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Abstract
In this paper, we propose a novel bimodal waveguide based on regional mode engineering (BiMW-RME). Leveraging the orthogonality of the guided modes, the form of patterned SiO2 cladding on the bimodal waveguide can reduce the interaction between the reference mode and the analyte, thereby significantly improving sensitivity. The proposed BiMW-RME sensor experimentally demonstrates a phase sensitivity of 2766 π rad/RIU/cm and a detection limit of 2.44×1−5 RIU. The sensitivity is 2.7 times higher than that of the conventional BiMW sensor on the same SOI platform. The proposed design strategy demonstrates a significant improvement in the sensor's sensitivity, presenting a novel approach to enhancing common-path interferometric sensor performance.
© 2024 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
On-chip interferometric sensors have been extensively studied during the last decade for various applications such as disease diagnosis [1–4], food safety [5,6], drug discovery [7,8], and environmental monitoring [9–11]. Compared to fiber sensors, on-chip interferometric sensors exhibit superior integration and multiplexing capabilities [12–16]. Many on-chip version of classic interferometer structures, such as Mach-Zehnder interferometers(MZI) [17,18] and Fabry-Perot interferometers(FPI) [19], have been demonstrated [20]. Due to the limited landscape on chip, substantial efforts have been devoted into reducing the footprint of on-chip interferometers [20]. Bimodal waveguides (BiMW) are considered as an appealing approach because they can potentially reduce the footprint of conventional on-chip MZIs by half and enable the multiplexing of a large number of sensors on-chip [21–26]. However, due to the nature of common path interferometry, both the reference and sensing channels response to analytes, consequently compromising the sensitivity. A number of methods have been explored in the hope of making the sensitivity of BiMW comparable with conventional MZIs [27–29]. As the sensitivity of BiMW relies on the sensitivity differences of guided modes, the sensitivity enhancement in both modes unfortunately cancels each other. As a result, the enhancement on the sensitivity difference is less significant [30,31]. Leveraging the special dispersion properties in slow light can effectively enhance the sensitivity difference. However, the high propagation loss limits the maximum length of the sensors and the experimental achievable sensitivity is far less than the theoretical prediction [32,33].
In this paper, we propose a universal approach based on regional mode engineering, which can be conveniently applied to improve the sensitivity of conventional BiMW sensors. Because of the orthogonality of the modes in multimode waveguide, there always exist regions in which the amplitude of one mode reaches its local maximum while the other mode reaches its local minimum. Engineering these regions can selectively alter one mode while leaving the other mode unperturbed. As a proof-of-concept, patterned SiO2 cladding layer is introduced into a BiMW to mitigate the interaction between the reference mode and the analyte while maintaining the sensitivity of the sensing mode. Significant sensitivity enhancement has been observed both theoretically and experimentally.
2. Sensor structures and analysis
The structure of a conventional BiMW on silicon-on-insulator (SOI) platform is illustrated in Fig. 1(a). The refractive index of the top cladding is set as 1.33 to resemble the aqueous environment. Figure 1(b) and (c) are the field distributions of the TM0 and TM1 modes simulated with the finite difference eigenmode (FDE) method. Figure 1(d) and (h) are the field distribution profiles at z = H/2. The purple region in Fig. 1(h) marks the position of the SiO2 in the y direction, in which the first-order mode reaches a local minimum and the fundamental mode reaches a local maximum. To assure the bimodal operation, the width of the waveguide is set as 930 nm. It can be observed that significant portion of both modes exists in the top cladding. Since the mode sensitivity is proportional to the mode overlap factor (f) [34], the sensitivity of the bimodal interferometer depends on the difference between the overlap factors of the fundamental mode and the first-order mode, which can be written as DiffTM (TE) = fTM1 (TE1)- fTM0 (TE0). Although thinner waveguide gives better sensitivity, using 220 nm ensures compatibility of the design with the standard commercial foundries. Additionally, in the absence of mode engineering, the overlap factors of TE0 and TE1 modes are 0.0228 and 0.0543, respectively, resulting in a DiffTE of 0.0315. Similarly, TM0 and TM1 modes have overlap factors of 0.1396 and 0.1866, corresponding to a DiffTM of 0.047. It can be noticed that although TM modes have larger overlap factors with ambient environment compared to TE modes, the improvement in Diff is insignificant. This is because any modifications, such as polarization or waveguide structure, alter both modes simultaneously. Therefore, more intricate tailoring of the mode distribution is necessary to further enhance the sensitivity of the BiMW.
Fig. 1. Structures and modes of BiMWs. (a) and (e) The schematic of the BiMWs without and with patterned SiO2 cladding, respectively. (b), (c), (f) and (g) are the corresponding electric field (|Ez|) distributions of transverse magnetic (TM) modes. (d) and (h) The field distribution profiles (|Ez|) of the BiMWs without and with patterned SiO2 cladding.
In light of the difference in the field distribution of TM0 and TM1 modes, we propose selectively reducing the sensitivity of one mode while minimizing the impact on the other mode. One intuitive approach is illustrated in Fig. 1(e). The center of the BiMW is covered with a patterned cladding material, e.g. SiO2. The patterned cladding prevents TM0 mode in this region from interacting with ambient environment. At the same time, the impact on TM1 mode is considerably smaller since the field of TM1 mode is weak in this region. With this configuration, TM0 mode should be used as reference channel and TM1 mode is the sensing channel. As shown by Fig. 1(f) and (g), the presence of SiO2 has little impact on the mode distribution. Similarly, we can also expose the center portion and cover the sides of the BiMW. In this configuration, the reference and sensing channels should be exchanged accordingly.
The correlation between the Diff and the structural parameters (the Si and SiO2 width Wb and Wc) is simulated and shown in Fig. 2(a). The width of the BiMW, in which only the fundamental mode and first-order mode exist, is scanned between 0.93 µm and 1.33 µm. It can be observed that Diff decreases as Wb widens. The introduce of the patterned cladding has pronounced impact on the Diff, which increases with Wc until reaches the maximum and then decreases afterwards. The maximum Diff is 0.103 when Wb = 930 nm and Wc = 420 nm, as shown by the star marker in Fig. 2(a). The corresponding mode distribution is shown in Fig. 2(b). The field distributions of another two representative points, marked with cross and circle, are also plotted for comparison. Cross represents the waveguide with same Wc and a larger Wb as the star point. As it can be seen that the increase of Wb improves the confinement of both TM0 and TM1 modes.
Fig. 2. Optimization of the waveguide structure. (a) Diff changes with Si (Wb) and SiO2 width (Wc). (b) Field distributions at the positions marked as star, cross, and circle in (a). (c) and (d) Diff changes with misalignment (m) and SiO2 height (Hc). Insets: Schematic diagrams and field distributions.
As a result, the enhancement on Diff decreases. Circle point presents the waveguide with the same Wb and a patterned cladding covers the entire top of the waveguide. In this configuration, the cladding covers both modes and predictably decreases the Diff. One should note that even in the worst case the introduce of patterned cladding offers a higher Diff compared to conventional BiMW.
As the misalignment is a common unavoidable fabrication error, its impact on the Diff is shown in Fig. 2(c). As the patterned cladding moves away from the sweet region, Diff decreases as fTM1 decreases. However, since part of the sweet region is still covered, the enhancement still exists. Besides, to simplify the fabrication, a thin layer of top cladding is desired. As can be seen in Fig. 2(d), Diff increases rapidly with Hc at first. However, after the SiO2 thickness reaches 200 nm, Diff gradually stabilizes. This indicates that a SiO2 with a thickness of 200 nm is adequate for blocking the fundamental mode.
The phase sensitivity at wavelength λ is defined as the ratio of the change in phase difference between two modes to the variation in refractive index of the external solution [31], i.e.,
Fig. 3. The simulated sensitivity of the BiMW-RME (a) Variation of phase sensitivity with Wb and Wc. (b) Variation of phase sensitivity with Hc and m.
3. Experiment and results
3.1 Fabrication of BiMW-RME and experimental setup
Figure 4(a) and (b) show schematic diagram and optical microscope image of the BiMW-RME structure. To stimulus both TM0 and TM1 modes, the input single mode waveguide is off-center aligned with the BiMW region. The output single mode waveguide is shifted accordingly to assist the transition of TM0 and TM1 modes in BiMW to the TM0 mode in the single mode waveguide. This simple design allows the demonstration of the proposed BiMW-RME sensor. The mode conversion efficiency can be further optimized with more intricate designs. The sensor is fabricated on SOI with a 220 nm thick top silicon layer and a 2 µm thick buried oxide layer. The structure in silicon layer is patterned with E-beam lithography and inductively coupled plasma etching. Hydrogen silsesquioxane (HSQ) is spin-coated and patterned to form SiO2. Figure 4(c) shows the junction utilized for mode excitation [28]. Figure 4(d) is the BiMW with patterned SiO2 cladding. Simulation shows that the extra loss induced by the introduce of SiO2 is less than 0.2 dB. As indicated in Fig. 4(d), there is ∼100 nm misalignment between the patterned cladding and the bimodal silicon waveguide. In addition, excess SiO2 covers the sidewall of the silicon waveguide. These fabrication imperfections could potentially compromise the sensitivity. The sensitivity of the sensor is characterized by solutions with different refractive indices. The experimental setup is illustrated in Fig. 4(e). A continuous-wave tunable laser is used as the light source. The polarization is adjusted through a polarization controller. Light is coupled into and out of the chip by grating couplers [28]. The output light is detected by a photodetector to obtain the interference pattern.
Fig. 4. (a) and (b) Schematic diagram and optical microscope image of the whole sensor. (c) and (d) Scanning electron microscope (SEM) images of the sensor. (e) Schematic diagram of the experimental setup. CWTL, continuous wave tunable laser; PC, polarization controller; AS, alignment stage; PD, photodetector; TC, temperature controller. (The black line: the light path; the blue line: data transmission; the orange arrow: the propagation direction of light.)
The entire system is controlled by a computer and the transmission spectrum is automatically monitored and saved. The temperature controller can minimize the temperature fluctuation to within 0.01 °C. The solutions with different refractive indices are obtained by altering the concentration of NaCl solutions [35]. Here, we use a needle tube to drop the NaCl solution directly onto the chip, and the monitoring time for each concentration is 200 seconds.
3.2 Experimental results
Figure 5(a) summarizes the evolution of the spectrum as the concentration of NaCl solution increases. The distinct extinction ratios of the dips are caused by unequal excitation of the two modes [29], which can be solved with more intricate couplers. As the ambient refractive index increases, the increasing optical path difference (OPD) between TM0 and TM1 modes leads to the redshift of the transmission minima. By tracking the dips marked by pink arrows in Fig. 5(a), the wavelength sensitivity is measured to be ∼1469.7 nm/RIU. The results obtained by peak/dip tracking is susceptible to spectral noise [36]. Thus, classic phase demodulation is used to relieve the impact of spectral noise and improve the limit-of-detection (LoD) [37,38]. The upper and lower panels of Fig. 5(b) show the amplitudes and phases of the spatial frequency spectra, respectively. According to the theoretical OPD = 284.2 nm between TM0 and TM1 modes, the spatial frequency at 0.12 nm-1 (OPD ∼288.3 nm), representing the bimodal interference, is selected to analyze the phase variation. The phase changes are monitored and plotted in Fig. 5(c). During the monitoring of NaCl solutions with different concentrations, data points are collected every 10 seconds. Due to the noise originated from the sensing system, the phase fluctuation (as shown in the inset of Fig. 5(c)) can be observed throughout the whole measurement. Figure 5(d) demonstrates a refractive index sensitivity of 221.3π rad/RIU with good linearity (R2 = 0.997). For comparison, the performance of a conventional BiMW sensor is fabricated and characterized. Its refractive index sensitivity is ∼140.9 π rad/RIU. This result indicates the refractive index sensitivity is enhanced by 1.57 times through the SiO2 deposition. Although the enhancement is lower than the theoretical prediction due to fabrication errors, the improvement is still significant. The slope can be improved by a few methods, such as increasing the sensing length and employing higher order modes [31].
Fig. 5. Experimental measurements of the BiMW-RME sensor (a) Interference spectra of the BiMW-RME sensor. (Light colors represent the raw experimental data; dark colors represent the fitting curve.) (b) Amplitudes (upper panel) and phases (lower panel) of spatial frequency spectra under different concentrations (c = 0%, 2%, 4%, 6%, and 8%). (c) Real-time phase changes for applying NaCl solution with different concentrations. (d) Variation of phase change with refractive index of NaCl solution.
3.3 Improvement of the LoD
LoD is another important parameter for sensor performance evaluation, which is defined by [39]
σexp is the phase noise, which equals 0.0018 π rad in this experiment. s is the phase sensitivity of the BiMW-RME sensor. The LoD of the BiMW-RME sensor reaches 2.44 × 10−5 RIU, which can be further improved by minimizing external disturbances induced noises. The noise can be divided into three categories [39], amplitude noise σamp, temperature noise σtem, and the spectral noise σspe. Here, we assume that individual noise sources are statistically independent, and σexp could be expressed as [40]
Here, by reducing the impact of amplitude noise on measurement noise, manifested as a smaller σamp, a lower LoD is achieved. A model for the relationship between LoD and amplitude noise is established based on Monte Carlo simulation [39]. By using less noisy detectors and sources or averaging and other signal processing techniques [41], amplitude noise can be reduced, thereby lowering the LoD. In this simulation, σamp is evaluated to be approximately 1.6 × 10−3 π rad and σothers (σ2others=σ2spe+σ2tem) to be about 8.2 × 10−4 π rad. Assuming that the effects of temperature and spectral noises on the experiment are fixed, a better LoD can be achieved by reducing σamp. The evolution of LoD with σamp is simulated as shown in Fig. 6. The LoD of the BiMW-RME sensor is always better than that of the conventional BiMW sensor. The circular point in Fig. 6 represent that σamp is 1.6 × 10−3 π rad, correlating with a LoD of approximately 2.0 × 10−5 RIU. When σamp is reduced to 1.55 × 10−4 π rad, the LoD is improved to ∼8.0 × 10−6 RIU, which is indicated by the triangular point in Fig. 6.
Table 1 summarizes the performance of the BiMWs reported in recent years. The sensitivity of typical BiMW on SOI is 1007 π rad/RIU/cm. Leveraging more intricate structures and/or material platforms with relatively smaller index contrast, the sensitivity can be enhanced [22,42]. The vertical BiMW on silicon nitride can reach ∼2700 π rad/RIU/cm [24]. The slow light enhancement could significantly increase the sensitivity by one order of magnitude. However, the interaction length limited by the high loss makes the approach less attractive [32,33]. For the proposed approach, theoretical analysis predicts that it can achieve a sensitivity around 3912 π rad/RIU/cm. Although the experimental result is lower than the theoretical prediction, its sensitivity still increases 2.7 times compared to conventional spiral BiMW [23], and achieves a similar level of LoD with a shorter sensing length.
Table 1. Experimental results comparison for the BiMW interferometers
4. Conclusion
In this paper, we propose and demonstrate a regional mode engineering based universal approach to increase the sensitivity of common path multimode interferometers. The experimental results show the sensitivity of the proposed BiMWs increases 2.7 times compared to conventional BiMWs on the same SOI platform. Theoretically, the enhancement can reach ∼4x if the fabrication imperfections could be minimized. This simple and effective method not only can be applied to BiMW sensors for sensitivity enhancement but can also be leveraged to improve the performance of devices involving multimode structures.
Funding
Science, Technology and Innovation Commission of Shenzhen Municipality (JCYJ20210324131614040, JCYJ20220531095604009); Basic and Applied Basic Research Foundation of Guangdong Province (2020B1515130006, 2021B515120056, 2023A1515011944); National Natural Science Foundation of China (U22A2093).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper may be obtained from the authors upon reasonable request.
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