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A tapered plasmonic channel waveguide can be used for index sensing by spatial mapping of the scattering field intensity. A numerical simulation shows that this waveguide reflects the plasmonic channel waveguide mode at various points as the refractive index of an analyte changes, and a strong outgoing scattering wave appears at the reflection point. One can measure the index change by detecting variations in the scattering point. In the case of a unit index change, the scattering point moved 2670 nm, which can be observed by an imaging system. Detection limit of the index change is estimated as 0.12. However, the limit can be further reduced by increasing the tapered length or decreasing the tapered angle of the structure.
© 2015 Optical Society of America
1. Introduction
Refractive index sensing using surface plasmon resonance (SPR) has been widely used for analyzing various materials in biochemical research [1,2]. Surface plasmon polaritons (SPPs) are the surface waves propagated by oscillating conduction electrons that excited from electromagnetic waves on a metal-dielectric interface. The resonance that appears in metal nanoparticles for the SPPs at particular wavelength satisfying resonant condition is called localized surface plasmon resonance (LSPR). As this resonance responds very sensitive to a change of refractive index of the material that fields are placed, the LSPR has received strong attention for applying to index sensors [3–10]. Recently, index sensing using various types of plasmonic nanostructures that use the LSPR such as a perfect absorber [3], a double split nanoring cavity [4], double nanopillars [5], nanoring arrays [6], a hybrid nanoparticle-microcavity [7], a hybrid coupler [8], a plasmonic nanocavity based on channel waveguides [9], and parallel disks [10], was reported [3–10]. The plasmonic sensors have many advantages for index sensing such as label-free real-time detection, a very small mode volume, and high sensitivity [1,2,11]. These advantages result from unique properties of the LSPR. The small mode volume is achieved by their subwavelength dispersion property that gives rise to good confinement of the fields, and good sensitivity is attributed to the strong field enhancement and high field overlap ratio of the analyte to the total mode volume.
Sensors based on the resonance use a spectral shift in a resonant spectrum to measure the index change; thus, reducing the linewidth of the spectral peaks becomes important [3–6,8,9,11]. However, resonance-based index sensors have an inevitable resolution limit. Any plasmonic resonator must have intrinsic energy losses, including a metallic absorption loss and a radiation loss, which result in linewidth broadening [10]. We cannot completely eliminate this metallic absorption loss, whereas the radiation loss can be minimized by rational design of the resonance mode [9]; therefore, the linewidth limits the measurable index change because of the small signal change of the broadened resonance.
Studies of plasmonic sensors that do not use resonance have also been reported. Mach–Zehnder interferometer (MZI) plasmonic sensors have been introduced that use the plasmonic waveguide mode of a metal–insulator–metal structure [12–14] or the long-range surface plasmon polariton mode of a metal stripe structure [15]. These SPP-based sensors, which use the propagating mode of the surface plasmons over the extended metal surface, measure the changing output power of the interferometers due to the optical path difference resulting from changes in the refractive index of the analyte. Therefore, they can avoid the linewidth broadening problem observed in plasmonic resonance. However, MZI plasmonic sensors have a larger scale than LSPR sensors; their size must reportedly be tens of micrometers to provide a large enough path difference [14].
We propose a plasmonic square groove tapered channel waveguide structure for use as a refractive index sensor in which the index change is detected by imaging the scattered light from the structure. The cutoff frequency of the square groove channel waveguide produces scattering waves at the cutoff point [9,16,17], which moves as the index of a material filling the groove changes. Thus, one can measure the index change by observing the variation in the scattering point. Because this index sensor is based on spatial mapping of the refractive index by means of scattering in the structure, the sensitivity, defined as the displacement of the scattering point for a unit refractive index change, is independent of the metallic absorption loss. Our index sensor structure has a submicrometer physical size of 0.3 × 0.5 × 3 μm3 = 0.45 μm3, which is suitable for application to lab-on-a-chip devices.
2. Cutoff frequency of a square groove plasmonic channel waveguide
Our refractive index sensor is based on a plasmonic channel waveguide that has a square groove with a depth d and a width w in silver. The groove is filled with a liquid solution with a refractive index n, as shown in Fig. 1(a). Figure 1(b) shows the electric field (Ez) mode profile of the waveguide mode with a wavelength of 651 nm in a waveguide with (w, d) = (200 nm, 500 nm). The electric field is strongly confined at the metal–dielectric interface, and most of it is located in the solution. Therefore, the propagation properties of the plasmonic mode are expected to change sensitively depending on the refractive index of the solution.
Fig. 1 (a) Schematic of a square groove plasmonic channel waveguide. Width and depth of the groove are represented by w and d, respectively. (b) Electric field (Ez) profile of the waveguide mode with a wavelength of 651 nm, where (w, d) = (200 nm, 500 nm).
We investigated the frequency dependence of the waveguide mode on the waveguide width and the refractive index of the solution by calculating dispersion curves, as shown in Figs. 2(a) and 2(b). At a fixed refractive index of 1.318, as the waveguide width increases, the dispersion curve moves to a lower frequency region, as shown in Fig. 2(a). On the other hand, when the waveguide width is fixed at 200 nm, the dispersion curve also has a lower frequency with increasing refractive index, as shown in Fig. 2(b). This is because an increase in the waveguide width or refractive index can be considered as an enlargement of the waveguide cross section.
Fig. 2 Dispersion curves of the plasmonic channel waveguide mode as functions of (a) the waveguide width w, and (b) the index of the solution n. Refractive index is fixed at 1.318 for the dispersion curves in (a). Red circles indicate the cutoff frequencies. (c) 2D color contour mapping of cutoff wavelengths vs. waveguide width and refractive index. Black line represents a cutoff wavelength of 650 .
In a plasmonic channel waveguide with a finite width, there exists a cutoff frequency, i.e., the lowest allowed frequency of the propagating waveguide modes [9,16,17]. When the waveguide mode has a frequency below the cutoff frequency, the mode cannot propagate and should be reflected or scattered. In Figs. 2(a) and 2(b), the cutoff frequencies are marked with red circles at a wave vector of 0, where the dispersion curve has the lowest frequency. According to the dispersion curve dependences, the cutoff frequency decreases with increasing width or index. For example, when the index is fixed at 1.318, the cutoff frequency of the waveguide is 2896 ´ 1012 rad/s for w = 200 nm and becomes 2087 ´ 1012 rad/s for w = 300 nm in Fig. 2(a). When the waveguide width is fixed at 200 nm, the cutoff frequencies for liquid indices of 1.318 and 1.518 are 2896 ´ 1012 rad/s and 2547 ´ 1012 rad/s, respectively.
In Fig. 2(c), a two-dimensional (2D) color contour map of the cutoff wavelength is plotted as a function of the waveguide width and refractive index. The waveguide width ranges from w = 70 nm to w = 270 nm in 50 nm steps, and the refractive index changes from n = 1.318 to n = 1.718 in steps of 0.1. Red (violet) indicates the maximum (minimum) cutoff wavelength of 1058 nm (389 nm). As expected from Figs. 2(a) and 2(b), the cutoff wavelength increases with increasing width or index. In this cutoff wavelength 2D map, the waveguide width and refractive index correspond to the cutoff wavelength of 650 nm, which is indicated by a black line. Here, we assume that 650 nm is the wavelength of the injected light for the index sensor, which will be shown in Section 3. The waveguide width that yields the same cutoff wavelength changes as the refractive index of the solution varies. For example, when the index is 1.318, the waveguide width for a cutoff wavelength of 650 nm is 199 nm, as shown by the black line. However, if the index becomes 1.718, the width must decrease to 145 nm to have the same cutoff wavelength.
If we design a waveguide having various widths, the plasmonic waveguide mode has different cutoff wavelengths at each point for the different widths. Consequently, the waveguide mode has a different reflecting position depending on the input wavelength, where the cutoff wavelength of the width at that point corresponds to the input wavelength. On the other hand, because the refractive index of the filling material is also the factor determining the cutoff wavelength, the reflecting position can also be changed by varying the refractive index. By fixing the input wavelength and changing the refractive index, the reflection point moves according to the index change.
All data obtained in this paper were calculated using the three-dimensional (3D) finite-difference time-domain (FDTD) method. Silver is modeled by a Drude-critical points model [18,19]. The model with two critical points is expressed as follows:
The parameters introduced in the equation are the background dielectric constant ε∞, plasma frequency in the Drude model ωD, collision frequency γ, amplitudes Ap, phases φp, critical point frequencies ΩP, and broadening parameters Γp. The first and second terms arise from the Drude model, and the later terms are added by introducing critical points in order to consider interband transitions of metals [18].The Drude parameters shown in Table 1 are fitted by experimentally measured dielectric functions [20]. Perfectly matched layers are used as boundary layers to represent free space, and a periodic boundary condition is applied to the calculated dispersion curves.
Table 1. Drude Parameters of Silver in Drude-Critical Points Dispersive Model for FDTD Simulation
3. Index sensing using a tapered channel waveguide
On the basis of the cutoff wavelength mechanism, we propose a tapered channel waveguide structure as a refractive index sensor, as shown in Fig. 3(a). The structure consists of an entrance waveguide with a width wa of 300 nm, a tapered waveguide with a length l of 2000 nm, and an exit waveguide with a width wb of 100 nm. In the tapered region, the waveguide width decreases linearly from wa to wb. For waveguides with these parameters, the propagation length is estimated to be about 10 μm, which is sufficient to maintain the power over the entire sensing region. When input light with a monochromatic wavelength (λ0) is injected as the plasmonic waveguide mode by grating coupling [21], slot coupling [22], or tapered-fiber coupling [23], the waveguide mode will propagate along the y axis direction, and the mode cannot propagate beyond a certain point in the tapered region if the waveguide width at that point has a cutoff wavelength of λ0, as shown in the upper image in Fig. 3(b). At that point, the waveguide mode will be reflected or scattered out into free space. As the refractive index increases from n to n′, the cutoff wavelength of the channel waveguide becomes longer, as we discussed in section 2. Therefore, the reflection point of input light with the same wavelength also moves to a narrower part of the tapered region. The refractive index change can be sensed by observing the change in the propagation length in the tapered region from y to y′.
Fig. 3 (a) Plasmonic tapered channel waveguide structure. Waveguide width decreases linearly in the tapered region from wa to wb over length l. (b) Schematics of refractive index sensing using the proposed tapered waveguide. For different refractive indices, the reflection point, at which a waveguide of that width has a cutoff wavelength that is the same as the input light wavelength, changes from y to y′.
Figures 4(a) and 4(b) show the reflection and scattering of the plasmonic waveguide mode at the tapered region for solutions with different refractive indices. The electric field intensity maximum, indicated by red spots, propagates along the bottom of the channel waveguide, representing the observed mode as a surface plasmon mode. Note, on the other hand, that the plasmonic waveguide mode cannot propagate further than certain positions in the tapered region because of the cutoff wavelength mechanism. The reflection point, which is obtained from the center of the last intensity maximum, moves to a narrower part of the tapered region as the index increases. The propagation length in the tapered region increases from 855 nm (y) to 1200 nm (y′) as the index changes from 1.318 to 1.518. Thus, the reflection point moves 345 nm for an index change of 0.2.
Fig. 4 Electric field intensity profiles (log scale) in the y–z plane for an index of (a) 1.318 and (b) 1.518 in a tapered structure with wa = 300 nm, wb = 100 nm, l = 2000 nm, and d = 500 nm. Left inset indicates top and bottom of the waveguide. A white line placed 500 nm above the top of the waveguide represents the plane where outgoing Poynting vector images are obtained.
However, in practical applications, it is difficult to directly measure the reflection point at the bottom of the submicrometer-sized channel waveguide. On the other hand, in Figs. 4(a) and 4(b), the scattered light leaving the waveguide also moves to a narrower part in the tapered region as the index of the analyte increases. Because the scattered light can be easily observed, we examined images of the scattered light, which were obtained from the outgoing Poynting vectors (Sz) at the top of the waveguide, as a function of the refractive index. In Fig. 5(a), one bright spot at the uppermost end of each scattering image is observed for all of the investigated refractive indices, which are also identified from the strongest scattering near the reflection points in the y–z plane electric intensity profiles of Figs. 4(a) and 4(b). As the refractive index increases in steps of 0.05, the scattering spot clearly moves to a narrower part of the tapered region, as indicated by blue lines in Fig. 5(a). The scattering energy is estimated as 14% of the incident light energy, which can be further enhanced by reducing the depth of the groove or making the angled sidewall. The lights of the scattering spots can be collected by a microscope objective lens and be taken by a CCD camera. The vertical components of the Poynting vector image just above the sensor surface can be observable in the conventional microscope system, as reported in the lasing images of nanolasers [24, 25].
Fig. 5 (a) Time-averaged outgoing Poynting vector (Sz) images in x–y plane, which are obtained at 500 nm above the top of the waveguide for refractive indices ranging from 1.318 to 1.518. (b) Scattering positions (red) and reflection points (black) are plotted as functions of the refractive index. The positions indicate the distance from the beginning of the tapered region. Scattering points and reflection points are obtained from 500 nm above the waveguide and bottom of the waveguide, respectively. The position indicated by orange, where the width of the tapered region is the waveguide width for a cutoff wavelength of 650 nm, is calculated from 2D contour mapping of the cutoff wavelength in Fig. 2(c).
We investigated the movement of the scattering bright spot as the refractive index increases in Fig. 5(b). The scattering position (red) increases linearly in proportion to the refractive index. The reflection point (black) measured at the bottom of the waveguide also increases linearly. On the other hand, the position (orange) at which the width corresponds to the waveguide width for a cutoff wavelength of 650 nm also increases linearly. The three curves have the same dependence on the refractive index except for small discrepancies in the absolute values. This means that the movements of the reflection point and scattering position in the proposed tapered channel waveguide index sensor with respect to the index change originated from the dependence of the cutoff wavelength on the refractive index and waveguide width. Because scattering does not occur along the orthogonal direction to the waveguide, and the position that the waveguide mode can reach is longer than the reflection points measured by the intensity maximum, the small discrepancies are observed.
4. Definition and dependence of the sensitivity
Because the proposed sensing mechanism differs from that of other refractive index sensors, which use the resonant wavelength shift due to the index change [3], we can define a new sensitivity (S) as the ratio of the displacement of the scattering spot (Δy) to a change in the refractive index (Δn), as follows:
Here, the scattering position is obtained from the center of the bright spot. If the index changes from 1.318 to 1.518, the scattering point at h = 500 nm moves from 730 nm to 1120 nm. The sensitivity is estimated to be 1950 nm/RIU, where RIU is a refractive index unit.To understand the dependence of the sensitivity on the structural parameters of the tapered structure, we investigated the sensitivities for various tapered structures. Figures 6(a)–6(c) show the changes in the sensitivity versus the tapered length (l), difference between the entrance (wa = 300 nm) and exit widths (wb), and scaled size of the entire structure. First, when the other structure parameters are fixed (wa = 300 nm, wb = 100 nm) and only the tapered length (l) increases, the sensitivity increases linearly in proportion to the tapered length because the change in the cutoff position becomes larger in a longer taper, as shown in Fig. 6(a). The sensitivity of the scattering point increases from 1150 nm/RIU (l = 1000 nm) to 2670 nm/RIU (l = 3000 nm). On the other hand, if the width difference of the tapered region changes for a fixed tapered length (l = 2000 nm), the sensitivity is inversely proportional to the width difference, as shown in Fig. 6(b). Because the width difference increases and the tapered region has a larger angle, a smaller change in the position in the tapered region results in the same change in the waveguide width, corresponding to the given index change. To check that, we increased the entrance width of wa = 300 nm to 500 nm, fixing wb at 100 nm and l at 2000 nm. The sensitivity decreases from 1950 nm/RIU to 1180 nm/RIU. Finally, we investigated the scaling effect of the size of the entire structure while maintaining the tapered angle [ = (wa - wb)/2l], as shown in Fig. 6(c). In detail, we simultaneously changed the entrance width of wa = 300 nm to 500 nm and the tapered length of l = 1000 nm to 2000 nm, with a fixed wb = 100 nm. The sensitivity in Fig. 6(c) was almost constant near 1150 nm/RIU regardless of the size of the entire structure. These results show that the sensitivity depends only on the angle of the tapered region. Figures 6(a)–6(c) suggest design rules for a sensitive index sensor. To obtain higher sensitivity, a longer tapered length and smaller difference between the two widths are desirable. When the scattering spot is observed by the microscope imaging system, the minimum observable movement corresponds to the diffraction limit of the imaging system. If the numerical aperture of the system is 1.0, the diffraction limit is 325 nm, which suggests the minimum detectable index change as 0.12. Because the spot moved 2670 nm for a unit index change. The detection limit of 0.12 can be further reduced by increasing the taper length without the limit since the scattering spot shape is almost kept for the different taper length.
Fig. 6 Sensitivity dependence of the scattering point on (a) tapered length (l) with fixed waveguide width (wa = 300 nm, wb = 100 nm), (b) waveguide width difference ( = wa - wb) with fixed tapered length (l = 2000 nm) and exit width (wb = 100 nm), and (c) tapered length (l) with fixed tapered angle [ = (wa - wb)/2l]. Inset schematics show how structural parameters are changed.
5. Conclusion
In this paper, we proposed a plasmonic square groove tapered channel waveguide structure for application as a refractive index sensor. The operation of this index sensor is based on the cutoff frequency mechanism, which produces an outgoing scattering wave at the point in the tapered region where the cutoff wavelength is the same as the injection wavelength. Because this scattering point moves as the refractive index of the material filling the groove changes, one can measure the index change by detecting the variation in the scattering wave. Indeed, spatial mapping of the refractive index by observing the scattering point becomes possible in the proposed plasmonic waveguide structure. This index sensing scheme is totally different from that of previously studied plasmonic sensors, which use the resonant wavelength shift, and is not limited by resonance broadening due to metallic absorption loss.
By investigating the dispersion relations of a simple channel waveguide, we found that the cutoff frequency was inversely proportional to the refractive index of the filling material and the waveguide width. On the basis of this, we designed the tapered channel waveguide with input/output waveguide widths of 300 nm and 100 nm, respectively, and a tapered region length of 2000 nm. In the proposed structure, the newly defined sensitivity, a ratio of the displacement (Δy) of the scattering spot to the index change (Δn), is obtained as 1950 nm/RIU. The sensitivity is linearly proportional to the tapered length, and the maximum sensitivity was 2670 nm/RIU for a length of 3000 nm. In contrast, as the difference between the input/output waveguide widths increases, the sensitivity decreases somewhat. Therefore, a longer tapered region and smaller difference between the input/output waveguides are desirable for a high-sensitivity index sensor. In addition, the proposed dependence of the cutoff wavelength on the waveguide width and refractive index can be applied to design submicrometer-sized plasmonic devices that can control light depending on the wavelength.
Acknowledgments
This work was supported in part by the National Research Foundation of Korea through the Korean Government under Grant NRF 2013R1A2A2A01014491, and in part by the National Research Foundation of Korea through the Korean Government under Grant NRF 2013M3C1A3065051.
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