## Introduction

Low-frequency noise with the spectral density S(f) = 1/fγ (where f is the frequency, and γ commonly ranges from 0.5 to 1.5), well known as 1/f noise, flicker noise, or excess noise, has been a ubiquitous phenomenon in both electrical and optical systems1,2,3,4. In general, the 1/f noise originates from the carrier instability inside photoelectric materials4,5 or the current flowing through electrical circuits6,7. Effectively suppressing the low-frequency noise is critical but fundamentally challenging to both electrical and optical transducers, especially to the ultrahigh-sensitivity detection and analysis. For example, in optical evanescent sensors based on resonant structures8,9,10 and nanowaveguides11,12,13,14,15, 1/f noise poses serious difficulties for resolving dynamic signals, such as biomolecule motions, binding, and trapping which are typically charaterized by hertz to kilohertz frequencies16,17,18,19,20,21,22. To date, while much effort has been devoted to suppressing the optical fluctuations in evanescent sensors, such as self-reference mode splitting23,24,25,26, frequency tracking27,28,29,30, and lock-in amplifying14,19, the 1/f noise suppression in optical sensors has never been explored.

Here, we propose an ultralow-noise optical sensing scheme, which can effectively suppress the 1/f noise, via an integrated heterodyne interferometer and an up-conversion amplifying technique. In experiment, the sampling noise is reduced by two orders of magnitude, compared with conventional lock-in amplifying method that focuses on suppressing optical fluctuations14,19. The ultralow-noise sensor is applied to detect single polystyrene and HIV-1 virus-like particles with the detection limit down to a few attograms. The 1/f-noise-free sensing scheme, combined with conventional enhancement mechanisms based on plasmonic nanostructures15,17,31 or surface charges on the analytes19,30, can provide a powerful way towards studying single-molecule dynamics in fundamental biophysics research and practical biological applications.

## Results

### 1/f-noise-free scheme

The 1/f-noise-free scheme is presented in Fig. 1a. We consider a weak photoelectric signal within sub-kilohertz frequency, which falls into the low-frequency 1/f noise band and could not be resolved through a conventional sensing method (Fig. 1a–i). To extract this tiny signal, first, the probe light carrying the sensing signal is shifted by fRF and optically amplified through a heterodyne interferometry. To greatly reduce the effect of 1/f noise, the beat frequency fRF is typically chosen to be tens of megahertz. Second, the beat-frequency photoelectric response is electrically boosted and down converted to a bias frequency Δf, considering a finite sampling rate during the long-term observation. For a conventional data acquisition card, the sampling frequency fsampling is approximately hundreds of kilohertz. The Δf should fall into fsampling but still be beyond the low-frequency 1/f noise band. In this way, the low-frequency signals can be detected with greatly suppressed noise and high-gain amplification in the electric domain.

The above scheme is applied to detect single nano-objects with the experimental set-up shown in Fig. 1b. The heterodyne interferometer, fabricated via a commercial silicon photonics foundry process, consists of a local waveguide and a probe waveguide. They are perpendicularly patterned with a gap serving as the joint sensing area. Since very little of the probe field is collected into local waveguide in the absence of nanoparticles, this dark-field waveguide configuration enables minimal background noise introduced by the probe light (Fig. 1b and Supplementary Fig. 1)19,32. The traveling light in the local (probe) waveguide has the frequency f0 (blued shifted by fRF = 80.15 MHz, f0 + fRF).

When single nanoparticles are deposited into the joint area, due to the elastic scattering, a part of the probe light is collected by the local waveguide via evanescent-wave coupling, which interferes with the local light (Fig. 1b). The generated beat-frequency envelop together with a reference light is subsequently detected by a balanced photodetector where the laser noise can be significantly suppressed21. In this scheme, the scattered signal is boosted by a dual amplification strategy. First, it is optically amplified in dark-field heterodyne configuration by a strong local field, and the enhancement factor reads $$2\sqrt{{P}_{{\rm{local}}}/{P}_{{\rm{probe}}}}$$ with Plocal and Pprobe being the power of local and probe light, respectively. The beat-frequency signal is further boosted by ~ 500 times using a radio-amplifier. After the cross-phase down conversion with the frequency fLO = 80.18 MHz, two channel electrical signals ($${A}_{{\rm{beat}}}^{{\rm{I}}}$$ and $${A}_{{\rm{beat}}}^{{\rm{Q}}}$$) are recorded at the bias frequency Δf = fLO − fRF = 30 kHz without distortion, which is also beyond the 1/f noise band. The beat intensity Ibeat = $${({A}_{{\rm{beat}}}^{{\rm{I}}})}^{2}+{({A}_{{\rm{beat}}}^{{\rm{Q}}})}^{2}$$ scales linearly with the scattering efficiency of the nanoparticle (Supplementary Note 1).

### Noise analysis

To study the noise performance in the low-frequency band, the power spectra of $${A}_{{\rm{beat}}}^{{\rm{I}}}$$ are obtained with or without light input as shown in Fig. 1c. In both cases, the significant electronic noise with the 1/f spectral shape emerges below ~100 Hz. In addition, a mass of spikes can be found with frequencies within 1 kHz that are introduced by the electrical elements. To eliminate these disturbances during extracting process, the beat-frequency signal is thus sampled at a bias frequency Δf far away from the low-frequency noise band (red curve in Fig. 1c). Furthermore, the noise amplitude of $${A}_{{\rm{beat}}}^{{\rm{I}}}$$ is plotted as a function of the bias frequency Δf as shown in Fig. 1d, and it is fitted by 1/(Δf)0.61 below the corner frequency of ~300 Hz. It is found that the sampling noise amplitude is suppressed by two orders of magnitude than that of the conventional lock-in amplifying method (1.87 × 10−6 V at Δf = 30 kHz versus 6.22 × 10−4 V at Δf = 0). Here, the sampling noise amplitude is calculated from the standard deviation of the cross-correlation $$\frac{2}{T}\mathop{\int}\nolimits_{-T/2}^{T/2}{A}_{{\rm{beat}}}^{{\rm{I}}}(t+\tau )h(\tau ){\mathrm{d}}\tau$$ between the signum function h(t) = sgn(t) and the signals $${A}_{{\rm{beat}}}^{{\rm{I}}}$$ in the duration time T = 1 s (Supplementary Note 2). With such a 1/f-noise-free extraction method, the corresponding real-time signals Ibeat in Fig. 1e show a significant suppression of 12.3 dB on the Ibeat fluctuations.

### Sensing characterization with a near-field nanotip

The on-chip waveguide sensor enables quantitative characterization of its sensing performance through a near-field nanotip as shown in Fig. 2a, b. A silica nanotip with a radius of 200 nm is applied as a controllable nano-object to observe the local topography of the joint sensing region (Methods). Experimentally, the nanotip is horizontally and vertically scanned in the range of 1.5 μm and 0.8 μm as shown in the insets of Fig. 2a, b, respectively. The beat intensity Ibeat as a function of nanotip position is in good agreement with the simulation results. In the three-dimensional finite element method (3D FEM) simulation, the power of probe light collected by the local waveguide Pcol is calculated as a function of the particle position (200-nm-radius silica nanosphere). As expected, the Ibeat increases as the nanotip approaches the joint sensing area, in which the signal-noise ratio (SNR) as high as 2 × 103 is observed. Note that the signal Ibeat reaches its maximum when the nanotip is about 300 nm away from the center of probe waveguide in Fig. 2a, which shows a directional scattering behavior (Supplementary Note 3)33.

### Real-time detection of single nanoparticles

The waveguide sensor is then tested by the standard polystyrene nanobeads. Experimentally, the nanobeads (30, 41, and 55 nm in radius) are blown onto the joint sensing area using a glass nozzle via a syringe pump (Methods). The binding events of nanoparticles are clearly recognized by the discrete increasing steps in real-time beat signal Ibeat as shown in Fig. 2c–e. As expected, the height of the discrete steps in $$\delta {I}_{\text{beat}}=\frac{2}{T}\mathop{\int}\nolimits_{-T/2}^{T/2}{I}_{{\rm{beat}}}(t+\tau )h(\tau ){\mathrm{d}}\tau$$ increases with the particle size. A few decreasing steps are also observed, which is due to the nanoparticles blown away by the air flow from the glass nozzle or the interference effects induced by multiple nanoparticles12,13. For the 30-nm-radius nanobeads, discrete steps of beat intensity Ibeat with the SNR as high as 14.5 dB are observed, while a SNR below 0 dB is observed at the same time with the conventional waveguide sensor through directly monitoring the transmission loss12,13 (Supplementary Fig. 4). The enhanced SNR is contributed by the dual signal amplification strategy and the 1/f noise suppression.

To estimate the detection limit, the statistical steps in the interval [δIbeat − σ/2, δIbeat + σ/2] with σ = 3 × 10−6 in Fig. 3a–c, originated from the particles deposited closely to the joint sensing area, are selected to analyze the size-dependent behavior. The mean values and standard deviations of the selected δIbeat are plotted in Fig. 3d, which are in good agreement with the simulation results. In the 3D FEM simulation, the power of probe light collected by the local waveguide Pcol is calculated as a function of particle size when the scatterer is placed in the joint sensing area. Since the beat intensity is proportional to the collected power of probe light δIbeat = rPcol (Supplementary Note 1), the equipment-dependent coefficient r is obtained according to the simulated Pcol and the corresponding measured δIbeat induced by 55-nm-radius polystyrene nanobeads. The noise levels derived from 3σ of Ibeat is 6.64 × 10−6 (1.12 × 10−4) at Δf = 30 kHz (Δf = 0), where σ is the standard deviation. According to the fitting curve of simulated results in Fig. 3d, the detection limit is 17.5 nm in radius for Δf = 30 kHz, while it is 47.3 nm for Δf = 0. This indicates that the ultrasensitive and low-noise sensor enables detection of single nanoparticles with the mass down to a few attograms (10−18 g).

Detecting and characterizing viruses in aerosol are of paramount importance for disease control and diagnosis34. Here, as a proof-of-concept demonstration for airborne biosensing, we applied the low-noise sensor to detect single viruses. The virus-like particles (VLPs) assembled from living cells expressing the human immunodeficiency virus (HIV) gag protein (Methods) are detected. Figure 4a presents clear discrete steps in the beat intensity Ibeat when single particles are blown onto the sensing area. In order to make a clearer comparison between the height of Ibeat steps versus the noise level, the absolute value of δIbeat calculated through cross-correlation is shown in Fig. 4b. The maximum SNR as high as 20 dB is obtained for the HIV-1 virus-like particles, suggesting our sensor has the ability to detect smaller viruses. Furthermore, the δIbeat of detected VLPs in an ensemble measurement is shown in Supplementary Fig. 5. Considering the difference in refractive index between virus and polystyrene nanobeads, the estimated radius of VLPs is about 52.1 ± 1.9 nm, which is close to the expected size of an HIV-1 VLP (~50 nm in radius).

### Multiplexed and rapid sensing

The ultralow-noise sensor is realized with the high-density integrated waveguide arrays via a commercial silicon photonics foundry process (Fig. 5a). This feature enables to explore multiplexed and rapid sensing.

A radio-frequency multiplexing concept is proposed as shown in Fig. 5b. The lights (f0) shifted by the radio frequencies (fRF1, fRF2, fRF3, -) are coupled into different probe waveguide units, from which all the scattering probe light interferes with the local light in the same bus waveguide. The multiplexed signals can be independently extracted by switching the down-conversion frequency fLO. This concept combined with surface functionalizations in different frequency channels may serve as an alternative approach for detecting several target analytes at the same time, which is highly desirable for practical applications such as medical diagnostics. In addition, we experimentally demonstrate that the probe-waveguide array can enhance the nanoparticle capture efficiency. As shown in Fig. 5c, representative beat intensity Ibeat for the nine-waveguide (one-waveguide) configurations contains 21 (4) discrete steps induced by nanobead binding in 20 s. For the long-term monitoring over 450 s, the statistical analyses of time intervals between sequential nanobead-binding events are shown in Fig. 5d. The 1/e decay time is 0.95 s (2.96 s) for the nine-waveguide (one-waveguide) configurations, which indicates a 3-fold enhancement in capture efficiency.

### Discussion

We have demonstrated a 1/f-noise-free sensing scheme with an integrated heterodyne interferometer. Compared with the conventional lock-in amplifying technique, the sampling noise is suppressed by two orders of magnitude, pushing the single-particle detection limit down to the attogram level. The proposed scheme with ultra-low noise and high-gain signal amplification could significantly enhance the sensitivity and lower the detection limit, which gives an insight into the low-frequency dynamics of unlabeled nano-objects, such as antigen–antibody reactions and cell motions. Note that, with the low-frequency 1/f noise suppressed, the detection limit of the heterodyne interferometer is determined by the optical background noises in the probe and local light. Especially, the intensity of background probe light scattered due to the sidewall roughness of waveguides, which could be shifted beyond 1/f noise band with the signal and thus cannot be removed by the 1/f-noise-free scheme, hinders its ability operated at a precision limited by fundamental shot and thermal noises.

Since the 1/f-noise-free sensing scheme is compatible with previous enhancement mechanisms based on plasmonic nanostructures15,17,31 or surface charges19,30 on the target nanoparticles/molecules, the ultra-low noise optical sensor has a high potential for single-molecule dynamic detection. Furthermore, the CMOS-compatible heterodyne interferometer combined with the microfluidics and the chemical-functionalization technology could be widely applied in the fields of biology, medicine, pharmacology, physics, and environmental science.

## Methods

### Fabrication of on-chip waveguide sensor

The waveguide sensor is fabricated through a standard CMOS-compatible process on a silicon-on-insulator (SOI) 8" wafer with a 220-nm-thick top silicon layer and a 2-μm-thick buried oxide layer. The layout is patterned through deep ultraviolet lithography and inductively coupled plasma etching. All the grating couplers involved are designed for inducing the transverse electric (TE) field in waveguides, of which the measured insertion loss is about 7.5 dB/facet. We design and fabricate two kinds of sensing structures around the joint sensing area. For the first kind, the probe waveguides are sparsely arranged with a center pith of 50 μm, and each one together with the local waveguide form an independent sensing area. This structure is used to characterize the local image of the sensing region and the detection limit of the waveguide heterodyne sensing system. For the other kind, nine probe-waveguide and one local-waveguide are integrated to construct the joint sensing area. These probe waveguides with a center pitch of 5 μm are connected in parallel by a power splitter to form a dense array. The designed widths of the probe waveguide and local wavguide around joint sensing area are 1 μm and 500 nm, respectively (Fig. 5, insets).

### Experimental set-up

The wavelength of the laser source is 1550 nm. The AOM (Gooch & Housego Inc., PM FIBER-Q) is driven by an arbitrary function generator with a sinusoidal wave. The 1/f-noise-free signal extracting system consists of a high-pass filters (55 MHz), a BPD (Torlabs Inc., PDB570C), two low-noise photodetectors (Newport Inc. 1811-FC), a radio-frequency amplifier (Mini-circuits Inc., ZHL-1-2W-S+), a 90 power splitter centered at 80.18 MHz, two microwave mixers (Mini-circuits Inc., ZFM-2-S+), and a data acquisition system (National Instruments). The 2-way downcoverted signals ($${A}_{{\rm{beat}}}^{{\rm{I}}}$$ and $${A}_{{\rm{beat}}}^{{\rm{Q}}}$$), as well as 1% power of the probe field and 10% power of the signal field for normalization are synchronously sampled by the DAQ.

### Sening characterization

In the experiment of nanotip scanning around joint sensing area, we use the one-probe-waveguide structure with a 1-μm-width gap. The nanotip is fabricated from a silica fiber through thermal-pulling (CO2 laser) and buffered hydrofluoric acid solution etching. The glass nozzle with an inner radius of 50 μm is fabricated by thermal-pulling the capillary glass tube (inner radius, 0.5 mm) using the hydrogen flame. The 3-axis translation stage drives the nanotip under the velocities of 0.45 μm/s (Fig. 2a) and 0.6 μm/s (Fig. 2b). Single nanobeads and HIV-1 VLPs are first diluted to tens of picomoles in the DI water (QDSphere Inc., radius of 30 nm; Nano-Micro Inc., radius of 41 nm; Invitrogen Inc., radius of 55 nm and HIV virus-like particles, radius of ~50 nm). The air flow with nanoparticles are then generated through the ultrasonic atomizer. The nanoparticles are deposited to the joint sensing area by a syringe pump (Harvard, Model PHD22/2000) at the flow rates of 15 ml min−1 for nanobeads and 10 ml min−1 for virus-like particles.

In the nanoparticles detection, the polystyrene nanobeads are measured using the waveguide sensor with a gap of 0.4, 1, and 1.4 μm for reducing the possible size correlations between the nanoparticles and the gap width. The step-finding algorithm is applied to extract the step signal. The step heights of the binding events are derived follows three steps: 1. Calculating the δIbeat through cross-correlation method from Ibeat to identify the locations of the possible binding events. 2. Calculating all the possible step heights and recording the corresponding time. 3. Comparing all the step heights with the system noise level and preserving those that are greater than ~ 3σ. The total numbers of the deduced scattering events are 186 for the 30 nm nanoparticles, 195 for the 41 nm nanoparticles, and 156 for the 55 nm nanoparticles (Fig. 3).

### Cell culture and plasmid transfection

HEK293T cells (American Type Culture Collection) were cultured in Dulbecco’s Modified Eagle’s Medium (DMEM, Mediatech), supplemented with 10% (v/v) FBS (PANTM Biotech), 1 × GlutaMAXTM (Thermo Fisher) at 37 °C, 5% (v/v) CO2, and 90% relative humidity. Cells reaching 50–70% confluency in a T-75 tissue culture flask were transfected with 10 μg of the CMV-driven expression plasmid encoding HIV-1 Gag (pCR3.1-Gag, a kind gift of Dr. Sanford Simons at the Rockefeller University, New York, NY) using FuGENE® 6 (Promega) as per manufacturer’s protocols.

### Virus particle collection

Virus-like particles were collected as previously described35,36. Briefly, culture supernatant of HEK293T cells harvested at 24 h after transfection of viral constructs was centrifuged at 1000 g for 10 min, followed by removal of cell debris and large aggregates with a 0.45 μm filter.