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Cost-effective silicon-photonic biosensors using doped silicon detectors and a broadband source

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Abstract

We propose and demonstrate a cost-effective, microring-based, silicon photonic sensor that uses doped silicon detectors and a broadband source. Shifts in the sensing microring resonances are electrically tracked by a doped second microring, which acts as both a tracking element and a photodetector. By tracking the power supplied to this second ring, as the sensing ring’s resonance shifts, the effective refractive index change caused by the analyte is determined. This design reduces the cost of the system by eliminating high-cost, high-resolution tunable lasers, and is fully compatible with high-temperature fabrication processes. We report a bulk sensitivity of 61.8 nm/RIU and a system limit of detection of 9.8x10-4 RIU.

© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement

1. Introduction

Miniaturized biosensing devices are crucial for the advancement of global healthcare as they offer fast, reliable, and affordable detection [1,2]. Services that are typically performed in a lab can be combined into a single compact device allowing for a cost-effective sensor that can produce results using an extremely small sample. Silicon-based photonic sensors can perform real-time, label-free measurements, eliminating long wait times [3]. These devices have been shown to detect various pathogens and disease markers, including breast and lung cancer [4,5], neurodegenerative disorders [6], and SARS-CoV-2 [7]. Also, these sensors are compatible with complementary-metal-oxide-semiconductor (CMOS) fabrication processes, which can be leveraged to produce silicon photonic sensors at a very low cost [8,9]. Finally, the silicon photonic sensors presented here hold the additional promise of reducing the cost of the overall measurement system. Current signal interrogation configurations for silicon photonic sensors require an expensive, high-resolution, tunable laser or optical spectrum analyzer, which inhibits their widespread use, especially for point-of-care diagnosis. Additionally, on-chip photodetectors must be implemented in a way that simplifies electronic controls and keeps costs to a minimum. Some alternatives to tunable lasers have been suggested, such as fixed wavelength laser systems [1013]; however, intensity-interrogation systems are often very sensitive to fluctuations in input optical power from the laser-source and either coupling or on-chip losses, which can result in decreased sensing performance [14,15]. Another fixed wavelength laser architecture is introduced in [16], but measurement results are not provided.

In this paper, rather than improving the performance of the individual components, we propose and demonstrate a low-cost silicon photonic sensor that uses doped silicon detectors and a broadband source, thus eliminating the need for spectrum analyzers, tunable lasers, and/or germanium photodetectors (Ge PDs). The approach demonstrated here uses an in-resonance photoconductive heater-detector (IRPHD) [17] to electrically track the output of a sensing microring, while also acting as the PD detecting the signal. As compared to Ge PDs, IRPHDs: (1) reduce the overall cost of photonic biosensors; (2) reduce the number of pads for electrical I/O by half (from four pads required by the Ge PD system [18] to only two pads required by the IRPHD system [19]), thus reducing the on-chip real-estate; (3) have higher quantum efficiencies [17,20]; (4) can be used to monitor the optical power inside the ring and can thus generate high photocurrents across a large optical dynamic range [17]; (5) are compatible with high-temperature CMOS fabrication processes. We demonstrate this method by first using thermally-tuned microrings in simulated biosensing experiments to compare the IRPHD performance to a Ge PD, and, second, in real-time sensing measurements of isopropyl alcohol, reporting a sensitivity of 61.8 nm/RIU and a system limit of detection of 9.8x10-4 RIU. The results demonstrated here are similar to those of other, higher-cost implementations [3].

2. Operating principle

Song et al. suggested a voltage scanning method using a tracking microring that electrically tracked the changes in the sensing microring [18]. Figure 1(a) shows the layout of the photonic sensor that was proposed by Song et al. [18]. As in Tsuchida [21], who used broadband, incoherent light sources to characterize optical resonators, this system uses a broadband light source as the input to the sensing micoring. The drop-port of the sensing microring is then coupled to the tracking microring. To align the resonances of these two rings, an initial electrical power is applied to the heater above the tracking microring. If a photodetector is placed at the drop port of the tracking microring, an optical signal will be detected by the photodetector. The strength of the signal from the photodetector is an indication of the alignment of the resonances of the tracking and sensing microring. When the resonance of the sensing ring is perturbed due to an interaction with an analyte, the transmission spectra of the rings will be misaligned, and a low output signal will be measured. To realign the resonances, the electrical power applied to the tracking ring is adjusted. By monitoring the change in the applied electrical power required to maximize the signal in the photodetector, which ensures that the two resonances (that of the sensing and the tracking rings) are aligned, the wavelength resonance shift caused by the analyte exposure can be determined.

 figure: Fig. 1.

Fig. 1. Layout and simulations of the photonic sensor consisting of two microrings, a sensing ring and a tracking ring. (a) The architecture presented by Song et al. [18] and (b) the architecture we are proposing in this paper, which replaces the Ge PD and 4 pads with a single IRPHD and 2 pads (for both tuning the heater and detecting the optical power). A cross-section of the IRPHD tracking microring is shown as an inset in the subfigure. (c) The optical spectrum that will be sensed by the IRPHD in (b), above, and by the Ge PD in (a), above. (d) The integrated power that will be measured by the IRPHD (in (b)) and by the Ge PD (in (a)) as functions of the electrical power that is applied to either of the heaters. In both (c) and (d), the optical power is normalized to the power in the input waveguide (as indicated by the light source in (a) and (b)).

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Figure 1(b) shows our proposed architecture, where, instead of using a Ge PD at the drop port of the tracking ring, we place the photodetector inside the tracking ring as detailed in [19]. By doping the waveguides, an IRPHD [22] is formed, which acts as both a heater and a photodetector. This has several advantages. First, a Ge PD is not needed anymore since the IRPHD will act as a heater and detector. Second, the pads associated with the Ge PD will be unnecessary and thus will be eliminated, resulting in a smaller sensor footprint. Third, since the IRPHD detects the light inside the ring, the optical power built-up can be orders of magnitude higher than the light detected by the Ge PD, as indicated in Fig. 1(c) and Fig. 1(d). The optical power inside the ring (on resonance), $P_\text {inner}$ can be expressed as

$$P_\text{inner} = \frac{\kappa_1\sqrt{\gamma}}{\left(1-\gamma\sqrt{(1-\kappa_1)(1-\kappa_2)}\right)^2}$$
where $\kappa _1$ is the cross-power coupling coefficient of the input bus coupler, $\kappa _2$ the cross-power coupling coefficient of the bottom coupler, $\gamma$ is the ring’s field round-trip transmission and is given by $\gamma =10^{-\alpha L/20}$, where $\alpha$ is the propagation loss inside the ring in dB/cm. The optical power at the drop port of the ring (on resonance) is expressed as
$$P_\text{drop} = \frac{\kappa_1\kappa_2\gamma}{\left(1-\gamma\sqrt{(1-\kappa_1)(1-\kappa_2)}\right)^2}$$
Thus, the ratio of the power inside the ring to the power at the drop port is given by
$$\frac{P_\text{inner}}{P_\text{drop}} = \frac{1}{\kappa_2 \sqrt{\gamma}}$$
This means that the smaller $\kappa _2$ is, more power stays in the ring cavity, the larger the optical power built-up inside the ring, and thus, the higher the optical signal read-out from a photodetector inside the ring compared to that placed at the drop port of the ring. Figure 1(c) and Fig. 1(d) compare the optical powers sensed by the Ge PD and the IRPHD as functions of wavelength, and electrical heater power, respectively. In our current configuration, $\kappa _2$ was set to 0.1 and the transmission inside the ring was set to unity, therefore the optical power sensed by the IRPHD is 10 times the optical power sensed by the Ge PD, as shown in Fig. 1(d). It is worth mentioning that Ge PDs have a responsivity of 0.8 A/W [23], which is higher than that of our IRPHDs. IRPHDs have a responsivity that varies with the voltage applied across the IRPHD as well as the optical power impinging on the IRPHD. However, due to their high quantum efficiencies, IRPHDs can generate much larger photocurrents with minimal optical power absorbed, especially when placed inside the ring [17], where the optical power can be several orders of magnitudes higher than that at the drop port.

3. Device design, fabrication, and experimental setup

The photonic sensor shown in Fig. 1(b) consists of two microrings in a Vernier configuration, a sensor and a tracker, with radii of 10 and 8 microns, respectively. This corresponds to rings free-spectral ranges (FSRs) of 9.1 nm and 11.4 nm, respectively. The overall rings’ FSR due to the Vernier’s configuration is $\sim 50$ nm. The rib waveguides used in our IRPHD and microring were formed using 500 nm and 220 nm core widths and heights, respectively, with a 90-nm thick slab (as indicated by the inset in Fig. 1(b)). The tracking ring had a straight-ring gap of 200 nm, which resulted in a cross-power coupling strength of $\sim$11%. The measured 3-dB bandwidth was $\sim$42 GHz, giving a quality factor of $\sim$4600. The IRPHD waveguide core was n-doped with a concentration of $5\times 10^{17}$ cm-3 and the sides were n++ doped to form Ohmic contacts. While the n-type doping in the waveguide core is low enough to allow for low-loss (doping loss = 5 dB/cm) propagation [17], it is sufficient to: (1) lower the electrical resistance across the waveguide, enabling the device to function as a thermo-optic tuner over appreciable wavelength ranges driven by the low voltages compatible with CMOS circuitry; (2) increase the measurable photocurrent to micro-amperes (for micro-watt input optical powers), allowing the device to also function as a precise power monitor inside our optical circuit. To operate as a photodetector, current-voltage (IV) curves of the IRPHD are taken with and without light in the circuit. By subtracting the curves, we can get a direct measurement of the photocurrent [22]. In our sensing system, since the IRPHD photocurrent is maximized when the sensing and tracking rings’ resonances are aligned, the power applied to the IRPHD tracking ring is proportional to the analyte perturbing the microring.

Figure 2(a) displays a block diagram of the experimental setup. A LUXMUX BeST-SLED was used as our optical broadband source. Since the FSRs of the sensing and tracking microrings are not identical, other resonance peak overlaps are possible. To ensure only a single resonance mode overlap, we used a 6 nm bandpass tunable filter (BPTF) followed by an erbium-doped fiber amplifier (EDFA); The EDFA compensates for both the BPTF and the on-chip grating coupler losses, and was placed after the BPTF due to the gain saturation of the EDFA. Although some work can be done to match the FSRs of the microrings, the peaks will remain aligned only over a narrow wavelength range. The group indices of the sensing and tracking microrings will be different because of their cladding materials (water vs oxide), causing two independent FSRs as a functions of wavelength. A filter will always be needed as long as the broadband source’s spectrum is larger than the microring FSRs. In the future, an on-chip BPF could be utilized [24,25]. Our devices were fabricated using 248 nm optical lithography at the Advanced Micro Foundry (previously A*STAR IME) in Singapore. Fig. 2(b) shows an optical microscope image of a test device, which included a Ge PD that was used for a comparison to the IRPHD.

 figure: Fig. 2.

Fig. 2. (a) Block diagram of our experimental setup, with measured spectrum shown to the right. An SLED broadband source was filtered using a bandpass tunable filter (BPTF) and amplified by an erbium-doped fiber amplifier (EDFA), before being coupled to the chip. (b) Optical microscope image of a test device. Here we include a thermally-tunable ring to simulate a biosensing experiment, and a germanium photodetector (Ge PD) to compare to our doped photodetectors (IRPHDs).

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4. Experimental results and analysis

As a proof-of-concept, we simulated a biosensing experiment by replacing the sensing ring with an electrically tunable microring. By setting the voltage of the sensing microring, while scanning the voltage of the tracking microring, a simulated bio-experiment was performed. Figure 3(a) shows the IRPHD photocurrent as a function of the tracking microring voltage for various sensing microring voltages (Vsensor). Since a measured dark current curve was subtracted from the photocurrent curves, as described in [17], and due to small fluctuations over time, some of the curves display negative values. Furthermore, the peak photocurrent value decreases due to the decreased quantum efficiency at higher voltages [17]. The sensitivity was extracted from this curve in units of Wtracker/Vsensor, where Wtracker represents the power consumed in the tracking microring. To convert sensitivity ($S_\text {MRR}$) into units of Wtracker/RIU, we can use the following equation:

$$S_\text{MRR} \left[ \frac{\text{W}}{\text{RIU}} \right] = \frac{S_\text{MRR} \left[ \frac{\text{W}}{\text{V}} \right] \times \frac{\delta \lambda}{\delta n_\text{eff}} \times \frac{\delta n_\text{eff}}{\delta n_\text{clad}} }{\frac{\delta \lambda}{\delta V}}$$
The change in resonant wavelength due to the change in voltage ($\frac {\delta \lambda }{\delta V}$) can be extracted by monitoring the transmission of the microring as various voltages are applied to the IRPHD. The change in resonance wavelength due to a change in the effective index ($\frac {\delta \lambda }{\delta n_\text {eff}}$) can be calculated using $\Delta \lambda _\text {res} = \frac {\lambda }{n_\text {g}}\Delta n_\text {eff}$. In this experiment, the change in effective index is due to the temperature change in both the core and cladding of the waveguide; however, in standard sensing measurements, the effective index change would only be due to the cladding index change. To account for this, we multiplied by the waveguide mode sensitivity ($\frac {\delta n_\text {eff}}{\delta n_\text {clad}}$), which describes the change in effective index due to a change in the cladding index, and was extracted from our simulations. Using this conversion, a sensitivity of 0.98 W/RIU was determined.

 figure: Fig. 3.

Fig. 3. (a) The IRPHD photocurrent difference as compared to the dark current as a function of the tracking ring voltage at various sensing ring voltages (indicated as legends on the line plots). (b) Tracker voltage to maximize the photocurrent from each photodetector (IRPHD and Ge PD) at various sensing ring voltage setpoints across time, implemented using a maximum search algorithm (the dither signal can be seen).

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Sensitivity values for silicon photonic sensors are typically reported in units of nm/RIU. This conversion can be made using:

$$S \left[ \frac{\text{nm}}{\text{RIU}} \right] = S \left[ \frac{\text{W}}{\text{RIU}} \right] \times \frac{\delta \lambda}{\delta P} \left[ \frac{\text{nm}}{\text{W}} \right]$$
where $\delta \lambda / \delta P$ is the change in wavelength due to a change in applied power. This can be determined by monitoring the output transmission as a function of applied power. For this design, the extracted value was 80 nm/W. This gave a sensitivity of 78.8 nm/RIU.

The high dynamic ranges of IRPHDs suggest that low optical input powers (<-30 dBm) can be detected. To compare and contrast the IRPHD performance to that of the Ge PD, we tuned the sensing microring in real-time and tracked the voltage change of the tracking microring, once by maximizing the IRPHD photocurrent and once by maximizing an on-chip Ge PD (placed at the drop port of the tracking microring (Fig. 2(b)). Figure 3(b) shows the real-time tracking, for the IRPHD and the Ge PD, using a maximum search algorithm [22]; similar performance was obtained, suggesting that the IRPHDs are suitable in a sensing system.

To investigate the limit of detection of the system beyond the work described in [19], the noise of the IRPHD was extracted from Fig. 3(b), as was the noise of the Ge PD. Figure 4 displays the noise floor of the power at the maximum current for each detector. After detrending, a 110 $\mathrm {\mu }$W and 51 $\mathrm {\mu }$W standard deviation was obtained for the IRPHD and Ge PD, respectively, indicating a detection limit of 3.4$\times$10-4 RIU and 1.6$\times$10-4 RIU, respectively. While the Ge PD has slightly better performance compared to the IRPHD, both limit of detections are similar to values reported for other silicon photonic sensors, which range from 10-3 to 10-6 RIU [3]. Furthermore, the noise reported here is significantly higher than the intrinsic noise for both PDs [26], as well as the source-measurement unit that was used to measure the detectors’ photocurrents. The rms noises of the Ge PD and the IRPHD are much smaller than the values reported here (see [17,23]), however, the values reported here more closely resemble the limit of detection of our system, as the fluctuations shown in Fig. 3(b) are due to the locking algorithm used to track the tracking ring resonance which, as a result, limits the detection of our system. By further improving the locking detection algorithm, a lower limit of detection could be obtained.

 figure: Fig. 4.

Fig. 4. System noise of the (a) IRPHD architecture and (b) GePD architecture, extracted from Fig. 3(b). Histogram of noise distribution with standard deviation results.

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A second test device was fabricated with the oxide removed from the sensor microring, allowing it to be directly exposed to sample analytes, which had previously not been investigated in [19]. The performance of the sensor was characterized by using a series of isopropyl alcohol (IPA) dilutions from 0% to 20% v/v (Fig. 5). The voltage corresponding to the maximum IRPHD photocurrent was recorded for each IPA concentration by sweeping the applied voltage of the tracking microring, obtaining a bulk sensitivity of 101.7 V/RIU (61.8 nm/RIU) and a limit of detection of 9.8$\times$10-4 RIU. Although this sensitivity is lower than the state-of-the-art microring sensors [3], it is similar to standard TE microring sensitivities. Since these experiments were designed to validate the IRPHD as the tracking microring and detector, no effort was made to optimize the performance of the sensing microring. However, the sensitivity and limit of detection of this system could be improved by replacing the simple TE strip waveguide with TM, slot, or SWG rings, which have been shown to produce higher sensitivities [3]. Furthermore, by optimizing the coupling method and efficiency of the broadband source to the chip (such as using edge couplers in place of the current grating couplers), the SNR can be increased, further lowering the limit of detection.

 figure: Fig. 5.

Fig. 5. Sensogram of the sensor/IRPHD system response to the introduction of IPA dilutions to the sensing ring. For the $\sim$28 mW operating point of our IRPHD, a sensitivity of 101.7 V/RIU (or 61.8 nm/RIU) was extracted.

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5. Results discussion and system optimization

By using a broadband source, rather than a tunable laser, the cost of implementing silicon photonic sensor systems is significantly reduced. Furthermore, in a tunable laser architecture, the system limit of detection is constrained by the resolution of the laser. In order to lower the limit of detection, the wavelength resolution of the laser must be increased, which further increases costs. In broadband source architectures, the limit of detection is dictated by the resolution of the power supply, which can be increased in a much more cost-effective way.

A broadband source can also simplify the coupling process in multiplexing systems. Designs that include multiple sensors need methods to couple light to each sensor. One such technique, implemented by Genalyte, Inc., uses a mechanical mirror system to focus laser light onto and from grating couplers for each sensor [27]. While very precise and effective, these additional components add cost, size, and complexity to the system. In lieu of using mechanical coupling systems, both the tunable laser and broadband coupling will be limited by the number of input channels that can be be attached to the chip. In order to route light to multiple sensors, the light needs to be split on chip. This reduces the optical power available to each sensor, and can reduce performance. While the optical power can be scaled, laser amplification significantly increases the noise [28], thus reducing sensor performance.

Furthermore, the sensor-tracker broadband source architecture does not have to suffer from reduced optical power when multiplexing, since only a small portion of the total bandwidth of light is used for each sensor. Instead of splitting the optical power, this system could split the light based on wavelength, sending separate wavelength bands to each sensor. The broadband source used in our experiments has a bandwidth of 35 nm, however, we only use a small portion of the available bandwidth (corresponding to the band over which the sensor and tracker FSRs remain similar). In these experiments, a single 6 nm window was used due to the limitations of the off-chip BPTF. By moving to on-chip bandpass filters [24,25], multiple filters centered at different frequencies could be implemented, allowing for a multiple sensor design (Fig. 6). The number and bandwidth of the filters will depend on the expected sensor range (i.e., the maximum resonant wavelength shift from an expected RIU shift), the Q-factor, and the bandwidth of the broadband source. This design offers the benefits of multiplexing without sacrificing the optical power in each ring.

 figure: Fig. 6.

Fig. 6. Proposed multiplexing system. Each on-chip contradirectional coupler (CDC) filter can be centered at a different wavelength, allowing for different light bands to be coupled to each sensor. Each sensor ring has its own IRPHD to track transmission shifts.

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Additionally, using IRPHDs in place of Ge PDs broadens the range of applications in two ways. Firstly, rapid prototyping foundries (such as AMO and Applied Nanotools Inc. [29]) often do not have germanium available in their fabrication processes. By replacing Ge PDs with IRPHDs, designers can create fully functional sensor systems, that do not rely on off-chip detectors, at a fraction of the turnaround time for tapeouts with traditional CMOS foundries [30]. Secondly, the high temperature processing required to grow germanium on silicon introduces challenges when integrating with CMOS processes [3134], although several foundries have solved these challenges, to various degrees [35,36]. In the future, the control for the sensor could be accomplished using an electronic CMOS circuit integrated onto the same chip as the sensor, further reducing costs. Since IRPHDs do not require high temperature processing, they will enable silicon photonic sensors to be fully integrated with CMOS devices, allowing for low-cost fabrication, and an overall more cost-effective sensing platform.

6. Summary and conclusion

We proposed and demonstrated a cost effective, CMOS-compatible silicon photonic sensor that uses a broadband source and doped silicon detectors. We demonstrated a bulk sensitivity of 61.8 nm/RIU with a system limit of detection of 9.8x10-4 RIU. Further work includes lowering this limit, as it is currently bound by the system noise and is much higher than the intrinsic limit. In addition, future work can consider including the optical bandpass filter on the chip, for a more complete solution [24,25]. By integrating bandpass filters on chip, this design can be used for analyte multiplexing. Overall, this design is promising for affordable sensing system as it eliminates the need for high-resolution tunable lasers and utilizes photodetectors that are compatible with high-temperature CMOS processing and rapid prototyping foundries.

Funding

Natural Sciences and Engineering Research Council of Canada (2014-05271, 414122-12).

Acknowledgements

This work was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) (2014-05271, 414122-12). Access to CAD tools was facilitated by CMC Microsystems, and the broadband SLED source was provided by Luxmux, for which we are very grateful.

Disclosures

The authors declare no conflicts of interest.

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Figures (6)

Fig. 1.
Fig. 1. Layout and simulations of the photonic sensor consisting of two microrings, a sensing ring and a tracking ring. (a) The architecture presented by Song et al. [18] and (b) the architecture we are proposing in this paper, which replaces the Ge PD and 4 pads with a single IRPHD and 2 pads (for both tuning the heater and detecting the optical power). A cross-section of the IRPHD tracking microring is shown as an inset in the subfigure. (c) The optical spectrum that will be sensed by the IRPHD in (b), above, and by the Ge PD in (a), above. (d) The integrated power that will be measured by the IRPHD (in (b)) and by the Ge PD (in (a)) as functions of the electrical power that is applied to either of the heaters. In both (c) and (d), the optical power is normalized to the power in the input waveguide (as indicated by the light source in (a) and (b)).
Fig. 2.
Fig. 2. (a) Block diagram of our experimental setup, with measured spectrum shown to the right. An SLED broadband source was filtered using a bandpass tunable filter (BPTF) and amplified by an erbium-doped fiber amplifier (EDFA), before being coupled to the chip. (b) Optical microscope image of a test device. Here we include a thermally-tunable ring to simulate a biosensing experiment, and a germanium photodetector (Ge PD) to compare to our doped photodetectors (IRPHDs).
Fig. 3.
Fig. 3. (a) The IRPHD photocurrent difference as compared to the dark current as a function of the tracking ring voltage at various sensing ring voltages (indicated as legends on the line plots). (b) Tracker voltage to maximize the photocurrent from each photodetector (IRPHD and Ge PD) at various sensing ring voltage setpoints across time, implemented using a maximum search algorithm (the dither signal can be seen).
Fig. 4.
Fig. 4. System noise of the (a) IRPHD architecture and (b) GePD architecture, extracted from Fig. 3(b). Histogram of noise distribution with standard deviation results.
Fig. 5.
Fig. 5. Sensogram of the sensor/IRPHD system response to the introduction of IPA dilutions to the sensing ring. For the $\sim$28 mW operating point of our IRPHD, a sensitivity of 101.7 V/RIU (or 61.8 nm/RIU) was extracted.
Fig. 6.
Fig. 6. Proposed multiplexing system. Each on-chip contradirectional coupler (CDC) filter can be centered at a different wavelength, allowing for different light bands to be coupled to each sensor. Each sensor ring has its own IRPHD to track transmission shifts.

Equations (5)

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P inner = κ 1 γ ( 1 γ ( 1 κ 1 ) ( 1 κ 2 ) ) 2
P drop = κ 1 κ 2 γ ( 1 γ ( 1 κ 1 ) ( 1 κ 2 ) ) 2
P inner P drop = 1 κ 2 γ
S MRR [ W RIU ] = S MRR [ W V ] × δ λ δ n eff × δ n eff δ n clad δ λ δ V
S [ nm RIU ] = S [ W RIU ] × δ λ δ P [ nm W ]
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