Single-molecule optofluidic microsensor with interface whispering gallery modes

Edited by Douglas Shepherd, Arizona State University, Tempe, AZ; received May 13, 2021; accepted December 23, 2021 by Editorial Board Member John W. Sedat
February 3, 2022
119 (6) e2108678119

Significance

Optical microresonators have emerged as promising platforms for label-free detection of molecules. However, approaching optimum sensitivity is hindered due to the weak tail of evanescent fields. Here, we report the implementation of the interface modes for ultrasensitive sensing in a microbubble resonator. With the electromagnetic field peaked at the interface between the optical resonator and the analyte solution, interface modes enable sensing of biomolecules with a detection limit of 0.3 pg/cm2. Single-molecule detection is further demonstrated using the plasmonic-enhanced interface modes. In addition, intrinsically integrated into a microfluidic channel, the sensor exhibits ultrasmall sample consumption down to 10 pL, providing an automatic platform for biomedical analysis.

Abstract

Label-free sensors are highly desirable for biological analysis and early-stage disease diagnosis. Optical evanescent sensors have shown extraordinary ability in label-free detection, but their potentials have not been fully exploited because of the weak evanescent field tails at the sensing surfaces. Here, we report an ultrasensitive optofluidic biosensor with interface whispering gallery modes in a microbubble cavity. The interface modes feature both the peak of electromagnetic-field intensity at the sensing surface and high-Q factors even in a small-sized cavity, enabling a detection limit as low as 0.3 pg/cm2. The sample consumption can be pushed down to 10 pL due to the intrinsically integrated microfluidic channel. Furthermore, detection of single DNA with 8 kDa molecular weight is realized by the plasmonic-enhanced interface mode.
Detecting biological molecules and monitoring their dynamics are of crucial importance in biomedical analysis and disease diagnosis (1, 2). Practical applications generally involve complex biological environments, in which an engineered interface is highly desirable to enable the enrichment, detection, and analysis of specific biomolecules (3). Over the past decades, many techniques on interfacial molecular analysis have been developed, such as lateral flow immunoassay, electrochemical analytical techniques, and optical biosensors (47). Among them, optical evanescent microsensors, such as microspheres (8, 9), microtoroids (1014), and nanowaveguides (1518), have attracted considerable research interest since they can detect unlabeled molecules and monitor their interactions in real time and in situ with ultrahigh sensitivity, fast response, and miniature footprint.
Despite these advantages, potentials of optical evanescent microsensors have not been fully explored. With the peak field intensity confined inside the cavity, these sensors can utilize the weak tail of the evanescent field only on the sensing surface (8, 1012, 15, 16), thus limiting their sensitivities. Moreover, ultrasmall sample consumption is desired for high-efficiency sensing yet challenging in evanescent microsensors, since they require delicate sample delivery designs such as an additional chamber (9, 12) or a precisely aligned fluidic channel (19, 20). Therefore, an integrated microfluidic platform with ultimate sensitivity is highly demanded.
In this work, we demonstrate an ultrasensitive optofluidic microbubble biosensor by exploiting the whispering gallery modes (WGMs) peaked at the interface between the optical resonator and the analyte solution, which are termed as the interface modes. Previously, the microbubble resonator has been widely used for measuring refractive index, biomolecule concentration, and single nanoparticle generally by the mode localized in the liquid core (2129). Here, we find that the profile of the WGM field can be tuned by varying the wall thickness, and the interface mode emerges when the maximum of the field intensity is drawn onto the interface. Compared with conventional evanescent sensors, the present scheme utilizing interface modes promises maximum sensitivity for interfacial molecular analysis, pushing the detection limit down to 0.3 pg/cm2. The scheme is also compatible with the widely adopted techniques to enhance signal- to-noise ratio (SNR) such as plasmonic hybridization (3033) and frequency tracking (12, 15, 18). As a proof of concept, single-molecule detection is demonstrated with a plasmonic-enhanced interface mode. Naturally integrated into a microfluidic system, the sensor with single-molecule sensitivity exhibits ultrasmall sample consumption down to 10 pL, providing an automatic platform for biomedical analysis.

Results

The optofluidic microbubble biosensor utilizes its inner interface to capture and detect analytes (Fig. 1A), and thus the optical field intensity at this interface is crucial to the sensitivity. In cylindrical coordinates (r,ϕ,z), WGMs of a microbubble cavity can be described by the radial mode number q, azimuthal mode number m, and axial mode number j (SI Appendix). The radial field distributions in such a structure can be described by the Helmholtz equation, which is analogous to the time-independent Schrödinger equation (28, 34, 35) with the effective radial potential of the transverse-electric modes written as
V(ρ)=m21/4ρ2,
[1]
Fig. 1.
Optofluidic microbubble cavity for interfacial molecular detection. (A) Schematic of the optofluidic microbubble biosensor. Analytes enter the naturally integrated microfluidic channel and are captured by the interior surface of the cavity. (B) Effective potential of the microbubble cavity (black curve), radial field distributions (pink curves) of three typical kinds of resonance modes (Left), and the corresponding cross-sectional field distributions (Right). From bottom to top: wall mode, interface mode, and core mode. (C) Minimum detectable surface density of molecules using the interface mode (red curve), wall mode (blue curve), and core mode (orange curve) in a microbubble cavity and the fundamental mode of a microsphere (black curve) as a function of the equatorial radius.
where ρ=nr with n being the refractive index and r the radial position, and m denotes the azimuthal mode number. Due to the discontinuity of refractive indexes in the radial direction, steep potential barriers exist at the inner and outer surfaces of the silica wall, shown as the black curve in Fig. 1B. Depending on the relative magnitude between the effective kinetic energy kq2 of the WGM with radial mode number q and the barrier height at the sensing interface Vint, the WGMs can be classified into three types, wall modes, interface modes, and core modes, as follows: 1) When kq2<Vint, optical fields are concentrated in the silica wall, forming the wall modes; 2) when kq2>Vint, optical fields are localized in the liquid core, forming the core modes; and 3) when kq2Vint, a special mode family emerges with the field peak located exactly at the interface between the silica wall–liquid core, termed the interface mode. The three types of modes are suitable for different applications. For example, wall modes can be used for temperature sensing with less environmental disturbance (36), while core modes are advantageous for refractive index monitoring and nanoparticle detection inside bulk solutions (2628). In particular, interface modes ensure the maximum sensitivity for interfacial molecular detection and analysis.
Theoretically, analytes adsorbed on the inner surface of a microbubble cavity introduce a resonance wavelength shift δλ, which could be obtained by (SI Appendix)
δλλ=DnsσdnsdCs,
[2]
where λ is the resonance wavelength, ns is the refractive index of the analyte solution (ns1.33 for the aqueous solution with low analyte concentration), and σ and Cs denote surface mass density for analyte adsorbed on the sensing surface and the concentration of analyte solution. For typical biological molecules, refractive index increment dns/dCs0.2cm3/g (37). The parameter D=ε0E2dS/2U, in which ε0 is the vacuum permittivity, E is the electric field magnitude, and U represents the total energy stored inside the resonator. The smallest detectable resonance shift is typically 1/50 to 1/100 of the mode linewidth Δλ reported in previous works (15, 3840), also confirmed in our experiment (SI Appendix, Fig. S8). Thus, here a resolution of Δλ/50 is used to quantitatively estimate the detection limit of the microsensor. As shown in Fig. 1C, compared with the core mode and the wall mode, the interface mode exhibits a much lower detection limit in surface density down to 0.3 pg/cm2. The detection limit remains nearly unchanged even when the equatorial radius of the microbubble approaches 10 µm, where sample with volume down to 10 pL can be analyzed by the naturally integrated microfluidic channel. In comparison, for typical evanescent microsphere sensors, the detection limit deteriorates exponentially when the cavity radius is below 45 µm due to the strongly reduced Q factor. In addition, the detection limit of molecular concentration can be estimated according to the binding affinity between the analyte molecules and the functionalized cavity surface (SI Appendix).
A method has been developed to identify different modes through the thermo-optic effect. Characterized by different field profiles, the three kinds of modes exhibit distinctive thermal responses to temperature disturbance δT, which can be described as
δλλ=(iαifini+βsilica)δT,
[3]
where i = liquid, silica, or air; αi, fi, and ni are the corresponding thermo-optic coefficient, energy distribution ratio, and refractive index; and βsilica denotes the linear expansion coefficient of the silica wall. Different types of modes can be classified by their energy ratio in the liquid core fliquid. According to numerical analysis (SI Appendix), for the microbubble resonator with wall thickness of 0.5 to ∼2.5 µm, 0.1<fliquid<0.4 for low-order interface modes, while fliquid<0.1 and fliquid>0.4 for the wall and core modes, respectively. Explicitly, as αliquid=9.16×105K1 and αsilica=1.19×105K1, core modes have the strongest and negative thermal shifts; on the contrary, wall modes manifest weak and positive thermal shifts; and interface modes, distributed in both silica and water, generally present weak and negative thermal responses.
Experimentally, a microbubble resonator with the wall thickness of about 1 µm (Fig. 2 A, Inset) is fabricated from a microcapillary by CO2 laser irradiation (Materials and Methods). The wall thickness of the microbubble cavity can be well adjusted by controlling the microbubble diameter (SI Appendix, Fig. S3). WGMs are excited by a tunable laser via a side-coupled tapered fiber, and the transmission spectrum is monitored in real time. After intentionally perturbing the environmental temperature by a local heat source, core modes with the largest thermal shifts are first identified (orange curves in Fig. 2A). According to numerical simulations, fliquid of the core mode with the largest thermal shift throughout the mode family is around 1 (SI Appendix). Referencing to the core mode, the values fliquid of all other modes are obtained subsequently, according to which different kinds of modes can be identified.
Fig. 2.
Interfacial analysis of specific interaction between proteins in an optofluidic microbubble sensor. (A) (Top) Environmental temperature drift of the microbubble cavity with time. Inset shows optical image of the microbubble resonator. (Scale bar: 50 µm.) (Bottom) Experimental response of wall modes, core modes, and interface modes during the environmental temperature drift. (B) Resonance shifts of the three kinds of modes during the sequential addition of citrate buffer (i), biotinylated BSA molecules in citrate buffer (ii), citrate buffer (iii), and streptavidin proteins in citrate buffer (iv and v).
The sensing capabilities of different modes are then characterized by microfluidic experiments with two kinds of analytes, biotinylated bovine serum albumin (BSA-biotin) molecules and streptavidin proteins. To eliminate the influence of environmental thermal fluctuations, the microbubble cavity is kept in a thermostatic chamber. As 1 µM BSA-biotin molecules gradually enter the microfluidic channel, all WGMs experience red shifts (Fig. 2 B, ii) due to the molecular adsorption onto the hydroxylated silica surface. After removing the surplus BSA-biotin molecules with citrate buffer rinsing (Fig. 2 B, iii), streptavidin proteins with the concentration down to 50 nM are then delivered into the microbubble cavity. Further red shifts occur due to specific binding between the two kinds of molecules (Fig. 2 B, iv). In addition, the specific interaction is confirmed by two control experiments. First, no evident resonance shift is observed when 150 nM streptavidin proteins is injected into the microbubble cavity without BSA-biotin molecule functionalization (SI Appendix, Fig. S4). Second, the interface mode experiences almost the same red shifts when the mixed solutions of 20 nM target streptavidin proteins with and without 180 nM control BSA molecules are injected into the microbubble cavity with BSA-biotin molecule functionalization (SI Appendix, Fig. S5).
Relative sensitivities of different modes are extracted from the mode shifts and summarized as a function of the corresponding fliquid, which are also compared with numerical simulations (Fig. 3). In simulation, the wall thickness of the microbubble cavity is scanned between 1.0 and ∼1.2 µm to account for the inevitable nonuniformity during the fabrication process. All the experimental data fall into the zones of the numerical prediction, confirming an at least twofold sensitivity improvement of the interface modes compared with both the wall and core modes. With the interface mode of the highest sensitivity, the minimal detectable concentration of streptavidin proteins is deduced to be 1 aM, taking into account the functionalization density and the intermolecular binding affinity (SI Appendix).
Fig. 3.
Interfacial sensitivity of the wall modes, interface modes, and core modes. Shown are experimental (red circles) and numerical (purple shadow) results of the sensitivity versus the energy distribution ratio in the water core of different modes. Parameters for simulation: radial mode number q= 1 (wall modes), 2 (interface modes), and 3 (core modes) for the wall thickness of 1.0 to ∼1.2 µm with the azimuthal nonuniformity <0.3 µm.
The proposed scheme is readily compatible with the widely adopted SNR enhancement techniques. Here, single-molecule detection is demonstrated by the plasmonic-enhanced interface mode (Fig. 4A). With a gold nanorod adsorbed onto the inner surface of a microbubble, numerical simulation predicts a field enhancement factor γp=2,500 at the hotspot. An additional plasmonic enhancement factor γe at the range of 101 to 102 has been reported owing to surface roughness of the gold nanorod or the ion layer around the molecules in the aqueous environment (9, 15, 41). In contrast to the collective molecule detection, sensitivity of single-molecule detection relies on both the radial and axial mode numbers of WGMs (SI Appendix). As shown in Fig. 4B, the fundamental axial interface mode with axial mode number 1 and radial mode number 2 could result in the largest resonance shift. With m=8kDa and γe=25, the maximum resonance shift reaches ∼65 fm, which is much higher than the noise level Δλ/50=15.6fm (Q>106) due to the frequency fluctuation that mainly arises from the thermal-refractive noise, laser jitter, and 1/f technical noise (42, 43). Although there are a few low-order wall modes that have the potential for single-molecule detection, the SNR is very low. The resonance shifts of most wall modes and all the core modes are too small to be resolved the single-molecule signals.
Fig. 4.
Single-molecule detection with the plasmonic-enhanced interface mode. (A) Schematic of the Au-decorated microsensor. A gold nanorod is functionalized on the interior surface of the microbubble cavity. (B) Calculated resonance shifts induced by a single DNA oligo for the modes with different radial and axial mode numbers with plasmonic enhancement. Parameters for the calculation: microbubble wall thickness 0.88 µm, molecular weight 8 kDa, and plasmonic enhancement factor γpγe=6.25×104. (C) Resonance shift and linewidth broadening of fundamental interface mode during the nanorod binding process. (D) Real and imaginary parts of the polarizability of the gold nanorod near the plasmonic resonance. (E) Resonance shift induced by a single DNA oligo of a fundamental interface mode (orange curve), a wall mode (black curve), and a core mode (brown curve) with plasmonic enhancement.
The fundamental interface mode is experimentally identified by combining the aforementioned thermo-optic effect with an axial field mapping technique, in which a taper fiber is scanned along the axial direction to depict the field profile (SI Appendix, Fig. S2). Then, the microbubble cavity is functionalized with a gold nanorod while the fundamental interface mode is monitored in real time (Materials and Methods). A linewidth broadening without mode shift confirms the adsorption of the gold nanorod, due to the zero real polarizability of the gold nanorod at the resonance condition (Fig. 4 C and D) (44). The intrinsic Q factor of the fundamental interface mode before and after gold nanorod adsorption is 2.6×108 and 8.6×106, respectively (SI Appendix, Fig. S7).
Single-strand DNA molecules are then delivered into the Au-decorated microsensor. The resonant wavelengths of three representative modes are traced, as presented in Fig. 4E. Transient steps and spikes are observed on the trace of the fundamental interface mode, corresponding to the adsorption and the transient movements of single DNA molecules, respectively. In contrast, on the trace of the wall mode and the core mode, single-molecule signals are buried in the frequency noises and difficult to be resolved. The noise levels are 3.1 and 23 fm for the high-Q interface mode with Δλ=0.2pm and low-Q core mode with Δλ=2.5pm, respectively (SI Appendix, Fig. S8). In addition, the quasi-static resonance shift induced by the slow drifting of the laser wavelength is observed with less than 0.1 pm in the period of 30 s. As this drift is slower than any physical processes (molecule adsorption, transient movement, etc.), it is negligible in the sensing experiments.
Single-molecule signals detected by the fundamental interface mode are analyzed statistically. Single-molecule steps and spikes are extracted from the resonance wavelength trace according to the noise level and summarized in Fig. 5 A and B, respectively. It can be found that a single-strand DNA molecule with m8kDa can induce the resonance shift up to ∼70 fm (Fig. 5A), revealing γe25, consistent with the numerical estimation. Both the wall and core modes fail to resolve the single-molecule signals even under such a large plasmonic enhancement factor γpγe=6.25×104, highlighting the improved sensing capability of the interface mode. Fig. 5B reveals that the time interval between spikes follows the exponential distribution with an average value of about 3 s. Furthermore, measurements of DNA molecules with different concentrations illustrate a linear dependence of average step rate on the concentration, indicating that the detected signals are from single-molecule adsorption (45). In addition, replicated experiments confirm the reproducibility of the single-molecule detection (SI Appendix, Fig. S9).
Fig. 5.
Statistical analysis of single-molecule signals of the plasmonic-enhanced fundamental interface mode. (A) Statistical distribution of step heights induced by the adsorption of single DNA molecules onto the gold nanorod that is placed on the inner surface of the microbubble cavity. (B) Statistical distribution of the time interval between two sequential spikes due to the transient movements of single DNA molecules around gold nanorods. (C) Cumulative step counts for DNA molecules with different concentrations. (D) Average step rates as a function of DNA concentration.
In conclusion, we proposed an optofluidic biosensor with the interface modes in a microbubble resonator. The interface mode features both the peak field intensity at the sensing surface and high-Q factors, enabling a detection limit as low as 0.3 pg/cm2. Furthermore, the proposed scheme can be directly incorporated with other SNR enhancement methods, enabling multifold sensitivity enhancement. As an example, single-molecule detection was demonstrated with the plasmonic-enhanced interface mode. In addition, naturally integrated with the microfluidic system, the optofluidic biosensor allows for rapid biochemical sensing with an ultrasmall sample consumption, and the sensing efficiency could be well adjusted by controlling the flow rate of analyte solution and cavity size (46, 47) (SI Appendix, Fig. S6). Combining sample preparation and delivery with the ultrasensitive analysis technique, the biosensor provides a promising platform for ultrasensitive biochemical analysis in practical applications such as biomedical analysis and early-stage diagnostics (48, 49).

Materials and Methods

Microbubble Resonator Fabrication.

The microbubble resonator is fabricated from a silica glass capillary (27, 50, 51) (TSP100170, Polymicro). First, the capillary is tapered to a diameter below 40 µm via heating and pulling procedures using a hydrogen flame. Consequently, the tapered capillary is transferred to a holder and pressurized inside to several atmospheres. Two focused CO2 laser beams are irradiated on the capillary from opposite directions, providing a uniform heating. Finally, with a well-controllable heating power, a microbubble cavity with desired diameter and wall thickness is formed near the focus point. The wall thickness of the microbubble changes with the diameter when a capillary taper is irradiated by a CO2 laser to form a microbubble cavity, as simulated by finite-element modeling. A microbubble cavity array on a same silica capillary is presented to demonstrate the repeatability of microbubble fabrication (SI Appendix, Fig. S3).

Experimental Setup.

A microbubble resonator (about 100 µm in radial diameter and ∼1 µm in wall thickness) is integrated in a microfluidic system and probed by a tunable diode laser (780-nm wavelength band; TLB-6712, New Focus) via the tapered-fiber coupling. Real-time transmission spectra are monitored by a photoreceiver (model 1801, New Focus) and recorded using a data acquisition (DAQ) card (USB6251-BNC, National Instruments). The whole system is sealed inside a poly(methylmethacrylate) (PMMA) chamber to minimize environmental disturbance.

Experimental Details for Protein Adsorption.

To improve the reusability, the aqueous solution of 0.5 to ∼2 M sodium hydroxide (NaOH) is used to hydroxylate the microbubble inner surface. Slight blue shift (<1pm/min) of the resonance wavelength for interface modes can be observed due to the surface reaction. The BSA-biotin proteins exhibit efficient adsorption when pH5.0 for citrate buffer, which is near the isoelectric point of the BSA protein, while the desorption appears at a higher or lower pH (i.e., phosphate-buffered saline with pH = 7.2 in our experiment) on such a hydroxylated surface. The BSA-biotin (purchased from OKA) and streptavidin (purchased from Sigma-Aldrich) are stepwisely diluted for more precise concentration control.

Gold Nanorod Functionalization.

The gold nanorod we used is 10 nm in diameter and 40 nm in length with the plasmonic resonance wavelength at about 780 nm (purchased from nanoseez). The concentration of the gold nanorod solution with positive charges is diluted down to 2 pM to avoid multiple-binding events, and the pH value is controlled using hydrochloric acid (HCl) to enable surface binding. After the injection of the gold nanorod solution, the nanorod starts to collide with and bind to the inner surface of the microbubble. The binding events of gold nanorods can be observed in the imaging system due to the large scattering cross-section. Furthermore, the monodispersion of gold nanorod adsorbed on the microbubble surface can be characterized by the linewidth broadening with zero mode shift (44).

DNA Preparation.

The stock solution of thiol-modified DNA oligo (5-SH-C6-TTTTGAGATAAACGAGAAGGATTGAT-3, Sangon Biotech) is prepared by dissolving the single-strand DNA oligo into 1× Tris-EDTA (TE) buffer (purchased from Sangon Biotech) to a final concentration of 100 µM. Before the experiment, 10 mM of tris(2-carboxyethyl)phosphine hydrochloride is added to the solution to reduct the thiol agent.

Data Availability

All study data are included in this article and/or SI Appendix.

Acknowledgments

This project is supported by the National Key R&D Program of China (Grant 2018YFB2200401), the National Natural Science Foundation of China (Grants 11825402, 11654003, 62105006, 11974341, and 62035017), and the High-performance Computing Platform of Peking University. X.-C.Y. is supported by the China Postdoctoral Science Foundation (Grant 2018M630020) and the Fundamental Research Funds for the Central Universities. S.-J.T. is supported by the China Postdoctoral Science Foundation (Grants 2021T140023 and 2020M680187).

Supporting Information

Materials/Methods, Supplementary Text, Tables, Figures, and/or References

Appendix 01 (PDF)

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Information & Authors

Information

Published in

Go to Proceedings of the National Academy of Sciences
Proceedings of the National Academy of Sciences
Vol. 119 | No. 6
February 8, 2022
PubMed: 35115398

Classifications

Data Availability

All study data are included in this article and/or SI Appendix.

Submission history

Received: May 13, 2021
Accepted: December 23, 2021
Published online: February 3, 2022
Published in issue: February 8, 2022

Keywords

  1. optofluidic biosensor
  2. whispering gallery microresonator
  3. interfacial molecular detection

Acknowledgments

This project is supported by the National Key R&D Program of China (Grant 2018YFB2200401), the National Natural Science Foundation of China (Grants 11825402, 11654003, 62105006, 11974341, and 62035017), and the High-performance Computing Platform of Peking University. X.-C.Y. is supported by the China Postdoctoral Science Foundation (Grant 2018M630020) and the Fundamental Research Funds for the Central Universities. S.-J.T. is supported by the China Postdoctoral Science Foundation (Grants 2021T140023 and 2020M680187).

Notes

This article is a PNAS Direct Submission. D.S. is a guest editor invited by the Editorial Board.

Authors

Affiliations

Xiao-Chong Yu1
State Key Laboratory for Mesoscopic Physics, School of Physics, Peking University, Beijing 100871, China
Frontiers Science Center for Nano-optoelectronics, Peking University, Beijing 100871, China
Department of Physics, Beijing Normal University, Beijing 100875, China
Applied Optics Beijing Area Major Laboratory, Beijing Normal University, Beijing 100875, China
State Key Laboratory for Mesoscopic Physics, School of Physics, Peking University, Beijing 100871, China
Frontiers Science Center for Nano-optoelectronics, Peking University, Beijing 100871, China
State Key Laboratory for Mesoscopic Physics, School of Physics, Peking University, Beijing 100871, China
Frontiers Science Center for Nano-optoelectronics, Peking University, Beijing 100871, China
Yinglun Xu
State Key Laboratory for Mesoscopic Physics, School of Physics, Peking University, Beijing 100871, China
Frontiers Science Center for Nano-optoelectronics, Peking University, Beijing 100871, China
Qihuang Gong
State Key Laboratory for Mesoscopic Physics, School of Physics, Peking University, Beijing 100871, China
Frontiers Science Center for Nano-optoelectronics, Peking University, Beijing 100871, China
State Key Laboratory on Integrated Optoelectronics, Institute of Semiconductors, Chinese Academy of Sciences, Beijing 100083, China
State Key Laboratory for Mesoscopic Physics, School of Physics, Peking University, Beijing 100871, China
Frontiers Science Center for Nano-optoelectronics, Peking University, Beijing 100871, China
Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, China
Yangtze Delta Institute of Optoelectronics, Peking University, Nantong 226010, China
National Biomedical Imaging Center, Peking University, Beijing 100871, China

Notes

2
To whom correspondence may be addressed. Email: [email protected] or [email protected].
Author contributions: X.-C.Y., S.-J.T., and Y.X. performed the experiments; X.-C.Y. carried out the simulation and numerical calculation; X.-C.Y., S.-J.T., W.L., Q.G., and Y.-L.C. analyzed the data; X.-C.Y., S.-J.T., W.L., Y.X., Q.G., Y.-L.C., and Y.-F.X. contributed to the discussions and wrote the manuscript; S.-J.T. and Y.-F.X. conceived the idea; and Y.-L.C. and Y.-F.X. supervised the project.
1
X.-C.Y. and S.-J.T. contributed equally to this work.

Competing Interests

The authors declare no competing interest.

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