2.2. Design and Optimization of Fishbone SWG Waveguides
In order to optimize fishbone SWG waveguides for sensing applications and compare their performance to conventional boneless SWG waveguides, we performed fully vectorial 3D-FDTD band structure simulations using Bloch boundary conditions, as described in Section 2.1.1. These simulations were used to predict the effective index, neff, and bulk sensitivity, Sb , of SWG waveguides operating with C-band and O-band light in the TE mode. Compared to Sb , surface sensitivity (Ss) is the more important metric for biosensors in the study of target molecule quantification, but it must be defined for a specific molecule of interest, meaning that Sb is a more suitable criterion for the general comparison of sensors when the target is unknown or the sensors are used for different biosensing assays [3,40]. As such, Sb was used in this work to compare sensing architectures. For all simulations, a waveguide width of 500 nm, waveguide thickness of 220 nm, and BOX thickness of 2 µm, were used. The grating period, Λ, was initially fixed at 250 nm. This grating period was selected, as it is below the Bragg threshold (Λ << λ/2neff) for all studied geometries. Further, others [19,39] have studied boneless SWG waveguides with this grating period, providing a valuable benchmark for comparison. The waveguides were optimized by performing simulation sweeps in which the duty cycle, δ, was varied from 0.2 to 0.8 for SWGs with fishbone widths, wfb, of 0, 60, 100, 140, 180, and 220 nm. Simulations performed with water cladding were used to extract neff and the group index, ng, for each waveguide geometry. To extract Sb , band structure simulations were additionally performed using an index-shifted water cladding material to simulate a dilute salt solution. For this indexshifted material, the real part of the refractive index of water was shifted by 0.01 (∆nbulk) at all wavelengths in the water material model; it was assumed that material absorption, and therefore, the imaginary term of the refractive index, remained constant. By simulating neff in both materials to extract ∆neff, the susceptibility, ∂neff/∂nbulk, could be estimated as ∆neff/∆nbulk. Using this susceptibility alongside the group index, Sb was calculated according to Equation (2).
Figure 3 presents the results of these simulations. Increasing δ and wfb led to an increase in neff for the C-band and O-band structures. This reflects an increase in light confinement as the volume fraction of silicon in the SWG structure increases. This increased light confinement decreases the interaction of light with the bulk material. As seen in Figure 3, this is generally accompanied by a decrease in Sb . However, when neff approaches and falls below ~1.44, which is the refractive index of the BOX, the waveguide no longer effectively guides light, and a considerable decrease in Sb is observed when δ and wfb are decreased further . For the C-band devices, the greatest value of Sb out of all the simulated structures was roughly 470 nm/RIU, whereas that for the O-band devices was roughly 400 nm/RIU. The greater sensitivities of the C-band structures can be attributed to lower mode confinement at longer wavelengths at the defined waveguide geometry of w = 500 nm and t = 220 nm .
The sensitivity results highlight that fishbone SWG waveguides can achieve comparable sensitivities compared with boneless SWG waveguides for appropriate combinations of δ and wfb. For both fishbone and boneless SWG structures, the electric field is highly concentrated in the gaps between the silicon blocks, as shown in Figure 4. This allows for strong interaction between the evanescent field and the bulk medium.
Based on this analysis, we selected two C-band and two O-band fishbone SWG waveguide designs for fabrication. Given the small effect of Λ on waveguide performance, we chose devices with Λ = 250 nm. Three evaluation criteria were used to select the best combinations of δ and wfb for the fabricated structures. First, the minimum feature size had to exceed 60 nm, which was the minimum fabricable feature size of the ANT electronbeam foundry process used in this work . Next, the reduced modal confinement of SWG waveguides can lead to considerable optical losses to the substrate [3,80]. SarmientoMerenguel et al. reported that these substrate leakage losses are independent of SWG geometry and established a direct relationship between leakage losses and neff, along with practical design guidelines . In particular, for a 2 µm BOX layer, for C-band light, substrate leakage losses are negligible when neff > 1.65. Therefore, in this work, only fishbone SWG designs with simulated neff values above this cutoff were considered for fabrication. It should be noted that this leakage loss cutoff was only previously validated for a wavelength range of 1.5–1.6 µm . The leakage loss cutoff is expected to be lower for the O-band than the C-band due to the higher modal confinement at lower wavelengths , making 1.65 a conservative estimate for this wavelength range. A comprehensive investigation of O-band substrate leakage losses, although beyond the scope of this work, would validate this assumption and establish a more precise substrate leakage loss cutoff for the O-band. As such, in this work, we used the same leakage loss cutoff of 1.65 for both the C-band and O-band devices. Lastly, among the fishbone SWG designs that satisfied the first two selection criteria, the two C-band and two O-band devices with the highest values of Sb were selected. When selecting the optimized C-band devices, an exception was made, as the geometry with the greatest Sb (δ = 0.6 and wfb = 60 nm) only exceeded the neff leakage loss cutoff by ~0.02. To mitigate the risk of leakage losses due to smaller-than-predicted feature sizes, we selected the C-band waveguide geometries with the second- and third-greatest simulated Sb values. The selected C-band (C1 and C2) and O-band (O1 and O2) designs, along with their simulated neff values, are provided in Table 1
In addition to these optimized fishbone SWG designs, an additional six fishbone and boneless SWG waveguides (C3–C6 and O3–O4) with similar neff values to the optimized designs were included on the fabricated photonic chips. Their geometries and simulated neff values are provided in Table 1. These additional geometries were included to experimentally investigate variations between ring resonators fabricated with fishbone SWGs and conventional SWGs, and to experimentally investigate the effect of grating period on device performance.
2.3. Sensor Chip Design and Fabrication
The SWG MRR photonic circuits were designed using KLayout mask editing software, the open-source SiEPIC tools library, SiEPIC EBeam process design kit, and Applied Nanotools process design kit [82–84]. One half of the chip layout was dedicated to the C-band resonators, whereas the other half was dedicated to the O-band resonators. All fabricated resonator designs are included in Table 1. The layout included input and output grating couplers to couple light between the chip and benchtop tunable lasers and detectors. 500 nm-wide strip routing waveguides were used to transmit C-band light between the I/Os and resonators, whereas 350 nm-wide strip waveguides were used for the O-band routing. Waveguide bends were designed with a bend radius of 5.0 µm and a Bezier bend parameter of 0.2 . 15 µm-long tapers were used to create smooth transitions between the routing waveguides and the SWG bus regions of the resonators.
The photonic chips were fabricated on silicon-on-insulator (SOI) wafers by Applied Nanotools Inc. (Edmonton, AB, Canada) using 100 keV electron beam lithography and reactive ion etching . All waveguides and photonic structures consisted of silicon. The chips were fabricated with a 220 nm silicon device layer, comprising the patterned photonic circuit, on top of a 2.0 µm SiO2 buried oxide (BOX) layer, on top of a 725 µm silicon wafer layer. For this work, the chips were fabricated without cladding. No photoresist or hard mask remained on the waveguide surfaces after fabrication. The chips were used as received for testing. The water contact angle of the sensor chips was found to be 28–30◦ , representing the hydrophilicity of the BOX layer, which comprises most of the chip’s surface area. It is possible, however, that the silicon waveguides with native oxide exhibit different wetting behavior .
2.4. Sensor Characterization
The photonic sensors’ transmission spectra were measured to characterize their performance in terms of ng, free spectral range (FSR), extinction ratio, and Q. These measurements were made using a custom optical testing setup (Maple Leaf Photonics, Seattle, WA, USA) mounted on a pneumatic vibration isolation table (Newport Corporation, Irvine, CA, USA).
The photonic chip was placed on a motorized XY stage (Corvus Eco, Micos GmbH, Eschbach, Germany), maintained at 22 ◦C with a thermoelectric cooler controlled by a laser diode controller (Stanford Research Systems LDC500, Sunnyvale, CA, USA) and illuminated by a cold light illumination source (Hund, Wetzlar, Germany). A 12-channel lidless fiber array (VGA-12-127-8-A-14.4-5.0-1.03-P-1550-8/125-3A-1-1-0.5-GL-NoLid-Horizontal, OZ Optics, Ottawa, ON, Canada) mounted to a motorized Z stage was aligned to the on-chip grating coupler inputs and outputs. Alignment was performed using open-source PyOptomip software (Python 2.7, 32-bit) , which controlled the position of the XY and Z stages and communicated with the tunable lasers and detectors. The relative positions of the photonic chip and fiber array were monitored using top- and side-view microscope cameras (Pixelink, Ottawa, ON, Canada) mounted to 12× zoom lenses (Navitar, Ottawa, ON, Canada). To test the C-band devices, the fiber array was connected to an Agilent 8164A mainframe (Agilent Technologies, Inc. Santa Clara, CA, USA) with a C-band swept tunable laser (Agilent 81682A); to test the O-band devices, the fiber array was connected to another Agilent 8164A mainframe with an O-band swept tunable laser (Agilent 81672B). Eight fiber array channels were connected to Agilent 81635A and Keysight N7744C (Keysight Technologies, Santa Rosa, CA, USA) optical detectors; therefore, up to eight resonators could be probed simultaneously. PyOptomip software was used to control and interface with the tunable lasers and optical detectors.
Prior to the measurements, the resonators were pipette-spotted with ~20 µL of ultrapure water from a NANOpure water purification system (Thermo Fisher Scientific Inc., Waltham, MA, USA). Measurements were then performed by sweeping the tunable laser input and recording the transmission spectra of the resonators. All of the SWG MRR sensors were characterized on five replicate chips.
To extract the sensor performance criteria from the optical spectra, a custom semiautomated script was written in MATLAB (MathWorks, Natick, MA, USA). First, the user was presented with a plot of the overlaid optical spectra of the simultaneously measured 8 resonators and prompted to select the wavelength range to be analyzed. On each optical spectrum, the script then performed (1) peak-finding (findpeaks() function) to identify resonance peak positions and approximate peak widths, (2) fitting of the baseline (non-peak) regions of the spectra to a third-degree polynomial function (polyfit()) and subtraction of that baseline from the optical spectra, (3) linearization of the decibel-scale baselinesubtracted data, (4) nonlinear least-squares fitting of each resonance peak to a Lorentzian function (lorentzfit() 184.108.40.206 by Jered Wells on the MATLAB File Exchange). During step (1), peaks of interest were automatically distinguished from noise by setting the arguments passed to findpeaks() based on the expected form of the data. Specifically, the minimum peak prominence (height of the peak, or extinction ratio) was set to 2 dBm, and the minimum distance between neighboring peaks (FSR) was set to 2 nm. The script also plotted and saved figures highlighting the found peaks on the optical spectra so that the user could check for anomalous results during or after analysis. The fit was performed on the linearized, baseline-subtracted data, and the peak was inverted and normalized prior to Lorentzian fitting (the fitted peak was positive and extended from 0 to 1). If the goodness-of-fit was sufficiently high (R2 > 0.85), the center wavelength of the Lorentzian function was used as the resonance peak position in subsequent computations, and the peak’s FWHM was calculated from the Lorentzian fit. If the goodness-of-fit was insufficient, the raw peak location was used as the resonance peak position and the FWHM was not computed (the peak was not counted in subsequent quality factor analysis). The peak prominence from the peak-finding function was taken as each peak’s extinction ratio, the FSR was calculated as the average distance between the resonance peaks in the spectrum (and ng was computed from the FSR as ng = λ 2 L·FSR ), and the quality factor was calculated from Equation (4) using the FWHM extracted from the Lorentzian fit.
2.5. Microfluidic Design and Fabrication
Microfluidic gaskets to deliver aqueous solutions for sensor performance characterization were fabricated using Sylgard™ 184 poly(dimethylsiloxane) (PDMS) (Ellsworth Adhesives, Hamilton, ON, Canada) molded against 3D printed molds using soft lithography. 2D layouts of the microfluidic channel and mold geometry were designed using KLayout mask editing software (aligned with the photonic design in the same layout), and the microfluidic layers of the layout (separate layers for the outside of the mold, the interior mold cavity, the channel features, and the input/output through holes) were exported as a .dxf file which was subsequently imported into SolidWorks (Dassault Systèmes, Vélizy-Villacoublay, France) and extruded into the final 3D geometry of the mold. The mold created gaskets with two parallel microfluidic channels, each designed to be 200 µm in width and 200 µm in height over the region of the photonic chip containing the sensors, expanding into 500 µm diameter circular input/output regions. The inset region of the mold into which PDMS was cast was designed to be 4 mm in thickness, and the mold also contained 500 µm diameter circular through-hole features to serve as input/output ports. All through-hole features were extruded to a 0.1 mm taller height than the walls of the mold to ensure that thin PDMS membranes did not remain atop through-hole features (the results of experimental testing suggested that 0.1 mm additional height was sufficient to create effective through-holes, whereas 0 mm height differential was insufficient). The gasket mold also contained 3 mm diameter through hole features to self-align the gaskets to the photonic chip, with the chip positioned in a precision-machined recess in a custom-made aluminum mounting plate with matched 4–40 tapped bolt holes. The cast gasket was designed to have ~3.3 mm of extra PDMS on the long edge closest to the channels to reduce any demolding-related feature distortion. This extra PDMS was manually cut off of the fabricated gasket using a single-edge razor blade after demolding.
The molds were printed on a ProFluidics 285D digital light processing (DLP) 3D printer (CADworks3D, Toronto, ON, Canada) at 50 µm using Master Mold resin (CADworks3D). Standard post-processing (isopropanol wash, compressed air dry, and 40 min ultraviolet cure in a Creative CADworks CureZone UV curing chamber (CADworks3D)) was performed on the molds to prepare for soft lithography. The root-mean-squared roughness of the fabricated molds had an upper bound of approximately 65 nm . No mold release agent was used. Sylgard™ 184 silicone elastomer prepolymer base and curing agent gent (Ellsworth Adhesives, Hamilton, ON, Canada) were mixed at a 10:1 ratio by hand-stirring and a planetary centrifugal mixer (THINKY ARE-310, THINKY USA, Laguna Hills, CA, USA), cast in the 3D printed molds (slightly overfilling the mold so that the PDMS liquid surface was convex and approximately 1 mm above the top of the mold), and degassed in a vacuum desiccator for 30–60 minutes. A sheet of overhead projector transparency material (Apollo, ACCO Brands Corporation, Lake Zurich, IL, USA) was cut to ~4 × 7 cm in size and slowly and carefully laid upon the mold, starting from one corner, to reduce the incidence of bubbles between the PDMS and transparency film . A piece of 1/8”-thick acrylic was then placed atop the transparency and a weight (~500–1000 g) was placed on the acrylic to press the stack together and remove residual PDMS prepolymer between the through-hole features and the transparency film. The use of the transparency and weight system during fabrication produces flat gaskets with complete through holes. The gaskets were cured overnight at 65 °C in an oven (Fisher Isotemp® Incubator 255D, Thermo Fisher Scientific, Hampton, NH, USA), the transparency film was carefully peeled off, and the gasket was then demolded and cut to size. After inspection with optical microscopy (Aven MicroVue Digital Microscope, Aven Tools, Ann Arbor, MI, USA), the gasket was ready for assembly with the photonic chip and mounting plate.
To assemble the setup for fluidic testing (Figure 6), the photonic chip was first placed in the machined recess of the mounting plate. A rectangular washer of the same dimensions as the fluidic gasket and with 4.5 × 2.5 mm rectangular holes aligned with the fluidic I/Os was custom laser-cut from ⅛” acrylic (McMaster-Carr, Elmhurst, IL, USA) using a Universal Laser Systems VersaLaser VLS2.30 laser cutter (Universal Laser Systems, Inc., Scottsdale, AZ, USA). 4–40 brass bolts (McMaster-Carr, Elmhurst, IL, USA) were threaded through the bolt holes in the acrylic washer (first, so that the washer sat against the bolt head) and the PDMS fluidic gasket to align the two pieces together. The bolts were then aligned with the threaded holes in the mounting plate and screwed into place to align and seal the fluidics against the photonic chip. The washer serves to provide even pressure to the flat PDMS gasket to maintain a good seal without a permanent plasma bond between the PDMS and the photoni
2.6. Bulk Sensitivity Testing
Bulk sensitivity measurements were performed by measuring the resonance wavelength shifts of the SWG MRRs during exposure to NaCl (Fisher Scientific S271-3, Thermo Fisher Scientific, Hampton, NH, USA) solutions with five different salt concentrations (0 M, 0.0625 M, 0.125 M, 0.250 M, and 0.375 M) and known refractive indices. The solutions prepared using ultra-pure water. The refractive indices of the solutions were measured with an Abbe refractometer (Spectronic Instruments, Inc., Rochester, NY, USA). From lowest to highest concentration, the measured refractive indices of the solutions were 1.3335, 1.3341, 1.3346, 1.3360, and 1.3373. It should be noted, however, that these are visible wavelength refractive indices and do not account for chromatic dispersion. The photonic chip was assembled with the microfluidic gasket and mounting plate, as described in Section 2.5. To perform the bulk refractive index sensing measurements, the photonic chip assembly was secured on the stage of the custom optical testing setup (Maple Leaf Photonics, Seattle, WA, USA) using thermally conductive tape. A Fluigent LineUp™ series fluid control system (Fluigent, Le Kremlin_Bicêtre, France) was used to supply fluid to the photonic chip assembly. Further details about this setup are provided in Section S2 of the Supplementary Materials.
Prior to the experiment, all tubing in the Fluigent system was primed with fluid by flowing the NaCl solutions at 500 mbar from each of the five reservoirs of both channels in sequence for two minutes each. The primed PEEK tubing (Idex 1531B, Cole-Parmer Canada, Quebec, QC, Canada) connected to the bubble trap outlets (Diba Omnifit® #006BT-HF, ColeParmer Canada, Quebec, QC, Canada) was then inserted into the microfluidic inlets of the PDMS gasket. Water was flowed continuously through the microfluidic channels at 10 µL/min until the beginning of the bulk refractive index sensing experiment. The fiber array, connected to the tunable laser and optical detectors, was aligned to the photonic chip, as described in Section 2.4.
During the experiment, the salt solutions were flowed over the MRR sensor via the two microfluidic channels in sequence at 30 µL/min for 20 minutes each. In the first replicate of the experiment, the salt solutions were flowed over the MRR sensor in order of ascending concentration, starting with water (0 M NaCl), followed by 0.0625 M, 0.125 M, 0.250 M, and lastly 0.375 M NaCl solutions. In the second replicate, the salt solutions were flowed over the MRR sensor in order of descending concentration. This was repeated four more times to reach a total of ten replicates. It is important to note that a known limitation of PDMS is that it can leach uncured oligomers into microchannels, with the oligomer concentration being inversely proportional to the flow rate . Given the relatively high flow rate of 30 µL/min used in this study (corresponding to a residence time of ~2 s in the microchannels), in addition to the considerable precedent for use of PDMS-based microfluidics in SiP assays [3, 28,71,90], oligomer leaching was expected to have a negligible effect on the bulk refractive index sensing experiments performed in this work. PDMS is also known to absorb small hydrophobic molecules, with absorption increasing with increasing residence time [91,92]. While not a concern in this study, which only used aqueous salt solutions and short residence times, this would be a relevant consideration in sensing assays using longer residence times and precious, low-concentration, and hydrophobic samples.
During the experiment, a custom Python acquisition script was used to sweep the tunable laser source over a 20 nm wavelength range (1540–1560 nm for the C-band devices and 1290–1310 nm for the O-band devices) and record the output transmission spectra from the photonic chip every 20–30 s. The fiber array alignment was monitored and adjusted every 30 sweeps using a fine align function to ensure good coupling to the on-chip grating couplers throughout the experiment.
Acquired optical spectra were analyzed using a custom Python script to Lorentzian-fit each resonance peak and track the cumulative peak shifts, generating plots and datasets of average resonance peak shift vs. time for each measured microring resonator sensor. Briefly, the custom Python script identified resonance peaks in the optical spectra and fit each resonance peak to a 4-parameter Lorentzian function (x-position of the peak center, height of the peak baseline, height of the peak, and peak width at vertical midpoint). It thus parameterized each resonance peak into a 4-element vector and each optical spectrum with n resonance peaks as an n × 4 matrix. It then matched resonance peaks in consecutively acquired spectra by computing the cosine similarity of the vectors , and computed the differential displacement in the x-position of the peak centers of the matched peaks. Finally, it averaged the computed differential displacement of all of the matched resonance peaks in the spectra to calculate the overall differential displacement for that sweep iteration (δλ). The overall resonance peak shift at time point i (∆λ(ti)) was calculated as the sum of all preceding displacements: ∆λ(ti) = ∑ i 1 δλ.
All resonances demonstrated a gradual blue drift throughout these experiments. Therefore, prior to further analysis, the peak shift data were drift-corrected by performing a linear fit to the baseline of each peak shift plot and subtracting this linear fit from the data. From the resonance peak shift vs. time data, the bulk refractive index sensitivity values were computed using a custom MATLAB script. The MATLAB script plotted the resonance peak shift vs. time data and prompted the user to click on the regions of the plot corresponding resonator response to each bulk refractive index standard saline solution. For each refractive index standard region, the script averaged the resonance peak shift data in a 20-timepoint region (corresponding to approximately 400s of acquisition) centered at the user’s click location. The bulk refractive index difference was computed as the difference between the measured refractive index of each refractive index standard saline solution and that of water. It then performed a linear regression on the peak shift vs. measured bulk refractive index difference (forcing zero intercept), and the slope of the linear regression was taken to be the bulk refractive index sensitivity.
2.7. SEM Imaging
A Zeiss Sigma scanning electron microscope (SEM, Carl Zeiss AG, Jena, Germany) was used to image the fabricated photonic chips. Imaging was carried out to compare the designed dimensions to the fabricated structures and identify any fabrication limitations or unexpected effects. In-lens and secondary electron detectors were used to take topview and angled-view (45◦ tilt) images of the photonic devices. ImageJ was used to measure the dimensions of the fabricated SWG waveguides on top-view SEM images taken at 50,000× magnification. For each geometrical parameter (w, Λ, δ, and wfb), five measurements were taken and then averaged to give a more representative estimation.
3.1. Simulation Overestimates In-Water Group Indices of SWG Waveguides
Silicon microring resonators with the waveguide geometries outlined in Table 1 were fabricated on a SOI wafer with no oxide cladding using ANT’s electron-beam lithography process . A circular ring geometry was used for the sensors instead of a racetrack geometry to eliminate mode-mismatch losses . All microrings were designed with a radius, R, of 30 µm, which was selected to ensure low bend losses [3,94]. To characterize the fabricated microring resonators, a tunable laser was coupled to the devices and their transmission spectra were collected while sweeping the wavelength of the input laser from 1530–1560 nm for the C-band devices or 1270–1310 nm for the O-band devices. This characterization was performed with a droplet of water fully covering the regions of the chip containing the resonators. The measurements were performed on five replicate chips and the measured spectra were analyzed using a custom script, as described in Section 2.4.
Table 2 reports the simulated and measured group indices and FSRs of the fabricated ring resonators. All measured group indices were lower than those predicted by simulations, with the boneless SWG devices generally exhibiting a slightly greater difference in ng between the measured and simulated values compared with the fishbone devices. Accordingly, the measured FSRs were greater than the simulated values for all geometries.
Our group has previously fabricated boneless SWG microring resonators using the identical geometry as design C6 from this work, using a different electron-beam lithography fabrication process . Previously, 30 µm-radius ring resonators fabricated with this waveguide geometry (Λ = 250 nm, δ = 0.7, w = 500 nm, t = 220 nm) exhibited an experimental ng of 3.27 and FSR of 3.936 nm, which align well with the simulated values reported here. This indicates that simulation inaccuracies are unlikely to be the source of variation in ng and FSR between the simulated and measured results. Instead, these variations are likely attributable to experimental factors, such as differences between the designed and fabricated structures. In particular, we hypothesized that the low experimental group indices may be due to smaller-than-designed feature sizes on the fabricated chips. To test this hypothesis, SEM imaging was performed on the fabricated structures and feature sizes were measured
Another possible explanation for the low experimental group indices is incomplete wetting of the SWG structures. Nanostructured surfaces can be susceptible to this phenomenon, which leads to the entrapment of air between narrow features during wetting . As such, air may have been trapped between the silicon pillars when the photonic chips were coated with water for measurements. Because air has a lower refractive index than water, this is expected to decrease neff . The group index can be related to neff according to ng(λ) = ne f f(λ) − λ· dne f f /dλ , where dne f f /dλ < 0 for the designed waveguides. While the first term of this equation should decrease in the case of incomplete wetting, the magnitude of the second term should also decrease when air is added to the SWG metamaterial, as air is less dispersive than water . Depending on the relative effect of trapped air on these two terms, incomplete wetting may cause a decrease in ng. To theoretically test this hypothesis, simulations were performed with fishbone SWG design C1 in which the gaps between the silicon pillars were filled with air up to a height tair (Figure S2). The fabricated waveguide geometry, as measured from SEM images, was used. Further details regarding these simulations are provided in the Supplementary Materials (Section S3). These simulations showed that the combination of reduced feature sizes and air entrapment considerably reduced ng and an increase in tair led to a decrease in ng (Figure S3). An air pocket height of tair = 120 nm yielded ng = 2.825, which is very close to the experimentally measured value of ng = 2.83. It should be noted that this model does not account for the curvature of the air–water interfaces enclosing the air pocket. Regardless, these simulation results suggest that the low experimental ng values may, indeed, be the result of incomplete wetting. Similarly to stiction during drying, incomplete wetting can cause deformations and damage to structures adjacent to the trapped air due to capillary pressure . This may have contributed to the feature collapse seen in Figure 7c. Another similar phenomenon that may have contributed to the low group indices is nanobubble formation on the waveguide surfaces due to etch roughness . The presence of a thin native oxide layer on the waveguide surface is yet another factor that may have contributed to these results .
3.2. Empirical Characterization of Extinction Ratio vs. Coupling Gap Reveals Insights for Further Optimization and Highlights Performance Degradation Due to Peak Splitting
Critical coupling is achieved when the coupling gap, gc, between the bus waveguide and ring resonator is such that the power coupled into a ring resonator is equal to the round-trip losses in the ring . At critical coupling, the extinction ratios (ERs) of the resonance peaks are maximized, thus enhancing the signal-to-noise ratio; this is a desirable condition for robust peak tracking and sensitive analyte detection . When gc is relatively small, the resonator is over-coupled, giving rise to increased power losses. This decreases both ER and Q. When gc is relatively large, the resonator is under-coupled, which increases Q, but decreases ER. Indeed, under-coupling can be used to enhance iLoD, although a tradeoff with ER exists for noisy systems that necessitate higher ERs for robust peak tracking . In this work, we aimed to optimize ER to facilitate straightforward extraction of the sensor intrinsic quality factor for comparison with propagation loss simulations, as well as facilitate meaningful comparison to previously reported sensors operating near critical coupling [3,21,28]. Subsequent system design (building upon the optimization framework presented here) should consider the tradeoff between Q and ER in choosing the best coupling condition for the application, and may choose to under-couple the resonators.
To achieve critical coupling, gc can be selected based on numerical simulations. For example, the critical coupling condition can be estimated based on simulated coupling coefficients extracted from FDTD simulations of the entire coupling region, along with simulated propagation losses [20,101]. However, one drawback of this approach is that FDTD simulations of the coupling region are very computationally intensive for SWG resonators. Additionally, while these FDTD coupling coefficient and loss simulations account for loss contributions due to material absorption and substrate leakage, they often do not accurately recapitulate the effects of optical scattering, which depend on the surface roughness of the fabricated waveguides and can increase losses and affect the coupling condition . Scattering has an increased effect on SWG waveguides compared to conventional strip waveguides owing to the increased surface area of SWG structures [3,39]. Considering these limitations, we decided to take an empirical approach to optimize gc for close-to-critical coupling.
Each resonator was fabricated with four different coupling gaps. The fabricated coupling gaps for the C-band devices were based on our group’s previous empirical findings for conventional SWG ring resonators with similar expected effective indices. As outlined in Table 1, coupling gaps of gc = 450, 500, 550, and 600 nm were fabricated for devices C1, C2, C4, and C5, which had simulated effective indices between 1.70–1.71. Smaller coupling gaps of gc = 400, 450, 500, and 550 nm were selected for C3 and C6 due to their greater predicted effective indices and, therefore, increased optical confinement. It has been reported that coupling increases with increasing wavelengths due to reduced optical confinement at the defined waveguide geometry of w = 500 nm and t = 220 nm . As such, smaller coupling gaps were selected for the O-band devices, relative to their predicted effective indices. Coupling gaps of gc = 400, 450, 500, and 550 nm were fabricated for O1 and O4, whereas coupling gaps of gc = 350, 400, 450, and 500 nm were fabricated for O2 and O3 due to their higher simulated effective indices.
The extinction ratios for all resonator designs were measured, as described in Section 2.4, and the results are presented in Figure 8 and Table 3. This characterization was performed for five replicate chips and mean values are reported. Details regarding the number of resonance peaks included from each chip in each mean calculation are provided in Section S4, Table S1. As shown in Figure 8b, all C-band devices, excluding C3, exhibited maximum extinction ratios at their largest coupling gaps. Consequently, it cannot be concluded that critical coupling was achieved for these devices, and future work should include the fabrication of these resonators with larger coupling gaps to avoid over coupling. In SEM images, the measured coupling gaps were 20–40 nm smaller than designed, which may be related to proximity effect correction in the lithography process . This may have contributed to this requirement for larger coupling gaps. As illustrated in Figure 8c, devices O1, O2 and O3 exhibited maximum extinction ratios at intermediate values of gc within their fabricated ranges. However, the variations in extinction ratio between different values of gc are similar in magnitude to the standard deviations of the measurements, so these results may not confirm critical coupling. Resonator O4 achieved an extinction ratio at its largest fabricated coupling gap, further highlighting that future work should extend the coupling gap ranges investigated here
Quality factors for the fabricated ring resonators were calculated from the measured spectra, as described in Section 2.4, and the results are provided in Table 4. For the C-band devices, the simulated quality factors were 1.3–1.6 times as large as the experimental values. This difference between simulated and experimental values is likely due to scattering and coupling losses, which were not accounted for in the simulations. Scattering losses arise due to roughness introduced on the waveguide surfaces during fabrication, which makes them challenging to model. These losses are typically non-negligible for SWG waveguides owing to their large surface area [3,94]. Next, overcoupling leads to greater optical losses compared to critical coupling . As discussed in the previous section, many of the C-band resonators were likely overcoupled, giving rise to this loss mechanism. Since the simulated quality factors were calculated based on the critical coupling assumption, these losses are another likely source of variation between the simulated and experimental results. It should be noted that the propagation loss simulations described in this work also did not include bending losses. Based on previously reported results, we expected negligible bending losses at the large ring radius of 30 µm considered here .
The simulated quality factors for the O-band resonators ranged from 4.40 × 104 to 5.11 × 104 , whereas the experimentally measured values were 6.3–7.2 times lower (Table 4). While scattering and coupling losses, combined with the smaller-than-designed feature sizes of the fabricated structures, likely contributed to this discrepancy, peak splitting appeared to be the dominant source of this variation. In an ideal ring resonator, there exist two counterpropagating circulating modes, clockwise and counterclockwise, which are uncoupled, and degenerate, meaning they resonate at the same frequency [104,105]. In this case, the resonator exhibits single peaks. A small mode perturbation, however, can couple these modes and break their degeneracy leading to a resonance shift that manifests as split resonance peaks [20,103,104]. In silicon waveguides, this perturbation typically occurs due to stochastic backscattering arising from sidewall roughness [20,103,104]. In the spectra measured for all O-band resonators, peak splitting was prevalent, comprising 18–51% of all resonances. Conversely, split peaks were far less common in the C-band resonator spectra, comprising roughly 2–12% of all resonances. While all resonators studied in this work were fabricated using the same foundry process and, therefore, were subject to similar sidewall corrugations, the exaggerated peak splitting observed among the O-band devices suggests that sidewall scattering is exacerbated at lower wavelengths. This is consistent with analytical models for scattering losses in which the losses are proportional to the square of the ratio of surface roughness to the wavelength of light in the material . Thus, the effects of scattering, and therefore, peak splitting, increase with decreasing wavelength. Additionally, the higher water absorption at 1550 nm may be hiding peak splitting, whereas a 10× lower water absorption at 1310 nm would reveal scattering induced peak splitting.
The analysis script used to extract the quality factors from the measured spectra performed Lorentzian fitting on the resonance peaks to measure the FWHM, from which the quality factors were calculated. In the case of split peaks, the Lorentzian was typically fit to the doublet, leading to an underestimation of Q (Figure 9). In this analysis, a R2 cutoff of 0.85 dictated which peaks were used in the calculation of Q. The split peaks typically exhibited poor R2 values compared with single peaks (Figure 9b); however, there was considerable overlap, with some apparent split peaks exhibiting higher R2 values than some single peaks (Figure 9c). However, it should be noted that some peaks, such as the one shown in Figure 9c, exhibited apparent peak splitting that had a similar magnitude to the spectral noise, making it challenging to confidently confirm the identity of these peaks as split or non-split. Biosensors 2022, 12, x FOR PEER REVIEW 24 of 35 given spectrum, it may also be challenging to confirm the identity of split peaks with high confidence. Overall, the prevalence of these split peaks is likely to cause deleterious effects in the analysis of binding assays. Therefore, a more robust solution for improving sensor performance is to des