Optical selection and sorting of nanoparticles according to quantum mechanical properties

Optical trapping and sorting system

To understand the sorting of particular person nanoparticles, we use counterpropagating different-colored lasers that may extract the resonant absorption drive by cancelling out the scattering forces. The counterpropagating beam programs had been constructed utilizing a pair of lenses with massive numerical aperture positioned reverse to one another (21) and the inversely directed evanescent waves (16). Nonetheless, it’s tough to exclude the affect of the gradient drive that simply negates the small impact of the quantum resonance drive. Thus, we centered on tapered optical fibers, i.e., nanofibers (22, 23). We ready a nanofiber with a diameter of a number of hundred nanometers and size of a number of millimeters (24), which exhibited the traits of single-mode propagation, thereby forming an intense evanescent subject across the fiber and enabling long-distance propagation whereas sustaining a tightly centered beam of sunshine. Utilizing these traits, a uniform electrical subject distribution might be generated alongside the fiber by which the particle movement was restricted to 1 dimension. As well as, the optical gradient drive and thermophoretic drive, arising from the temperature gradient (e.g., Soret impact), had been exerted in a course perpendicular to the fiber axis such that the particle movement alongside the nanofiber was pushed solely by the resonant absorption and scattering forces. Moreover, as a result of the momentum of the photons in a waveguide is dependent upon the propagation constants of the person modes, the single-mode wave in our nanofiber had the fixed photon momentum; this supplies a perfect platform for analyzing the optical forces exerted on the nanoparticles. On the premise of the steadiness of the absorption and scattering forces induced by the different-colored lasers counterpropagating alongside the nanofiber, we succeeded in attaining the selective transportation of single nanoparticles in accordance with the quantum resonant absorption (Fig. 1A).

Along with the choice and sorting, the proposed system can exactly decide the resonant absorption cross sections of single nanoparticles. Fluorescence and photothermal spectroscopies have been extensively used for characterizing single nanoparticles and nanomaterials due to their excessive sensitivity on the degree of single-molecule detection (25, 26). Nonetheless, these strategies probe the comfort processes emitting a photon and thermal vitality, that are thought to be oblique absorption measurements. When the excited states of the supplies irreversibly transit to different states with out present process rest processes, reminiscent of photochemical reactions, these strategies can now not observe the resonant absorption. Absorption spectroscopy, which straight measures the excitation processes, is an indispensable instrument for analyzing the interplay strengths between mild and matter. Specifically, absolutely the values of the absorption cross sections of single nanoparticles/nanomaterials are important for experimental physics in materials science and are essential for designing nanostructured supplies at a single-quantum state degree (27). Nonetheless, it’s nonetheless difficult to detect extraordinarily small absorption alerts of single nanoparticles and nanomaterials. In our technique, correct measurement of quantum resonant absorption is realized by exactly observing the optical drive–pushed motions of the nanoparticles, referred to as as optical drive spectroscopy. This spectroscopy based mostly on the optical momentum change as a substitute of the vitality change is conceptually totally different from the traditional strategies.

Figure 1B illustrates the experimental setup. A nanofiber with a diameter of 400 nm was fabricated from a industrial single-mode optical fiber (24). The diameter is fixed within the waist a part of the fiber over a size of a number of hundred micrometers. The nanofiber was soaked in an aqueous answer of diamond nanoparticles, i.e., nanodiamonds (NDs). As a result of nitrogen-vacancy facilities (NVCs) in NDs have superior properties, reminiscent of no photobleaching, excessive sensitivity to the encircling surroundings, and sharp zero phonon line absorption, they’ve been gaining consideration as luminescent and magnetic-responsive nanomaterials that can be utilized for organic imaging, sensing, and single-photon supply (17, 18). Thus, choice and sorting of NDs with and with out NVCs are extremely fascinating. We ready two sorts of NDs; one contained NVCs (>300 per particle), i.e., quantum resonant ND (r-ND), and the opposite was nearly free from the NVCs, i.e., nonresonant ND (n-ND). The diameters of each r-NDs and n-NDs had been 50 ± 15 nm. Steady-wave inexperienced (GR; 532 nm) and near-infrared (NIR; 1064 nm) diode lasers had been launched from each ends of the nanofiber. The NVCs exhibit absorption on the GR area however not on the NIR area (28, 29). Moreover, we introduce a weak crimson laser within the fiber as a probe mild (690 nm, 0.1 mW) to watch the movement of the NDs, which was recorded by an optical microscope outfitted with a charge-coupled system (CCD) digital camera.

Selective transportation of single nanoparticles

Figure 2A depicts the trapping and transportation of a single r-ND, the place solely the GR laser (70 mW) is incident from the left finish of the fiber and the movement of the r-ND is noticed within the waist a part of the fiber. The outcome reveals that the r-ND is attracted by the gradient drive of the evanescent subject and strikes alongside the fiber due to the dissipative forces. The particle pace is fixed at 110 μm/s (see a trajectory in fig. S1). We consider the drive exerted on the r-ND as 89 fN by contemplating the steadiness between the optical drive and viscous drag utilizing the Faxen method for correcting the impact of the fiber floor [(23) and see the Supplementary Materials). When the NIR laser is simultaneously incident from the other end of the fiber (from the right), where the NIR laser power is fixed at 250 mW, and the GR laser power is varied from 70 to 0 mW, we achieve the motion control of a single r-ND (Fig. 2B). At the GR laser power of 70 mW, the r-ND moves toward the propagation direction of the GR laser (from left to right). As the GR laser power decreases, the motion decelerates and subsequently stops (~8 s). On further decreasing the GR laser power, the r-ND moves toward the opposite direction. The motion control experiment for an n-ND is illustrated in the Supplementary Materials (fig. S3).

The dissipative optical force exerted on an r-ND along a nanofiber is composed of two components, namely, absorption and scattering forces (F_abs, F_sca), which are represented by the absorption and scattering cross sections (σ_abs, σ_sca), as follows

(1)where I and c represent the intensity and velocity of light in a vacuum, respectively, and n_eff is the effective refractive index of the nanofiber (n_eff = 1.354 at 532 nm). The scattering cross section for Rayleigh particles is theoretically given by

(2)where n₁ and n₂ are the refractive indices of diamond and surrounding water, respectively, λ is the incident laser wavelength in vacuum, and V is the volume of the particle. In the case of r-NDs including NVCs, σ_abs is given by the transition dipole strength of an NVC and the number of NVCs in r-ND. The NIR laser induces only the scattering force, as NVCs exhibit no absorption at 1064 nm.

We perform a motion control experiment for an n-ND without NVCs to measure the balanced powers of the GR and NIR lasers for restricting the motion of the particle. The NIR laser power was fixed at 160 mW, corresponding to the intensity of 108 MW/cm² estimated from the mode profile of the nanofiber, while the observed balanced power of the GR laser was 7.61 mW (intensity, 6.06 MW/cm²). As F_abs is not exerted on the n-ND, scattering forces (F_sca) by the GR and NIR lasers balance each other. Moreover, σ_sca strongly depends on the wavelength (Eq. 2), which is compensated by the large difference between the intensities of the GR and NIR lasers. As σ_sca is proportional to the square of the particle volume, the scattering force also changes significantly depending on the particle size. Fortunately, the ratio of the scattering forces at 532 and 1064 nm is constant for any particle size. This is because the volume dependence of σ_sca is the same (∝V²) for both wavelengths. Thus, it is noted that the balanced powers of the two counterpropagating lasers remain unchanged for n-NDs of any size.

Furthermore, we demonstrate the selective transportation of r-NDs and n-NDs (Fig. 3 and movie S1). The same experimental setup and nanofiber were used, and the NIR laser power was 160 mW. The GR laser power was adjusted to 7.40 mW to drive different motions of the r-NDs and n-NDs. This value is slightly lower than the balanced power of the n-ND such that the scattering force exerted by the NIR laser is stronger for n-NDs than that by the GR laser, whereas the resonant absorption force on the r-NDs by the GR laser reverses the force strength relation. By switching the probe laser on and off, we can measure the emission from the NVCs and thus distinguish between the r-NDs and n-NDs. The two particles at both ends are r-NDs (numbered 1 and 4) and the other two particles are n-NDs (numbered 2 and 3). Scattered light spots of four NDs have nearly the same intensities when the probe laser is off, while the spots of r-NDs are brighter than the spots of n-NDs in Fig. 3 because the NVC emission is added to the scattered light. The r-NDs slowly move to the right (along the propagation direction of the GR laser), whereas the n-NDs move in the opposite direction (see trajectories in fig. S2). This result clearly demonstrates the selective transportation of NDs according to the quantum resonant absorption of NVCs by using the optical forces.

Determination of the absorption cross section

Next, we analyze the absorption cross section (σ_abs) of a single r-ND. We prepared the same experimental conditions and used the same nanofiber that was used for the balanced power measurement of an n-ND. At the NIR laser power of 160 mW, the balanced power of the GR lasers for an r-ND was measured to be 6.75 mW (intensity, 5.37 MW/cm²). Then, by turning the NIR laser off, the motion of r-NDs driven by the GR laser was observed to determine the strength of the optical force. On the basis of the balance with the viscous drag, the optical force composed of F_abs and F_sca was calculated as 6.30 fN. As a reference, the data of the n-ND were used for the present absorption analysis. By comparing the balanced powers of the GR laser for the r-ND (P_r-ND = 6.75 mW) and n-ND (P_n-ND = 7.61 mW), we obtain the ratio of F_abs and F_sca exerted on the r-ND as (P_n-ND − P_r-ND):P_r-ND (Fig. 4) such that the measured optical force on the r-ND (F = 6.30 fN) can be decomposed into F_abs = 0.71 fN and F_sca = 5.59 fN. This result demonstrates that the absorption and scattering forces exerted on a single r-ND can be separately determined with subfemtonewton order accuracy. Thus, from Eq. 1, we evaluate the σ_abs to be 2.9 × 10⁻¹⁴ cm². We repeated the measurements for 10 different r-NDs using the same nanofiber to perform the experiments under the same conditions. The average and SD of the evaluated σ_abs were 3.3 × 10⁻¹⁴ and 1.1 × 10⁻¹⁴ cm², respectively. The deviations in σ_abs can be attributed to the variations in the number of NVCs contained in the r-NDs with different sizes and defect densities. The detailed distribution of σ_abs and estimated number of NVCs are shown in the Supplementary Materials (see fig. S4).

Here, we emphasize that the present method can detect the absorption cross section in the order of a square nanometer, which is close to those of single molecules (typically as large as 10⁻¹⁵ cm²). Under the diffraction-limited illumination condition, this absorption cross section corresponds to a transmittance of ~10⁻⁶. Recently, Kukura et al. (30) and Celebrano et al. (31) succeeded in measuring the extremely small absorption using highly sensitive detectors, and the accuracy of their method is comparable with that of our method. However, in their technique, the Rayleigh scattering caused by nanoparticles and nanomaterials attenuates the transmitted light intensity as well such that the absorption signals cannot be extracted separately from the scattering components. In contrast, our proposed optical force spectroscopy can separately determine the absorption and scattering cross sections of single nanoparticles from the momentum change. The sensitivity is not limited by the signal-to-noise ratio of light intensity detection but restricted by the accuracy of the motion detection. Although nanometer-level position sensing techniques are available, the random thermal motion is the main factor that determines the accuracy. If the experiment is performed using superfluid helium at the cryogenic temperature, then the detection accuracy will be ultimately improved.

We demonstrated the selective transportation of single nanoparticles based on the relation between the quantum mechanical properties of nanomaterials and their macroscopic motion driven by the quantum resonant optical forces. This selective transportation is applicable to the precise sorting of nanocrystals, quantum dots, and molecular nanoparticles according to their resonant absorption properties. Optical force spectroscopy directly and sensitively measures the interaction between light and nanoparticles separately from the scattering effects based on the photon momentum change and not the energy change. It is noted that even if the reference nanoparticle having the same parent material but without absorbers is unavailable, the proposed absorption detection can still be achieved (see Materials and Methods). Although we focus on NDs as the samples for the first demonstration, note that other kinds of nanoparticles can be equally interesting targets. Size-selective optical transport of semiconductor quantum dots has been successfully demonstrated (32). Furthermore, it was reported that organic dye-doped nanoparticles have unique optical trapping characteristics according to their quantum resonance properties (33, 34). Applying the present technique to these nanomaterials will be our future endeavor. In conclusion, we believe that our scheme can enable a new class of optical force methodologies to investigate the characteristics of advanced nanomaterials and quantum materials and develop state-of-the-art nanodevices.