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Abstract
We report experimental results of an interferometric chemical sensor integrated on a silicon chip. The sensor measures refractive index variations of the liquid that contacts exposed spiraled silicon waveguides on one branch of a Mach-Zehnder interferometer. The system requires neither laser tuning nor spectral analysis, but a laser at a fixed wavelength, and a demodulation architecture that includes an internal phase modulator and a real-time processing algorithm based on multitone mixing. Two devices are compared in terms of sensitivity and noise, one at 1550 nm wavelength and TE polarization, and an optimized device at 1310 nm and TM polarization, which shows 3 times higher sensitivity and a limit of detection of 2.24·10−7 RIU.
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1. Introduction
In the last years, the development of integrated photonic biochemical sensors has been remarkable, spanning many applications such as clinical diagnosis, food safety, and surveillance for chemical and biological warfare [1]. In the biomedical field, for example, non-invasive techniques for cancer screening and diagnosis are challenging objectives, which lately has been investigated by using photonic integrated technology, in addition to electrochemical and micro-mechanical devices [2]. The capability to provide reliable real-time measurements with high sensitivity, resolution and integrability is one of the advantages of integrated photonic sensors. In particular, silicon photonics stands out as a technological platform with a great potential for high production volumes at a remarkably low cost per chip. This cost-effectiveness makes it possible to dispose of the device after a single or a few measurements, opening possibilities for a variety of lab-on-chip point-of-care applications. In addition, the great increase in the availability of fabrication platforms around the world makes prototyping new devices much easier than before.
To make a photonic chemical sensor for a liquid, light propagating through the waveguide must interact with the liquid containing the analyte. This is typically achieved by removing the top cladding of the waveguide and exposing the core to the liquid, making light interact with the liquid through its evanescent field. Changes in refractive index of the liquid translate into a change in the phase of the light which can be measured by using photonic devices such as interferometers, ring resonators, photonic crystals, etc [3]. To make the sensor specific to a target molecule, the surface of the waveguide can be functionalized with a substance that chemically binds only to that molecule.
The main problem of the evanescent coupling is that it typically has low responsivity, because a change of the refractive index of the liquid generates a change in the guiding effective index which is quite small. In silicon photonic waveguides with typical dimensions of 220 × 500 nm2, the responsivity is around 17% for transverse-electric (TE) polarization and 1550 nm wavelength. It is well known that transverse-magnetic (TM) polarization provides a higher responsivity (by a factor around 2 to 3), with the additional advantage that the evanescent field is higher along the top surface of the core. To maximize sensitivity, TM polarization is a better choice, as shown in previous works [4,5,6,7], even though it is not the standard polarization in most available building blocks.
The choice of the wavelength is also important; silicon waveguides are transparent in wavelengths longer than 1.1 µm. The C-band, which is centered at 1.55 µm, is a very common choice as it corresponds to the third telecom window, which yields minimum loss in silica optical fibers. However, water has a significant optical loss at this wavelength, which limits the maximum interaction length in biosensors. For water-based sensing, a better choice would be the O-band, which is centered around 1.31 µm, where optical losses of water are 10 times lower, as shown in [6]. The O-band also corresponds to the second telecom window, so it is not difficult to find fiber-optic component devices in that wavelength range.
Finally, another common issue is the sensor read-out. The simplest way to measure the sensing response that generates a phase shift is by spectral analysis. However, this requires either an expensive source such as a tunable laser, or an expensive detector such an Optical Spectrum Analyzer (OSA). A low-cost interrogation method would yield a much more inexpensive system, which would have a higher impact in the market. Either in ring resonators or interferometers, a shift in the fringe or peak pattern is proportional to the change of effective refractive index [6]. Interferometers can use a fixed-wavelength laser, using different techniques to recover the phase, such as using a coherent 120° or 90°-hybrid coupler [8]. Alternatively, the interferometer can also be interrogated with a single readout port by actively dithering the phase with an internal phase modulator using a Phase Generated Carrier (PGC) scheme [9], which allows the extraction of the phase by monitoring different harmonics of the output signal. In [10], a multitone mixing (MTM) technique was proposed, which showed to improve the response linearity in presence of modulation depth variations in the device over the standard PGC technique.
In this paper, we show experimental results of an interferometer-based chemical sensor in the O-band using TM polarization, which features a low-cost real-time phase demodulation scheme based on the MTM method, requiring only a fixed-wavelength laser as an optical source. The system response is compared to a similar version designed for the C-band and TE polarization. The TM version in the O-band shows ∼3 times higher responsivity values, which allowed reaching a limit of detection as low as 2.24·10−7 RIU.
2. Design
The geometries of the waveguides were designed to be compatible with the most common silicon-photonic platform, which is based on 220 nm-thick silicon-on-insulator technology; these wafers fix the waveguide height to 220 nm, leaving the width as a free design parameter. The rectangular shape of the waveguides generates a strong birefringence in the modes which must be considered in the design. In waveguides with the horizontal dimension larger than the vertical, which is the typical case, the fundamental mode is polarized in the horizontal direction, which is the so-called TE mode (strictly, the precise term would be quasi-TE because they have small regions with vertical polarization too). However, single-mode waveguides can also propagate the TM mode with a lower effective refractive index. Nevertheless, these modes are not typically considered higher-order modes (HOMs) because having a perpendicular polarization makes them very unlikely to be excited in curves or in any structure with width variations. Therefore, TM modes are more difficult to handle, because width variations can generate intercrossings with higher-order TE modes which can scatter a significant part of the light to these undesired modes [11]. For these reasons, most silicon-photonic devices based on 220nm-thick SOI are designed for TE polarization. Our reference device is in fact based on the fundamental TE-mode of a 220 × 480 nm2, which is the one used in [12].
In order to improve performance, we have proposed to change the polarization to TM to improve sensitivity, and the wavelength to 1.31 µm to decrease water absorption. Therefore, for selecting the best width for our waveguide, we have reduced it to 400 nm to keep the single-mode condition, while maintaining a reasonable confinement to keep the loss low in bends.
Simulations of the mode profiles are computed with the finite-difference Eigen-mode (FDE) solver, using MODE Solutions from Lumerical Inc software. Figure 1 shows the simulated electric field intensity in the case of TE and TM polarization at 1550 nm and 1310 nm wavelength respectively, using the nominal structure dimensions. As expected from electromagnetic boundary conditions, the TM mode has higher evanescent fields towards the top and bottom surfaces of the core, while TE mode enhances the evanescent field at the sidewalls. As roughness is mostly concentrated in the sidewalls, this is the reason why losses are typically lower in TM modes.
Fig. 1. Intensity of the electric field for the reference (a) and improved (b) waveguide designs, in presence of water as top cladding material. (a) TE mode at 1550 nm wavelength, (b) TM mode at 1310 nm wavelength.
The sensitivity of the device is calculated as the phase shift per refractive index unit (RIU) of the liquid, $S = \varDelta \phi /\varDelta {n_l}$. The relationship between the phase shift and the refractive index variation of a liquid covering the sensing MZI branch, can be expressed as follows:
The optical system on the chip included grating couplers, multimode interference (MMI) couplers, and metal heaters for phase modulation. For the TE-polarization grating couplers and MMI couplers the standard devices from the foundry photonic design kit were used. For the TM-polarization components, we designed our own components. The TM grating couplers at 1310 nm were designed with a period of 710 nm, etch depth of 70 nm and duty cycle of 50%. The grating lines had elliptical shape to directly focus the light from the optical fiber to the 400 nm-wide waveguide. On the other hand, the 2 × 2 MMI coupler for TM polarization at 1.31 µm was designed using FDTD, yielding a total length of 44 µm, width 6 µm, input port width 1.5 µm, and port distance 2.1 µm. The heaters were designed as a single metal track of length 200 µm and width 2 µm. The decision to set the length of the resistor of 200 µm, is related to the purpose of having a good trade-off between the chip’s compactness and avoiding reaching high temperature. We could have made the resistor shorter, which should work with higher temperatures, but a thermal cross talk could occur, introducing errors in the measurements. This heater yielded a tuning efficiency of 32 mW/2π and a ${V_{2\pi }}$= 6.7 V. The response time is calculated as 13.1 µs in [13].
In order to measure the phase changes induced by the liquid, the exposed waveguide was set on one branch of a Mach-Zehnder interferometer (MZI), with a reference waveguide of the same length with a silica cladding. The length of the exposed waveguide was set to L = 2.5 mm. The total length of the MZI branches was more than twice longer, because a certain separation was needed between the heaters and the sensing windows, but this extra distance should not have an impact on the responsivity because the waveguides are both cladded, thus all through this section the phase gets compensated. The exposed waveguide, which was bent on a spiral to reduce footprint, was set right next to a symmetrical reference spiral. The liquid flows on top of both spirals, to minimize temperature differences, even though the liquid only touches the core of the exposed one, while the reference one remains covered by the silica cladding.
Regarding the extraction of the interferometer phase, we used an active phase demodulation technique that just requires a fixed laser as a source, and a photodiode as a detector. As shown in Eq. (1), an effective refractive index variation entails phase changes at the output of the interferometer. If the interferometer is not actuated, extracting the phase just from the intensity becomes difficult when the signal moves away from the quadrature points due to responsivity fading. To overcome this issue, the PGC technique is typically applied, which consists in introducing a sinusoidal modulation and a demodulation stage in the signal processing. The extraction of in-phase and quadrature components of the signal and the subsequent application of the arc-tangent function enables the phase calculation with no fading [9] [14]. In [10], an improved algorithm called multitone mixing is proposed, which reduces the distortion in presence of modulation depth variations, by introducing higher order harmonics in the demodulation. Therefore, this is the technique used in this work. In particular, the active modulation is applied using an integrated heater on top of one of the MZI branches. As the phase shift is proportional to the square of the voltage applied, a zero-offset sinusoidal signal at a frequency ω/2 generates a sinusoidal phase shift at a frequency ω. This modulation generates a current in the photodiode which follows the equation:
where A and B are related to the mixing efficiency of the interferometer, C is the phase modulation depth, ω is the modulation angular frequency and $\varDelta \phi (t )$ is the phase difference between the two branches that we want to calculate. If we expand this equation in terms of Bessel functions IQ components can be extracted, respectively, from the even and odd harmonics of the signal:The PGC technique extracts the first and second harmonics of the signal to estimate the I and the Q components of the phase with no responsivity fading. However, distortion-free results can only be obtained when the modulation depth C is fixed and equal to 0.84π. To reduce the dependence on variations of C we used the MTM technique, which makes use of a linear combination of harmonics of the modulating signal that strongly reduces the distortion even in presence of remarkable variations in modulation depth, [10]. To do the demodulation, instead of using sinusoidal functions, synthetic functions are digitally generated which combine different harmonics:
In the MTM technique up to the third harmonic, we fixed a4 = 0 and a1 = 1, and we calculate the other two parameters to equalize the derivatives of the combinations of the Bessel functions by imposing the matrix equation:
For the nominal modulation depth $C = 0.84\pi $, the solution of Eq. (6) is obtained for ${a_2} = 2.5806$ and ${a_3} ={-} 3.0339$. Finally, we calculate the phase from the ratio of the mixing:
Where the symbol ${\otimes} $ indicates the mixing, intended as a digital multiplication followed by a low-pass filter with a cut-off lower than the modulation frequency.The processing was entirely done in real-time using a digital acquisition board to collect the data, and the processing was done in real-time in a PC with LabView.
3. Fabrication and experimental set-up
The chip was fabricated in a multiproject wafer (MPW) run by Advanced Micro-Foundry (AMF) [15]. The layout of the chip is shown in Fig. 2, starting from the grating coupler and following the path to the heaters and the MZIs. The heaters were used for modulating the signal and therefore for computing the MTM processing technique. In the figure, the sensing window corresponding to the exposed spiral is visible as well.
Fig. 2. Optical microscope image of the photonic chip. The central part shows magnified areas of the TM grating couplers, TE spirals and the heaters.
The etching of the top cladding in the spirals was also carried out by the foundry, and the result is shown in the SEM images of Fig. 3. It is worth noting an over-etching of several hundred nm; in addition, the shape of the silicon waveguide core is also affected by this process, slightly reducing its dimensions. This phenomenon is responsible for a higher responsivity in experimental results with respect to the simulations, especially in the case of TM polarization MZI. The average dimensions of the core calculated using the SEMs images are around 200 nm x 442 nm for TE spirals and 200 nm x 360 nm for TM ones. However, the over-etching depth was around 250 nm.
Fig. 3. SEM images. In (a) covered spirals and in (b) exposed spirals are shown. The difference between the two branches of the MZI is clear: on the right side spiral the top cladding is removed. The difference is enhanced in the lower pictures, where an over etching is visible in the exposed spiral.
A fiber array is used for the optical input and output coupling. The fibers were standard single-mode fibers with a pitch of 127 µm, polished at an angle of 8°. Once the light is propagating in the integrated system, before it reaches the spirals, in one branch it is modulated by a heater present in the path, shown in Fig. 2.
The complete system is outlined in the scheme in Fig. 4. The experimental set-up includes the integrated optical on-chip system, the fluidic system, the signal acquisition, and the data processing.
Fig. 4. Sensing system schematic design. The figure describes the light path, starting from the laser source, passing through the chip, where its phase varies with respect to the liquid sliding in the sensing window, being detected by the acquisition board through the photodiode and finally being processed in the PC.
Regarding the optical system, we used the following lasers: one at 1550 nm with 10 mW power and 400 kHz linewidth, and one at 1310 nm with 10 mW power and 3 MHz linewidth. In general, considering that the interferometer is balanced, there are no strong requirements regarding the linewidth of the laser. Typical single-frequency sources such as distributed feedback (DFB) lasers or vertical-cavity surface-emitting lasers (VCSEL) would be adequate for the proposed device. The output was coupled into the chip through grating couplers. A polarization controller was used to optimize the maximum signal into the chip. The light in the MZIs was modulated with a resistor of 1.4 kΩ used as a heater, at a frequency of 1 kHz to generate the phase modulation at 2 kHz. The light out of the chip was collected through the same fiber array, sent to InGaAs photodiodes, and their output current was converted into voltage with a transimpedance amplifier with a gain of 300 kΩ and 1 MHz bandwidth. The data was acquired by an acquisition board MCC USB-1808X with an acquisition rate of 50 kS/s. The acquisition board is used both for generating the modulating signal and for the acquisition stage, in such a way to ensure the synchronization of the signals involved in the processing. Finally, the data was processed in real-time with Labview software that performed the phase calculation using the MTM technique with a low pass filter of 20 Hz bandwidth and a phase-unwrapping step to enable continuous measurements beyond a full fringe. The low frequencies involved in the processing allow using a software for real-time phase demodulation.
As far as the fluidic system is concerned, a valve MUX Microfluidic Flow Switch Distributor was used to switch between de-ionized water (DIW) and aqueous solutions with 1%, 2% and 5% glycerol volume concentration, with 480 s waiting time for giving to the system a stabilization time to detect the correspondent phase variation. A constant continuous flow of 40 µL/min was provided by the Syringe TWO Programmable Syringe Pump in suction mode. FEP tubing conveyed the liquids from the valve to the polydimethylsiloxane (PDMS) cell attached to the chip, in which a channel funneled the fluids over the spirals, including the sensing window, and finally to the pump. The dimensions of the channel are a length of 3.8 mm, a width of 0.45 mm and a height of 200 µm so as to make the liquid flow on top of both interferometers and cover them totally within the edges of the chip.
The PDMS fluidic cell is fabricated by mixing an elastomer with a curing agent with a mixing ratio of 10:1, and pouring the mixture on the mold for 48 hours at room temperature. The PDMS cell is then fixed to the chip using a methacrylate (PMMA) slab, which is pressed on top of the cell using two screws fixed on a metal plate where the chip is placed (Fig. 5).
Fig. 5. Fluidic system design. The metal holder is necessary to make the PMMA plate fixed to the chip by using two screws.
The configuration described above ensured sufficient stability for the device to conduct the experiments.
4. Results and discussion
After the fiber array alignment, the MZIs spectra were collected for both TE and TM polarizations, as shown in Fig. 6. The measurements were acquired before exposing the waveguides to water. The fringes are clearly visible in both cases, which means that both the exposed and non-exposed spirals have a balanced signal transmission. The signal levels were lower for the TM case, as at 1310 nm we used a broadband source and optical spectrum analyzer instead of the tunable laser used at 1550 nm.
Fig. 6. In red the MZI spectra from fiber array alignment in TE polarization (a) and TM polarization (b); in blue the reference signal from the input and output grating couplers.
The sensing measurements, however, were performed at fixed wavelengths (at 1550 nm for the TE and 1310 nm for the TM polarization). We started by injecting DIW to determine a baseline. After 8 minutes the valve was switched, the 5% glycerol aqueous solution started flowing in the sensing region, and the induced phase shift with respect to the baseline was measured. The procedure was repeated, alternating between DIW and glycerol aqueous solution with decreasing percentage, waiting 8 minutes between a solution and the subsequent one. The acquired traces are shown in Fig. 7, for both devices (the measurements were not simultaneous). In the TM experiment, a very slight linear phase drift with a final value of -0.955 rad, attributed to a temperature drift, was detrended to facilitate the comparison. It is worth noting that the introduction of glycerol solutions generated strong phase shifts which decreased when the glycerol concentration was reduced. The response was also very repeatable as observed during the 5% repetition cycle. Regarding the responsivity, the measured phase variation was, as expected, higher with the TM polarization. The responsivity plots are shown in Fig. 8. The linear fittings showed a responsivity for the TM interferometer which is 3.38 times higher than for the TE device.
Fig. 7. Signal detected from TE and TM interferometers during fluidics measurements. The expressed percentages are the glycerol volume concentrations.
As the sensor measures refractive index change, we have calculated the responsivity of the devices to refractive index by using tabulated values of refractive index of aqueous solutions of glycerol. At room temperature, the refractive index of DIW water is ${n_{DIW}} = 1.318$ at 1550 nm, and ${n_{DIW}} = 1.3223$ at 1310 nm [16]; the refractive indices of glycerol are ${n_{gly}} = 1.4585$ at 1550 nm, and ${n_{gly}} = 1.4609$ at 1310 nm [17]. For calculating the refractive indices of aqueous solutions of glycerol we used a 3rd-degree polynomial model which was reported in [18]:
where w is the weight concentration, and the parameters are $A = \; - 0.0215,\; B = 0.0512,\; C = 0.111,\; D = 1.318$ for 1550 nm. As we could not retrieve data for 1310 nm in the literature, we assumed the same shape, but shifting the extreme values of 0 and 100% to be the ones at 1310 nm. With this assumption, the estimated coefficients for 1310 nm wavelength were $A = \; - 0.0216,\; B = 0.0512,\; C = 0.109,\; D = 1.3223$. With this model, the calculation of the refractive indices for each concentration and wavelength are shown in Table 1.
Table 1. Refractive index values of glycerol aqueous calculated from the model
Applying this model for the refractive index of aqueous solutions of glycerol, we can convert the measured phase changes to refractive index for each device, with Eq. (1), using the responsivities calculated from the slopes of the linear fits of Fig. 8. The results are shown in Fig. 9, where indeed very similar results are found for both devices.
Fig. 9. Plot showing for TE and TM the time variation of the refractive index of the liquid flowing on the surface of the chip. The expressed percentages are the glycerol volume concentrations.
Finally, we can also calculate the experimental waveguide sensitivity from the following equation, derived from Eq. (1):
The experimental responsivity values yielded waveguide sensitivity ($\partial {n_{eff}}/\partial {n_l}$) values of 17.24% for the TE polarization case, and 49.94% for the TM polarization. The TE responsivity agrees very well with the nominal calculation (17.31%), while the TM responsivity is higher than the calculated one (38.3%). A possible reason can be the over-etching phenomenon that occurred during the chip fabrication, as detected by SEM images, that has a larger impact on TM polarization. Knowing the responsivity of the device, the refractive index of a generic liquid is detectable by using Eq. (9), once the phase variation is experimentally measured through the sensor.
Finally, concerning the noise measurement, in Fig. 10 we show the noise of the signal during 5 seconds of measurement. The analysis conducted is purely statistical, for which a period of 5 seconds has been chosen, given the high response speed of the sensor. In particular, the attention has been focused on the part of the chart in which the liquid with 5% glycerol concentration was flowing over the chip and the measurement became stable. From this trace, the limit of detection analyte has been calculated as 3σ, where σ is the standard deviation of the trace. The results for each case are $3{\sigma _{TE}} = 3.64\cdot{10^{ - 7}}$ RIU and $3{\sigma _{TM}} = 2.24\cdot{10^{ - 7}}$ RIU, which means that the TM polarization device has lower noise than the TE, due to its higher responsivity. These noise levels are in line with the state of the art of this kind of devices used for chemical sensing [1]. In particular, with respect to the proposed sensor, in [19] the calculated LOD is slightly lower ($1\cdot{10^{ - 7}}$), while in [20] and in [21] is slightly higher, with the values of $7\cdot{10^{ - 6}}$ and $9.2\cdot{10^{ - 7}}$ respectively. Looking at the obtained outcomes, we could state that the proposed device outperforms the reference one, as expected from the simulation’s results, being able to detect low refractive index variation with higher response. The improvement with respect to the reference device is related to the higher responsivity of the device. We foresee that chemical functionalization of the exposed waveguides can convert this system into a specific chemical sensor suitable for label-free detection. An advantage of working with integrated photonic circuits is the possibility of increasing the number of sensors easily and in a compact way, since they have a very small footprint. Analyzing this aspect, the challenge is to functionalize each MZI differently, to make them specific for detecting particular analytes. This can be attained for example using microdroplet delivery instruments which are well known in the biochemical industry or through a microfluidic system. Additionally, another potential improvement to transform the device into a market-ready product would involve integrating the laser source directly into the chip, which is something feasible [22].
Fig. 10. Zoom in the time variation of the refractive index, to show the noise level in the measurements for both TE and TM.
5. Conclusions
In this paper, we have presented an interferometric chemical sensor integrated on a silicon chip. The sensing measurements entail the detection of the refractive index of liquids by employing a photonic integrated circuit, which is based on Mach-Zehnder interferometers, and a phase demodulation scheme using the MTM technique. The described system requires only a fixed-wavelength laser as an optical source. The conducted experiments demonstrate the optimization of the chemical sensor through the use of a 1310 nm wavelength and TM polarization compared to a prior version where a 1550 nm wavelength and TE polarization were used. The results show that with the TM version in the O-band, an increase of the responsivity value of around 3 times and a limit of detection of 2.24·10−7 RIU are detected. The enhancement of the LOD and a responsivity of 49.94% guarantee low refractive index variation detection capability. Therefore, the performance of this device is suitable for label-free chemical sensing, and the fabrication technology used enables its application in point-of-care devices due to its potential low cost. The detection of protein biomarkers [23], nucleic acids [24], small organic molecules and infectious pathogens [25] are some examples of applications in which the usage of the proposed device could have a significant role.
Funding
Ministero dell'Università e della Ricerca (IR0000036).
Acknowledgments
The authors would like to thank Ana Sánchez, Iñigo Molina and Gonzalo Wangüemert for fruitful discussions.
Part of the research was funded by the Italian Ministry of University and Research under the grant “Fondo per la promozione e lo sviluppo delle politiche del Programma nazionale per la ricerca (PNR) 2021”, project title: Samarcanda, to D.A. We acknowledge the support of the BRIEF “Biorobotics Research and Innovation Engineering Facilities” project (Project identification code IR0000036) funded under the National Recovery and Resilience Plan (NRRP), Mission 4 Component 2 Investment 3.1 of Italian Ministry of University and Research funded by the European Union – NextGenerationEU”.
Disclosures
The authors declare that there are no conflicts of interest related to this article.
Data availability
Raw data referred to MZI spectra are available in Dataset 1 Ref. [26], Dataset 2 Ref. [27]. Raw data referred to fluidics’ measurements are available in Dataset 3 Ref. [28] and Dataset 4 Ref. [29].
References
1. M. C. Estevez, M. Alvarez, and L. M. Lechuga, “Integrated optical devices for lab-on-a-chip biosensing applications,” Laser & Photon. Rev. 6(4), 463–487 (2012). [CrossRef]
2. C. Ciminelli, P. Colapietro, G. Brunetti, et al., “Lab-on-chip for liquid biopsy: a new approach for the detection of biochemical targets,” in 2023 23rd International Conference on Transparent Optical Networks (ICTON), Bucharest, Romania (2023).
3. W. Lukosz, “Integrated optical chemical and direct biochemical sensors,” Sens. Actuators, B 29(1-3), 37–50 (1995). [CrossRef]
4. A. Densmore, M. Vachon, D.-X. Xu, et al., “Silicon photonic wire biosensor array for multiplexed real-time and label-free molecular detection,” Opt. Lett. 34(23), 3598–3600 (2009). [CrossRef]
5. S. TalebiFard, S. Schmidt, W. Shi, et al., “Optimized sensitivity of Silicon-on-Insulator (SOI) strip waveguide resonator sensor,” Biomed. Opt. Express 8(2), 500–511 (2017). [CrossRef]
6. L. Castelló-Pedrero, M. I. Gómez-Gómez, J. García-Rupérez, et al., “Performance improvement of a silicon nitride ring resonator biosensor operated in the TM mode at 1310 nm,” Biomed. Opt. Express 12(11), 7244–7260 (2021). [CrossRef]
7. A. Sánchez-Ramírez, J. M. Luque-González, J. G. Wangüemert-Pérez, et al., “Comparing dielectric and plasmonic waveguides in a Mach-Zehnder architecture with coherent readout for sensing applications,” Opt. Laser Technol. 168, 109813 (2024). [CrossRef]
8. R. Halir, L. Vivien, X. Le Roux, et al., “Direct and Sensitive phase readout for integrated waveguide sensors,” IEEE Photonics J. 5(4), 6800906 (2013). [CrossRef]
9. A. Dandridge, A. B. Tveten, T. G. Giallorenzi, et al., “Homodyne demodulation scheme for fiber optic sensors using phase generated carrier,” IEEE Trans. Microwave Theory Techn. 30(10), 1635–1641 (1982). [CrossRef]
10. Y. Marin, P. Velha, and C. J. Oton, “Distortion-corrected phase demodulation using phase-generated carrier with multitone mixing,” Opt. Express 28(24), 36849–36861 (2020). [CrossRef]
11. J. Guo and Y. Zhao, “Analysis of mode hybridization in tapered waveguides,” IEEE Photon. Technol. Lett. 27(23), 2441–2444 (2015). [CrossRef]
12. Y. Marin, V. Toccafondo, P. Velha, et al., “Silicon photonic biochemical sensor on chip based on interferometry and phase-generated-carrier demodulation,” IEEE J. Select. Topics Quantum Electron. 25(1), 1–9 (2019). [CrossRef]
13. J. Elaskar, F. Bontempi, P. Velha, et al., “Ultracompact microinterferometer-based fiber Bragg grating interrogator on a silicon chip,” J. Lightwave Technol. 41(13), 4397–4404 (2023). [CrossRef]
14. C. Kirkendall and A. Dandridge, “Overview of high performance fibre-optic sensing,” J. Phys. D: Appl. Phys. 37(18), R197–R216 (2004). [CrossRef]
15. S. Y. Siew, B. Li, F. Gao, et al., “Review of silicon photonics technology and platform development,” J. Lightwave Technol. 39(13), 4374–4389 (2021). [CrossRef]
16. G. M. Hale and M. R. Querry, “Optical constants of water in the 200-nm to 200-µm wavelength region,” Appl. Opt. 12(3), 555–563 (1973). [CrossRef]
17. M. Nyakuchena, C. Juntunen, P. Shea, et al., “Refractive index dispersion measurement in the short-wave infrared range using synthetic phase microscopy,” Phys. Chem. Chem. Phys. 25(34), 23141–23149 (2023). [CrossRef]
18. J. E. Saunders, C. Sanders, H. Chen, et al., “Refractive indices of common solvents and solutions at 1550 nm,” Appl. Opt. 55(4), 947–953 (2016). [CrossRef]
19. K. Zinoviev, L. Carrascosa, J. Sánchez del Río, et al., “Silicon photonic biosensors for lab-on-a-chip applications,” Advances in Optical Technologies 2008, 1 (2008). [CrossRef]
20. F. Prieto, B. Sepúlveda, A. Calle, et al., “An integrated optical interferometric nanodevice based on silicon technology for biosensor applications,” Nanotechnology 14(8), 907–912 (2003). [CrossRef]
21. J. J. Lillie, M. A. Thomas, N.-M. Jokerst, et al., “Multimode interferometric sensors on silicon optimized for fully integrated complementary-metal-oxide-semiconductor chemical-biological sensor systems,” J. Opt. Soc. Am. B 23(4), 642–651 (2006). [CrossRef]
22. J. Yang, M. Tang, S. Chen, et al., “From past to future: on-chip laser sources for photonic integrated circuits,” Light: Sci. Appl. 12(1), 16 (2023). [CrossRef]
23. B. Senf, W.-H. Yeo, and J.-H. Kim, “Recent advances in portable biosensors for biomarker detection in body fluids,” Biosensors 10(9), 127 (2020). [CrossRef]
24. C. Sánchez and L. Lechuga, “Ultrasensitive label-free nucleic-acid biosensors based on bimodal waveguide interferometers,” Methods in Molecular Biology 2393, 89–125 (2022). [CrossRef]
25. M. Soler, M. C. Estevez, M. Cardenosa-Rubio, et al., “How nanophotonic label-free biosensors can contribute to rapid and massive diagnostics of respiratory virus infections: COVID-19 case,” ACS Sens. 5(9), 2663–2678 (2020). [CrossRef]
26. F. Piretta, F. Samà, F. Bontempi, et al., “MZI spectrum at 1550 nm wavelength and TE polarization,” figshare, (2024). https://doi.org/10.6084/m9.figshare.25075907.
27. F. Piretta, F. Samà, F. Bontempi, et al., “MZI spectrum at 1310 nm wavelength and TM polarization,” figshare, (2024). https://doi.org/10.6084/m9.figshare.25075919.
28. F. Piretta, F. Samà, F. Bontempi, et al., “Phase changes due to refractive index variations (TE 1550 nm),” figshare, (2024). https://doi.org/10.6084/m9.figshare.25075925.
29. F. Piretta, F. Samà, F. Bontempi, et al., “Phase changes due to refractive index variations (TM 1310 nm),” figshare, (2024). https://doi.org/10.6084/m9.figshare.25075931.
