Current Issue

In the optical waveguide structure as shown in Fig. 3, the analytes filled in the slot were assumed to be H₂0 (n_s = 1.31), isopropanol (n_s = 1.377), ethylene glycol (n_s = 1.505), and sodium chloride (n_s = 1.5443), and then computational analysis was performed. First, the width and height of the rail were set to 200 nm and 320 nm, respectively, and the ratio of the fundamental mode distributed to the slot was examined through a confinement factor defined by Eq. (10) while increasing the width of the slot from 40 nm to 200 nm.

Fig. 3. 
Cross-sectional schematic of the vertical slot optical waveguide for computational analysis.

Fig. 4(a) shows the tendency of the overall confinement factor to increases as the slot width increases and then decrease after a certain maximum value. In the case of H₂O and isopropanol, the confinement factor at a slot width of approximate 60 nm shows a high value of about 0.58 or more, and then decreases rapidly. On the other hand, ethylene glycol and sodium-chloride show a flat maximum value for widths in the range of 100 to 120 nm and then gradually decrease. As can be seen in Fig. 4(a), the confinement factor decreases after the maximum values because the width of the slot widens, as a result, a small portion of the incident light wave begins to be transmitted through the rail acting as an SOI optical waveguide rather than a slot. Furthermore, as the width of the slot increases, the effective refractive index of the fundamental mode decreases, as shown in Fig. 4(b), because a large portion of light is confined within the slot, which has a low refractive index.

Fig. 4. 
Change in the (a) confinement factor and (b) effective refractive index of TE mode in the slot region with an increase in the slot width for various analytes (rail width = 200 nm; rail height = 320 nm).

To examine the effect of the rail width on the confinement factor, the slot width and height were set to 120 nm and 320 nm, respectively, the rail width was gradually increased within the range of 140 to 240 nm, and the confinement factor was calculated for the aforementioned analytes. As shown in Fig. 5, as the rail width increases, the confinement factor tends to increase until the rail width is 180-210 nm. Until the rail width reaches the appropriate width, it cannot sufficiently serve as the strip optical waveguide, and then, from the amount of light confined to the slot, the amount of light that escapes to the rail is small. Therefore, the confinement factor increases. On the other hand, when the rail width is increased beyond the optimal width and the rail itself begins to act as a strip optical waveguide, the confinement factor starts to decrease again because the light waves confined to the slot can be transmitted through the rail.

Fig. 5. 
Change in the confinement factor of the TE mode in slot region with an increase in the rail width for various analytes (slot width = 120 nm; rail height = 320 nm).

In order to examine the effect of the rail height on the light wave confinement factor, the rail and slot widths were set to 200 nm and 120 nm, respectively, the rail height was increased within the range of 240 nm to 360 nm, and the amount of light waves confined to the slot was examined as the confinement factor. Fig. 6 shows that, as the height of the rail increases, the confinement factor increases. This indicates that, the higher the rail height, the more difficult it is for the light waves confined to the slot to escape to the upper cladding region; as a result, the confinement coefficient increases. However, in the manufacturing process of the slotted optical waveguide, it is desirable to determine an appropriate height, given the difficulty of the etching process, its processing time, and its cost. After consulting various references [16-19], a height of approximately 320 nm was estimated as an appropriate height.

Fig. 6. 
Change in the confinement factor of the TE mode in the slot region as the rail width is increased for various analytes (slot width = 120 nm; rail width = 200 nm).

Therefore, based on the results of the previous computational analysis, the rail width, rail height, and slot width of the optimized slot optical waveguide in the 1.5 μm wavelength range were set at 200 nm, 320 nm and 120 nm, respectively. Fig. 7 shows the two-dimensional field distribution and the field components corresponding to each direction of the x and y axis for the TE mode E_y(x). As expected, the intensity of the mode field was strongly distributed in the slot, and the confinement factor was calculated to be over about 0.56. In SOI and Si₃N₄ ridge or rib optical waveguide structures, weak evanescent waves appearing in the upper cladding contribute to sensing; however, in slot optical waveguides, more than 50 % of the fundamental mode field propagates through the slot, and excellent sensing performance can be expected.

Fig. 7. 
Calculated two-and one-dimensional mode distributions for the E_y(x, y), E_y(x, 0) and E_y(0, y) of the TE fundamental mode in the slot waveguide.

Computational analysis of the normalization transmission power of the slot optical waveguide with a 5000 μm channel length was then performed, focusing on the previous-derived optimized specifications. First, the rail width and height were set to 200 nm and 320 nm, respectively, and the result, as shown in Fig. 8, was obtained through transmission power analysis while varying the slot width in the range of 20–180 nm. As the slot width increased, the transmission power increased until it reached the maximum power and then decreased. As the refractive index of the analyte increased, the slot width corresponding to the maximum power tended to increase. Overall, the graph shows a trend very similar to that shown in Fig. 5, which was obtained based on the confinement factor.

Fig. 8. 
Change in the normalized transmission power of the TE mode in the slot region with an increase in the slot width for various analytes (rail width = 200 nm; rail height = 320 nm).

In succession, the change in transmission power was analyzed computationally, as shown in Fig. 9, while increasing the rail width for slot widths of 60 nm and 120 nm. The maximum transmission power was obtained at a rail width of approximate 185 nm for both slot widths, which was shorter by approximately 20 nm than the optimized value derived based on the confinement factor, as shown in Fig. 5, but showed a very similar trend overall.

Fig. 9. 
Change in the normalized transmission power of the TE mode in the slot region with an increase in the rail width for various analytes and slot widths (a) 60 nm and (b) 120 nm (rail height = 320 nm).

Finally, we set the slot widths to 60 nm and 120 nm and the rail widths to 200 nm, and analyzed the transmission power while increasing the rail height to obtain the results shown in Fig. 10. Regardless of the value of the refractive index of the analytes, the transmission power tended to increase as the rail height increased, and it was confirmed that the increase slowed as the rail width increased. It also showed a very similar trend to that shown in Fig. 6.

Fig. 10. 
Change in the normalized transmission power of the TE mode in the slot region with an increase in the rail height for various analytes and slot widths (a) 60 nm and (b) 120 nm (rail width = 200 nm).

Various figures of merit, such as sensitivity, limit of detection, selectivity, reproducibility, stability, and resolution, are widely used to evaluate sensor performance. Among these indicators, the sensitivity of a sensor is one of its most important characteristics. In particular, the sensitivity of an optical waveguide-based sensor consists of the optical waveguide sensitivity (S_w) and the architecture sensitivity (S_a). The former reflects the effect of the change in the analyte refractive index or binding thickness on the variation in the effective refractive index of the mode. The effective refractive index of a waveguide mode is not a directly measurable quantity; therefore, it must be determined from a quantity that can be readily detected. To estimate the effective refractive index, a device with photonic sensing architecture is employed. Such devices can be broadly categorized into two different types: interferometric devices such as Mach-Zehnder interferometers, Young interferometers, and multimode interferometers, and resonant devices such as ring resonators and Fabry-Perot resonators. In devices with interferometric architectures, the variations of effective refractive index are related to optical phase shifts, Δϕ whereas in those with resonant architectures they are related to a resonant wavelength changes, Δλ.

In evanescent field sensors, the waveguide sensitivity is determined by the strength of the interactions between matter and the fraction of light in solution or at the surface. According to the status of the target molecules, two specific types of sensitivities, as mentioned in the introduction (refer to Fig. 1), are defined in biochemical sensing applications: (i) homogeneous (or bulk) sensitivity (S_wh), which considers the refractive index changes in the waveguide’s entire cladding; and (ii) surface sensitivity (S_ws), which assesses refractive index changes within the first few tens to hundreds of nanometers above the surface. Homogeneous sensitivity is defined as the slope of the phase (or wavelength) shift versus the change in the refractive index. Therefore, the overall photonic device sensitivity S for the interferometric configuration can be defined as

where λ₀ is the incident light wavelength, L is the interaction length, and n_a is the refractive index of the analyte (i.e., cover material) [34,35]. The sensitivity of the resonant configuration can also be defined as

where λ_r is the resonant wavelength, n_g is the waveguide group index, and t_a is the analyte thickness. Therefore, in this study, we focused on the effects of slot optical waveguide specifications on the waveguide sensitivity of homogeneous sensing and surface sensing. The sensitivity mentioned hereafter refers to the sensitivity of the waveguide.

In the optimized slot optical waveguide, the extent to which the effective refractive index (n_eff) of the fundamental mode was affected by the change in the analyte refractive index (n_a) was examined through computational analysis, and the sensitivity was evaluated.

First, the rail width and height of the slot optical waveguide were set to 200 nm and 320 nm, respectively, and the change in the effective refractive index of the fundamental mode was analyzed within the range of 1.3 to 1.55 of the index of the analyte for slot widths of 80 nm, 120 nm, and 160 nm. As shown in Fig. 11(a), as the refractive index of the analyte increases, the effective refractive index of the fundamental mode formed in the slot generally increases linearly. The sensitivity was evaluated using Eq. (11) based on the rate of change in the effective refractive index. As shown in Fig. 11(b), in the case of a slot width of 120 nm, the deviation of the sensitivity was evaluated at a level of about 0.015 [au/RIU]. Although the 80 nm and 160 nm slot widths show higher sensitivities in a specific refractive index section, the small deviation in sensitivity in the overall sensing range is more important for the evaluation of sensor performance. Therefore, when the numerical value and deviation of the sensitivity are considered at the same time, the optimized slot width is considered to be 120 nm. Furthermore, it confirmed that a high confinement factor can be achieved with the slot width selected in the optimization process.

Fig. 11. 
Changes in the (a) effective refractive index of the TE mode and (b) waveguide sensitivity with an increase in the analyte refractive index for various slot widths (rail width = 200 nm; rail height = 320 nm).

Next, the slot width and rail height were set to 120 nm and 320 nm, respectively, and the refractive index of the analyte was increased from 1.3 to 1.55 for rail widths of 150 nm, 200 nm, and 250 nm; then, the change in the effective refractive index was analyzed. As shown in Fig. 12(a), as the refractive index of the analytes increases, the effective refractive index of the fundamental mode generally increases linearly. In this case, the sensitivity was also evaluated, and as shown in Fig. 12(b), the deviation in the sensitivity was evaluated as less than approximately 0.01 [au/RIU] for a rail width of 200 nm. Therefore, even in this case, it can be confirmed that the rail width of 200 nm selected in the optimization process results in a high confinement factor.

Fig. 12. 
Changes in the (a) effective refractive index of the TE mode and (b) waveguide sensitivity with an increase in the analyte refractive index for various rail widths (slot width = 120 nm; rail height = 320 nm).

The change in the effective refractive index of the fundamental mode was analyzed when the slot and rail widths of the optimized slot optical waveguide were set to 120 nm and 200 nm, respectively, and the refractive index of the analyte was varied within the range of 1.3-1.55 for rail heights of 240 nm, 320 nm, and 370 nm. As shown in Fig. 13(a), as the refractive index of the analytes increases, the effective refractive index of the fundamental mode generally increases linearly. The sensitivity was also evaluated, as shown in Fig. 13(b), and the deviation in the sensitivity was evaluated as 0.03 [au/RIU] for a 320 nm rail width.

Fig. 13. 
Changes in the (a) effective refractive index of the TE mode and (b) sensitivity with an increase in the analyte refractive index for various rail heights (slot width = 120 nm; rail width = 200 nm).

The confinement factor was comprehensively evaluated based on the ratio of a fundamental mode distributed in the slot. Furthermore, the effective refractive index of the fundamental mode based on the refractive index of the analyte in the slot and the sensitivity were evaluated. The same results were achieved by using both approaches: when the slot width, rail width, and height were set to 120 nm, 200 nm, and 320 nm, respectively, the confinement factor was evaluated as –56% and the waveguide sensitivity was –0.9 [au/RIU] or higher. If the optimized slot optical waveguide is used as an integrated-optic biochemical sensor, excellent performance can be expected.

Surface sensing is based on the immobilization of a very thin layer of receptors on the bottom of the slot and the top surfaces of rail. The interaction between the analyte and receptor produces a change in the specific molecular (n_a) adlayer thickness (t_a), affecting the effective refractive index of the propagating optical mode, as shown in Fig. 14. By functionalizing the waveguide surface with specific receptors, sensing can be used for specific detection of certain analytes, such as antibody-antigens including biotin-streptavidin and prostate specific antigen (PSA)-bovine serum albumin (BSA), and pollutants in water. In this section, we focus on how the specifications of the slot waveguide affect the surfacing sensing using the quasi-TM mode, in which the dominant transverse magnetic field component is parallel to the surface of the slot and rail.

Fig. 14. 
Cross-sectional schematic of the vertical slot optical waveguide for computational analysis of surface sensing.

First, a computational analysis was performed on the modal effective refractive index for a 1-40 nm change in the thickness of the sodium chloride layer and the sensitivity based on Eq. (11) was calculated as shown in Fig. 15. As the thickness of sodium chloride layer increases, the effective refractive index of the quasi-TM mode increases because the refractive index of sodium chloride is larger than that of the cover cladding material (water). On the other hand, the narrower the slot width in the computational analysis, the more difficult it is to drive a mode close to the TM. Therefore, it was confirmed that a slot width ≥ 150 nm is needed to obtain a quasi-TM mode ≥ 90%. As shown in Fig. 15(b), a sensitivity of approximately 6-9 × 10^-4 [RIU/nm] can be achieved for a 150 nm slot width and a 2-40 nm thickness range. Meanwhile, Fig. 16 shows the effective refractive index and sensitivity according to the thickness of isopropanol, ethylene glycol, and sodium chloride materials for a slot, rail width, and rail height of 150 nm, 200, nm and 320 nm, respectively. In Fig. 16(b), it can be observed that, the smaller the refractive index of the analyte, the smaller the deviation of the sensitivity according to the thickness.

Fig. 15. 
Change in the (a) effective refractive index of the TM mode and (b) sensitivity with an increase in sodium-chloride thickness for various slot widths (rail width = 200 nm; rail height = 320 nm).

Fig. 16. 
Change in the (a) effective refractive index of the TM mode and (b) sensitivity with an increase in the layer thickness of the analyte for various materials (slot width = 150 nm; rail width = 200 nm; rail height = 320 nm).

Fig. 17 show the change in the effective refractive index of the TM mode and sensitivity according to the thickness of the sodium-chloride layer for various rail widths and a slot width and rail height of 150 nm and 320 nm, respectively. By the way, Fig. 18 show the change in the effective refractive index of the TM mode and sensitivity according to the thickness of the sodium-chloride layer for various rail height and a slot width and rail width of 150 nm and 200 nm, respectively. It was confirmed that the change in sensitivity with changes in the rail width or height and analyte thickness was relatively small. The rail width and height of 200 nm and 320 nm, respectively, show the smallest deviations in the sensitivities, as shown in Fig. 17(b) and Fig. 18(b), as we expect. Therefore, even in this case, it can be confirmed that the rail width and height of 200 nm and 320 nm, respectively, selected in the optimization process results in a high confinement factor.

Fig. 17. 
Change in the (a) effective refractive index of the TM mode and (b) sensitivity with changes in the thickness of the sodium-chloride layer for various rail widths (slot width = 150 nm; rail height = 320 nm).

Fig. 18. 
Changes in the (a) effective refractive index of the TM mode and (b) sensitivity with changes in the thickness of the sodium-chloride layer for various rail heights (slot width = 150 nm; rail width = 200 nm).