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Abstract
A waveguide-mode sensor with a planar sensing chip, consisting of two waveguiding layers and a glass substrate, is a promising candidate for a near-field illumination biosensor. Aiming at using fluorescent labeling induced by ultraviolet light, we optimize the structure of a waveguide-mode sensing chip, based on the mechanism for enhancing ultraviolet near-field light revealed by numerical calculations. Candidates of optimal materials are also presented. The chip optimized as above should be able to enhance the intensity of ultraviolet near-field light 25 times as high as an Al surface plasmon resonance sensing chip.
© 2017 Optical Society of America
1. Introduction
Near-field light is generated when light is totally internally reflected at the interface between two substances such as a glass substrate and liquid. As the penetration depth or the illumination space of the near-field light is limited, total internal reflection fluorescence (TIRF) microscopy utilizing near-field light is more suitable for observing a substance put on the surface of a substrate than other techniques such as epi-illumination microscopy and confocal microscopy [1]. Therefore, TIRF microscopy is used, for example, for a cell imaging [1,2] and for detecting fluorescent-labeled protein [3] in an aqueous buffer solution. Here, the electric field strength of the near-field light can be enhanced by surface plasmon resonance (SPR) [4–7]. Therefore, surface plasmon enhanced TIRF microscopy can excite fluorescent molecules more effectively than conventional TIRF microscopy [8–10].
Many fluorescent labels adequate for the above fluorescence have been developed in recent years. Their excitation wavelengths range from UV to near-infrared. Especially, fluorescent labels using quantum dots have attracted much attention, since they can emit bright fluorescence with a large Stokes shift and have a high resistance against breaching [11].
Aiming at developing methods to excite fluorescent labels more efficiently, much research has been carried out. However, most research focuses on SPR in a visible region using a metal thin film such as Au and Ag [12,13]. Compared to the visible region, research has scarcely been done for the UV region. Although attempts to enhance SPR using Al thin layers have been reported [14,15], their enhancement ratios of electric field are lower than those for the visible region. Moreover, Al is oxidized easily in air, which makes the electric field enhancement by SPR smaller, although Al oxide has an advantage of preventing fluorescence quenching by the Al layer [15].
A waveguide structure is another candidate to induce evanescent field with enhanced electric field. Figure 1 shows a schematic configuration of a waveguide-mode (WM) sensor [16–21]. The sensing chip is composed of two waveguiding layers such as Si and SiO2 on a SiO2 substrate. When light with a proper wavelength illuminates the sensing chip at an appropriate incident angle, it can be propagated within the layers. The WM resonance can be excited by both p- and s-polarized lights, but the sensitivity of WM resonance is higher for s-polarized light than for p-polarized light [16]. Therefore, s-polarized light is assumed in the following chapters in this study.
From this viewpoint, we optimize the structure of a WM sensing chip to realize high-efficiency UV near-field illumination. We analyze the relationship between the refractive index and the optimal thickness for the layers theoretically. In addition, we calculate the normalized electric field strength at the interface between the sensing chip and the buffer using a transfer matrix method [22,23] and select optimal materials for the layers based on the calculation results.
2. Theory
The WM sensing chip has the configuration and optical arrangement shown in Fig. 1. Figure 2(a) shows a schematic of the cross section of the sensing chip and a buffer solution. On the Cartesian coordinate system shown on the right, the interface between the sensing chip and the buffer with analytes is set to z = 0. When light, which is a coherent plane wave, illuminates the sensing chip from the side of a substrate via a prism, the electric field intensity in the sensing chip is approximated one-dimensionally as a function of z [23]. When E(z) denotes the electric field of light at position z on the light incident surface, which is perpendicular to the interface between the chip and the buffer, the normalized electric field strength squared N(z) [23] is defined as
where E0 denotes the electric field of incident light before the light illuminates the prism. Fluorescent-labeled analytes show strong fluorescence if N(0) is large [8]. Therefore, the structure of the sensing chip must be optimized to maximize N(0).
Fig. 2 Schematic views of the cross-sectional structure of the WM sensing chip. The directions of the light reflection and transmission (a) and the change in value of N(z) in the chip when θ = θc (b) or θ > θc (c), θc: critical angle of total reflection (not to scale). n’s, n’1, n’2, and n’b denote the complex refractive indices of the substrate, the layer 1, the layer 2, and the buffer, respectively. Yellow areas in (b) and (c) are conceptual images of near-field light.
Light is reflected and transmitted in the sensing chip as shown in Fig. 2(a), depending on the values of complex refractive indices of the substrate, the layer 1, the layer 2, and the buffer. Here, complex refractive index n’ of a substance is expressed as n’ = n - ik, where the real part n is the refractive index in a narrow sense and k is the extinction coefficient that represents the absorption of light. When k of a substance is large, light is much absorbed in the layer and the intensity of reflected light is decreased. Thus, the values of k of the layers 1 and 2 are assumed to be zero in this chapter.
In Fig. 2(a), the equation,
is satisfied according to Snell’s law. Here, ns, n1, and n2 respectively represent the refractive indices of the substrate, the layer 1, and the layer 2, while θin, θ1, and θ2 respectively denote the incident angles to the layer 1, to the layer 2, and to the buffer. When materials of the prism and the substrate are assumed to be SiO2 as in our previous work [16–21], θin agrees with that to the substrate.Total internal reflection occurs when θ2 satisfies the relation
at the interface between the layer 2 and the buffer. Here, θc is the critical angle for total internal reflection and nb is the refractive index of the buffer. In this case, near-field light is generated and the position where light is totally reflected is slightly inside the buffer as shown in Fig. 2(a).The energy reflectivity R at the interface between the layer 2 and the buffer is expressed as [24]
where θb denotes the complex angle of refraction in the buffer. Here, Φ in Eq. (5) is the Goos-Hänchen shift of the near-field light.In Fig. 2(a), the distance δ from the surface of the chip to the position, at which light is totally reflected, is expressed as [24]
When θ2 is equal to the critical angle θc, Φ = 0 is satisfied from Eq. (5). Then, the distance δ becomes δ = λ/(4n2cosθ2) from Eq. (6). In this case, the maximum light intensity appears at the interface between the layer 2 and the buffer. That is, the maximum of N(z) is N(0) as shown in Fig. 2(b). On the other hand, when θ2 becomes larger than θc, Φ becomes larger and δ becomes smaller. That is to say, the position of the maximum of N(z) shifts toward the inside of the layer 2 and N(0) becomes smaller, as shown in Fig. 2(c). This means that θ2 should be as close to θc as possible but slightly larger because analytes in the buffer or temperature of the buffer may increase nb in an actual system.Next, the thicknesses of the layers are optimized. In order to increase N(0), the thicknesses of the layers must be set so that the phase of the light reflected at the interface between the substrate and the layer 1, that of the light reflected at the interface between the layer 1 and the layer 2, and that of the light reflected at the position of the distance δ from the surface of the chip are synchronized. Here, when light transmitted through a medium is reflected by a medium with a higher n, its phase is shifted by π whereas when light is reflected by a medium with a lower n, the phase shift does not occur. In case of the WM sensing chips [16–21], which satisfy ns < n1 and n1 > n2, the first reflection at the interface between the substrate and the layer 1 causes a phase-shift of π. On the contrary, the second reflection at the interface between the layer 1 and the layer 2 and the third reflection at the distance δ from the surface of the chip do not cause the phase shift.
For the thickness d1 of the layer 1, the optical path difference between the two lights reflected at the first interface and the second interface is 2d1cosθ1. Therefore, the most suitable d1 can be determined by the equation,
where m1 is zero or a positive integer.For the thickness d2 of the layer 2, when we assume a virtual thickness,
the suitable thickness is determined by the equation,where m2 is a positive integer. If we set m1 = 0 and m2 = 1, we obtainandWhen d1 and d2 satisfy the conditions calculated from Eqs. (10)a) and (10b) and θ2 is set to be slightly larger than θc, N(z) changes as shown in the solid red line in Fig. 3.Fig. 3 Change in value of N(z) in the WM sensing chip when the real part of n’1 is higher than those of n’s and n’2. Yellow area is a conceptual image of near-field light.
3. Optimization of the structure and materials for a WM sensing chip
The materials of the layers 1 and 2 of the WM sensing chip are optimized to enhance UV near-field light effectively. Born and Wolf calculated reflection and transmission coefficients in a multilayered medium using a numerical method called “transfer matrix method” for solving the Maxwell equations [22]. Using software based on a similar transfer matrix method, the electric field distribution in a multilayered medium with parallel boundaries of layers can be calculated [23]. Assuming that the incident light, which is a coherent plane wave, illuminates the multilayered medium, N(z) in Eq. (1) is calculated by multiplying 2 × 2 characteristic matrices of the multilayers. The phase of the reflected light can also be calculated by inputting the complex refractive index of each layer in the matrix [23].
In this chapter, N(z) of a WM sensing chip was calculated by the software under the following conditions. The incident light with a wavelength λ of 375 nm is assumed to be s-polarized and both the prism and the glass substrate are assumed to be made of SiO2 as mentioned in Chapter 1 and 2. As a buffer solution to be dropped on a chip, water (nw = 1.354, kw = 0.000 [25]) is assumed for simplicity. From Eqs. (2) and (3), θc is calculated to be 66.8° for a SiO2 substrate with ns = 1.473 and ks = 0.000 [25]. Based on this calculation, θin is set as 67.0°.
As a first step, the layer 2 is assumed to be SiO2 and the layer 1 is optimized as for its d1, n1, and k1. Namely, N(0) at the interface between the sensing chip and the water is calculated as a function of n1 and k1, where d1 is optimized to give the maximum value of N(0) for given values of n1 and k1.
Figure 4(a) shows the results of the maximum value of N(0), which is referred to as NM(0). Note that the ranges of abscissa and ordinate of Fig. 4(a) are chosen by taking account of complex refractive indices of possible applicable materials shown in the figure. The values of NM(0) are indicated by the colors shown on the right in a logarithmic scale. That is, warm colors represent high values of NM(0). As shown in Fig. 4(a), for realizing high values of NM(0), n1 should be as high as possible, while k1 should be as low as possible. The values of n1 and k1 at the wavelength of 375 nm of several candidates for the layer 1, ITO (i), diamond (ii), SiC (iii), TiO2 (iv), ZnO (v), and Si (vi) [25–28], are also shown in Fig. 4(a). Furthermore, in Fig. 4(b), the values of NM(0) calculated for the above candidates of layer 1 are shown, together with the corresponding thickness d1 [nm] in parentheses that yields each value of NM(0). In Fig. 4(b), it is clear that d1 agrees with the value calculated from Eq. (10)a). The thickness of the SiO2 layer 2 is 176 nm in all cases of (i) – (vi), which also agrees with the value calculated from Eq. (10)b). As for Si (vi), which is used as the layer 1 for the WM sensors [16–21], NM(0) is only 20.3 even though it is as thin as 14 nm. Therefore, Si is not suitable for near-field illumination in a UV region. TiO2 (iv) increases NM(0) to 138 which is 6.8 times as high as that of Si.
Fig. 4 (a) Calculation results of NM(0) as a function of n1 and k1. White squares stand for the values of ITO (i), diamond (ii), SiC (iii), TiO2 (iv), ZnO (v), and Si (vi). The layer 2 is assumed to be SiO2. (b) Values of NM(0) for the candidates (i) – (vi). Numerals in parentheses are the optimized thicknesses d1 [nm] that yield these values of NM(0).
Next, the material is optimized for the layer 2. In this case, we want to maximize NM(0), on the condition that the layer 1 is TiO2. The results are shown in Fig. 5. In Fig. 5(a), it is clearly indicated that n2 and k2 should be as low as possible. Although not shown here, NM(0) is not enhanced for n2 < 1.356 because the light is totally reflected between the layers 1 and 2 and it does not reach the interface between the layer 2 and the water. The values of n2 and k2 of several materials, namely, MgF2 (vii), CaF (viii), SiO2 (ix), PMMA (x), and BK7 (xi) are plotted in Fig. 5(a) [25,29,30]. In Fig. 5(b), the values of NM(0) in addition to the corresponding optimized values of d2 are shown. It is clear that d2 agrees with the value calculated from Eq. (10)b). The thickness of the TiO2 layer 1 is always 28 nm, which also agrees with the value calculated from Eq. (10)a). MgF2 (vii) can increases NM(0) most effectively in (vii) – (xi) to 387.
Fig. 5 (a) Calculation results of NM(0) as a function of n2 and k2 and for MgF2 (vii), CaF (viii), SiO2 (ix), PMMA (x), and BK7 (xi). The layer 1 is assumed to be TiO2. (b) Values of NM(0) and the corresponding optimized values of d2 [nm] in parentheses.
As shown in Figs. 4 and 5, the combination of materials, which can yield the highest NM(0), are TiO2 28 nm thick for the layer 1 and MgF2 315 nm thick for the layer 2. Therefore, the distribution of N(z) is calculated for the sensing chip composed of the 28-nm TiO2 layer 1 and the 315-nm MgF2 layer 2 as shown in Fig. 6. Here, the solid black vertical line drawn at z = 0 shows the interface between the layer 2 and the water. Furthermore, z < −343 (broken blue line), −343 < z < −315 (dotted orange line), −315 < z < 0, and z > 0 show the SiO2 prism and the SiO2 substrate, the TiO2 layer, the MgF2 layer, and the water, respectively. The distance δ from the surface of the chip to the position where light is totally reflected is calculated to be 239 nm from Eq. (6), which is shown by the broken black line.
Fig. 6 Normalized electric field strength squared N(z) in the WM sensing chip composed of the 28-nm TiO2 layer and the 315-nm MgF2 layer as a function of distance z from the interface between the MgF2 layer and the water. The interfaces between the substrate and the TiO2 layer, the TiO2 layer and the MgF2 layer, and the MgF2 layer and the water are indicated by the broken blue line, the dotted orange line, and the solid black line, respectively. The position where the light is totally reflected is shown by the broken black line.
To evaluate the allowable ranges of the thicknesses of the TiO2 and MgF2 layers, N(0) is shown in Fig. 7 as a function of thicknesses of the two layers. It is clear that N(0) can be enhanced similarly even if the thickness of each layer varies by a few nm.
4. Comparison of the electric field enhancement effect with an Al SPR sensing chip
An SPR sensing chip is commonly used to obtain enhanced UV near-field light. In this chapter, the electric field enhancement effect is compared between the above-mentioned optimized TiO2/MgF2 WM sensing chip and an SPR sensing chip. It is well known that UV light is enhanced significantly by an Al SPR [15]. Therefore, we calculate the value of N at the interface between the Al layer of the SPR sensing chip and water, Nsp(0), when p-polarized light at a wavelength λ of 375 nm illuminates the chip. Here, the prism and the substrate of the sensing chip are assumed to be SiO2. We use nAl = 0.347 and kAl = 4.535 as the values of the real and imaginary parts of the complex refractive index of Al, based on our measurement result obtained using a spectroscopic ellipsometer (VASE, J.A. Woollam). For calculations, thickness of Al, dAl, is set to be in a range from 5 to 50 nm. Since the incident angle to the Al layer, θsp, which can excite SPR, depends on dAl, θsp is optimized to maximize Nsp(0).
Figure 8 shows calculation result of NspM(0), which is the maximum value of Nsp(0) (solid red line, left axis), and θsp (broken blue line, right axis) as a function of dAl. It is indicated that we can obtain the highest NspM(0) of 15.5 at θsp of 73.5° when dAl is 20 nm. This value of NspM(0) is about 1/25 of the highest NM(0) of 387 obtained for the optimized TiO2/MgF2 WM sensing chip.
Fig. 8 Calculation results of NspM(0) (solid red) obtainable for the Al SPR sensing chip and the incident angle to the Al layer θsp (broken blue) as a function of dAl.
There have been several papers that attempted to enhance the electric field strength of UV light by SPR. In many cases, Al nanoparticles [31,32] or Al nanostructured films [33] were used, but they required sophisticated skills for fabrication. In addition, they would not suitable for near-field illumination since hot spots, where an enhanced electrical field is induced by the nanostructures, are limited.
The optimized WM sensing chip with appropriate thicknesses of TiO2 and MgF2 can enhance N(0) by 387 times theoretically. This enhancement factor is 25 times that of the SPR sensing chip, which is the most important advantage of our WM sensing chip. In the WM sensing chip, the light is transmitted through the layers 1 and 2 after it was reflected at the interfaces between the substrate and the layer 1 and between the layers 1 and 2, if the phase matching condition is fulfilled. If the reflection occurs more, the electric field is enhanced more due to the near-field effect. This is the main reason for the high electric-field enhancement of our chip. Furthermore, since the chip is composed solely of inert inorganic dielectrics, quenching of fluorescence would not occur.
We have already reported that a WM sensing chip with layers of Si and SiO2 can enhance near-field light in a visible region in a similar manner to what is expected by numerical calculations [16–21]. The present research reveals that the enhancement mechanism of our chip. Moreover, it reports numerically optimized structures and materials for our chip usable in an UV region. Experimental evidence supporting the calculations developed and the mechanism proposed in this paper will appear in the near future. Highly effective and stable UV near-field illumination would be realized, by applying the above-mentioned optimization to a sensing chip of a WM sensor.
5. Conclusions
The structure and materials of a WM sensing chip, which can effectively enhance the electric field strength in the UV region, was optimized for high-sensitivity detection of fluorescent-labeled materials. Based on calculation results using a transfer matrix method, we found that the WM sensing chip composed of a layer with a high refractive index and a low extinction coefficient and a layer with a low refractive index and a low extinction coefficient is the best. The thicknesses of the two waveguiding layers are set so that reflected lights have the same phase. The WM sensing chip composed of such optimized TiO2 and MgF2 layers can enhance the intensity of UV near-field light at a wavelength of 375 nm more efficiently than an Al SPR sensing chip. The optimized WM sensing chip would realize high-efficiency UV near-field illumination.
Funding
Japan Society for the Promotion of Science (JSPS) (16J10336).
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