Simulation of optomechanical interaction of levitated nanoparticle with photonic crystal micro cavity.

We propose and analyze theoretically a promising design of an optical trap for vacuum levitation of nanoparticles based on a one-dimensional (1D) silicon photonic crystal cavity (PhC). The considered cavity has a quadratically modulated width of the silicon wave guiding structure, leading to a calculated cavity quality factor of 8 × 105. An effective mode volume of approximately 0.16 µm3 having the optical field strongly confined outside the silicon structure enables optical confinement on nanoparticle in all three dimensions. The optical forces and particle-cavity optomechanical coupling are comprehensively analyzed for two sizes of silica nanoparticles (100 nm and 150 nm in diameter) and various mode detunings. The value of trapping stiffnesses in the microcavity is predicted to be 5 order of magnitudes higher than that reached for optimized optical tweezers, moreover the linear single photon coupling rate can reach MHz level which is 6 order magnitude larger than previously reported values for common bulk cavities. The theoretical results support optimistic prospects towards a compact chip for optical levitation in vacuum and cooling of translational mechanical degrees of motion for the silica nanoparticle of a diameter of 100 nm.

Complex colloidal structures with non-linear optical properties formed in an optical trap.

Illumination of a colloidal suspension of dielectric nanoparticles (50 nm in radius) with counter-propagating non-interfering laser beams of sufficient power leads to spatial redistribution of particles due to associated optical forces and formation of colloidal structures composed of thousands of nanoparticles along the beams. We employ a weak probe beam propagating through the colloidal structure and demonstrate that the colloidal structure acts effectively as a non-linear optical medium, similar to a gradient index lens, with optical transformation properties externally tunable by trapping laser power. With an increasing number of nanoparticles we observe the formation of a more complex colloidal structure axially and even laterally and we explain the origin of this process.

Optical Trapping, Optical Binding, and Rotational Dynamics of Silicon Nanowires in Counter-Propagating Beams.

Silicon nanowires are held and manipulated in controlled optical traps based on counter-propagating beams focused by low numerical aperture lenses. The double-beam configuration compensates light scattering forces enabling an in-depth investigation of the rich dynamics of trapped nanowires that are prone to both optical and hydrodynamic interactions. Several polarization configurations are used, allowing the observation of optical binding with different stable structure as well as the transfer of spin and orbital momentum of light to the trapped silicon nanowires. Accurate modeling based on Brownian dynamics simulations with appropriate optical and hydrodynamic coupling confirms that this rich scenario is crucially dependent on the non-spherical shape of the nanowires. Such an increased level of optical control of multiparticle structure and dynamics open perspectives for nanofluidics and multi-component light-driven nanomachines.

Optomechanical properties of optically self-arranged colloidal waveguides.

When a suspension of wavelength-sized polystyrene spheres is illuminated with non-interfering counter-propagating Gaussian beams, the particles self-arrange into a colloidal waveguide (CWG). Mutual force interaction among particles is mediated by scattered light, referred to as the optical binding. We analyzed the longitudinal and lateral motion of particles in such CWGs made of an increasing number of particles with diameters of either 520 or 657 nm. We observed the enhancement of the binding stiffness of neighboring particles by more than an order of magnitude. This enhancement is done by optical means, mainly due to a local increase of optical intensity due to multiple light scattering in an optically bound structure.

Diffusing up the Hill: Dynamics and Equipartition in Highly Unstable Systems.

Stochastic motion of particles in a highly unstable potential generates a number of diverging trajectories leading to undefined statistical moments of the particle position. This makes experiments challenging and breaks down a standard statistical analysis of unstable mechanical processes and their applications. A newly proposed approach takes advantage of the local characteristics of the most probable particle motion instead of the divergent averages. We experimentally verify its theoretical predictions for a Brownian particle moving near an inflection in a highly unstable cubic optical potential. The most likely position of the particle atypically shifts against the force, despite the trajectories diverging in the opposite direction. The local uncertainty around the most likely position saturates even for strong diffusion and enables well-resolved position detection. Remarkably, the measured particle distribution quickly converges to a quasistationary one with the same atypical shift for different initial particle positions. The demonstrated experimental confirmation of the theoretical predictions approves the utility of local characteristics for highly unstable systems which can be exploited in thermodynamic processes to uncover energetics of unstable systems.

Dynamics of an optically bound structure made of particles of unequal sizes.

This theoretical study based on the coupled dipoles model focuses on the dynamics of two optically bound dielectric spheres of unequal sizes confined in counter-propagating incoherent Bessel beams. We analyzed the relative motion of the particles with respect to each other and defined conditions where they form a stable optically bound structure (OBS). We also investigated the motion of the center of mass of the OBS and found that its direction depends on the particle separation in the structure. Besides the optical interaction between objects, we also considered a hydrodynamic coupling in order to obtain more precise results for moving an OBS.

Chiral particles in the dual-beam optical trap.

We investigate the dynamics of chiral microparticles in a dual-beam optical trap. The chiral particles have the structure of spherical chiral microresonators, with a reflectance deriving from the supramolecular helicoidal arrangement. Due to the strong asymmetric response of the particles to light with a specific helicity and wavelength, their trapping position and rotational frequency can be controlled by proper combination of the polarization state of the two light beams. Here symmetric and asymmetric polarization configurations of dual- interfering beam traps have been investigated. Based on the polarization controlled asymmetric transmission of the chiral particles, a tunable wash-board potential is created enabling the control of the trapping position along the beams axis. Asymmetric configurations display polarization controlled rotation of the trapped particles. Optical binding of rotating particles exhibits a complex dynamics.

Non-spherical gold nanoparticles trapped in optical tweezers: shape matters.

We present the results of a theoretical analysis focused on three-dimensional optical trapping of non-spherical gold nanoparticles using a tightly focused laser beam (i.e. optical tweezers). We investigate how the wavelength of the trapping beam enhances trapping stiffness and determines the stable orientation of nonspherical nanoparticles in the optical trap which reveals the optimal trapping wavelength. We consider nanoparticles with diameters being between 20 nm and 254 nm illuminated by a highly focused laser beam at wavelength 1064 nm and compare our results based on the coupled-dipole method with published theoretical and experimental data. We demonstrate that by considering the non-spherical morphology of the nanoparticle we can explain the experimentally observed three-dimensional trapping of plasmonic nanoparticles with size higher than 170 nm. These results will contribute to a better understanding of the trapping and alignment of real metal nanoparticles in optical tweezers and their applications as optically controllable nanosources of heat or probes of weak forces and torques.

Complex rotational dynamics of multiple spheroidal particles in a circularly polarized, dual beam trap.

We examine the rotational dynamics of spheroidal particles in an optical trap comprising counter-propagating Gaussian beams of opposing helicity. Isolated spheroids undergo continuous rotation with frequencies determined by their size and aspect ratio, whilst pairs of spheroids display phase locking behaviour. The introduction of additional particles leads to yet more complex behaviour. Experimental results are supported by numerical calculations.

Spectral tuning of lasing emission from optofluidic droplet microlasers using optical stretching.

We introduce tunable optofluidic microlasers based on active optical resonant cavities formed by optically stretched, dye-doped emulsion droplets confined in a dual-beam optical trap. To achieve tunable dye lasing, optically pumped droplets of oil dispersed in water are stretched by light in the dual-beam trap. Subsequently, resonant path lengths of whispering gallery modes (WGMs) propagating in the droplet are modified, leading to shifts in the microlaser emission wavelengths. Using this technique, we present all-optical, almost reversible spectral tuning of the lasing WGMs and show that the direction of tuning depends on the position of the pump beam focus on the droplet. In addition, we study the effects of temperature changes on the spectral position of lasing WGMs and demonstrate that droplet heating leads to red-tuning of the droplet lasing wavelength.

Optical manipulation of aerosol droplets using a holographic dual and single beam trap.

We present optical trapping and manipulation of pure water and salt water airborne droplets of various sizes ranging from sub-micrometers up to several tens of micrometers in a holographic dual and single beam trap. In the dual beam trap, successful fusion of droplets as well as precise delivery of many droplets and manipulation of multiple droplets are demonstrated. Furthermore, employing the transfer of the orbital angular momentum of light from Laguerre-Gaussian beams, we show that the water droplets orbit around the beam propagation axis and their tangential speed can be controlled by beam waist magnitude. We also demonstrate that sub-micrometer sized pure water droplets can be trapped and manipulated by a single beam trap with a relatively low numerical aperture. In this case, multiple stable trapping positions were observed, both theoretically and experimentally, which were due to the optical intensity oscillations in the focal region of the laser beam.

Synchronization of spin-driven limit cycle oscillators optically levitated in vacuum.

We explore, experimentally and theoretically, the emergence of coherent coupled oscillations and synchronization between a pair of non-Hermitian, stochastic, opto-mechanical oscillators, levitated in vacuum. Each oscillator consists of a polystyrene microsphere trapped in a circularly polarized, counter-propagating Gaussian laser beam. Non-conservative, azimuthal forces, deriving from inhomogeneous optical spin, push the micro-particles out of thermodynamic equilibrium. For modest optical powers each particle shows a tendency towards orbital circulation. Initially, their stochastic motion is weakly correlated. As the power is increased, the tendency towards orbital circulation strengthens and the motion of the particles becomes highly correlated. Eventually, centripetal forces overcome optical gradient forces and the oscillators undergo a collective Hopf bifurcation. For laser powers exceeding this threshold, a pair of limit cycles appear, which synchronize due to weak optical and hydrodynamic interactions. In principle, arrays of such Non-Hermitian elements can be arranged, paving the way for opto-mechanical topological materials or, possibly, classical time crystals. In addition, the preparation of synchronized states in levitated optomechanics could lead to new and robust sensors or alternative routes to the entanglement of macroscopic objects.

Optical forces induced behavior of a particle in a non-diffracting vortex beam.

An interaction between a light field with complex field spatial distribution and a micro-particle leads to forces that drag the particle in space and may confine it in a stable position or a trajectory. The particle behavior is determined by its size with respect to the characteristic length of the spatially periodic or symmetric light field distribution. We study theoretically and experimentally the behavior of a microparticle near the center of an optical vortex beam in a plane perpendicular to the beam propagation. We show that such particle may be stably trapped either in a dark spot on the vortex beam axis, or in one of two points placed off the optical axis. It may also circulate along a trajectory having its radius smaller or equal to the radius of the first bright vortex ring.

Using the transient trajectories of an optically levitated nanoparticle to characterize a stochastic Duffing oscillator.

We propose a novel methodology to estimate parameters characterizing a weakly nonlinear Duffing oscillator represented by an optically levitating nanoparticle. The method is based on averaging recorded trajectories with defined initial positions in the phase space of nanoparticle position and momentum and allows us to study the transient dynamics of the nonlinear system. This technique provides us with the parameters of a levitated nanoparticle such as eigenfrequency, damping, coefficient of nonlinearity and effective temperature directly from the recorded transient particle motion without any need for external driving or modification of an experimental system. Comparison of this innovative approach with a commonly used method based on fitting the power spectrum density profile shows that the proposed complementary method is applicable even at lower pressures where the nonlinearity starts to play a significant role and thus the power spectrum density method predicts steady state parameters. The technique is applicable also at low temperatures and extendable to recent quantum experiments. The proposed method is applied on experimental data and its validity for one-dimensional and three-dimensional motion of a levitated nanoparticle is verified by extensive numerical simulations.

High quality quasi-Bessel beam generated by round-tip axicon.

We study theoretically and experimentally the spatial intensity distribution of the zero-order Bessel beam formed by the axicon which possess a rounded tip. Such a tip generates a refracted beam that interferes with the quasi-Bessel beam created behind the axicon. In turn an undesired intensity modulation occurs that significantly disturbs the unique properties of the quasi-Bessel beam--namely the constant shape of the lateral intensity distribution and the slow variation of the on-axis beam intensity along the beam propagation. We show how the spatial filtration of the beam in the Fourier plane improves this spatial beam distribution and removes the undesired modulation. We use an efficient numerical method based on Hankel transformations to simulate the propagation of the beam behind the axicon and filter. We experimentally measure the intensity distribution of the beam in many lateral planes and subsequently reconstruct the spatial intensity distribution of the beam. Computed and measured beam distributions are compared and the obtained agreement is very good.

Enhancement of the 'tractor-beam' pulling force on an optically bound structure.

Recently, increasing attention has been devoted to mastering a new technique of optical delivery of micro-objects tractor-beam'1, 2, 3, 4, 5, 6, 7, 8, 9. Such beams have uniform intensity profiles along their propagation direction and can exert a negative force that, in contrast to the familiar pushing force associated with radiation pressure, pulls the scatterer toward the light source. It was experimentally observed that under certain circumstances, the pulling force can be significantly enhanced6 if a non-spherical scatterer, for example, a linear chain of optically bound objects10, 11, 12, is optically transported. Here we demonstrate that motion of two optically bound objects in a tractor beam strongly depends on theirs mutual distance and spatial orientation. Such configuration-dependent optical forces add extra flexibility to our ability to control matter with light. Understanding these interactions opens the door to new applications involving the formation, sorting or delivery of colloidal self-organized structures.

Thermally induced micro-motion by inflection in optical potential.

Recent technological progress in a precise control of optically trapped objects allows much broader ventures to unexplored territory of thermal motion in non-linear potentials. In this work, we exploit an experimental set-up of holographic optical tweezers to experimentally investigate Brownian motion of a micro-particle near the inflection point of the cubic optical potential. We present two complementary views on the non-linear Brownian motion. On an ensemble of stochastic trajectories, we simultaneously determine (i) the detailed short-time position statistics and (ii) the long-distance first-passage time statistics. We evaluate specific statistical moment ratios demonstrating strongly non-linear stochastic dynamics. This is a crucial step towards a possible massive exploitation of the broad class of complex non-linear stochastic effects with objects of more complex structure and shape including living ones.

Three-dimensional optical trapping of a plasmonic nanoparticle using low numerical aperture optical tweezers.

It was previously believed that larger metal nanoparticles behave as tiny mirrors that are pushed by the light beam radiative force along the direction of beam propagation, without a chance to be confined. However, several groups have recently reported successful optical trapping of gold and silver particles as large as 250 nm. We offer a possible explanation based on the fact that metal nanoparticles naturally occur in various non-spherical shapes and their optical properties differ significantly due to changes in localized plasmon excitation. We demonstrate experimentally and support theoretically three-dimensional confinement of large gold nanoparticles in an optical trap based on very low numerical aperture optics. We showed theoretically that the unique properties of gold nanoprisms allow an increase of trapping force by an order of magnitude at certain aspect ratios. These results pave the way to spatial manipulation of plasmonic nanoparticles using an optical fibre, with interesting applications in biology and medicine.