1. Introduction

With the increasing presence of nanoparticles in daily lives, there is a growing interest in assessing their benefits and risks. Meanwhile, there is also a strong need to detect and characterize biological nanoparticles such as viruses, which are responsible for the outbreak of many infectious diseases. A critical step in this assessment is to establish label-free, reliable and cost-effective techniques for real-time and on-site detection and quantification of individual viruses and nanoparticles. This will facilitate studies of physical and biological properties of single viruses, and of size and material dependent properties of nanoparticles at single particle level.

Among various techniques [1–13], micro/nano-sized photonic [3–8] and electromechanical [9, 10] resonators are emerging as forerunners for label-free detection of single nanoparticles and molecules due to their immense susceptibility to perturbations in their environments which enhances sensitivity and resolution, and due to the increasing demand for shrinking device dimensions to achieve massive parallelism and integration with the existing micro/nanosystems.

The sensing mechanism used in the existing photonic and electromechanical resonators relies on the detection of the spectral shift of a resonance mode upon the landing of a nanoparticle within the mode volume. The amount of the spectral shift depends on both the position of the particle and its properties such as mass, size, refractive index or polarizability. Thus, although each arriving particle or virion can be detected, accurate quantitative measurement of the properties of each arriving particle and virion cannot be done. Instead, statistical analysis, such as building histograms of event probability versus spectral shift for ensembles of sequentially arriving particles of similar properties, is used to extract the required information (e.g., size, mass or polarizability) [4, 10]. This prevents single-shot measurement of each particle and real-time sizing capabilities. Moreover, an equally important issue affecting these schemes is the absence of a reference. The shift induced by a nanoparticle is very small, and it is sensitive to instrumental noise and environmental disturbances. Thus, discriminating between the interactions of interest and the interfering perturbations becomes difficult.

Recently, we have introduced position-independent size measurement for a single nanoparticle by using scattering-induced mode-splitting in an ultra-high-quality (Q) WGM microtoroid resonator [14]. Although this prototype scheme allowed to overcome some difficulties (i.e., position-dependence and lack of reference) associated with measurement of nanoparticles, there remained critical issues to be solved. First, the sizing method is applicable only for WGM without observable splitting. One has to find a splitting-free WGM for measurement of the particle. Since intrinsic mode splitting (e.g., not intentionally induced or caused by the target scatterers) [15,16] takes place in almost all practical realizations of ultra-high-Q resonators due to contaminations or structural inhomogeneities, it is difficult to find such an initially splitting-free WGM. Second, position independent size estimation was valid only for the first nanoparticle as the previous model did not explain how the split modes are affected when the particles sequentially enter the mode volume after the first one.

In this study, we demonstrate a technique which overcomes the above mentioned limitations of existing resonator-based schemes thus allowing the detection, counting and size measurement of consecutively adsorbed nanoparticles and virions one-by-one at single particle resolution. This new mode splitting based approach requires neither simultaneous excitation, frequency-locking and tracking of multiple modes of a resonator nor histogram preparations or stochastic analysis.

We achieved label-free detection and accurate size-measurement of InfA virions, gold (Au) and polystyrene (PS) particles down to R=30 nm. The ability to detect and measure single virions/nanoparticles allows determining their polarizability and size distributions. The demonstrated techniques offer the possibility of an ultra-compact single nanoparticle/biomolecule size spectrometry system for in-lab or in-field use.

2. Experiments

Single Virus/Nanoparticle Size Spectrometry

Figure 1(a) schematically depicts our experimental system. Microresonators used in our experiments are silica microtoroids prepared by photolithography followed by CO₂ laser re-flow [17]. The resonators have quality factors above 10⁷ and diameters below 40 μm. A tunable 670 nm band laser is used in experiments with virions and nanoparticles smaller than R=70 nm, and a 1550 nm band laser is used in experiments with bigger particles. A fiber taper prepared from a standard single mode fiber by heat-and-pull technique is used to couple light into and out of the microresonator. Transmitted light is detected by a photodetector which is connected to an oscilloscope for monitoring the transmission spectra (Fig. 1(b)). The spectra are acquired to the computer at rate of 10 frames per second, and processed by double Lorenzian curve fitting to find the frequencies and linewidths of the resonances.

 

Fig. 1 Experimental Setup (a) Simplified schematic of the virion/nanoparticle size spectrometry system, showing the virion/nanoparticle deposition through a nozzle onto a fiber taper coupled microtoroid resonator. The inset displays the scanning electron micrograph of single InfA virions adsorbed on the surface of a resonator. (b) Typical transmission spectrum of the system showing virion induced mode splitting.

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Mode splitting can be induced either by the scattering centers due to structural inhomogeneities (i.e., intrinsic mode splitting) [15,16] or by the scatterers intentionally introduced into the resonator mode volume [14, 15, 18]. The underlying physics of the interaction between a resonant mode and a single sub-wavelength scatterer in the mode volume was studied using the dipole approximation [18]. The resonator-scatterer interaction lifts the frequency-degeneracy of the two counter-propagating WGMs of the resonator and splits the single resonance into two, leading to two standing wave modes (SWMs). Consequently, the two SWMs are identified in the transmission spectrum as a doublet with two spectrally shifted resonance modes of different linewidths (Fig. 1(b)).

For the deposition of nanoparticles and viruses, a set-up consisting of a differential mobility analyzer (DMA) and a nozzle with an inner tip diameter of 80 μm was used. First, particles are carried out by compressed air using a collision atomizer. The solvent in droplets is then evaporated in a dryer with the silica gel desiccants. Solid particles are further neutralized by a radioactive source such that they have a well-defined charge distribution. Then they are sent to the DMA where they are classified according to their electrical mobility. Particles within a narrow range of mobility can exit through the output slit. The nozzle was placed at about 300 μm away from the microtoroid, and particles are blown directly towards the microtoroid. Purified and inactivated Influenza virus X-31 A/AICHI/68 was purchased in 4-(2-hydroxyethyl)-1-piperazineethanesulfonic acid (Hepes) buffer from Charles River Laboratories. The virus sample was passed through a 0.2 μm nylon membrane filter to remove aggregates. Gold nanoparticles (50 and 100 nm) were purchased from British Biocell International Limited. PS nanoparticles (50–135 nm) are from Thermo Scientific (Duke Standards 3K series).

Figure 2 shows the mode splitting spectra induced by InfA virions entering the resonator mode volume one-by-one. With the arrival of the first virion, the single resonance splits into two. The subsequent single virion adsorptions lead to redistribution of the existing SWMs and abrupt jumps in the splitting spectra (Fig. 2(a)). The sudden changes in the frequencies and linewidths of the resonance modes signal the detection of particle adsorption events, and the amount of change depends on the virion size and its position in the mode volume. In the next section, we will explain how to take advantage of the split modes for constructing a position-independent measurement scheme for individual scatterers. The mode splitting resonance frequencies and linewidths extracted from the spectra in Fig. 2(a) show step changes corresponding to each individual virion adsorption event (Figs. 2(b) and 2(c)). Processing this data allows to extract the polarizability and hence the size of each virion (Fig. 2(g)), as will be shown in the next section. Note that particles deposited outside the mode volume do not affect the WGM, so they have no effect on the resonance spectrum.

 

Fig. 2 Real-time records of single InfA virion adsorption events using mode splitting phenomenon in a microtoroid optical resonator. (a) Evolution of transmission spectra as the single virions are adsorbed onto the resonator mode volume. The single resonance splits into a doublet with the first virion binding event. The subsequent binding events lead to abrupt changes in the mode splitting spectra. Each abrupt change corresponds to detection of a single virion, and the amount of change depends on the polarizability and the position of the adsorbed virion in the mode volume (see Eqs. (4) and (5)). A video showing the detection of R=100 nm PS particles is also included (Media 1). (b) Frequencies and (c) linewidths of the two split modes extracted from the data in (a) by curve fitting. (d) Sum of the frequency shifts of the two split modes with respect to frequency of the initial single mode resonance mode, ${\delta }_N^{+}$, and (e) sum of the linewidths of the split modes, ${\rho }_N^{+}\hspace{0.17em}+\hspace{0.17em}2{\gamma }_0$. Lines are for eye guide. (F) Evolution of splitting quality $Q_{\text{sp}}\hspace{0.17em}=\hspace{0.17em}2{\delta }_N^{-}/({\rho }_N^{+}\hspace{0.17em}+\hspace{0.17em}2{\gamma }_0)$ as a function of time. Note that mode splitting is observable in the transmission spectrum if Q _sp > 1. (g) Size of each adsorbed single virion calculated from the data in (d) and (e) using Eqs. (9) and (10). The horizontal line designates the average size. In (d) and (g), the ’*’ signs mark the point of single virus adsorption events, and circles mark the events from which accurate size information could be extracted.

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3. Theory

Single Particle Model

Let’s denote the two SWMs formed after the adsorption of a single nanoparticle/virion as lower and higher frequency modes with the corresponding resonance frequencies and linewidths denoted as ( ${\omega }_1^{-}$, ${\gamma }_1^{-}$) and ( ${\omega }_1^{+}$, ${\gamma }_1^{+}$). The dipole approximation predicts that the spectral distance of these two modes is given by the coupling coefficient between the counter-propagating WGMs as 2g = −αf ²(r)ω/V, and the linewidth difference due to coupling of the WGMs to the environment via scattering is given as 2Γ = α ² f ²(r)ω ⁴/3πν ³ V. Here ω is the angular resonant frequency, V is the microcavity mode volume, $\nu \hspace{0.17em}=\hspace{0.17em}c/\sqrt{{\varepsilon }_m}$ with c representing the speed of light, and f (r) is a scalar quantity and designates the normalized mode intensity distribution. The polarizability α of the scatterer is α = 4πR ³(ɛ_p − ɛ_m)/(ɛ_p + 2ɛ_m) for a spherical particle of radius R and electric permittivity ɛ_p in a surrounding medium of electric permittivity ɛ_m (e.g., ɛ_m = 1 for air). Subsequently, the frequency shift ( $\mathrm{\Delta }{\omega }_1^{-}$, $\mathrm{\Delta }{\omega }_1^{+}$) and linewidth change ( $\mathrm{\Delta }{\gamma }_1^{-}$, $\mathrm{\Delta }{\gamma }_1^{+}$) of the split modes (doublet) with respect to the resonance frequency ω ₀ and the linewidth γ ₀ of the initial (pre-scatterer) WGM are

Multi-Particle Model

In the case of multiple scatterers, with each new scatterer entering the resonator mode volume, the resonator-scatterer interaction changes, leading to redistribution of SWMs. Consequently, the locations of nodes and anti-nodes of the SWMs with respect to the individual scatterers are modified (Media 1).

The locations of each scatterers with respect to each other in the resonator mode volume determines the distribution of SWMs. Assuming N-scatterers in the mode volume, we define ϕ_N as the spatial phase distance between the antinode of the ${\omega }_N^{-}$ mode and the 1st scatterer, and β_i as the spatial phase distance between the i-th and the 1st scatterer. We can write the frequency shift and the linewidth broadening experienced by the split modes as

Next, we define ${\delta }_N^{-}\hspace{0.17em}=\hspace{0.17em}\mathrm{\Delta }{\omega }_N^{+}\hspace{0.17em}-\hspace{0.17em}\mathrm{\Delta }{\omega }_N^{-}\hspace{0.17em}=\hspace{0.17em}{\omega }_N^{+}\hspace{0.17em}-\hspace{0.17em}{\omega }_N^{-}$ as the mode splitting between the two modes and ${\delta }_N^{+}\hspace{0.17em}=\hspace{0.17em}\mathrm{\Delta }{\omega }_N^{+}\hspace{0.17em}+\hspace{0.17em}\mathrm{\Delta }{\omega }_N^{-}\hspace{0.17em}=\hspace{0.17em}{\omega }_N^{+}\hspace{0.17em}+\hspace{0.17em}{\omega }_N^{-}\hspace{0.17em}-\hspace{0.17em}2{\omega }_0$ as the total frequency shift. Similarly, ${\rho }_N^{-}\hspace{0.17em}=\hspace{0.17em}\mathrm{\Delta }{\gamma }_N^{+}\hspace{0.17em}-\hspace{0.17em}\mathrm{\Delta }{\gamma }_N^{-}\hspace{0.17em}=\hspace{0.17em}{\gamma }_N^{+}\hspace{0.17em}-\hspace{0.17em}{\gamma }_N^{-}$ corresponds to the linewidth difference between the two split modes and ${\rho }_N^{+}\hspace{0.17em}=\hspace{0.17em}\mathrm{\Delta }{\gamma }_N^{+}\hspace{0.17em}+\hspace{0.17em}\mathrm{\Delta }{\gamma }_N^{-}\hspace{0.17em}=\hspace{0.17em}{\gamma }_N^{+}\hspace{0.17em}+\hspace{0.17em}{\gamma }_N^{-}\hspace{0.17em}-\hspace{0.17em}2{\gamma }_0$ corresponds to the sum of the linewidth change. Using the definitions of ${\delta }_N^{\pm }$ and ${\rho }_N^{\pm }$ and Eqs. (4) and (5), we find

4. Discussion

Mode Splitting Size Spectrometry of Single InfA Virions

The spectrogram shown in Fig. 2(a) presents examples of transmission spectra obtained in experiments with InfA virions. With each consecutive individual nanoparticle adsorption, the frequency and the linewidth of the split modes change abruptly. The heights of discrete jumps depend on the positions of the virions relative to the SWMs according to Eqs. (4)–(6).

Extracted frequencies and linewidths of the split resonances from the experimental data shown in Fig. 2(a) are depicted in Figs. 2(b,c). This information is subsequently used to calculate ${\delta }_N^{+}$ and ${\rho }_N^{+}$ (Fig. 2(d) and 2(e)). Single virion adsorption events are clearly visible as discrete jumps in Figs. 2(d) and 2(e). Although the height of each discrete jump depends on the position of each virion within the resonator mode volume, we can accurately measure the size regardless of the virion position. Using Eqs. (9) and (10), we estimated the polarizability from which the size of the adsorbed virions was derived and presented in Fig. 2(g). Assuming a refractive index of 1.48 [11] for virions, we calculated the radii of the adsorbed virions to be in the range 46 – 55 nm, for the data in Fig. 2. As seen in Fig. 2(e), the change in total linewidth ${\rho }_N^{+}$ for the fourth virion adsorption event is within the noise level of our system. Although the estimated size for this virion differs from the expected nominal size, this does not prevent detecting this virion thanks to the distinct change in total frequency ${\delta }_N^{+}$ (Fig. 2(d)).

We obtained the polarizability and size distributions of InfA virions by performing many experiments using different resonators. The results are depicted in Figs. 3(a) and 2(b). Measured radius R = 53.2 ± 5.5 nm for InfA virions agrees very well with the values reported in the literatures [4, 11, 22].

 

Fig. 3 Single virus/nanoparticle size spectrometry using mode splitting in microtoroid resonators. Polarizabilities and sizes are calculated from transmission spectra according to Eqs. (9) and (10). (a) Measured polarizability distributions of InfA virions and 50 nm Au nanoparticles. (b) Measured size distribution of InfA virions with average radius at 53.2 nm. (c) Measured polarizability distributions of 50 nm and 100 nm Au particles. (d) Measured size distrbutions of 100 nm and 135 nm polystyrene (PS) particles. Red curves are Gaussian fits to the experimentally obtained distributions.

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Having identified that the developed model and the scheme allow measuring the polarizability and size of individual InfA virions, we set out to measure polarizability and size distributions of Au and PS nanoparticles. For comparison, we show in Figs. 3(a) and 3(c) the experimentally obtained polarizability distributions of Au nanoparticles with R = 50 nm and R = 100 nm. Figure 3(d) depicts the distribution of estimated sizes for PS particles of R = 100 nm and R = 135 nm. The measured distributions of the tested nanoparticles are significantly different correlating with their sizes and material properties.

Size Resolution and Detection Limit

For PS particles with nominal radius of R = 100±1.7 nm and R = 135 ± 2.1 nm, our size estimation yielded R = 101.2 ± 9.05 nm and R = 135.9 ± 9.96 nm, respectively. The standard deviations of measured polarizability distributions (Fig. 3(a) and 3(c)) for Au particles are 32% and 31%, respectively for R = 50 nm and R = 100 nm. These are slightly larger than the 24% polarizability deviation estimated from the 8% size deviation claimed by the manufacturer.

The standard deviation of the estimated particle sizes and polarizabilities using our technique have four main contributions: (i) Standard deviation of the particles, (ii) detection noise and the laser frequency fluctuations, (iii) curve fitting noise in extracting the resonance frequencies and linewidths of the split modes, and (iv) fluctuations in the taper-resonator gap. We performed all experiments in normal laboratory environment with no active control of the conditions. Thus, we believe that the reported results can be improved by proper conditioning and control of laser phase and intensity noise as well as taper-resonator gap fluctuations.

Theoretical detection limit of our scheme is mainly dependent on Q/V of the resonator and the wavelength of the resonance. For a dielectric nanoparticle of refractive index 1.5, detection limit is around R = 10 nm with an ultra-high-Q resonance in the 670 nm wavelength band. In our experiments using microtoroids with Q ≥ 10⁸, the smallest detected PS particles were of radii R = 20 nm (nominal value provided by the manufacturer), and the smallest PS particles detected and accurately measured were of radii R = 30 nm. These are the smallest dielectric nanoparticles ever detected and measured using optical resonators.

We performed accurate size measurement of up to 50 nanoparticles consecutively deposited on a single WGM resonator with high-Q, without cleaning of the resonator. On the other hand, hundreds of virions or nanoparticles can be detected with the same resonator. This discrepancy in the detection and measurement limits can be explained as follows. In order to detect a single virion/nanoparticle binding event, it is sufficient to detect any change in either the resonance frequencies or the linewidths. However, accurate size measurement requires that the changes in both the frequencies and the linewidths are accurately measured. Thus, size measurement imposes a much stricter condition. For example, as the number of particles in the resonator mode volume increases, the increasing scattering loss leads to broadening of the resonance linewidths. Eventually, the change induced in the linewidths by a single virion/nanoparticle falls within the noise level (i.e., similar to the fourth virion event in Fig. 2). In such a case, linewidth information is partially or completely lost, and size information cannot be extracted correctly. However, there may still be a discernible change in frequency which would allow detection of particle binding. Indeed, accurate detection of resonance frequency changes has a higher saturation limit and is less prone to noise than the linewidth measurement.

Measurement of Nanoparticle Mixtures

We challenged our system with a mixture of PS and gold nanoparticles with radii R = 50 nm. The measured polarizability distributions are shown in Fig. 4. The two maxima are easily seen and the two distributions have small overlap suggesting that our method can be reliably used to detect multiple components of a homogenously mixed ensemble of particles and to decide whether the given composition of particle ensemble is mono or poly-modal. This is expected as our scheme measures nanoparticles one-by-one. No apriori information is needed to differentiate particles of different polarizabilities.

 

Fig. 4 Measured polarizability distributions of a homogenous mixture of PS and Au particles with radii 50 nm. Bimodality of the mixture is accurately determined from the processing of mode splitting spectra. Red curves are the Gaussian fits to the experimentally obtained distributions. The left peak corresponds to PS particles and the right peak corresponds to Au particles.

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Resolvability of Mode Splitting

In order to resolve mode splitting in the transmission spectra after the deposition of the N-th particle, ${\delta }_N^{-}\hspace{0.17em}>\hspace{0.17em}{\rho }_N^{+}/2\hspace{0.17em}+\hspace{0.17em}{\gamma }_0$ should be satisfied [23, 24]. Consequently, mode splitting quality $Q_{\text{sp}}\hspace{0.17em}=\hspace{0.17em}2{\delta }_N^{-}/({\rho }_N^{+}\hspace{0.17em}+\hspace{0.17em}2{\gamma }_0)$ should be larger than one, Q _sp > 1 [23]. The change in Q _sp as the InfA virions bind to the resonator is shown in Fig. 2(f) where we see that Q _sp > 1 is satisfied during the measurements. As the particle binding continues, each additional scatterer increases the linewidths, at some point Q _sp may become less than one and mode splitting can no longer be resolved. However, even in such cases, one can extract some useful information if we assume that mode splitting is much smaller than the individual linewidths ${\omega }_N^{+}\hspace{0.17em}-\hspace{0.17em}{\omega }_N^{-}\hspace{0.17em}\ll \hspace{0.17em}{\gamma }_N^{-},{\gamma }_N^{+}$, and the two resonances have similar linewidths ${\gamma }_N^{-}\hspace{0.17em}\simeq \hspace{0.17em}{\gamma }_N^{+}$. In such a case, the transmission spectrum will show a single lorentzian peak with a linewidth of ${\gamma }_N\hspace{0.17em}=\hspace{0.17em}\sqrt{{\gamma }_N^{-}{\gamma }_N^{+}}\hspace{0.17em}\simeq \hspace{0.17em}({\gamma }_N^{-}\hspace{0.17em}+\hspace{0.17em}{\gamma }_N^{+})/2$ and a resonance at ${\omega }_N\hspace{0.17em}\simeq \hspace{0.17em}({\omega }_N^{-}\hspace{0.17em}+\hspace{0.17em}{\omega }_N^{+})/2$. This expressions then can be used in Eqs. (9) and (10) to calculate the polarizability and the size of the N-th particle, provided that γ_N – γ _N−1 and ω_N − ω _N−1 are resolvable [25]. It should be noted that working in the split mode regime allows a lower measurable particle size for single particle analysis.

Measurement of Ensembles of InfA Virions

Discussions and experimental results presented in the previous sections clearly demonstrate that our scheme is very effective and efficient in estimating the polarizability of individual nanoparticles entering the resonator mode volume one-by-one. Indeed, during continuous deposition of nanoparticles, mode splitting spectra at any instant is related to the effective polarizability of already deposited nanoparticles. If we assume that N-particles are deposited to the mode volume of the resonator, we can assign an effective polarizability α _eff sensed by the resonator using

 

Fig. 5 Estimation of the size of InfA virions by applying Eq. (11) on the data in Fig. 2. The fluctuations in size estimation decreases as the splitting quality Q _sp increases (Fig. 2(f)).

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5. Conclusion

We have shown that adsorption of individual viruses and nanoparticles leads to discrete changes in the mode splitting spectra of a WGM microcavity. We developed an accurate and efficient method to detect and measure individual nanospecies one-by-one as they are adsorbed in the mode volume of a microresonator and experimentally verified it using InfA virions, PS and Au nanoparticles of various sizes. We achieved this by developing a new theoretical model and measurement strategy which take into account the effect of multiple scatterers deposited on an optical WGM resonator. Contrary to the existing schemes, this new approach works equally well regardless of whether there is intrinsic mode splitting or whether a particle is deposited in the resonator mode volume before the actual measurement starts. The particles are characterized accurately regardless of their positions in the mode volume without the need for complicated processes such as stochastic analysis or excitation and tracking of multiple resonant modes. Moreover, our method is capable of identifying the modality of mixtures of nanoparticle ensembles. Thus, the proposed single nanoparticle size spectrometry technique provides a suitable platform for in-situ, real-time and highly sensitive detection and sizing of individual nano-sized particles and viruses.

Since nanoparticle induced mode splitting has been demonstrated in water [26], the techniques developed here could be effectively extended to aqueous environment and incorporated into microfluidic or lab-on-chip devices which will pave the way for detecting and sorting of single bio- molecules/particles based on their polarizability or size. Although in this work, we considered spherical particles and isotropic polarizability, our method could be applied to distinguish between spherical and nonspherical particles by probing the particles with light fields of orthogonal polarizations [27, 28]. Moreover, the demonstrated techniques are not limited to microtoroidal resonators and in principle can be used with any WGM resonator (e.g., microsphere, microdisk or microring), independent of the mode number and polarization. We should note that for spherical particles, the estimated polarizability using our technique is the same for all polarizations; however, for non-spherical particles different polarizations will give different polarizabilities. This can be used to estimate the shape and size of the particles. [25,30,31] Further improvements in detection and size measurement limits could be made by improving the system stability, using noise reduction methods (e.g. [8, 29]), as well as employing gain-media doped microresonators [32].

We believe that the abilities provided by this single nanoparticle size spectrometry scheme will find applications in in bio/chemical sensing, environmental monitoring, pharmaceutical diagnosis and biomedical researches and nanotechnologies where size dependent properties of individual particles and their interactions play significant roles.