1. Introduction

Localized surface plasmon resonant (LSPR) nanostructures can sense minute changes in their surrounding medium [1]; individual nanoantenna can detect up to a single molecule [2]. The free-space interrogation of a single nanoantenna, however, suffers from weak coupling efficiency (typically 0.1% [3]) due to the wide difference between the beam spot size and the aperture size of a nanoantenna. A dark-field setup can improve the signal to noise ratio (SNR) at the cost of a bulky setup with stringent alignment requirements [2,3]. Therefore, typically, arrays of resonant nanostructures are patterned on substrates and interrogated with free-space beams. However, fabrication related variation in array element dimensions leads to linewidth broadening of the LSPR resonance which degrades performance in refractometry as well as SERS sensing.

Biophotonic integrated photonic sensors [4] hold the possibility of multiplexed sensing in compact field-deployable multifunctional [5–8] packaging that readily provide sample-to-answer capabilities. Interrogation of individual plasmonic nanoantenna in integrated photonic configurations addresses several of the challenges noted previously by providing a compact and alignment-insensitive platform. Coupling of light to LSPR nanoresonators is also significantly improved due to higher confinement of light in waveguides as compared to free space illumination. On the other hand, the extreme sensitivity of plasmonic nanostructures to local perturbations could decrease Limit of Detection (LoD) and power consumption figures and increase the detection dynamic range and the multiplexing capacity [5,6] of integrated photonic sensing platforms. While silicon-on-insulator (SOI) is the mainstream integrated photonics material platform, silicon nitride ($Si_3N_4$) is emerging as a competitive alternative, especially, for biophotonics applications [9]. The $Si_3N_4$ platform offers low absorption loss (compared to silicon) in the visible and near IR bands where biological entities and the background (water) are non-absorbing. Besides this, low cost and easier integration with light sources and photodetectors is possible in these wavelengths [7]. The advantages have to be balanced against the fact that the lowered index contrast increases the device footprint [9], especially, for resonators. On the other hand, the reduced index contrast dampens the deleterious effects of fabrication imperfections.

Computational and experimental studies on the incorporation of plasmonic nanoantenna has been reported in both SOI [10–19] and $Si_3N_4$ platforms [3,6,20–25]. The plasmonic nanoantenna is either loaded on the interrogating strip waveguide or on a microring resonator [6,22] coupled to the interrogating strip waveguide. Additionally, photonic crystal defect cavities and waveguides configurations [18,19,25,26] have also been reported. Monitoring the shift of resonance in the transmitted spectrum (spectral-shift modality) or the change in transmittance at a specific wavelength (intensity-shift modality) on the interrogating waveguide allows us to detect binding events on the nanoantenna. A monolayer of octadecanthiol (ODT) molecules was deposited on gold nanoparticle with SOI waveguide interrogation [11]. The authors claim ultra low analyte volume detection of 0.26 attoliters. Using chain of gold nanoparticles integrated with silica on silicon (SOS) waveguides, Ozikandathil et al. have performed antigen-antibody binding based detection of recombinant bovine somatoropin (rbST) molecules with detection limit of 20 ng/ml [27]. Chamanzar et al. detected 8% dextrose solution using an array of 40 gold nanorods loaded on top of strip waveguide [6] on silicon nitride platform. Each of the sensing technologies adopt spectral shift modality requiring bulky off the chip spectrometers. Intensity shift modality using the mentioned configurations is not yet explored. SERS signals resulting from the local field enhancement on the nanonantenna surface can be collected for off-chip readout. Losada et al. [20] and Peyskens et al. [21] characterized 4-nitrophenol (pNTP) molecules on silicon nitride platform by using gold Bow-Tie nanoantenna in the wavelength region of 700 nm-1000 nm.

The coupling efficiency achievable for the strip waveguide with its top surface loaded with a single plasmonic nanoantenna is only about 10% [3] as it is limited by the mode-fraction in the evanescent tail (coupling efficiency can be improved by resorting to multiple nanoantennae [11], but this has demerits as discussed earlier). Alternately, the nanoantenna can be inserted in a subwavelength cut created in a silicon waveguide in order to excite the nanoantenna by the intense light of the waveguide core [10,20]. Although the method showed a coupling efficiency of 90% at near infrared wavelengths, the cut reduces the transmission magnitude by 10 dB [10]. This affects the refractive index sensing performance particularly the intensity shift modality. Also there are fabrication problems such as difficulty in alignment of nanoantenna inside the gap and integration of microfluidic channel. For $Si_{3}N_4$ platform, the cut does not improve coupling due to reduced index contrast. The approaches where the nanoantenna loading happens on a waveguide-fed resonator are inspired by the fact that this coupling increases the Q/V ratio beyond that achievable with an individual nanoantenna or an individual microresonator. The improvement in sensing performance, however, occurs at the expense of increased footprint. The device footprint increase is more evident for the $Si_{3}N_4$ platform in aqueous cladding due to the reduced index contrast.

We numerically investigate the optical properties of structured waveguides loaded with plasmonic nanoantenna. Specifically, instead of using strip waveguides, we propose sub-wavelength grating (SWG) [28] and phase shifted Bragg grating (PSBG) configurations to enhance the interaction of light with nanoantenna in a low contrast setting. Both the SWG [29–31] and PSBG [32–34] have been found to improve the sensing performance in integrated photonics. However, the integration of plasmonics and SWG/PSBG structures is still in its nascent stage [35] and, to the best of our knowledge, this study is the first to comprehensively study the interaction between such structured waveguides and plasmonic nanoantenna. Following this introduction the geometry and numerically optical response of the strip, SWG and PSBG configurations loaded with individual nanoantenna has been discussed in section 2. The RI sensing performance for the intensity shift based modality have been evaluated for the proposed structures in section 3. Followed by this, effect of geometrical parameter variations in SWG and PSBG waveguides on sensing and intensity enhancement ability is predicted (section 3.1). The structures’ robustness to nanoantenna length and position variations has been predicted in section 3.2 before concluding the paper in section 4.

2. Geometry and optical response

2.1 Structure and simulation methodology

We investigate the interrogation of a simple plasmonic nanoantenna with three different waveguide geometries, namely: strip, PSBG and SWG as seen in Fig. 1. Silica substrate and aqueous background are considered throughout. For each waveguide, the top surface is loaded by a gold nanoantenna. The waveguide width $w$ and thickness $h$ are kept identical for all the three configurations. For the PSBG waveguide, the corrugation depth, duty cycle, periodicity and length of central rib are denoted as $w_1$, $DC_1$, $GP_1$ and $L_c$ respectively. For the SWG waveguide, the duty cycle and periodicity are denoted as $DC_2$ and $GP_2$ respectively. The nanoantenna length, width and thickness are denoted as $l_d$, $w_d$ and $t_d$ respectively. The waveguides are end-fire excited from one end and the output light is collected from the other end.

 

Fig. 1. Schematic (top view) of on-chip photonic waveguide configurations loaded with individual plasmonic nanoantenna. (a), (b), (c) show nanoantenna loaded top surfaces of strip (a), PSBG (phase shifted Bragg grating) (b) and SWG (sub-wavelength grating) waveguides (c). The waveguides rest on a silica substrate in an aqueous background.

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All results reported in this article are obtained via numerical full-wave electromagnetic solvers. Time domain electromagnetic analysis of the mentioned structures has been done using the commercial simulation tool CST Microwave studio which uses Finite Integration Technique. The structure is divided into hexahedral meshes with minimum 10 cells per wavelength. Open radiating boundary conditions are imposed along all the axes. Gold is modeled using Johnson-Christy model [36], silicon nitride, silica and water are modeled with constant refractive indices of 1.99, 1.45 and 1.33 respectively. The simulation setup has been verified by performing mesh convergence tests as well as by verification against previously published papers of waveguide/plasmonic nanoantenna geometry and against papers on SWG/PBSG waveguides.

2.2 Optical response of nanoantenna loaded systems

Here we investigate the optical response of the various waveguides to loading with the plasmonic nanoantenna. Figure 2 shows the transmission, absorption and near field responses of all the three waveguide configurations with and without nanoantenna loading. In the study, the waveguide geometrical parameters such as width ($w$=700 nm), thickness ($h$=220 nm) are kept constant for all the configurations.

 

Fig. 2. Comparison of the transmittance (T) and absorption (A) spectra for different waveguide configurations with and without plasmonic nanoantenna loading. We consider one strip waveguide, one PSBG waveguide and two different SWG waveguides (SWG 1 and SWG 2). The insets in (a), (b), (d) and (e) show the normalized near field plots of the bare waveguide modes on the top-surface. (g-j) show the near field plots around the plasmonic nanoantenna at resonance wavelengths for loaded waveguides (g – strip, h – SWG 1, i – SWG 2 and j – PBSG). (k) corresponds to a strip waveguide with a sub-wavelength cut for housing the nanoantenna [20]. $GP_1$=225 nm, $DC_1$=0.6, $GP_2$=225 nm, $DC_2$=0.5, $w$=700 nm, $h$=220 nm $l_d$=67 nm, $w_d$=$t_d$=30 nm. SWG 2: $GP_2$=250 nm, $DC_2$=0.5, $l_d$=62 nm.

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The simplest case of a strip waveguide is considered first. As seen in Fig. 2(a), the bare waveguide exhibits a near-unity transmittance over the entire region of interest and the familiar fundamental TE-like waveguide mode profile. On loading this strip waveguide with a plasmonic nanoantenna, LSPR is excited in it by the evanescent tail of the waveguide mode. The coupling results in a broadly resonant transmission dip and the transmission-modulation quantifies the degree of coupling between the mode and the LSPR. It is seen that the loading does not result in reflections. The transmission dip and absorption peak of 12% is much larger than that achievable in free-space; it is limited by spatial overlap of the evanescent tail and dipolar LSPR mode. Further improvement in coupling requires two contradicting requirements: (1) looser mode confinement which ensures that a larger fraction of the mode power is in the evanescent tail; and (2) faster evanescent decay which improves the fraction of the mode power in the evanescent tail that the nanoantenna can capture. In high index contrast waveguides, the second requirement is fulfilled but not the first. On the other hand, in low index contrast waveguides, the first requirement is satisfied but not the second. For a system with a given index contrast, we propose that longitudinal confinements introduced by the waveguide structuring can be used to improve the coupling.

Figure 2(b) and (c) show the transmission and absorption response of the PSBG waveguide with a defect created in the center. Unlike the strip waveguide, this resonant configuration exhibits a strong wavelength-dependent transmission. For the bare waveguide, a high Q transmission peak is observed inside the Bragg window of low transmission which corresponds to the excitation of the Fabry-Perot resonance in the defect region. This resonance can only be excited in a finite structure. On loading with nanoantenna, the same sharp resonance is seen (albeit, with a reduced transmission). This is dramatically different from the case of a strip waveguide which preserves the naturally broad linewidth of the plasmonic dipolar mode. Of the transmission reduction of about 60% seen in Fig. 2(c), around 32% is coupled to the nanoantenna, 18% is scattered by the corrugating ribs and the remaining is reflected.

Depending on the geometrical parameters of the SWG, most importantly, the grating pitch, its optical responses can be made to match that of the strip or the PSBG configuration. This is because SWGs can either guide or scatter light depending on the relation between grating period and wavelength of operation [28]. In the sub-wavelength regime it behaves as a homogeneous waveguide, whereas for the case of grating period comparable to wavelength, it radiates. In between the two regimes, it behaves as a Fabry-Perot resonator. We consider two cases of SWG: (1) SWG 1 that behaves as a homogeneous waveguide; and (2) SWG 2 that operates as a Fabry-Perot resonator. The transmission and absorption responses of SWG 1 with and without nanoantenna loading is seen in Fig. 2(d). The waveguide effective index is reduced in comparison to the strip waveguide, but the mode profile difference is bigger for larger index contrast. It is seen that the coupling to nanoantenna does not change significantly in SWG 1. In our previous work [37], we had reported a silicon SWG waveguide operating in the homogeneous mode with nanoantenna loaded at the sides of the waveguide where the coupling efficiency doubled. Such a change could not be achieved in low contrast silicon nitride waveguide with aqueous cladding. Figure 2(e) and (f) show the transmission and absorption responses for Fabry Perot resonant SWG 2 with and without nanoantenna loading. As found in PSBG waveguide, high Q of the Fabry Perot modes is preserved on nanoantenna loading. Coupling efficiency of 30% is observed at around 803 nm wavelength.

Given a light source with a certain output power, the power coupled to a nanoantenna using a waveguide can be thus considerably larger than the free space case [3]. The intensity enhanced hotspots can act as Raman centers resulting in considerable increase in Surface-enhanced Raman scattering, SERS [20] that can be collected using an objective placed above the nanoantenna. The E field distribution on the top surface of the bare waveguide configurations are shown in the insets of Figs. 2(a), (b), (d) and (e). In Fig. 2(b), a high amplitude standing wave mode can be observed in the Fabry Perot resonant wavelength of the bare PSBG waveguide and the field is observed to be enhanced two times. For the SWG operating in the waveguide mode, SWG 1, shown in Figs. 2(d), a low amplitude standing wave is observed along the longitudinal direction due to small reflections from the rib-cladding interfaces. The E-field strength is same as that observed for the strip waveguide. The effective index of the waveguide being lower than the strip waveguide, the mode is relatively expanded. An intense Fabry Perot mode in SWG 2 can be seen in the near field distribution shown in Fig. 2(e). The field is approximately 3 times more enhanced as compared to the strip waveguide. The electric field plots around the nanoantenna for the loaded waveguide configurations are shown in Figs. 2(g)-(k) respectively. The E-field enhancement due to nanoantenna loading is calculated taking the reference as maximum E-field inside the bare strip waveguide core ($E_o$) similar to that done by Losada et al. [20]. E-field of magnitude 18$E_o$ has been observed around nanoantenna for strip and SWG configurations as shown in Figs. 2(g) and (h) respectively. In Fig. 2(i), a considerable improvement of factor 40 (40$E_o$) has been observed for the case of loaded Fabry Perot resonant SWG 2. For PSBG configuration in Figs. 2(j), the field strength is 25$E_o$. Figure 2(k) shows the field distribution of nanoantenna inserted in a sub-wavelength cut waveguide in the same cladding environment. This structure has been proposed by Losada et al. for a top cladding of air [20]. A field enhancement of 29 has been observed.

Thus, an improved coupling and near field enhancement of nanoantenna are observed on replacing the strip waveguides with resonant PSBG and SWG configurations. Besides this, high $Q/V$ is obtained with high $Q$ attributed by Fabry Perot mode and small $V$ due to LSPR modes. The footprint for resonating SWG and PSBG based structures are 15 µm×0.7 µm, 70 µm×0.7 µm respectively, which is smaller than hybrid WGM LSPR resonators(40 µm×40 µm [6]). Although the optical response has been studied at wavelengths slightly higher than visible spectrum, the structure can be also redesigned to operate in the visible wavelength regime.

3. Results and discussion

In this section, we perform numerical studies on RI sensing using intensity shift modality. In a typical sensing experiment, the analyte molecules bind to the bioreceptor molecules attached to the nanoantenna surface, causing shift in its resonant wavelength. The bioreceptor adds specificity to the binding process ideally responding to a single target species and the intensity-shift modality uses a single-wavelength co-located with the resonant peak or dip. We adopt a simpler setup (similar to [11]) to emulate this process as seen in Fig. 3(a) by adding a homogeneous layer with thickness $t_a$=20 nm that covers all the sides of nanoantenna except the bottom with its effective refractive index $n_a$ ranging from 1.33 (the case where no binding occurs) to 1.45 (the case for complete coverage by analyte). If $I_0$ is the transmittance at the interrogating wavelength without the presence of analyte (i. e. $n_a = 1.33$) and $I_0 + \Delta I$, the transmittance in the presence of analyte (i. e. $n_a = 1.33 + \Delta n$). In an actual experiment, an additional noise signal ($I_{noise}$) is also measured at the output photodetector. The sensor performance is quantified with the sensitivity as $S= \dfrac {1}{\Delta n} \dfrac {\Delta I}{I_o}$ and its figure of merit depends on the ratio of $\Delta I$ and $I_{noise}$.

 

Fig. 3. Comparison of intensity shift based refractive index (RI) sensing performance for plasmonic nanoantenna interrogated by different waveguide configurations such as strip waveguide, PSBG waveguide, SWG operating in waveguide mode and Fabry Perot mode. (a) shows schematic of modeling analyte binding to the nanoparticle. (b) shows the relative intensity shift corresponding to varying analyte RI for all the configurations. (c)-(f) show the effect of varying analyte RI on their transmission spectra. The nanoantenna surface is covered by a 20 nm thick homegeneous layer. The waveguide, nanoantenna and background are modeled similar to Fig. 2.

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Figure 3(b) shows relative intensity shifts ($\Delta I$) corresponding to varying analyte refractive indices for the strip, SWG and PSBG waveguide interrogated nanoantenna. Two different SWG waveguides corresponding to SWG 1 and SWG 2 as discussed in section 2 are considered. The spectral shifts can be seen in Fig. 3(c)-(f). In all cases, it is seen that the shift $\Delta I$ exhibits a linear response (small fluctuations can be attributed to numerical round-off errors). For the Fabry Perot resonant SWG and PSBG interrogators, the change in output intensity per unit change in analyte refractive index ($dI/dn$) is 2 times greater than that for the strip and SWG 1 waveguides. Using PSBG, the corresponding sensitivity $S$ is 7 times higher than strip waveguide and 6 times higher than SWG 1 waveguides. Similar increment in sensitivity of resonating SWG 2 configurations is observed.

High Q in resonators with narrow linewidths limit the dynamic range for intensity shift sensing scheme [38]. This problem is not observed in PSBG and SWG resonators. Considering the spectra in the insets, red shift in resonant wavelength can be seen for the case of SWG 1 and strip waveguide systems, whereas no shift has been observed for the Fabry Perot resonant PSBG and SWG 2 interrogators. Even though PSBG and SWG 2 resonators possess high Q, their dynamic range is not affected as there is negligible spectral shift in response to analyte binding. Thus, with SWG and PSBG configurations operating on Fabry Perot mode, a considerable increase in sensitivity is observed compared to the commonly investigated strip waveguide based interrogation scheme. Additionally, the dynamic range of these structures is not affected unlike observed in other high Q resonator based sensors.

To get a sense of the magnitude of intensity shifts obtained in presence of analyte, we consider the PSBG interrogation scheme for detecting Bovine Serum Albumin (BSA) proteins. The nanoantenna surface area available for binding is 7830 nm$^{2}$, radius of BSA molecule is 3.4 nm. The maximum number of molecules that can bind to a single nanoantenna is approximately 216. The intensity change ($\Delta I$) due to binding of such molecules can be computed from the parameters such as device sensitivity ($S$=394%/RIU), local RI change due to analyte ($\Delta n$=0.12), initial intensity ($I_o$=12%). $\Delta I$ is 6% corresponding to binding of 216 BSA molecules. For input power of 1 mW, the power change in output is 60 µW, which is considerably larger than typical noise floor (<0.1 µW) observed in photodetectors.

3.1 Design space exploration

As mentioned in section 1, the nanoantenna loaded strip waveguide configurations have already been investigated extensively in the past for performance improvement in sensing and spectroscopy applications. For high Q PSBG and SWG resonator configurations, geometrical parameters can be tuned to investigate further scope of improvement. In Fig. 4(a), (b), the effect of varying corrugation depth $w_1$ and number of grating periods $N$ is observed for intensity shift sensing modality in PSBG configuration. For a given geometrical parameter value, the transmission spectra with analyte ($n_a = 1.45$) and without analyte ($n_a = 1.33$) is also noted. In each case, we also note the transmitted intensity changes at the resonant wavelength. As seen in Fig. 4(a), with increase in $w_1$ from 70 nm to 130 nm, $\frac {\Delta I}{I_o}$ increases from $28\%$ to $57\%$, beyond which, the Fabry-Perot resonance disappears. In Fig. 4(b), the number of grating periods, $N$, is changed. Increasing $N$ increases the $Q$ factor of of the cavity (due to increase in reflectivity of Bragg mirrors) thus enhancing the interaction of light with analyte. On increasing $N$ from 50 to 250, $\frac {\Delta I}{I_o}$ increases from 11% to 47%. However further increase in $N$ reduces the transmission intensity corresponding to Fabry-Perot resonance (result not shown in the figure). This is because of reduced coupling of light from Bragg mirrors (due to high Bragg reflectivity) into the cavity. For resonant SWG configuration, the effect of varying duty cycle $DC_2$ and $N$ on sensing performance is shown in Fig. 4(c) and (d) respectively. As shown in Fig. 4(c), $\frac {\Delta I}{I_o}\%$ is high for $DC_2$=0.5,0.6, however, on further increase or decrease, it reduces to 12% (the relative intensity change is computed for the best case out of multiple Fabry Perot resonances). In Fig. 4(d), the relative intensity change of $\frac {\Delta I}{I_o}>30\%$ is observed.

 

Fig. 4. Effect of geometrical parameter variations of Fabry Perot resonant PSBG, SWG interrogated nanoantenna configurations on its intensity sensing and enhancement ability. (a), (b) shows transmission change with/without analyte for varying PSBG corrugation depth $w_1$ and number of grating periods (N). The corresponding change in the electric field around the nanoantenna is shown in (e). For SWG resonator, the duty cycle $DC_2$ and $N$ are varied in (c), (d) and (f) respectively. The analyte is 20 nm thick with constant refractive index of 1.45. The fixed design parameter values are same as that used in Fig. 2.

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The effect of PSBG and SWG geometrical parameter variations on the electric field enhancement around the nanoantenna are shown in Fig. 4(e) and (f) respectively. As shown in Fig. 4(e), there is marginal decrease in the field enhancement (approximately $20E_o$) on changing the corrugation depth $w_1$ (field plots labelled as A, B). The enhancement factor is decreased from $25E_o$ for $N=250$ to $15E_o$ for $N=50$ (field plots labelled as C, D). In Fig. 4(b), on increasing the SWG duty cycle from $DC_2=0.4$ to $DC_2=0.8$, the enhancement increases from $30E_o$ to $40E_o$ (field plots labelled as E, F). On reducing the number of grating periods from 85 to 45, the field enhancement remains high at $40E_o$ (field plots labelled as G, H).

Reducing the number of grating periods has marginal effect on sensing and intensity enhancement performance of SWG resonator as opposed to PSBG configuration. Thus, SWG with further reduced footprint can be realized for sensing and SERS applications. For a certain range of corrugation depth $w_1=90-130 nm$ in PSBG, the sensing and intensity enhancement performance is not degraded thus providing flexibilty in choice of designing parameter values.

3.2 Impact of fabrication imperfections

Although the PSBG and SWG exhibiting high Q and high intensity Fabry Perot modes show better sensing and spectroscopy capabilites, their robustness to fabrication imperfections needs to be assessed. Such hybrid structures can be easily fabricated by adsorbing gold nanoparticles on waveguides patterned by lithography. The gold nanoparticles can be adsorbed on the waveguide surface by evaporating the aqueous solution containing the nanoparticles [27]. They can be accurately fabricated by two steps of e-beam lithography involving patterning of waveguide and nanoantenna [3,20,21,23,26]. Waveguide patterning using low cost deep UV photolithography has also been reported [11]. Three kinds of fabrication errors can be encountered in the proposed nanostructures: 1. SWG/PBSG rib width and thickness fluctuations, 2. alignment errors between nanoantenna and waveguide ribs and 3. nanoantenna dimension fluctuations. Errors 1 and 3 lead to change in resonance position while error 2 leads to reduction in sensitivity and field enhancement. Due to low index contrast in the proposed structure, error 1 has marginal effect on its optical response [9]. However, errors 2 and 3 can considerably affect its performance parameters. Such errors have also shown to affect the performance of the strip waveguide loaded nanoantenna configurations [39]. With the use of alignment markers, the nanoantenna position errors of less than 20 nm [3,26] have been reported. For the case of dispersion in nanoantenna dimensions, LSPR wavelength accuracy of 15 nm have been claimed in [11].

The influence of second and third kind of errors discussed above is studied and results are shown in Fig. 5. The field decaying nature of the Fabry Perot modes can be observed from the top surface intensity distribution of SWG and PSBG structures shown in Figs. 5(a) and (d) respectively. The effect of nanoantenna misalignment on sensing performance has been observed in Figs. 5(b) and (e) respectively. The nanoantenna position is changed along the transverse (y-axis) and longitudinal (z-axis) directions relative to SWG and PSBG resonator top surfaces. For the SWG interrogation scheme, the relative intensity change is marginally reduced on nanoantenna position changes of upto 50 nm in either direction. The PSBG configuration is equally robust on nanoantenna position variations of similar scale. Figures 5(c) and (f) show the effect of nanoantenna length variation on the sensing performance of SWG and PSBG interrogators. For nanoantenna length variation from 52 nm to 62 nm in SWG interrogator, $\frac {\Delta I}{I_o}$ changes marginally (remains above 35%), however for $l_d= 67$ nm, the change is moderate (23%). In PSBG interrogation scheme, there is a moderate change in $\frac {\Delta I}{I_o}$ on variations of such scale.

 

Fig. 5. Robustness of sub-wavelength grating (SWG) and phase shifted Bragg grating (PSBG) interrogation systems to variation in plasmonic nanoantenna position and dimension. (a) shows the normalized intensity distribution on the top surface of a Fabry Perot resonant bare SWG where nanoantenna is to be loaded. The normalized intensity distribution for the bare PSBG waveguide is shown in (d). The nanoantenna position is changed along transverse (y-axis) and longitudinal (z-axis) directions. The corresponding effect on the intensity shift based RI sensing performance is shown in (b), (e) for SWG and PSBG respectively. Effect of nanoantenna length variation on the sensing performance of SWG and PSBG interrogators is shown in (c), (f) respectively. The analyte is 20 nm thick with refractive index of 1.45. The waveguide, nanoantenna and background are modeled similar to Fig. 2 for PSBG and SWG interrogation system.

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4. Conclusion

To conclude, the numerical study has predicted that nanostructuring can improve the interaction of integrated waveguides with plasmonic nanoresonators in comparison to strip waveguides. The proposed concept is particularly beneficial in the $Si_3N_4$ integrated biophotonics platforms with aqueous cladding which has low index contrast. The application of refractive index sensing based on intensity shift modality has been investigated, which has not been explored for low analyte volume detection in the past. With nanostructuring, there is six fold increase in sensitivity and four fold enhancement in intensity compared to the strip waveguide configurations. The use of compound nanoantenna [40] could further improve the sensing and field enhancement capability of the device. The design space exploration and sensitivity analysis will be helpful for experimental realization of proposed concepts. The proposed structures are robust to nanoantenna positioning and dimension errors. The device robustness can be further improved by using alternate nanoantenna shapes.