, G.

Greve, J.

Hawkins, O. E.

J. A. Weidanz, K. L. Doll, S. Mohana-Sundaram, T. Wichner, D. B. Lowe, S. Gimlin, D. Wawro Weidanz, R. Magnusson, and O. E. Hawkins, “Detection of human leukocyte antigen biomarkers in breast cancer utilizing label-free biosensor technology,” J. Visualized Exp. (97), e52159 (2015).
[Crossref]

Hillier, A. C.

L. Liu, H. A. Khan, J. Li, A. C. Hillier, and M. Lu, “A strain-tunable nanoimprint lithography for linear variable photonic crystal filters,” Nanotechnology 27(29), 295301 (2016).
[Crossref]

Hong, R. J.

L. Y. Qian, D. W. Zhang, C. X. Tao, R. J. Hong, and S. L. Zhuang, “Tunable guided-mode resonant filter with wedged waveguide layer fabricated by masked ion beam etching,” Opt. Lett. 41(5), 982–985 (2016).
[Crossref]

L. Y. Qian, D. W. Zhang, Y. S. Huang, C. X. Tao, R. J. Hong, and S. L. Zhuang, “Performance of a double-layer guided mode resonance filter with non-subwavelength grating period at oblique incidence,” Opt. Laser Technol. 72, 42–47 (2015).
[Crossref]

Hsieh, W. H.

Hsu, H. Y.

H. Y. Hsu, Y. H. Lan, and C. S. Huang, “A gradient grating period guided-mode resonance spectrometer,” IEEE Photonics J. 10(1), 1–9 (2018).
[Crossref]

Huang, C. S.

H. Y. Hsu, Y. H. Lan, and C. S. Huang, “A gradient grating period guided-mode resonance spectrometer,” IEEE Photonics J. 10(1), 1–9 (2018).
[Crossref]

H. A. Lin and C. S. Huang, “Linear variable filter based on a gradient grating period guided-mode resonance filter,” IEEE Photonics Technol. Lett. 28(9), 1042–1045 (2016).
[Crossref]

Huang, Y. S.

L. Y. Qian, D. W. Zhang, Y. S. Huang, C. X. Tao, R. J. Hong, and S. L. Zhuang, “Performance of a double-layer guided mode resonance filter with non-subwavelength grating period at oblique incidence,” Opt. Laser Technol. 72, 42–47 (2015).
[Crossref]

Karrock, T.

Khan, H. A.

L. Liu, H. A. Khan, J. Li, A. C. Hillier, and M. Lu, “A strain-tunable nanoimprint lithography for linear variable photonic crystal filters,” Nanotechnology 27(29), 295301 (2016).
[Crossref]

Kim, S.

W. Zhang, S. Kim, N. Ganesh, I. D. Block, P. C. Mathias, H.-Y. Wu, and B. T. Cunningham, “Deposited nanorod films for photonic crystal biosensor applications,” J. Vac. Sci. Technol. 28(4), 996–1001 (2010).
[Crossref]

R. Magnusson, D. Wawro, S. Zimmerman, Y. Ding, M. Shokooh-Saremi, K. J. Lee, D. Ussery, S. Kim, and S. H. Song, “Leaky-mode resonance photonics: Technology for biosensors, optical components, MEMS, and plasmonics,” Proc. SPIE 7604, 76040M (2010).
[Crossref]

Ko, Y. H.

Ku, Y. F.

Lacour, D.

Laing, L.

B. T. Cunningham, P. Li, S. Schulz, B. Lin, C. Baird, J. Gerstenmaier, C. Genick, F. Wang, E. Fine, and L. Laing, “Label-free assays on the BIND system,” J. Biomol. Screening 9(6), 481–490 (2004).
[Crossref]

Lan, Y. H.

H. Y. Hsu, Y. H. Lan, and C. S. Huang, “A gradient grating period guided-mode resonance spectrometer,” IEEE Photonics J. 10(1), 1–9 (2018).
[Crossref]

Lee, K. J.

R. Magnusson, D. Wawro, S. Zimmerman, Y. Ding, M. Shokooh-Saremi, K. J. Lee, D. Ussery, S. Kim, and S. H. Song, “Leaky-mode resonance photonics: Technology for biosensors, optical components, MEMS, and plasmonics,” Proc. SPIE 7604, 76040M (2010).
[Crossref]

Lemarchand, F.

Levi, O.

Li, H. Y.

Li, J.

L. Liu, H. A. Khan, J. Li, A. C. Hillier, and M. Lu, “A strain-tunable nanoimprint lithography for linear variable photonic crystal filters,” Nanotechnology 27(29), 295301 (2016).
[Crossref]

Li, P.

B. T. Cunningham, P. Li, S. Schulz, B. Lin, C. Baird, J. Gerstenmaier, C. Genick, F. Wang, E. Fine, and L. Laing, “Label-free assays on the BIND system,” J. Biomol. Screening 9(6), 481–490 (2004).
[Crossref]

B. T. Cunningham, P. Li, B. Lin, and J. Pepper, “Colorimetric resonant reflection as a direct biochemical assay technique,” Sens. Actuators, B 81(2-3), 316–328 (2002).
[Crossref]

Lin, B.

B. T. Cunningham, P. Li, S. Schulz, B. Lin, C. Baird, J. Gerstenmaier, C. Genick, F. Wang, E. Fine, and L. Laing, “Label-free assays on the BIND system,” J. Biomol. Screening 9(6), 481–490 (2004).
[Crossref]

B. T. Cunningham, P. Li, B. Lin, and J. Pepper, “Colorimetric resonant reflection as a direct biochemical assay technique,” Sens. Actuators, B 81(2-3), 316–328 (2002).
[Crossref]

Lin, H. A.

H. A. Lin and C. S. Huang, “Linear variable filter based on a gradient grating period guided-mode resonance filter,” IEEE Photonics Technol. Lett. 28(9), 1042–1045 (2016).
[Crossref]

Lin, S. F.

S. F. Lin, C. M. Wang, Y. L. Tsai, T. J. Ding, T. H. Yang, W. Y. Chen, and J. Y. Chang, “A model for fast predicting and optimizing the sensitivity of surface-relief guided mode resonance sensors,” Sens. Actuators, B 176, 1197–1203 (2013).
[Crossref]

S. F. Lin, C. M. Wang, T. J. Ding, Y. L. Tsai, T. H. Yang, W. Y. Chen, and J. Y. Chang, “Sensitive metal layer assisted guided mode resonance biosensor with a spectrum inversed response and strong asymmetric resonance field distribution,” Opt. Express 20(13), 14584–14595 (2012).
[Crossref]

Liu, L.

L. Liu, H. A. Khan, J. Li, A. C. Hillier, and M. Lu, “A strain-tunable nanoimprint lithography for linear variable photonic crystal filters,” Nanotechnology 27(29), 295301 (2016).
[Crossref]

Liu, V.

Lowe, D. B.

J. A. Weidanz, K. L. Doll, S. Mohana-Sundaram, T. Wichner, D. B. Lowe, S. Gimlin, D. Wawro Weidanz, R. Magnusson, and O. E. Hawkins, “Detection of human leukocyte antigen biomarkers in breast cancer utilizing label-free biosensor technology,” J. Visualized Exp. (97), e52159 (2015).
[Crossref]

Lu, M.

L. Liu, H. A. Khan, J. Li, A. C. Hillier, and M. Lu, “A strain-tunable nanoimprint lithography for linear variable photonic crystal filters,” Nanotechnology 27(29), 295301 (2016).
[Crossref]

I. D. Block, N. Ganesh, M. Lu, and B. T. Cunningham, “A sensitivity model for predicting photonic crystal biosensor performance,” IEEE Sens. J. 8(3), 274–280 (2008).
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Y. H. Ko and R. Magnusson, “Flat-top bandpass filters enabled by cascaded resonant gratings,” Opt. Lett. 41(20), 4704–4707 (2016).
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R. Magnusson, D. Wawro, S. Zimmerman, Y. Ding, M. Shokooh-Saremi, K. J. Lee, D. Ussery, S. Kim, and S. H. Song, “Leaky-mode resonance photonics: Technology for biosensors, optical components, MEMS, and plasmonics,” Proc. SPIE 7604, 76040M (2010).
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S. S. Wang and R. Magnusson, “Theory and applications of guided-mode resonance filters,” Appl. Opt. 32(14), 2606–2613 (1993).
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S. S. Wang, R. Magnusson, J. S. Bagby, and M. G. Moharam, “Guided-mode resonances in planar dielectric-layer diffraction gratings,” J. Opt. Soc. Am. A 7(8), 1470–1474 (1990).
[Crossref]

J. A. Weidanz, K. L. Doll, S. Mohana-Sundaram, T. Wichner, D. B. Lowe, S. Gimlin, D. Wawro Weidanz, R. Magnusson, and O. E. Hawkins, “Detection of human leukocyte antigen biomarkers in breast cancer utilizing label-free biosensor technology,” J. Visualized Exp. (97), e52159 (2015).
[Crossref]

Mathias, P. C.

W. Zhang, S. Kim, N. Ganesh, I. D. Block, P. C. Mathias, H.-Y. Wu, and B. T. Cunningham, “Deposited nanorod films for photonic crystal biosensor applications,” J. Vac. Sci. Technol. 28(4), 996–1001 (2010).
[Crossref]

Moghaddas, S. A. J.

S. A. J. Moghaddas, M. Shahabadi, and M. Mohammad-Taheri, “Guided mode resonance sensor with enhanced surface sensitivity using coupled cross-stacked gratings,” IEEE Sens. J. 14(4), 1216–1222 (2014).
[Crossref]

Mohammad-Taheri, M.

S. A. J. Moghaddas, M. Shahabadi, and M. Mohammad-Taheri, “Guided mode resonance sensor with enhanced surface sensitivity using coupled cross-stacked gratings,” IEEE Sens. J. 14(4), 1216–1222 (2014).
[Crossref]

Mohana-Sundaram, S.

J. A. Weidanz, K. L. Doll, S. Mohana-Sundaram, T. Wichner, D. B. Lowe, S. Gimlin, D. Wawro Weidanz, R. Magnusson, and O. E. Hawkins, “Detection of human leukocyte antigen biomarkers in breast cancer utilizing label-free biosensor technology,” J. Visualized Exp. (97), e52159 (2015).
[Crossref]

Moharam, M. G.

Mure-Ravaud, A.

Nazirizadeh, Y.

Niraula, M.

Oertzen, F.

Pepper, J.

B. T. Cunningham, P. Li, B. Lin, and J. Pepper, “Colorimetric resonant reflection as a direct biochemical assay technique,” Sens. Actuators, B 81(2-3), 316–328 (2002).
[Crossref]

Plumey, J. P.

Qian, L. Y.

L. Y. Qian, D. W. Zhang, C. X. Tao, R. J. Hong, and S. L. Zhuang, “Tunable guided-mode resonant filter with wedged waveguide layer fabricated by masked ion beam etching,” Opt. Lett. 41(5), 982–985 (2016).
[Crossref]

L. Y. Qian, D. W. Zhang, Y. S. Huang, C. X. Tao, R. J. Hong, and S. L. Zhuang, “Performance of a double-layer guided mode resonance filter with non-subwavelength grating period at oblique incidence,” Opt. Laser Technol. 72, 42–47 (2015).
[Crossref]

Schulz, S.

B. T. Cunningham, P. Li, S. Schulz, B. Lin, C. Baird, J. Gerstenmaier, C. Genick, F. Wang, E. Fine, and L. Laing, “Label-free assays on the BIND system,” J. Biomol. Screening 9(6), 481–490 (2004).
[Crossref]

Sentenac, A.

Shahabadi, M.

S. A. J. Moghaddas, M. Shahabadi, and M. Mohammad-Taheri, “Guided mode resonance sensor with enhanced surface sensitivity using coupled cross-stacked gratings,” IEEE Sens. J. 14(4), 1216–1222 (2014).
[Crossref]

Shokooh-Saremi, M.

R. Magnusson, D. Wawro, S. Zimmerman, Y. Ding, M. Shokooh-Saremi, K. J. Lee, D. Ussery, S. Kim, and S. H. Song, “Leaky-mode resonance photonics: Technology for biosensors, optical components, MEMS, and plasmonics,” Proc. SPIE 7604, 76040M (2010).
[Crossref]

Song, S. H.

R. Magnusson, D. Wawro, S. Zimmerman, Y. Ding, M. Shokooh-Saremi, K. J. Lee, D. Ussery, S. Kim, and S. H. Song, “Leaky-mode resonance photonics: Technology for biosensors, optical components, MEMS, and plasmonics,” Proc. SPIE 7604, 76040M (2010).
[Crossref]

Su, W.

Talneau, A.

Tao, C. X.

L. Y. Qian, D. W. Zhang, C. X. Tao, R. J. Hong, and S. L. Zhuang, “Tunable guided-mode resonant filter with wedged waveguide layer fabricated by masked ion beam etching,” Opt. Lett. 41(5), 982–985 (2016).
[Crossref]

L. Y. Qian, D. W. Zhang, Y. S. Huang, C. X. Tao, R. J. Hong, and S. L. Zhuang, “Performance of a double-layer guided mode resonance filter with non-subwavelength grating period at oblique incidence,” Opt. Laser Technol. 72, 42–47 (2015).
[Crossref]

Tsai, Y. L.

S. F. Lin, C. M. Wang, Y. L. Tsai, T. J. Ding, T. H. Yang, W. Y. Chen, and J. Y. Chang, “A model for fast predicting and optimizing the sensitivity of surface-relief guided mode resonance sensors,” Sens. Actuators, B 176, 1197–1203 (2013).
[Crossref]

S. F. Lin, C. M. Wang, T. J. Ding, Y. L. Tsai, T. H. Yang, W. Y. Chen, and J. Y. Chang, “Sensitive metal layer assisted guided mode resonance biosensor with a spectrum inversed response and strong asymmetric resonance field distribution,” Opt. Express 20(13), 14584–14595 (2012).
[Crossref]

Ussery, D.

R. Magnusson, D. Wawro, S. Zimmerman, Y. Ding, M. Shokooh-Saremi, K. J. Lee, D. Ussery, S. Kim, and S. H. Song, “Leaky-mode resonance photonics: Technology for biosensors, optical components, MEMS, and plasmonics,” Proc. SPIE 7604, 76040M (2010).
[Crossref]

Wang, C. M.

S. F. Lin, C. M. Wang, Y. L. Tsai, T. J. Ding, T. H. Yang, W. Y. Chen, and J. Y. Chang, “A model for fast predicting and optimizing the sensitivity of surface-relief guided mode resonance sensors,” Sens. Actuators, B 176, 1197–1203 (2013).
[Crossref]

S. F. Lin, C. M. Wang, T. J. Ding, Y. L. Tsai, T. H. Yang, W. Y. Chen, and J. Y. Chang, “Sensitive metal layer assisted guided mode resonance biosensor with a spectrum inversed response and strong asymmetric resonance field distribution,” Opt. Express 20(13), 14584–14595 (2012).
[Crossref]

Wang, F.

B. T. Cunningham, P. Li, S. Schulz, B. Lin, C. Baird, J. Gerstenmaier, C. Genick, F. Wang, E. Fine, and L. Laing, “Label-free assays on the BIND system,” J. Biomol. Screening 9(6), 481–490 (2004).
[Crossref]

Wang, S. S.

Wawro, D.

R. Magnusson, D. Wawro, S. Zimmerman, Y. Ding, M. Shokooh-Saremi, K. J. Lee, D. Ussery, S. Kim, and S. H. Song, “Leaky-mode resonance photonics: Technology for biosensors, optical components, MEMS, and plasmonics,” Proc. SPIE 7604, 76040M (2010).
[Crossref]

Wawro Weidanz, D.

J. A. Weidanz, K. L. Doll, S. Mohana-Sundaram, T. Wichner, D. B. Lowe, S. Gimlin, D. Wawro Weidanz, R. Magnusson, and O. E. Hawkins, “Detection of human leukocyte antigen biomarkers in breast cancer utilizing label-free biosensor technology,” J. Visualized Exp. (97), e52159 (2015).
[Crossref]

Weidanz, J. A.

J. A. Weidanz, K. L. Doll, S. Mohana-Sundaram, T. Wichner, D. B. Lowe, S. Gimlin, D. Wawro Weidanz, R. Magnusson, and O. E. Hawkins, “Detection of human leukocyte antigen biomarkers in breast cancer utilizing label-free biosensor technology,” J. Visualized Exp. (97), e52159 (2015).
[Crossref]

Wichner, T.

J. A. Weidanz, K. L. Doll, S. Mohana-Sundaram, T. Wichner, D. B. Lowe, S. Gimlin, D. Wawro Weidanz, R. Magnusson, and O. E. Hawkins, “Detection of human leukocyte antigen biomarkers in breast cancer utilizing label-free biosensor technology,” J. Visualized Exp. (97), e52159 (2015).
[Crossref]

Wu, H.-Y.

W. Zhang, S. Kim, N. Ganesh, I. D. Block, P. C. Mathias, H.-Y. Wu, and B. T. Cunningham, “Deposited nanorod films for photonic crystal biosensor applications,” J. Vac. Sci. Technol. 28(4), 996–1001 (2010).
[Crossref]

Xu, L.

Yang, T. H.

S. F. Lin, C. M. Wang, Y. L. Tsai, T. J. Ding, T. H. Yang, W. Y. Chen, and J. Y. Chang, “A model for fast predicting and optimizing the sensitivity of surface-relief guided mode resonance sensors,” Sens. Actuators, B 176, 1197–1203 (2013).
[Crossref]

S. F. Lin, C. M. Wang, T. J. Ding, Y. L. Tsai, T. H. Yang, W. Y. Chen, and J. Y. Chang, “Sensitive metal layer assisted guided mode resonance biosensor with a spectrum inversed response and strong asymmetric resonance field distribution,” Opt. Express 20(13), 14584–14595 (2012).
[Crossref]

Yoon, J. W.

Zhang, D. W.

L. Y. Qian, D. W. Zhang, C. X. Tao, R. J. Hong, and S. L. Zhuang, “Tunable guided-mode resonant filter with wedged waveguide layer fabricated by masked ion beam etching,” Opt. Lett. 41(5), 982–985 (2016).
[Crossref]

L. Y. Qian, D. W. Zhang, Y. S. Huang, C. X. Tao, R. J. Hong, and S. L. Zhuang, “Performance of a double-layer guided mode resonance filter with non-subwavelength grating period at oblique incidence,” Opt. Laser Technol. 72, 42–47 (2015).
[Crossref]

Zhang, W.

W. Zhang, S. Kim, N. Ganesh, I. D. Block, P. C. Mathias, H.-Y. Wu, and B. T. Cunningham, “Deposited nanorod films for photonic crystal biosensor applications,” J. Vac. Sci. Technol. 28(4), 996–1001 (2010).
[Crossref]

Zheng, G.

Zhuang, S. L.

L. Y. Qian, D. W. Zhang, C. X. Tao, R. J. Hong, and S. L. Zhuang, “Tunable guided-mode resonant filter with wedged waveguide layer fabricated by masked ion beam etching,” Opt. Lett. 41(5), 982–985 (2016).
[Crossref]

L. Y. Qian, D. W. Zhang, Y. S. Huang, C. X. Tao, R. J. Hong, and S. L. Zhuang, “Performance of a double-layer guided mode resonance filter with non-subwavelength grating period at oblique incidence,” Opt. Laser Technol. 72, 42–47 (2015).
[Crossref]

Zimmerman, S.

R. Magnusson, D. Wawro, S. Zimmerman, Y. Ding, M. Shokooh-Saremi, K. J. Lee, D. Ussery, S. Kim, and S. H. Song, “Leaky-mode resonance photonics: Technology for biosensors, optical components, MEMS, and plasmonics,” Proc. SPIE 7604, 76040M (2010).
[Crossref]

Appl. Opt. (2)

IEEE Photonics J. (1)

H. Y. Hsu, Y. H. Lan, and C. S. Huang, “A gradient grating period guided-mode resonance spectrometer,” IEEE Photonics J. 10(1), 1–9 (2018).
[Crossref]

IEEE Photonics Technol. Lett. (1)

H. A. Lin and C. S. Huang, “Linear variable filter based on a gradient grating period guided-mode resonance filter,” IEEE Photonics Technol. Lett. 28(9), 1042–1045 (2016).
[Crossref]

IEEE Sens. J. (2)

S. A. J. Moghaddas, M. Shahabadi, and M. Mohammad-Taheri, “Guided mode resonance sensor with enhanced surface sensitivity using coupled cross-stacked gratings,” IEEE Sens. J. 14(4), 1216–1222 (2014).
[Crossref]

I. D. Block, N. Ganesh, M. Lu, and B. T. Cunningham, “A sensitivity model for predicting photonic crystal biosensor performance,” IEEE Sens. J. 8(3), 274–280 (2008).
[Crossref]

J. Biomol. Screening (1)

B. T. Cunningham, P. Li, S. Schulz, B. Lin, C. Baird, J. Gerstenmaier, C. Genick, F. Wang, E. Fine, and L. Laing, “Label-free assays on the BIND system,” J. Biomol. Screening 9(6), 481–490 (2004).
[Crossref]

J. Opt. Soc. Am. A (2)

J. Vac. Sci. Technol. (1)

W. Zhang, S. Kim, N. Ganesh, I. D. Block, P. C. Mathias, H.-Y. Wu, and B. T. Cunningham, “Deposited nanorod films for photonic crystal biosensor applications,” J. Vac. Sci. Technol. 28(4), 996–1001 (2010).
[Crossref]

Nanotechnology (1)

L. Liu, H. A. Khan, J. Li, A. C. Hillier, and M. Lu, “A strain-tunable nanoimprint lithography for linear variable photonic crystal filters,” Nanotechnology 27(29), 295301 (2016).
[Crossref]

Opt. Express (5)

Opt. Laser Technol. (1)

L. Y. Qian, D. W. Zhang, Y. S. Huang, C. X. Tao, R. J. Hong, and S. L. Zhuang, “Performance of a double-layer guided mode resonance filter with non-subwavelength grating period at oblique incidence,” Opt. Laser Technol. 72, 42–47 (2015).
[Crossref]

Opt. Lett. (3)

Proc. SPIE (1)

R. Magnusson, D. Wawro, S. Zimmerman, Y. Ding, M. Shokooh-Saremi, K. J. Lee, D. Ussery, S. Kim, and S. H. Song, “Leaky-mode resonance photonics: Technology for biosensors, optical components, MEMS, and plasmonics,” Proc. SPIE 7604, 76040M (2010).
[Crossref]

Sens. Actuators, B (2)

B. T. Cunningham, P. Li, B. Lin, and J. Pepper, “Colorimetric resonant reflection as a direct biochemical assay technique,” Sens. Actuators, B 81(2-3), 316–328 (2002).
[Crossref]

S. F. Lin, C. M. Wang, Y. L. Tsai, T. J. Ding, T. H. Yang, W. Y. Chen, and J. Y. Chang, “A model for fast predicting and optimizing the sensitivity of surface-relief guided mode resonance sensors,” Sens. Actuators, B 176, 1197–1203 (2013).
[Crossref]

Other (1)

J. A. Weidanz, K. L. Doll, S. Mohana-Sundaram, T. Wichner, D. B. Lowe, S. Gimlin, D. Wawro Weidanz, R. Magnusson, and O. E. Hawkins, “Detection of human leukocyte antigen biomarkers in breast cancer utilizing label-free biosensor technology,” J. Visualized Exp. (97), e52159 (2015).
[Crossref]

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Figures (7)

Fig. 1.
Fig. 1. (a) Schematic of a typical GMR structure. (b) Calculated relation between the incident angle and the value of λ/Λ, λ = 800 nm. (c) Calculated TE mode spectrum under normal incidence. (d) Calculated TE mode spectrum under an incident angle of 34.74°.
Fig. 2.
Fig. 2. (a) Simulated transmission spectrum at normal incidence for a TE mode. Simulated transmitted spectrum at an incident angle of (b) 34.74° and (c) 0°. The grating periods are 800 nm in both panels. (d) GMR wavelength as a function of incident angle. The black and red lines were calculated for nc = 1.33 and 1.39, respectively.
Fig. 3.
Fig. 3. Basic slab waveguides model.
Fig. 4.
Fig. 4. GMR wavelength shift as a function of incident angles: RCWA simulations (dashed line) and slab waveguide model (solid red line).
Fig. 5.
Fig. 5. SEM micrographs of the fabricated GMR samples. The measured grating periods in SEM are 450, 809, and 994 nm for (a), (b), and (c), respectively. (d) Photograph of the fabricated GMR samples.
Fig. 6.
Fig. 6. (a) Setup for transmission spectrum and sensitivity measurements. (b)-(d) Experimental transmission spectra for samples A, B and C, with different grating periods at incidence angles of 0°, 35°, and 45°, respectively. (e) Resonance wavelength versus the refractive index of the surrounding medium. The slopes of the fitting curves show that the refractive index sensitivities corresponding to data in (b)-(d).
Fig. 7.
Fig. 7. Transmission spectra for (a) sample B at incident angle of 15° and (b) sample C at incident angle of 35°.

Tables (2)

Tables Icon

Table 1. GMRs shift under various angles based on the RCWA (R) and slab waveguide model (M)

Tables Icon

Table 2. Bulk sensitivity comparison for different oblique incident angles

Equations (11)

Equations on this page are rendered with MathJax. Learn more.

max { n c , n s } | n c sin θ i λ / λ Λ Λ | < n e f f ,
S   =   Δ λ / Δ n c ,
arg R 1 + arg R 2 + 2 d w k _ z = 2 π m .
k _ x 2 + k _ z 2 = k 0 2 n w 2 ,
k _ x = k 0 n c sin θ + 2 π Λ i .
( 2 π m arg R 1 arg R 2 2 d w ) 2 = ( 2 π λ ) 2 n w 2 ( 2 π λ n c sin θ 2 π Λ i ) 2 .
( 2 π m arg R 1 arg R 2 2 d w ) 2 = ( 2 π λ 0 ) 2 n w 2 ( 2 π Λ i ) 2 .
( n c λ sin θ i Λ ) 2 ( i Λ ) 2 = n w 2 ( 1 λ 2 1 λ 0 2 ) .
λ = i n c λ 0 2 sin θ + λ 0 Λ 2 n w 4 + n c 2 ( i 2 λ 0 2 Λ 2 n w 2 ) si n 2 θ Λ n w 2 .
S   =   d λ d n c = λ 0 Λ n w 2 ( n c ( i 2 λ 0 2 Λ 2 n w 2 ) si n 2 θ Λ 2 n w 4 + n c 2 ( i 2 λ 0 2 Λ 2 n w 2 ) si n 2 θ + i λ 0 sin θ ) .
Δ λ = λ 0 Λ n w 2 ( n c ( λ 0 2 Λ 2 n w 2 ) si n 2 θ Λ 2 n w 4 + n c 2 ( λ 0 2 Λ 2 n w 2 ) si n 2 θ λ 0 sin θ ) Δ n c .

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