Transparent Microspheres Research Articles

Towards absolute calibration of optical tweezers

Aiming at absolute force calibration of optical tweezers, following a critical review of proposed theoretical models, we present and test the results of Mie-Debye-spherical aberration (MDSA) theory, an extension of a previous (MD) model, taking account of spherical aberration at the glass-water interface. This first-principles theory is formulated entirely in terms of experimentally accessible parameters (none adjustable). Careful experimental tests of the MDSA theory, undertaken at two laboratories, with very different setups, are described. A detailed description is given of the procedures employed to measure laser beam waist, local beam power at the transparent microspheres trapped by the tweezers, microsphere radius, and the trap transverse stiffness, as a function of radius and height in the (inverted microscope) sample chamber. We find generally very good agreement with MDSA theory predictions, for a wide size range, from the Rayleigh domain to large radii, including the values most often employed in practice, and at different chamber heights, both with objective overfilling and underfilling. The results asymptotically approach geometrical optics in the mean over size intervals, as they should, and this already happens for size parameters not much larger than unity. MDSA predictions for the trapping threshold, position of stiffness peak, stiffness variation with height, multiple equilibrium points, and "hopping" effects among them are verified. Remaining discrepancies are ascribed to focus degradation, possibly arising from objective aberrations in the infrared, not yet included in MDSA theory.

Theory of stimulated concentration scattering of light in a liquid suspension of transparent microspheres

A theory of stimulated light scattering in a nonlinear liquid suspension of transparent microspheres—an artificially created medium whose nonlinearity is caused by modulation of the concentration of microspheres by gradient forces in a field of spatially inhomogeneous laser radiation—is constructed. The threshold, angular, and spectral characteristics of the scattering are studied in the diffusion-limit approximation based on the solution of the system of wave equations in combination with the Planck-Nernst two-dimensional equation for the concentration of microspheres. The transient regime of scattering in the field of a specified step-like pump pulse is considered. A sharp angular dependence of the scattering efficiency on the microsphere radius is predicted and proposed for use in optical diagnostics of liquid suspensions of dielectric microspheres—highly efficient wideband nonlinear media.

Optical Trapping, Manipulation, and 3D Imaging of Disclinations in Liquid Crystals and Measurement of their Line Tension

We demonstrate optical trapping and manipulation of defects and transparent microspheres in nematic liquid crystals (LCs). The three-dimensional director fields and positions of the particles are visualized using the Fluorescence Confocal Polarizing Microscopy. We show that the disclinations of both half-integer and integer strengths can be manipulated by either using optically trapped colloidal particles or directly by tightly-focused laser beams. We employ this effect to measure the line tensions of disclinations; the measured line tension is in a good agreement with theoretical predictions. The laser trapping of colloidal particles and defects opens new possibilities for the fundamental studies of LCs.

Four-wave mixing in a liquid suspension of transparent dielectric microspheres

The process of four-wave mixing in an artificial heterogeneous nonlinear medium—a liquid suspension of transparent dielectric microspheres—is considered. The dynamics of the concentration response to gradient forces that act on microspheres in the interference field of interacting waves are investigated on the basis of the Smolukhovskii equation. Kinetic equations for the amplitudes of light-induced concentration gratings that take part in the four-wave mixing are obtained with the use of the Fourier series expansion of the distribution function of microspheres. The ratios of the microsphere radius to the grating periods are obtained under which the resultant gradient force vanishes and, hence, a suspension of dielectric microspheres does not exhibit nonlinear properties irrespective of the intensities of the interacting waves. The kinetics of the process of four-wave mixing is investigated under efficient energy exchange between reference, signal, and reversed waves. It is shown that a liquid suspension of transparent dielectric spheres is a highly effective wideband nonlinear medium for reversing the wave front of low-intensity radiation of continuous-wave lasers.

Strong optical force induced by morphology-dependent resonances

We consider the resonant optical force acting on a pair of transparent microspheres by the excitation of morphology-dependent resonance (MDR). The bonding and antibonding modes of the MDR correspond to strong attraction and repulsion, respectively. The dependence of the force on separation and the role of absorption are discussed. At resonance, the force can be enhanced by orders of magnitude such that it will dominate other relevant forces. We found that a stable binding configuration can be induced by the resonant optical force.

Four-wave mixing in a liquid suspension of dielectric microspheres

In this work a theory of the degenerate four-photon parametric scattering (FPS) is developed in a liquid suspension of transparent microspheres (heterogeneous medium), the nonlinearity of which is caused by the change in the microsphere concentration under the action of gradient forces in the electromagnetic field of interacting waves. It is shown that the water suspension of latex spheres with diameter d = 0.234 μm and concentrationN0 = 6.5·10 cm, in effect of the FPS process, corresponds to a cubic nonlinear medium with the optical Kerr coefficient n2 that is larger by a factor of 10 than in the case of CS2.

Fabrication of two-dimensional arrays of microlenses and their applications in photolithography

This paper describes several methods for the fabrication of microlenses, and demonstrates a lithographic technique that uses a microlens array to pattern the intensity of light incident on photoresist. Three different methods were used to fabricate microlenses: (i) self-assembly of transparent microspheres, (ii) melting and reflow of photoresist on glass substrates and (iii) self-assembly of liquid polymers on functionalized surfaces. These methods provide different advantages and convenience for the fabrication of microlenses. Microlens arrays produced by these techniques were used in photolithography to produce arrays of micropatterns in photoresist. The distribution of these micropatterns replicates the distribution of the microlenses in the array. Two types of illumination are used for exposure in this technique: collimated flood illumination and illumination through a mask. Depending on which type of exposure is used, a single microlens array can produce different patterns on its image plane: (i) an array of circular or noncircular microlenses under collimated illumination produces an array of optical micropatterns on an image plane positioned within micrometer distances from the lens array. The array of optical micropatterns corresponds to the distribution of spatial irradiance generated by simple lensing of the microlens array. The shapes of these micropatterns depend on the shapes and profiles of the microlenses. (ii) Under illumination patterned by a mask, each microlens approximately replicates the image of the patterned light source and produces a micro-scale image of this source on its image plane. The array of microlenses generates an array of repetitive micropatterns on the common image plane of the lens array. The shapes of the micropatterns depend on the patterns of the masks. Gray-scale masks can be used to produce repetitive microstructures with controlled profiles. Both techniques can generate microstructures with submicron resolution. We demonstrate that both methods produce arrays of uniform micropatterns over an area larger than 10 cm2.

Compositional dependence of up-conversion process in Tm 3+–Yb 3+ codoped oxyfluoride glasses and glass-ceramics

Up-conversion of infrared radiation to the visible and ultraviolet regions in PbF 2–GeO 2–Al 2O 3–Tm 2O 3–Yb 2O 3 oxyfluoride glasses and glass ceramics was obtained, exciting at 1.0 μm with a diode laser at room temperature. Transparent films and microspheres were prepared by a modified spin-coating technique. The effect of host composition on the up-conversion luminescence was studied in order to improve the ultraviolet radiation generation. In the glass samples, the Tm 3+ blue (4786 Å) and red (6500 Å) visible emissions got more intense as the PbF 2 content was increased. The main Tm 3+ blue emission (4786 Å, 1G 4→ 3H 6), results from a three-photon process. A second blue emission (4500 Å, 1D 2→ 3F 4), followed by a UV emission (3650 and 3850 Å, 1D 2→ 3H 6) was observed in the (2PbF 2/GeO 2) glass ceramics, in a narrow range of Al 2O 3 concentration. The 1D 2 level of the Tm 3+ ions is populated by a fourth photon from the cross-relaxation process given by ( 3F 4, 1G 4)→( 3H 6, 1D 2).

Self-Assembly of Uniform Spherical Aggregates of Magnetic Nanoparticles through π–π Interactions

Nanoparticles of Fe3O4 coated with 2-carboxyterthiophene (TTP-COOH) self-assemble through π–π interactions to form uniform transparent microspheres (see schematic representation). The interaction between individual particles is relatively weak and the spherical aggregates can be destroyed by sonication to leave the monodispersed nanoparticles.

Self-Assembly of Uniform Spherical Aggregates of Magnetic Nanoparticles through π-π Interactions.

Nanoparticles of Fe3 O4 coated with 2-carboxyterthiophene (TTP-COOH) self-assemble through π-π interactions to form uniform transparent microspheres. The interaction between individual particles is relatively weak and the spherical aggregates can be destroyed by sonication to leave the monodispersed nanoparticles.

Fabrication of arrays of two-dimensional micropatterns using microspheres as lenses for projection photolithography

This letter demonstrates the use of an array of transparent microspheres in forming repetitive, micrometer-scale patterns in photoresist, starting from masks with centimeter-scale patterns. A transparent microsphere with diameter d>1.5 μm acts as a lens and reduces centimeter-scale images into micrometer-scale images on its image plane. A planar array of microspheres projects the image of an illuminated mask onto a corresponding array of micropatterns on their common image plane. We have prepared arrays of polystyrene microspheres (d=1.5–10 μm) embedded in a transparent membrane to generate repetitive patterns in photoresist, and have transferred the resulting patterns into metal films by liftoff. The optical system of this technique is related to that used in conventional projection photolithography, but differs in that the lens that accomplishes size reduction is positioned within 10 μm of the photoresist. The microspheres generate uniform patterns over an area of ∼2 cm2, using a mask with area ∼25×25 cm2 illuminated with a white light source. This method can generate submicron features either within a micropattern or between neighboring patterns.

Axial and Lateral Displacement Measurements of a Microsphere Based on the Critical-Angle Method

A method has been developed for optically measuring nanometer-scale displacements of transparent and metal-coated microspheres in both the axial (vertical) and lateral (horizontal) directions. This method works by detecting changes in the internal reflection of a laser beam reflected from the microsphere after it passes through critical-angle prisms. For weakly reflective 10-µm-diameter polystyrene microspheres in water (relative refractive index n=1.2), the detection resolutions as estimated from the full-width at half maximum (FWHM) noise level in the frequency region above 500 Hz in the axial and lateral directions were experimentally found to be as good as 1.7 and 1.1 nm, respectively. Furthermore, the lateral displacement resolution (0.2 nm) of a 10-µm-diameter metal-coated microsphere was better than the axial displacement resolution (0.9 nm) of a conventional flat mirror by more than a factor of four.

Towards cavity-QED experiments with silica microspheres

We present experiments performed on highly transparent silica microspheres used as very high Q optical resonators for cavity quantum electrodynamics (CQED) studies. By coupling these microspheres to eroded optical fibers and fiber tips, direct mapping of the whispering-gallery modes has been achieved and the mode quantum numbers have been assessed. Low-threshold whispering-gallery modes lasers made with Nd-doped spheres are described and further CQED projects are proposed.

Spontaneous emission rate and level shift of an atom inside a dielectric microsphere

Abstract The transition frequency shift and the spontaneous decay rate (the radiative linewidth) variation of an atom placed in a transparent dielectric microsphere are presented. It is demonstrated that with the refractive index of the microsphere material (e.g. diamond) being high enough, the size of the microsphere can be selected such that the spontaneous decay rate decreases (or increases) several times, depending on the position of the atom. At the same time, the atomic transition frequency shift proves to depend more strongly on the position of the atom, reaching high values near the surface of the microsphere.

Spontaneous emission rate and level shift of an atom inside a dielectric microsphere

Abstract The transition frequency shift and the spontaneous decay rate (the radiative linewidth) variation of an atom placed in a transparent dielectric microsphere are presented. It is demonstrated that with the refractive index of the microsphere material (e.g. diamond) being high enough, the size of the microsphere can be selected such that the spontaneous decay rate decreases (or increases) several times, depending on the position of the atom. At the same time, the atomic transition frequency shift proves to depend more strongly on the position of the atom, reaching high values near the surface of the microsphere.

Optical properties of solid particle receiver materials: I. Angular scattering and extinction characteristics of Norton Masterbeads ®

As part of the Solar Thermal Technology Program, the direct absorption of sunlight by free-falling particles inside a cavity receiver is being evaluated. The objective of the on-going optical properties measurement program is to obtain information to be used as input to radiation transfer models for prediction of receiver performance. Instrumentation and data analysis techniques have been developed to determine both the angular scattering properties and the scattering and absorption components of the extinction coefficient of candidate materials. This report summarizes the measurement procedures and presents data for an iron-doped alumina spheroid, Masterbeads ®, manufactured by Norton Chemical Company. This material exhibits good optical absorption properties over the solar insolation spectrum and favorable thermal and mechanical properties for temperatures up to 1000°C. The optical scattering and extinction properties are spectral; measurements were performed at 632.8 nm for convenience. The measurements were also simplified by arranging the spheriods in a falling curtain geometry of one particle nominal thickness. Data were obtained over a range of mass flow rates and particle areal densities. Photographic documentation of curtain particle density enabled calculation of mean particle scattering and absorption loss components in the absence of multiple-particle optical interactions. Prediction of optical extinction properties at other wavelengths is anticipated to be straightforward using spectral hemispherical reflectance measurements on bulk samples. Additional scattering and extinction data were obtained on transparent glass microspheres for comparison and as a verification of the measurement apparatus and procedures.