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A waveguide-mode sensor of the spectral-readout type can be used to detect changes in the complex refractive index in the vicinity of the surface of a sensing plate by observing the change in the spectrum of light reflected on the surface. The sensor’s configuration can be simplified by adopting a parallel-incidence-type optical setup. To obtain a high sensitivity, the optimization of the sensing-plate structure, incidence angle, and detection wavelength band is essential for the sensor. In the present report, the results predicted by simulations are compared with experimental results in order to evaluate their validity. A discussion of the optimal design for the parallel-incidence-type sensor is also presented, according to the results obtained.
© 2015 Optical Society of America
1. Introduction
Sensors capable of detecting substances such as viruses, bacteria, contaminants, and in-vivo proteins with a high sensitivity are sought for controlling communicable diseases, environmental pollution countermeasures, and the early detection of diseases. A sensor capable of measuring the affinity between biological materials is also required in the field of drug development. Sensors based on surface plasmon resonance (SPR) are widely used for such purposes [1–3]. In recent years, there have also been reports of a ring resonator sensor, which utilizes the evanescent field of light propagating in a ring-shaped waveguide to perform detection similarly to the SPR sensor [4,5]. The waveguide-mode sensor, which has an optical system quite similar to that of the SPR sensor and detects substances using the evanescent field of propagating light, has been reported as well [6,7]. The concept of the waveguide-mode sensor resembles that of the resonant mirror biosensor [8–10].
The waveguide-mode sensor has a waveguide layer comprising a Si layer and an amorphous SiO2 layer (hereafter referred to as the “SiO2 layer”) formed on a transparent substrate, where the SiO2 layer supports leaky waveguide modes. The transparent substrate and substances on the SiO2 layer, which mainly consist of water, work as claddings. Enhanced electric fields due to the excitation of waveguide modes have been reported previously [7]. Theoretically, the substrate may be made of any plate material that is transparent; however, silica glass (SiO2 glass) is optimally suited owing to its optical characteristics, physical stability, and chemical stability [7]. Thus, because the sensing plate of the waveguide-mode sensor is comprised only of Si and SiO2, it is extremely stable compared with the SPR sensor, which has a sensor surface composed of metals. A dynamic range of the sensitivity of the waveguide-mode sensor has been reported to be in the order of 10 ng/mL to 10 μg/mL for label-free detection of proteins [11]. A variety of methods has been reported for enhancing the sensitivity of waveguide-mode sensors. For instance, it has been reported that the detection sensitivity of the protein adsorption was increased tenfold by forming nanopores 50 nm in diameter on the SiO2 layer at a rate of 5 × 109 per square cm [7].
Reflectometric interference spectroscopy [12,13] uses an optical setup similar to that of the waveguide-mode sensor. The difference is that the waveguide-mode sensor utilizes the propagating light confined within the waveguide. Since the propagating light suffers multiple reflection at the sensing plate surface, the waveguide-mode sensor sensitively detects changes in the imaginary part of the complex refractive index on the sensing plate surface [14,15]. A highly sensitive detection of influenza viruses achieved by taking advantage of this characteristic and by using gold nanoparticles as a labeling material has also been reported, where detection of influenza viruses with concentrations of 8 × 103 to 8 × 105 plaque forming unit per mL was demonstrated [16].
There have been many reports regarding detections performed with SPR sensors and waveguide-mode sensors, by utilizing the incidence angle dependence of the reflectance. This is achieved by irradiating light while varying the incidence angle, using the Kretschmann configuration [17]. Because this method requires the precise control of the incidence angle, making the structure of the sensor quite complicated, there have been reports of spectral-readout-type sensors with a fixed incidence angle and the incidence of white light [18–20]. As a spectral readout-type sensor, a fiber optic based SPR sensor, which is small and inexpensive owing to its simple structure, has also been reported [21].
The waveguide-mode sensor of the spectral-readout type uses the light from white-light sources such as LEDs and halogen lamps. The light is collimated with a collimator lens, s-polarized by a polarizer, and irradiated onto the sensing plate at a specific incidence angle via a prism. A region with a lower reflectance is observed at a particular wavelength in the spectrum of the light reflected by the sensing plate. Such a “dip” is a resonance dip generated by the excitation of the waveguide mode. The position of a resonance dip (λdip) and the reflectance at the resonance dip change with the adsorption of substances on the surface of the sensing plate, and this change makes it possible to detect the adsorption of the corresponding substances. A higher sensitivity was reported with the waveguide-mode sensor using the spectral-readout method, rather than the incidence-angle scanning method [20].
A parallel-incidence-type optical system in which the incidence and emission directions of the light are parallel to the bottom surface of the prism has been reported in relation to spectral-readout-type SPR sensors [19], and numerous reports have discussed its use with waveguide-mode sensors in recent years [16,22,23]. The optical system of the parallel-incidence-type waveguide-mode sensor is shown in Fig. 1. The incidence angle (θ) to the sensing plate in this optical system is determined by the bottom angle of the prism (α). The amount of change in the reflectance (⊿R) in relation to the change in the refractive index has been reported to depend on the thickness of the Si layer (tSi), as well as on the thickness of the SiO2 layer (tSiO2) and θ [7,20]. In this report, the detection of protein adsorption is used as a model case to clarify the relationship among such parameters, ⊿R, and the amount of changein λdip (⊿λ). Furthermore, a sensor of the parallel-incidence type was built and used to take measurements of ⊿R and ⊿λ, in order to evaluate the validity of the values obtained from the simulations. Additionally, a discussion is presented regarding the method for deducing optimal design values for the sensor, according to the simulation results.
2. Simulations
An incident light of a waveguide-mode sensor of the parallel-incidence type was irradiated onto a trapezoidal prism parallel to the sensing plate, as shown in Fig. 1. However, the optical system model shown in Fig. 2 was used for the simulation, for simplification. A Si layer and a SiO2 layer were arranged on the bottom surface of the semicylindrical prism, as shown in the figure. The surface of the sensing plate was assumed to be immersed in water. The incident light was irradiated onto the surface of the sensing plate at an incident angle of θ. The following relationship exists between θ (degrees) and α (degrees):
where nSiO2 represents the refractive index of the silica glass. The refractive index of air was assumed to be 1. The information obtained regarding θ could therefore be converted into conditions for α using Eq. (1). The simulation was performed using the transfer matrix method for a stratified medium, according to the Fresnel equations [24]. The s-polarized light, which can be expected to provide a higher sensitivity for the waveguide-mode sensor, was used as the incident light [6]. The complex refractive indices of the SiO2 glass and water used for the calculation were taken from a previous report [25]. The corresponding value for single-crystalline Si, described in [26], was used as the value of the complex refractive index for Si.The black line in Fig. 3(a) represents the reflection spectrum obtained from a calculation performed by setting tSi, tSiO2, and θ to 220 nm, 430 nm, and 70°, respectively. Two resonance dips with λdip at 545.4 and 632.1 nm are observed in the wavelength range between 500 and 700 nm. The reflection spectrum for the case where a protein layer, simulated by a layer with a refractive index of 1.45, extinction coefficient of 0, and thickness of 5 nm, was adsorbed on the surface of the sensing plate is represented by a red line. It is evident that λdip shifts to the longer-wavelength side owing to the adsorption of protein. The ⊿λ values for the two resonance dips of 545.4 and 632.1 nm were 0.8 and 4.1 nm, respectively. ⊿Rdip indicates the difference in the reflectance before and after the protein adsorption at λdip prior to the protein adsorption. ⊿R before and after the protein adsorption is indicated in Fig. 3(b). Hereafter, the maximum value of ⊿R at each resonance dip and the absolute value of ⊿R are expressed as Max ⊿R and |⊿R|, respectively. It should be noted that the wavelength at which Max ⊿R is obtained is different form λdip prior to the protein adsorption. Because the protein adsorption can be detected with a better sensitivity when ⊿λ and ⊿R are larger, they are good indicators for the sensitivity of the sensor [21].
Fig. 3 (a) Reflection spectra obtained from a calculation performed by setting tSi, tSiO2, and θ to 220 nm, 430 nm, and 70°, respectively. The black line represents the spectrum without a protein layer. The red line represents the spectrum for the case where a protein layer with a refraction index of 1.45, extinction coefficient of 0, and thickness of 5 nm, was adsorbed on the surface of the sensing plate. (b) ⊿R obtained by subtracting the spectrum without the protein layer from the spectrum with the protein layer.
The results from the calculation for the incident wavelength and tSiO2 dependency of the reflectance, with tSi set to 220 nm and θ set to 70°, are shown in Fig. 4(a). The regions with a smaller R correspond to the resonance dips. It is evident that multiple resonance dips with different tSiO2 are manifested for a specific wavelength. This is because when tSiO2 increases, a higher-order mode is excited. The results from the calculation for the incident wavelength and tSiO2 dependence of ⊿R before and after the protein adsorption, performed by setting tSi to 220 nm and θ to 70°, are shown in Fig. 4(b). Here, it is evident that a significant change in the reflectance cannot be observed with all the resonance dips seen in Fig. 4(a). For instance, |⊿R| is a small value regardless of what value tSiO2 is set to in the wavelength range of 460–480 nm, as well as 540–580 nm. This is because the waveguide mode excited in the wavelength regions with a small |⊿R| is strongly confined within the Si layer, and the electric field intensity of such a mode on the surface of the sensing plate is weak [20]. The tSiO2 at which resonance dips are observed with respective wavelengths, is represented by the white dotted line in Fig. 4(a). It is evident that, as described above, multiple resonance dips with different tSiO2 are manifested for a specific wavelength. For this reason, the smallest tSiO2 for the resonance dips with the largest ⊿Rdip with respective wavelengths are plotted here.
Fig. 4 (a) Incident wavelength and tSiO2 dependency of the reflectance, where tSi and θ are set to 220 nm and 70°, respectively. The regions with a smaller R indicated by blue color correspond to the resonance dips. The white dotted line indicates the smallest values of tSiO2 at which the resonance dips with the largest ⊿Rdip are observed with respective wavelengths. (b) Incident wavelength and tSiO2 dependence of ⊿R obtained by subtracting the reflectance without the protein layer from the reflectance with the protein layer, where tSi and θ are set to 220 nm and 70°, respectively.
The relationship between λdip and the smallest tSiO2 for the resonance dip with the largest ⊿Rdip, similar to the white dotted line in Fig. 4(a), is shown in Fig. 5(a), where the values were obtained by setting tSi to 220 nm and θ between 67° and 75°. The λdip dependencies of ⊿λ and Max ⊿R when the protein is adsorbed, calculated by assuming a waveguide-mode sensor with tSi set to 220 nm, are shown in Figs. 5(b) and 5(c), respectively, where the value of tSiO2 that corresponds to the respective λdip shown in Fig. 5(a) was used for tSiO2. The θ was set between 67° and 75°. It is evident from Figs. 5(b) and 5(c) that both ⊿λ and Max ⊿R have peaks in the vicinity of the wavelengths 440, 500, and 620 nm. ⊿λ is larger when θ is smaller, and Max ⊿R is larger when θ is larger at the peaks of 500 and 620 nm. On the other hand, when θ is smaller, both ⊿λ and Max ⊿R are larger at the peak of 440 nm. Both ⊿λ and Max ⊿R are minimized at wavelengths of 470 and 560 nm, which correspond to the wavelength region where |⊿R| is small regardless of what value tSiO2 is set to, as shown in Fig. 4(b).
Fig. 5 (a) Relationship between λdip and the smallest tSiO2 for the largest ⊿Rdip, similar to the white dotted line in Fig. 4(a), (b) between λdip and ⊿λ, and (c) between λdip and Max ⊿R. The values are obtained by setting tSi to 220 nm and θ between 67° and 75°. The ⊿λ and Max ⊿R are obtained by assuming that the protein layer is adsorbed on the sensing plate, where the values of tSiO2 that correspond to the respective λdip shown in Fig. 5(a) are used.
The results from plotting the relationship between λdip and tSiO2, similar to that in Fig. 5(a), with tSi also treated as a variable varying between 0 and 400 nm, are shown in Figs. 6(a) and 6(b). Figures 6(a) and 6(b) indicate the results of calculations performed with θ set to 68° and 75°, respectively. Figures 6(c) and 6(d) indicate the relationships of ⊿λ obtained with the protein adsorption with tSi and λdip for θ of 68° and 75°, respectively. Figures 6(e) and 6(f) indicate the relationships of Max ⊿R obtained with the protein adsorption with tSi and λdip for θ of 68° and 75°, respectively. The values of tSiO2 corresponding to the respective tSi and λdip of Fig. 6(a) were used as tSiO2 in the calculations for Figs. 6(c) and 6(e). The values of tSiO2 corresponding to the respective tSi and λdip of Fig. 6(b) were used as tSiO2 in the calculations for Figs. 6(d) and 6(f). It is evident from Figs. 6(c) and 6(d) that ⊿λ becomes larger as λdip becomes larger. However, in cases where tSi is considered to be a constant, ⊿λ changes periodically with respect to λdip. For instance, the results indicated in Fig. 5(b) show a periodical change in ⊿λ with respect to λdip when tSi is set to 220 nm. ⊿λ gradually decreases periodically as tSi increases. The Max ⊿R indicated a tendency that differed from that of ⊿λ. In particular, Max ⊿R decreases as λdip increases. It is evident from Fig. 6 that when θ is smaller, a larger ⊿λ is obtained, whereas when θ is larger, a larger Max ⊿R is obtained. This tendency agrees with the results from Fig. 5, but at the peak of 440 nm in Fig. 5, both ⊿λ and Max ⊿R are observed to have been larger with a smaller θ. This is because tSi was treated as a constant and set to 220 nm for the calculation for Fig. 5. It is evident from Fig. 6 that the combination of tSi, tSiO2, and λdip is important for obtaining a larger ⊿λ and Max ⊿R.
Fig. 6 Relationship among tSi, λdip and the smallest tSiO2 for the largest ⊿Rdip for θ of 68° (a) and 75° (b), among tSi, λdip, and ⊿λ for θ of 68° (c) and 75° (d), and among tSi, λdip, and Max ⊿R for θ of 68° (e) and 75° (f). The ⊿λ and Max ⊿R are obtained by assuming that the protein layer is adsorbed on the sensing plate. The values of tSiO2 that correspond to the respective tSi and λdip in Fig. 6(a) were used as tSiO2 in the calculations for Figs. 6(c) and 6(e). The values of tSiO2 that correspond to the respective tSi and λdip in Fig. 6(b) were used as tSiO2 in the calculations for Figs. 6(d) and 6(f).
In order to indicate how the changes in ⊿λ and Max ⊿R manifest with regard to spectra, the reflection spectra before and after the protein adsorption are shown for tSi, tSiO2, and λdip, which correspond to the white dots (1) and (2) in Fig. 6(a), in Figs. 7(a) and 7(b), respectively. The θ used for the calculation was 68°. The black and red lines represent the spectrum prior to and following the protein adsorption, respectively. The tSi, tSiO2, λdip, ⊿λ, and Max ⊿R at the white dots (1) and (2) are indicated in Table 1. Both ⊿λ and Max ⊿R are large at the white dot (1), as shown in Figs. 6(c), 6(e), and Table 1. It is evident that the deep resonance dip has shifted significantly under such conditions, as shown in Fig. 7(a). The ⊿λ is large, but the Max ⊿R is small at the white dot (2). It is evident from Fig. 7(b) that while the shift in the dip position was large, no significant change in the reflectance was observed, because the resonance dip was shallow. Such a phenomenon is observed when λdip is on the longer-wavelength side. This is because the dip is caused by light absorption by the Si layer. Si has strong absorption on the shorter-wavelength side and strongly absorbs the propagated light. This results in a smaller reflection light intensity, which leads to a deeper resonance dip. In contrast, on the longer-wavelength side, with a smaller absorption of Si, the dip becomes shallower owing to the stronger reflection light intensity at λdip. When the Si layer is thin, the absorption by the Si becomes smaller, and thus, the Max ⊿R becomes smaller with shorter wavelengths in regions with a smaller tSi, as shown in Figs. 6(e) and 6(f).
Fig. 7 Reflection spectra of the waveguide-mode sensor with tSi, tSiO2, and λdip corresponding to the white dot (1) in Fig. 6(a)-(a) and the white dot (2) in Fig. 6(a)-(b). The black and red lines represent the spectrum prior to and following the protein adsorption, respectively.
Table 1. Values of tSi, tSiO2, λdip, ⊿λ, and Max ⊿R at the white dots (1) and (2) in Fig. 6
3. Experimental details
In order to evaluate the aforementioned calculation results, we conducted a protein detection test using multiple sensing plates having various tSi and tSiO2. A sensing plate having a single-crystalline Si layer and a thermally grown SiO2 layer on a 1.2-mm-thick silica glass substrate was used in the experiments. The sensing plates were cut into plates measuring 18 × 14 mm. A silicon-on-quartz (SOQ) substrate (Shin-Etsu Chemical) with a single-crystalline Si layer on a silica glass substrate was used in fabricating this sensing plate. The SiO2 layer was formed by thermally oxidizing the surface of the single-crystalline Si layer of the SOQ substrate [7]. Four types of sensing plates with a tSi of 25 ± 2, 85 ± 2, 160 ± 2, and 220 ± 2 nm were prepared, where the tSiO2 was 440 ± 5, 480 ± 5, 530 ± 5, and 450 ± 5 nm, respectively. The fabricated sensing plates were then immersed in a 5% hydrochloric acid solution, and etching of the SiO2 layer was performed in order to control the SiO2 layer thickness. Four plates with different tSiO2 were prepared for each of the sensing plates.
An optical system of the parallel-incidence type, shown in Fig. 1, was used for taking measurements. A halogen lamp (HL-2000-FHSA, Ocean Optics) was used as the light source. The light from the halogen lamp was directed into an optical fiber and emitted as collimated light from the collimator lens fitted on the other side of the optical fiber. This emitted light was s-polarized by a polarizing plate and directed onto the prism. The light was then reflected on the surface of the sensing plate, emitted from the prism, directed into the optical fiber via a condensing lens, and directed to a spectrophotometer (HR4000, Ocean Optics). The prisms used had an α of 32° and 38°, and according to Eq. (1), the incidence angle θ was 67.6° and 70.7°, respectively, when the wavelength of the incident light was 633 nm. The sensing plate was optically attached onto the bottom surface of the prism using an index matching liquid (Cargille fused silica matching liquid, code 50350).
Streptavidin was used as the protein for the experiment, and biotin was immobilized on the top surface of the sensing plate in order to observe the specific adsorption of the streptavidin on the biotin. The sensing plate was first immersed in a solution containing (3-aminopropyl) triethoxysilane 0.5% v/v in ethanol for 24 h to modify the amino group on the top surface of the sensing plate. After the sensing plate was rinsed with ethanol, it was immersed in a 0.5 mM solution of 5-[5-(N-succinimidyloxycarbonyl)pentylamido]hexyl-d-biotinamide [biotin-(AC5)2-OSu] in phosphate-buffered saline (PBS buffer, pH 7.4, Wako Chemicals, code 163-25265) for one hour, and the biotin was immobilized on the top surface of the sensing plate. This sensing plate was then set on the prism, and a liquid cell was placed on the top surface of the sensing plate. A PBS buffer containing 50 nM streptavidin was used for the detection. The error in the measurement during the streptavidin detection was found to be within ± 20% during repeated experiments.
4. Results
Figure 8 shows reflection spectra obtained using a sensing plate with a tSi of 160 nm. A prism with an α of 32° was used in this experiment. The black line represents the spectrum measured by filling the liquid cell with the PBS buffer. Two resonance dips with a λdip of 515 and 622 nm were observed. The thicknesses of the Si and SiO2 layers were estimated to be 160 and 280 nm, respectively, by fitting the spectrum obtained from the transfer matrix method on this spectrum (as indicated by the blue dotted line in Fig. 8). The values of tSi and tSiO2 of the sensing plates prepared in the experiment estimated by the same way were summarized in Table 2. The red line represents the spectrum measured by filling the liquid cell with the PBS buffer after adding the 50 nM solution of streptavidin in the buffer in the liquid cell, which was left standing for ten minutes and then rinsed three times with the PBS buffer. Both resonance dips shifted to the longer-wavelength side owing to the adsorption of streptavidin. The ⊿λ and Max ⊿R could be obtained for the two resonance dips using these two spectrabefore and after the adsorption of the streptavidin. Figures 9(a) and 9(b) indicate the relationship between the observed position of the resonance dip λdip and ⊿λ using the sensing plates with tSi of 25 and 160 nm, respectively, whereas Figs. 9(c) and 9(d) indicate the relationship between λdip and Max ⊿R using the sensing plates with tSi of 25 and 160 nm, respectively. The prism with an α of 32° (θ = 67.6° at 633 nm) was used in this experiment. Figures 10(a) and 10(b) indicate the relationship between λdip and ⊿λ using the sensing plates with tSi of 85 and 220 nm, respectively, whereas Figs. 10(c) and 10(d) indicate the relationship between λdip and Max ⊿R using the sensing plates with tSi of 85 and 220 nm, respectively. The prism with an α of 38° (θ = 70.7° at 633 nm) was used in this experiment. The dotted lines shown in Figs. 9 and 10 represent values obtained from the simulation. As shown in Fig. 9(a), the sensing plates with tSi of 25 nm always showed large ⊿λ, whereas Max ⊿R decreased monotonically as λdip increased as shown in Fig. 9(c). The values of ⊿λ and Max ⊿R obtained using the sensing plates with tSi of 85, 160, and 220 nm oscillated with λdip, indicating that selection of an appropriate tSiO2 is essential for these sensing plates. These results are consistent with the results shown in Fig. 6 predicted by the simulation.
Fig. 8 Reflection spectrum obtained in the experiment measured by filling the liquid cell with the PBS buffer (black line) and reflection spectrum obtained after the adsorption of streptavidin on the biotin immobilized on the sensing plate (red line). A sensing plate with tSi of 160 nm and a prism with α of 32° were used in this experiment. The blue dotted line is a fitting curve of the black spectrum obtained using the transfer matrix method.
Table 2. Values of tSi and tSiO2 of the sensing plates estimated by the spectral fitting as shown in Fig. 8. These 16 plates were used for the detection of streptavidin.
Fig. 9 Relationship between λdip and ⊿λ observed using sensing plates with tSi of 25 nm (a) and 160 nm (b), and relationship between λdip and Max ⊿R observed using sensing plates with tSi of 25 nm (c) and 160 nm (d). The α of the prism used was 32°. The dotted lines represent values obtained from the simulation.
Fig. 10 Relationship between λdip and ⊿λ observed using sensing plates with tSi of 85 nm (a) and 220 nm (b), and relationship between λdip and Max ⊿R observed using sensing plates with tSi of 85 nm (c) and 220 nm (d). The α of the prism used was 38°. The dotted lines represent values obtained from the simulation.
5. Discussion
It should be noted that there are some differences between the experimental conditions and the conditions used for the theoretical calculations. In the theoretical calculations, for instance, the refractive index of the protein was treated as constant at 1.45 and did not have any wavelength dependence. Indeed, the refractive index of streptavidin has been reported to be 1.45 [27]. In reality, however, there is a high possibility that the refractive index is wavelength-dependent, and it is necessary to understand the wavelength dependence of the refractive index of streptavidin in order to reproduce more accurate experimental results. To obtain calculation results that are closer to experimental values with regard to the refractive index of the Si and SiO2 layers, it is desirable to use the measured values for the Si and SiO2 layers that are actually used on the sensing plates. Furthermore, while the layer of the adsorbed protein is assumed to have a uniform thickness (5 nm) during the calculations, it is highly likely that this is different from the thickness under actual conditions.
In addition, there is an aspect of parallel-incidence-type waveguide-mode sensors that does not agree with the calculation conditions. This pertains to the fact that θ is incidence-wavelength-dependent, owing to the wavelength dependence of the refractive index of the silica-glass prism. When the bottom angle of the prism α is 38°, for instance, the incidence angle θ of light with a wavelength of 500 nm would be 73.92°, whereas that of light with a wavelength of 700 nm would be 74.07°. In light of such factors, the calculation results can be considered to agree quite well with the experimental results.
As previously mentioned, some factors can potentially cause variance between the simulation and the actual sensing system, but as long as the complex refractive index and thickness of the substance subject to detection can be obtained at a prescribed level of certainty, the sensing characteristics of the waveguide-mode sensor can be estimated with good accuracy using the transfer matrix method. This means that the calculation method described in the chapter on the simulation can be extremely useful in building a highly sensitive waveguide-mode sensor.
The decision regarding which of ⊿λ and ⊿R should be used for the detections should be made according to the performance of the detector used. If a spectrophotometer with a high wavelength resolution is used, it is better to use ⊿λ for the detections, whereas if a detector that is capable of accurately measuring the light intensity is used, it is better to use ⊿R of a specific wavelength for the detections. In general, a compact spectrophotometer with an uncooled CCD array or an uncooled CMOS sensor, such as a spectrophotometer used in the present research, has considerable noise in measuring light intensity. In addition, light intensity of a lamp or a LED is not perfectly stable. Accordingly, in such a case using these apparatuses, a better resolution can be achieved using ⊿λ than using ⊿R.
For protein detection, if ⊿λ was used to perform the detection, the sensitivity was better with a smaller θ; i.e., it was better to use a prism with a smaller α, as indicated by Figs. 5(b), 6(c), and 6(d). A large ⊿λ that approaches double the value when θ is 75° can be expected when θ is 68°, as indicated by Figs. 6(c) and 6(d). However, when α is too small, the θ becomes smaller than the critical angle for the surface reflection, and the sensor no longer functions effectively. If an analyte to be examined has a refractive index similar to water, α must be at least 30° to ensure that θ is greater than the critical angle.
A larger θ, i.e., a larger α, is better for detections using ⊿R. However, according to Figs. 6(e) and 6(f), there is only a ~10% difference between the largest Max ⊿R that can be expected for cases with θ of 68° and 75°. That is, the sensitivity is not affected greatly by θ when the detection is performed using ⊿R. There is no need to acquire the spectrum when measuring ⊿R, and only the change in the reflectance for a specific wavelength must be monitored. However, the incident light intensity must be stable under such conditions. A mechanism for monitoring the incident light intensity must be implemented when using a light source with a readily variable incident light intensity or when it is necessary to detect a minute ⊿R.
In optical systems of the parallel-incidence type, α has an influence on the size of the beam spot on the surface of the sensing plate. Although the lateral width of the beam is not affected by α, the following relationship is established between the vertical width w and α:
where w0 is the width of the incident light in the vertical direction, and β is the refraction angle on the incident surface of the prism. Figure 11 indicates the relationship between α andw at a wavelength of 600nm when w0 is set to 1 mm. It is evident that w is ~4 mm at the minimum and increases as α increases. When measuring a liquid specimen in minute amounts, such as a biological specimen, it is desirable to have smaller liquid cells. Thus, because it is necessary to keep the beam spot on the sensing plate as small as possible in this instance, it is more desirable to have a smaller α. According to the aforementioned considerations, a high- performance sensor can be built by keeping α as small as possible within the range wherein it satisfies the total reflection conditions on the surface of the sensing plate for the purpose of protein detections, as was the case with our example. Selecting the optimal prism angle with considerations for the detection conditions in actual sensing systems can lead to the deduction of the optimal tSi, tSiO2, and λdip, by performing the calculation indicated in Fig. 6.6. Conclusions
The relationship among the parameters tSi, tSiO2, λdip, and θ of the waveguide-mode sensors of the spectral-readout type and the ⊿λ and Max ⊿R obtained by the sensor associated with spectrum changes were deduced using the transfer matrix method for the Fresnel equations. The spectrum changes occur when substances targeted for detections are adsorbed. The calculation was performed by assuming the adsorption of protein, and the calculation results obtained were confirmed to agree quite well with the results of the experiment performed using a waveguide-mode sensor of the parallel-incidence type. A higher sensitivity can be expected with a smaller θ if ⊿λ is used for the detection index. If ⊿R is used for the detection index, it is better to have a larger θ, but in such a case, the influence of θ on the sensitivity is small. Because the θ of a waveguide-mode sensor of the parallel-incidence type is determined according to the bottom angle α of the trapezoidal prism, α should be decided in such a way that θ is optimal. Configuring a sensing plate using the optimal values for tSi and tSiO2, obtained from the calculation performed for such an optimal α, would enable the construction of a highly sensitive sensor. This design method can be applied to any case, as long as the complex refractive index of the object targeted for the detection is known.
Acknowledgments
The authors thank the Advanced Functional Materials Research Center of Shin-Etsu Chemical Co., Ltd., for supplying the sensing plate.
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