Optical Trapping Force Research Articles

Optomechanical Thermometry of Nanoribbon Cantilevers

Cadmium sulfide (CdS) nanostructures have attracted a significant amount of attention for a variety of optoelectronic applications including photovoltaic cells, semiconductor lasers, and solid-state laser refrigeration due to their direct bandgap around 2.42 eV and high radiative quantum efficiency. Nanoribbons (NRs) of CdS have been claimed to laser cool following excitation at 514 and 532 nm wavelengths by the annihilation of optical phonons during anti-Stokes photoluminescence. To explore this claim, we demonstrate a novel optomechanical experimental technique for microthermometry of a CdSNR cantilever using Young’s modulus as the primary temperature-dependent observable. Measurements of the cantilever’s fundamental acoustic eigenfrequency at low laser powers showed a red-shift in the eigenfrequency with increasing power, suggesting net heating. At high laser powers, a decrease in the rate of red-shift of the eigenfrequency is explained using Euler–Bernoulli elastic beam theory, considering Hookean optical-trapping force. A predicted imaginary refractive index for CdSNR based on experimental temperature measurement agrees well with a heat transfer analysis that predicts the temperature distribution within the cantilever and the time required to reach steady state (<100 μs). This approach is useful for investigating solid-state laser refrigeration of a wide variety of material systems without the need for complex pump/probe spectroscopy.

Single nanoparticle trapping based on on-chip nanoslotted nanobeam cavities

Optical trapping techniques are of great interest since they have the advantage of enabling the direct handling of nanoparticles. Among various optical trapping systems, photonic crystal nanobeam cavities have attracted great attention for integrated on-chip trapping and manipulation. However, optical trapping with high efficiency and low input power is still a big challenge in nanobeam cavities because most of the light energy is confined within the solid dielectric region. To this end, by incorporating a nanoslotted structure into an ultracompact one-dimensional photonic crystal nanobeam cavity structure, we design a promising on-chip device with ultralarge trapping potential depth to enhance the optical trapping characteristic of the cavity. In this work, we first provide a systematic analysis of the optical trapping force for an airborne polystyrene (PS) nanoparticle trapped in a cavity model. Then, to validate the theoretical analysis, the numerical simulation proof is demonstrated in detail by using the three-dimensional finite element method. For trapping a PS nanoparticle of 10 nm radius within the air-slot, a maximum trapping force as high as 8.28 nN/mW and a depth of trapping potential as large as 1.15×105 kBT mW−1 are obtained, where kB is the Boltzmann constant and T is the system temperature. We estimate a lateral trapping stiffness of 167.17 pN·nm−1· mW−1 for a 10 nm radius PS nanoparticle along the cavity x-axis, more than two orders of magnitude higher than previously demonstrated on-chip, near field traps. Moreover, the threshold power for stable trapping as low as 0.087 μW is achieved. In addition, trapping of a single 25 nm radius PS nanoparticle causes a 0.6 nm redshift in peak wavelength. Thus, the proposed cavity device can be used to detect single nanoparticle trapping by monitoring the resonant peak wavelength shift. We believe that the architecture with features of an ultracompact footprint, high integrability with optical waveguides/circuits, and efficient trapping demonstrated here will provide a promising candidate for developing a lab-on-a-chip device with versatile functionalities.

Optical trapping and optical force positioning of two-dimensional materials.

In recent years, considerable effort has been devoted to the synthesis and characterization of two-dimensional materials. Liquid phase exfoliation (LPE) represents a simple, large-scale method to exfoliate layered materials down to mono- and few-layer flakes. In this context, the contactless trapping, characterization, and manipulation of individual nanosheets hold perspectives for increased accuracy in flake metrology and the assembly of novel functional materials. Here, we use optical forces for high-resolution structural characterization and precise mechanical positioning of nanosheets of hexagonal boron nitride, molybdenum disulfide, and tungsten disulfide obtained by LPE. Weakly optically absorbing nanosheets of boron nitride are trapped in optical tweezers. The analysis of the thermal fluctuations allows a direct measurement of optical forces and the mean flake size in a liquid environment. Measured optical trapping constants are compared with T-matrix light scattering calculations to show a quadratic size scaling for small size, as expected for a bidimensional system. In contrast, strongly absorbing nanosheets of molybdenum disulfide and tungsten disulfide are not stably trapped due to the dominance of radiation pressure over the optical trapping force. Thus, optical forces are used to pattern a substrate by selectively depositing nanosheets in short times (minutes) and without any preparation of the surface. This study will be useful for improving ink-jet printing and for a better engineering of optoelectronic devices based on two-dimensional materials.

Geometrical effect characterization of femtosecond-laser manufactured glass microfluidic chips based on optical manipulation of submicroparticles

Microfluidic devices provide a platform with wide ranging applications from environmental monitoring to disease diagnosis. They offer substantive advantages but are often not optimized or designed to be used by nonexpert researchers. Microchannels of a microanalysis platform and their geometrical characterization are of eminent importance when designing such devices. We present a method that is used to optimize each microchannel within a device using high-throughput particle manipulation. For this purpose, glass-based microfluidic devices, with three-dimensional channel networks of several geometrical sizes, were fabricated by employing laser fabrication techniques. The effect of channel geometry was investigated by employing an optical tweezer. The optical trapping force depends on the flow velocity that is associated with the dimensions of the microchannel. We observe a linear dependence of the trapping efficiency and of the fluid flow velocity, with the channel dimensions. We determined that the highest trapping efficiency was achieved for microchannels with aspect ratio equal to one. Numerical simulation validated the impact of the device design dimensions on the trapping efficiency. This investigation indicates that the geometrical characteristics, the flow velocity, and trapping efficiency are crucial and should be considered when fabricating microfluidic devices for cell studies.

Optical Forces at the Nanoscale: Size and Electrostatic Effects.

The reduced magnitude of the optical trapping forces exerted over sub-200 nm dielectric nanoparticles complicates their optical manipulation, hindering the development of techniques and studies based on it. Improvement of trapping capabilities for such tiny objects requires a deep understanding of the mechanisms beneath them. Traditionally, the optical forces acting on dielectric nanoparticles have been only correlated with their volume, and the size has been traditionally identified as a key parameter. However, the most recently published research results have shown that the electrostatic characteristics of a sub-100 nm dielectric particle could also play a significant role. Indeed, at present it is not clear what optical forces depend. In this work, we designed a set of experiments in order to elucidate the different mechanism and properties (i.e., size and/or electrostatic properties) that governs the magnitude of optical forces. The comparison between experimental data and numerical simulations have shown that the double layer induced at nanoparticle's surface, not considered in the classical description of nanoparticle's polarizability, plays a relevant role determining the magnitude of the optical forces. Here, the presented results constitute the first step toward the development of the dielectric nanoparticle over which enhanced optical forces could be exerted, enabling their optical manipulation for multiples purposes ranging from fundamental to applied studies.

Modified field confinement and enhanced optical forces in hybrid dielectric wedge tip-loaded plasmonic waveguide

We proposed and theoretically investigated a hybrid plasmonics waveguide consisting of a tiptilted quadrate nanowire, which was embedded in a low-permittivity dielectric and placed on a metal substrate with a small gap distance. Due to the corner effect, the hybrid mode with extremely local field enhancement has the long propagation length and strong coupling strength between the dielectric nanowire and metal. By employing the simulations with different geometric parameters, the proposed waveguide can obtain better performances than the previous hybrid plasmonics waveguide, particularly in the subwavelength confinement (as small as λ2/1600), long-range propagation (millimeter range), and optical trapping forces (2.12 pN/W). The use of a naturally dielectric wedge tip of quadrate nanowire that can be chemically synthesized provides an efficient approach to circumvent the fabrication difficulty of shape wedge tips. The present structure provides an excellent platform for nanophotonic waveguides, nanolasers, nanoscale optical tweezers, and biosensing.

All-dielectric structure for trapping nanoparticles via light funneling and nanofocusing

We propose a dielectric structure which focuses the laser light well beyond the diffraction limit and thus considerably enhances the exerted optical trapping force upon dielectric nanoparticles. Although the structure supports a Fabry-Perot resonance, it actually acts as a nanoantenna in that the role of the resonance is to funnel the laser light into the structure. In comparison with the lens illuminating the structure, the proposed structure offers roughly a 10000-fold enhancement in the trapping force - part of this enhancement comes from an 80-fold enhancement in the field intensity, and the remaining comes from a 130-fold enhancement in the normalized gradient of the field intensity (viz. the gradient of the field intensity divided by the field intensity). Also, the proposed structure offers roughly a 100-fold enhancement in the depth of the trapping potential. It is noteworthy that 'self-induced back-action trapping' (SIBA), which has recently been the focus of interest in the context of optical resonators, does not take place in the proposed resonator. In this paper, we also point out some misconceptions about SIBA together with some hitherto unappreciated subtleties of the dipole approximation.

Optical trapping forces of a focused azimuthally polarized Bessel-Gaussian beam on a double-layered sphere

We calculate the trapping forces exerted by a highly focused Bessel-Gaussian beam on a double-layered sphere by means of vector diffraction integral, T-matrix method and Maxwell stress tensor integral. The Bessel-Gaussian beam is azimuthally polarized. Numerical results predicate that the double-layered sphere with air core can be stably trapped in three-dimensions. The trapping forces and efficiencies are dependent on the refraction index and size of the inner core. The trapping efficiency can be optimized by choosing the refraction indices of the inner core and outer layer. Our computational method can be easily modified for other laser beams and particles with arbitrary geometries and multilayers.

Direct measurement of optical trapping force gradient on polystyrene microspheres using a carbon nanotube mechanical resonator

Optical tweezers based on optical radiation pressure are widely used to manipulate nanoscale to microscale particles. This study demonstrates direct measurement of the optical force gradient distribution acting on a polystyrene (PS) microsphere using a carbon nanotube (CNT) mechanical resonator, where a PS microsphere with 3 μm diameter is welded at the CNT tip using laser heating. With the CNT mechanical resonator with PS microsphere, we measured the distribution of optical force gradient with resolution near the thermal noise limit of 0.02 pN/μm in vacuum, in which condition enables us to high accuracy measurement using the CNT mechanical resonator because of reduced mechanical damping from surrounding fluid. The obtained force gradient and the force gradient distribution agree well with theoretical values calculated using Lorenz–Mie theory.

Low-loss nanowire and nanotube plasmonic waveguide with deep subwavelength light confinement and enhanced optical trapping forces

With the rapid development of the micro/nano fabrication technology, the semiconductor nanowires and nanotubes with size and dimensions controllable realize wide applications in nanophotonics. In this talk, we propose two kinds of hybrid plasmonics waveguides, one is consisting of nanowires, another is consisting of nanotubes. By employing the simulating with different geometric parameters, the basic waveguiding properties, including the effective mode area, the propagation length, the mode character and the optical trapping forces can be achieved. Compared with previous plasmonic waveguide with plane metal substrate, current plasmonics waveguides with ease of fabrication have the advantage of long propagation length and effectively optical trapping of nanoparticles with deep subwavelength light confinement, which may be very useful for nanophotonic integrated circuits, nanolasers and biosensing.

Tunable nanophotonic array traps with enhanced force and stability.

A nanophotonic trapping platform based on on-chip tunable optical interference allows parallel processing of biomolecules and holds promise to make single molecule manipulation and precision measurements more easily and broadly available. The nanophotonic standing wave array trap (nSWAT) device [Nat. Nanotechnol. 9, 448 (2014); Nano Lett. 16, 6661 (2016)] represents such a platform and can trap a large array of beads by the evanescent field of the standing wave of a nanophotonic waveguide and reposition them using an integrated microheater. In this paper, by taking a systematic design approach, we present a new generation of nSWAT devices with significant enhancement of the optical trapping force, stiffness, and stability, while the quality of the standing wave trap is resistant to fabrication imperfections. The device is implemented on a silicon nitride photonic platform and operates at 1064 nm wavelength which permits low optical absorption by the aqueous solution. Such performance improvements open a broader range of applications based on these on-chip optical traps.

Two-beam laser fabrication technique and the application for fabricating conductive silver nanowire on flexible substrate

In this study, a two-beam laser fabrication technique is proposed to fabricate silver nanowire (AgNW) on the polyethylene terephthalate (PET) substrate. The femtosecond pulse laser in the technique plays a role in generating Ag nanoparticles from the silver aqueous solution by multiphoton photoreduction. The continuous wave (CW) laser of the technique works as optical tweezers, and make the Ag nanoparticles gather to a continuous AgNW by the optical trapping force. The optical trapping force of the CW laser was calculated under our experimental condition. The flexibility and the resistance stability of the AgNW that fabricated by this technique are very excellent. Compared to the resistance of the AgNW without bending, the decreasing rate of the AgNW resistance is about 16% under compressed bending condition at the radius of 1 mm, and the increasing rate of the AgNW resistance is only 1.3% after the AgNW bended about 3500 times at the bending radius of 1 mm. The study indicates that the AgNW is promising for achieving flexible device and would promote the development of the flexible electronics.

Analytical calculations of optical trapping forces for drag calibration: Effects of mismatch between beam focus and particle center

We present analytical calculations of optical forces for drag calibrations via the geometrical optics approximation (GOA) for the case in which a single laser beam is strongly focused on a polystyrene microsphere dispersed in an aqueous phase. When the beam focus is mismatched with the particle center owing to the presence of vertical forces, such as gravity, buoyancy, and the radiation force caused by the laser beam, the trapped particle would be displaced in a radial direction when the lateral drag force is applied. Based on the analytical calculations of optical trapping forces and the force balance upon dragging, we found that the critical laser power at which the beam focus matches the particle center exhibits a power-law relationship with the particle radius a according to the empirical expression log(Pcrit (mW)) = 2.899 log(2a (µm)) - 2.316. We also found an empirical expression for the mechanical equilibrium position of the vertical displacement Δzeq0(Δy=0) as functions of the laser power P and the particle radius, \(\Delta z_{eq}^0 = \frac{{\left[ {{F_{gb}}\left( {pN} \right) - 0.068P\left( {mW} \right)} \right]\left[ {2.7a\left( {\mu m} \right) - 0.252} \right]}}{{P\left( {mW} \right)}}\), where Fgb is the sum of the gravitational and buoyant forces.

Simple and high efficient graded-index multimode fiber tweezers: simulation and experiment

We propose and demonstrate a novel single fiber optical tweezer based on a graded-index multimode fiber (GIMMF), which works with a free length GIMMF (>30 cm). We achieve a three-dimensional stable trap of yeast cells by using the GIMMF optical tweezers. Compared with the single-mode fiber optical tweezers, the GIMMF optical tweezers possess large optical trapping forces. Owing to the freedom of the GIMMF length, the fabrication of the GIMMF optical tweezers is simple, repeatable, and highly efficient. The GIMMF tweezers have the penitential to become a new member of the single fiber optical tweezers family and have a wide range of applications in the medical and biological cytology fields.

Working together

Strength lies in numbers and in teamwork: tens of thousands of artificial atoms tightly packed in a nanodiamond act cooperatively, enhancing the optical trapping forces beyond the expected classical bulk polarizability contribution.

Numerical analysis of an optical nanoscale particles trapping device based on a slotted nanobeam cavity.

A slotted nanobeam cavity (SNC) is utilized to trap a polystyrene (PS) particle with a radius of only 2 nm. The carefully designed SNC shows an ultrahigh Q factor of 4.5 × 107 while maintaining a small mode volume of 0.067(λ/nwater)3. Strongly enhanced optical trapping force is numerically demonstrated when the 2 nm PS particle is introduced into the central, slotted part of the SNC. In the vertical direction, the numerical calculation results show that a trapping stiffness of 0.4 pN/(nm · mW) around the equilibrium position and a trapping potential barrier of ~2000 kBT/mW can be reached. To our best knowledge, the trapping capability (trapping stiffness and trapping potential barrier) of the proposed structure significantly outperforms the theoretical results of those in previously reported work. In addition, the SNC system does not suffer from the metal induced heat issue that restricts the performance of state-of-the-art optical trapping systems involving plasmonic enhancement. Based on the proposed cavity, applications such as lab-on-a-chip platforms for nanoscale particle trapping and analysis can be expected in future.

Single fiber optical trapping of a liquid droplet and its application in microresonator

We propose and demonstrate an optical trapping of a liquid droplet and its application based on an annular core microstructured optical fiber. We grind and polish the annular core fiber tip to be a special frustum cone shape to make sure the optical force large enough to trap the liquid droplet non-intrusively. The axial and transverse optical trapping forces are simulated. In addition, we investigate the whispering gallery modes resonance characteristic of the trapped liquid droplet as the example of applications. The whispering gallery modes spectrum is sensitive to the size of the micro liquid droplet. Due to the simple construction and flexible manipulation, the fiber-based optical trapping technology for micro liquid droplets trapping, manipulating, and controlling has great application penitential in many fields, such as physics, biology, and interdisciplinary studies.

Optical trapping force and torque on spheroidal Rayleigh particles with arbitrary spatial orientations.

We investigate the spatial orientation dependence of optical trapping forces and intrinsic torques exerted on spheroidal Rayleigh particles under irradiation of highly focused linearly and circularly polarized beams. It is revealed that the maximal trapping forces and torques strongly depend on the orientation of the spheroid, and the spheroidal particle is driven to be stably trapped at the beam focus with its major axis perpendicular to the optical axis. For a linearly polarized trapping beam, the optical torque is always perpendicular to the plane containing the major axis and the polarization direction of the incident beam. Therefore, the spheroid tends to rotate its major axis along with the polarization direction. However, for a circularly polarized trapping beam, the optical torque is always perpendicular to the plane containing the major axis and the optical axis. What is different from the linear polarization case is that the spheroid tends to have the major axis parallel to the projection of the major axis in the transverse plane. The optical torque in the circular polarization case is half of that in the linear polarization case. These optical trapping properties may be exploited in practical optical manipulation, especially for the nonspherical particle's trapping.

Optical Manipulation of Micro / Nanoparticles Using Fiber-Based Optical Tweezers

Over forty years, the optical tweezers have been used to facilitate new scientific findings and benchmark single-molecule studies. One of the next steps, as far as applications is concerned, is expected to be their use as medical diagnostic tools, where in parallel, manipulation, sorting, and diagnosis of large number of biological particles, using the optical trapping technique will make the current clinical procedures quicker and cheaper. However, most of the current optical tweezers are based on objective lenses, which are bulky, expensive, and hard to integrate. Optical tweezers based on optical fibers have great potential to solve the abovementioned limitations. This paper attempts to provide solutions in order to overcome the limitations of current conventional optical tweezers with the objective of achieving fundamental understanding and improving the performance of fiber-based optical tweezers. Thus, we develop an optical fiber tweezers using a continuous wave diode GaAlAs laser operating at 659-nm for trapping dielectric nanoparticles (900-nm diameter and 3-?m diameter), suspended in deionized water. We systematically measure the optical trapping force and the effective trapping quality factor. We also investigate the dependence of the trapping force on both the insertion angle of the fiber into the sample chamber and the size of the trapped particle.

Plasmon optical trapping using silicon nitride trench waveguides

We theoretically demonstrate optical trapping using a silicon nitride (Si3N4) trench waveguide on which bow-tie plasmonic nanoantennas are employed for enhancing optical forces. The electric field tailing away from the waveguide is transformed and then enhanced by the plasmonic nanoantennas deposited on the waveguide surface. We show that, with gold bow-tie nanoantennas, the waveguide system exhibits outstanding trapping capability on a 10 nm radius polystyrene nanoparticle, due to a 60-fold electric field enhancement in the proximity of the nanoantenna gap. This enhancement causes a boost of the optical trapping force by 3 orders of magnitude. The gradient force in the vertical direction is also calculated semi-analytically by using a dipole approximation of a scattering polystyrene nanosphere, and the analytical solution well matches the full-wave simulations. Mode polarization effects are discussed in this paper as a way to switch trapping. These investigations indicate that the patterned Si3N4 trench waveguide is suitable for optical trapping and nanoparticle sensing applications.