1. Introduction

The optical planar waveguide-mode sensor has been developed as an alternative to the well-known surface plasmon resonance (SPR) sensor by introducing an extra rather thick dielectric layer on the top of the metal layer to form a planar waveguide [2]– [5]. As the waveguide mode resonance is generally sharper in the angular spectrum than SPR, it was expected that the waveguide-mode sensor has a finer resolution or better sensitivity [6]. After rigorously survey on the effects of various reflecting layer materials used in the waveguide-mode sensors [7, 8], our group has proposed a silica-based monolithic waveguide-mode sensor, where a SiO₂ wave-guide layer was formed by thermally oxidizing the surface of a single crystalline Si (c-Si) layer of a silicon-on-quartz (SOQ) substrate [1]. Though the silica-based sensor is slightly less sensitive when compared with waveguide sensors using noble metals, the monolithic type sensor has excellent chemical and mechanical stability because the materials used are chemically stable and the SiO₂ waveguide layer and the c-Si layer are atomically bonded (structurally monolithic), thus eliminating the inherent problems of insufficient adhesion and/or being chemically unstable in noble metal sensors.

The previously reported waveguide-mode sensors use a monochromatic light as the source and sense the dielectric variation on the waveguide surface by measuring the angular spectrum of reflectivity and detecting the dip variations. To position the angle precisely, two goniometers are usually employed; one to rotate the incidence angle, and the other to synchronize the optical detector to the corresponding specular reflection angle (see, for example, [1]). Because goniometers of high precision are usually bulky, slow and expensive, this makes the whole sensor system somewhat cumbersome and less attractive to field applications. Therefore, in this paper, to develop a more portable version of waveguide-mode sensor which is compact, swift and cheap, we propose an alternate sensor scheme which resolves the light wavelength instead of the incidence angle, similar to what has been reported for SPR sensors [9]– [11]. Concretely, in this proposed scheme, a broadband light source emits a white light to the sensor plate, then at the detector location, a spectrometer sweeps over the wavelength range of interests and takes the snapshot of spectrum. By taking the differential of the spectra before and after adsorption of an analyte, we will detect the characteristic variation caused by the analyte. We call this sensor a spectral readout type waveguide-mode sensor. Thanks to modern optical techniques, both a white light source and a spectrometer could be fabricated very compact and moderately cheap, thus the sensor system can be very lightweight and suitable for outdoor uses.

In this paper, we will investigate numerically the sensitivity and corresponding operation modes of a spectral readout type waveguide-mode sensor. The sensor is based on the aforementioned silica-type monolithic structure [1] but applied in a spectral readout fashion. We will also optimize its structure and operation conditions by numerical simulations to gain the best sensitivity.

2. The operation modes and their sensitivities of the spectral readout waveguide-mode sensors

Figure 1a shows a schematic model of the waveguide-mode sensor using the Kretschmann configuration. On the top there is a semi-cylindrical glass prism for coupling the incident light into the sensor. A c-Si layer and a SiO₂ waveguide layer are underneath the prism. In a real silica-based monolithic sensor, these layers are formed on a SOQ substrate, and the substrate is index-matched to the prism bottom by index-matching oil filled in between [1]. Under the waveguide layer, there is usually an aqueous buffer solution to hold biomolecules or other chemicals. For simplicity, here we assume the buffer layer to be water. When some target molecules are adsorbed on the surface of the waveguide, an extra adlayer is assumed to be inserted between the waveguide layer and water. In the simulations, to emulate a monolayer of protein, the ad-layer thickness is assumed to be 5 nm and the refractive index is assumed to be n = 1.45. This waveguide structure is the same as that of a normal angle-scan type waveguide sensor, except that now the wavelength is a variable to be resolved while the incidence angle θ is fixed during the measurement. Another new issue is that all materials have a wavelength dependence in the refractive indices which need to be taken into account in the analysis. Figure 1b shows the complex refractive indices (n + i × k) of the main materials used in the sensor, c-Si, SiO₂ and water, over a wavelength range of 280 nm to 1000 nm [12]. It is seen that, while SiO₂ and water have rather gentle variations in n, the refractive index of c-Si varies remarkably, especially at the short wavelength range. As the k values of SiO₂ and water are very close to zero, they are not plotted in the figure. In contrast to SPR sensors where only p-polarized light can excite the SPR modes, in waveguide-mode sensors, both p- and s-polarized lights are able to excite the waveguide-mode resonances. Nevertheless, the s-polarization mode is generally more sensitive than p-polarization mode, as numerically summarized in the reference [8]. The physical reason is that the s-polarized light has all its electric field rendered in the form of in-plane component of planar waveguide, contributing to form a sharp and intense resonance mode. When a semiconductor material such as Si is used as the reflecting layer, the s-polarization can have a moderate sensitivity while p-polarization has hardly any sensitivity. Therefore, in this paper we will focus only on the s-polarization mode.

 

Fig. 1 Schematic of the waveguide-mode sensor (a) and the wavelength dependent refractive indices of the materials used (b). The thicknesses of thin film layers are exaggerated for easy viewing. When the incidence angle θ is large enough and at suitable resonance condition, the incident optical power is partially reflected, partially coupled to waveguide mode, and also partially absorbed by the lossy layer (c-Si layer). The reflectivity responds sensitively to the presence of the adlayer.

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To simulate the light scattering as well as the electric field distribution, the transfer matrix method for a stratified medium was used [13, Section 1.6, p.51]. Figure 2a shows an example of the simulated angular spectra of a monolithic waveguide-mode sensor with a 220 nm thick c-Si layer, where the thickness is optimal for the incident wavelength of λ = 632.8 nm as reported by reference [1]. In [1], it has been shown that the sensitivity exhibits periodic peaks with increasing c-Si layer thickness. Each peak corresponds to an individual mode in the Si layer, and the peak at 220 nm thickness is a rather good one among them. In the current calculation, the thickness of the SiO₂ waveguide layer, t_WG, was set to be 350 nm. As can be seen in Fig. 2a, a sharp electromagnetic (EM) resonance dip at the incidence angle of 67.70° is observed for the s-polarization reflectivity. In a normal waveguide-mode sensor, this angular dip is detected and tracked by rotating the goniometers, to sense the adsorption of the target adlayer. In our current spectral readout scheme, however, the reflectivity spectrum in wavelength domain is preferred. Figure 2b shows the corresponding wavelength resolved spectra for the same waveguide structure with a s-polarized broadband white source incident at the angle of θ = 67.70°. The red and blue lines represent the spectra with and without the 5 nm adlayer of n = 1.45, respectively. Multiple dips are observed at specific wavelengths. They correspond to the dips in angular spectra of a normal angle-scan type waveguide sensor, implying that EM resonances happen at these wavelengths and the incident light is coupled into the guiding modes confined in the composite waveguide formed by the c-Si and SiO₂ layers. By examining the red and blue spectra of Fig. 2b carefully, it is found that after the adsorption of the adlayer, not all the dips shift by the same distance from their original positions. To view it more clearly, the differential of reflectivity (ΔR) between the blue and red spectra is plotted in Fig. 2c. It also shows that the differential amplitudes at these dips vary remarkably between each other. For example, the dip around 630 nm exhibits the most drastic reflectivity variation, while its neighboring dip at 540 nm shows only a moderate variation despite that the 540 nm dip itself is much deeper (i.e., of stronger resonance). This implies that not all the resonance modes are equally sensitive to the adsorption of exotic material. To explore the mechanism behind it, we have simulated more reflectivity spectra for a series of SiO₂ waveguide thickness t_WG and summarized them into a contour map as shown in Fig. 3a. In the calculations, the c-Si layer thickness t_Si and the incidence angle θ were fixed to be 220 nm and 67.70°, respectively.

 

Fig. 2 (a) Simulated angular reflectivity spectra of a monolithic waveguide-mode sensor with a 220 nm thick c-Si layer and a 350 nm thick SiO₂ layer. The light wavelength λ is fixed at 632.8 nm. (b) The wavelength resolved spectra for the same waveguide sensor but with a white light source. Only s-polarization results are shown and the incidence angle θ is assumed to be 67.70°. The red and blue lines represent the spectra with and without the 5 nm thick adlayer of n = 1.45. (c) The values of ΔR by subtracting the blue spectrum from the red one in (b).

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Fig. 3 Contour maps corresponding to the spectrum before the adsorption of adlayer (a) and the differential curve (b) of Fig. 2, for a series of SiO₂ waveguide thicknesses. Other parameters are the same as those used in Fig. 2. The amplitudes of reflectivity R and ΔR are indicated by the corresponding color bars. The white dots (i), (ii) and (iii) are three structures to be further examined.

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Figure 3a shows the simulated reflectivity as functions of the wavelength of incident light and the thickness of the SiO₂ waveguide when the adlayer is absent. It is seen that the spectrum dips form some clear mode tracks in the contour map, which reflects the mode evolution with the change in waveguide thickness t_WG. For each SiO₂ waveguide thickness, there exist simultaneously multi modes centered at different wavelengths. Furthermore, the mode tracks exhibit some remarkable turning points at certain locations (for example, point (ii) in Fig. 3a), where the mode slope dλ/dt_WG can be large. Since the refractive index of the protein layer, 1.45, is close to that of the SiO₂ waveguide layer, n_SiO2 ≈ 1.46, the adsorption of a protein layer is approximately equivalent to an increase in waveguide layer thickness t_WG. As a consequence, these turning points of mode tracks are expected to have very high sensitivity because here a small change in t_WG brings a large wavelength shift dλ. To confirm this, the corresponding spectrum differential of Fig. 2b is also summarized in a contour map as shown in Fig. 3b. Indeed, there appear large differential peaks and dips at the turning points, which means high sensitivity at these locations.

To understand the physical mechanism of the origin of high sensitivity at the turning points, we need to look into the EM resonance characteristics of modes at this region. Figure 4 plots the electric field distributions for three typical points around the turning point of a mode track, which are marked as white dots (i), (ii) and (iii) in Fig. 3. They represent three waveguide structures with the same thickness for c-Si layer, t_Si = 220 nm, but with different thicknesses for the SiO₂ waveguide layer, t_WG = 412 nm, 284 nm and 156 nm. In the simulations, the s-polarized light beams were incident at the same angle of 67.70°, but of different wavelengths at which waveguide modes are induced, as indicated in Fig. 4. For structures (i) and (iii), Figs. 4a and 4c show that the electric field is almost equally confined in the c-Si layer and SiO₂ waveguide layer in these two structures. In Fig. 4b, however, the electric field is much stronger in SiO₂ waveguide layer than in c-Si layer (please notice the difference in the scale bars of electric field for these figures). For a more quantitative comparison, the three electric field distribution curves are plotted in a single graph as shown by Fig. 4d. The vertical green solid lines indicate the prism/c-Si/SiO₂ interfaces, while the vertical dotted lines indicate the respective waveguide surface positions of the three structures. It is seen that, though the three electric field amplitudes are comparable inside the c-Si layer, the field in the SiO₂ layer of structure (ii) has a much larger amplitude than those of the other two structures (more than three times in amplitude). Consequently, the evanescent field intensity at its waveguide surface (red dotted line) is also much stronger and can interact intensely with the exotic adlayer. This accounts for the higher sensitivity of structure (ii) observed in Fig. 3b, which is located at the center of the turning point. If we look further into the EM mode profiles inside the c-Si layers, we observe that the electric fields are nearly symmetric around the interface between c-Si and SiO₂ layers for structures (i) and (iii). For structure (ii), however, the electric field is asymmetric or exhibits a node at the c-Si/SiO₂ interface. The difference of waveguide mode profiles results in the big difference in EM field strength on the waveguide layer surface.

 

Fig. 4 Electric field distributions for the three points marked as (i), (ii) and (iii) in Fig. 3. They represent three waveguide structures with the same thickness for c-Si layer (t_Si = 220 nm), but different thicknesses for the SiO₂ waveguide layer. The strengths of the electric field are normalized by the incident electric field amplitude, indicated by the scale bars in (a)–(c) and numerically plotted in (d) for a comparison. The glass prism, the c-Si layer, the SiO₂ waveguide layer and the water layer are lined up along the positive z-direction with the interfaces indicated by green lines. In (d), the waveguide surfaces are marked by vertical dotted lines with the same color as that of the corresponding |E| curves.

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Now let us go back to Fig. 3a for a more detailed look. It is observed that the mode tracks appear the most clearly in the wavelength range of 420 – 700 nm. Correspondingly, the differential spectra are also the most distinct in this region (Fig. 3b). At the short wavelength range below 400 nm, though there appear more high order modes crammed here, their contrasts are very low and show almost no sensitivity. This is because in the short wavelength region, c-Si has a remarkable increase in its extinction coefficient k as shown in Fig. 1b. The large optical loss renders the resonance modes into very shallow dips. On the other hand, in the long wavelength region where λ > 700 nm, because the k value of c-Si approaches zero, the c-Si reflecting layer becomes almost completely transparent and it hinders the formation of leaky modes, leaving only the normal total internal reflection dominant there. In fact, these trends had also been observed in reference [8] for the semiconductor region, where a moderate k brings the best sensitivity.

3. Optimal design of spectral readout type waveguide-mode sensors

As described above, in order to design a spectral readout type monolithic waveguide-mode sensor which has the best sensitivity, we need to make the sensor work at the asymmetric-like modes around the turning points of mode tracks (Fig. 3). To realize this goal, besides the SiO₂ layer thickness and the optical wavelength, we have two more parameters to scan, the c-Si layer thickness and the incidence angle of light. In addition, in the simulations, to evaluate the performance of a spectral readout waveguide-mode sensor, its sensitivity can be defined either as the wavelength shift of spectrum dips (Δλ), or as the amplitude of differential spectrum (|ΔR|), as shown in Fig. 3b when an adlayer is adsorbed on the waveguide surface. Here, for simplicity of simulation, we use ΔR as the criterion and do a global search for maximum ΔR over all structure and operation parameters. It should be pointed out that the wavelength shift Δλ can be an as effective criterion. In a real sensor system design, due to the limitation in wavelength resolution or signal fluctuation, we may need to make some compromise in either criterion while pursuing the optimal waveguide structure.

Figure 5 shows the optimized results obtained by a computer-aided automatic searching. Our strategy is as follows, for each pair of c-Si layer thickness and SiO₂ layer thickness, the incidence angle and wavelength were first scanned in coarse steps so that the mode tracks could be recognized by the computer program. Then for each mode track, the value of ΔR was locally maximized at each turning point. By summarizing and comparing all the local bests, a globally best ΔR value was selected. By this way, the global optimal solution could be located very efficiently, while at the same time the mode “hopping” or local maximum trapping in computation could be avoided.

 

Fig. 5 Optimized sensitivity (a) and the corresponding optimal operation wavelength (c), incidence angle (d) for a spectral readout type monolithic waveguide-mode sensor. They are plotted as functions of the thicknesses of c-Si layer and SiO₂ layer. The optimal sensitivity for an angle-scan type monolithic waveguide-mode sensor working at 632.8 nm is given in (b) as a comparison. The small noisy area seen in (c) and (d) for t_Si ≈ 50 nm t_WG < 300 nm is due to numerical errors in the automatic maximum searching.

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Figure 5a shows an achievable maximum sensitivity map such obtained for a spectral readout type monolithic waveguide-mode sensor. As a comparison, the optimal sensitivity for a regular angle-scan type monolithic silica-based waveguide-mode sensor is also shown in Fig. 5b, where the operation wavelength was fixed at 632.8 nm and the incidence angle was scanned and optimized. From Fig. 5b, it is seen that there is hardly any sensitivity when the SiO₂ layer thickness t_WG is less than 200 nm because there is no sensitive asymmetric mode existing in this region. For t_WG > 200 nm, multi mode characteristic is observed along the c-Si thickness axis, i.e., the optimal mode will shift to a higher order mode as the thickness of c-Si layer increases. There exist dark (low sensitivity) regions between the periodic sensitivity peaks, where the turning points of mode tracks (as shown in Fig. 3) are moving out of the working wavelength of 632.8 nm. On the other hand, for the current spectral readout type waveguide-mode sensor as shown in Fig. 5a, although the multi mode characteristic is still visible along the c-Si thickness axis, it is much blurred and the sensitivity is generally better than that of Fig. 5b. The reason is that in the spectral readout type sensor, we have one more degree of freedom to optimize the sensor — the working wavelength. The sensitive asymmetric modes can always be tracked and captured somewhere in the wide wavelength range, thus alleviating the periodic dark regions of Fig. 5b. As a consequence, at almost any c-Si layer thickness the spectral readout type sensor could have a rather good sensitivity. This brings about a big relief to the thermal oxidization condition for fabricating the monolithic sensing plate because we have a looser requirement in Si thickness. In addition, for a thin c-Si layer (t_Si < 50 nm), the sensor can be operated even at a short wavelength around 400 nm, to take advantage of the large n of c-Si at this wavelength range (see Fig. 1b). The simulation results of reference [8] showed that the waveguide sensor has a rather sensitive region when the refractive index of the reflecting layer is around n > 5 and k ≈ 0.5. As a result, the sensitivity as high as 0.8 could be achieved for region of t_Si < 50 nm.

Figure 5c shows the corresponding optimal wavelength to achieve the best sensitivity of Fig. 5a. It exhibits a similar multi-mode profile as that shown in Fig. 5a. Within each operation mode, the lines of equal wavelength are observed to line up vertically. This means the optimal wavelength depends only on the thickness of c-Si layer, but not on that of SiO₂ layer unless a mode hopping happens. The physical meaning is that the optimal EM mode is mainly determined by the c-Si layer because of its larger refractive index, while SiO₂ layer plays more like a waveguide cladding here. In each mode, the wavelength increases with an increase in c-Si layer thickness to keep the EM mode profile not perturbed. Finally, Fig. 5d summarizes the optimal incidence angle corresponding to Figs. 5a and 5c. Generally, as the SiO₂ layer becomes thicker, the incidence angle will become larger in order to cancel the thickness increasing effect by reducing the wavevector along the thickness direction.

Using these contour maps shown in Fig. 5 as a design guide, we can choose appropriate thicknesses for the c-Si layer and SiO₂ layer, design a proper dove prism to incorporate the optimal incidence angle, and adopt suitable white light source to cover the target wavelength range, so as to construct a miniaturized highly sensitive sensor device. In fact, a palm-size highly sensitive sensor of this principle is being developed by our group.

4. Conclusion

To make the waveguide-mode sensor closer to practical applications, we have proposed the spectral readout type waveguide-mode sensor because it can be more compact, swifter and cheaper than normal angle-scan type waveguide-mode sensors. By numerically simulating the reflectivity spectra and electric field distributions of this type of sensor, we found that not all the waveguide modes have the same high sensitivity. Only the asymmetric-like mode has a very strong evanescent electric field tail across the waveguide surface, thus a good sensitivity to the exotic materials adsorbed on waveguide. This asymmetric-like mode exists at the turning point of a mode track when an symmetric-like mode is shifting to a higher order mode. Since the spectral readout type sensor could track the sensitive turning point of a mode track in a wide range of wavelength, it gains an extra degree of freedom to optimize the sensitivity when compared with previously reported angle-scan type waveguide-mode sensors. As a result, the optimal sensitivity of a spectral readout type sensor is generally better than that of an angle-scan type waveguide-mode sensor. This makes the spectral readout type sensor more attractive as a promising portable biosensor.