Soo Chang

Theoretical calculations of optical force exerted on a dielectric sphere in the evanescent field generated with a totally-reflected focused gaussian beam

Abstract We investigate theoretically the optical force exerted on a dielectric sphere in the evanescent field, by which the small particles can be pushed or pulled on the scale of the optical wavelength. In our approach we derive an expression of the evanescent field formed at the plane interface with a totally-reflected gaussian laser beam, assuming that the sphere does not affect the boundary conditions. We then solve the scattering problem for the evanescent field incident on a sphere to find the analytical formulas of the cartesian components of optical force. Numerical results show that the magnitude of the optical force for a sphere of radius a =0.5 λ is ≈ 10 −6 (dyne) in the evanescent field of a 1 W gaussian laser beam and the z -component of optical force F z changes the sign according to the refractive index n of the sphere.

Force of surface plasmon-coupled evanescent fields on Mie particles

Forces acting on Mie particles by surface plasmon-coupled evanescent fields are theoretically analyzed. An expression of the evanescent field produced in Kretschmann (or Sarid) geometry is derived in terms of vector spherical wave functions, while multiple reflections between the Mie particle and the metal boundary are taken into account. The Cartesian components of the force on a Mie particle by the evanescent field are analytically formulated and numerically evaluated. We show that forces are increased by one or two orders at metal boundaries than at dielectric boundaries. For a glass bead, the force normal to the metal boundary is strong compared with the tangential force. For a silver-coated glass bead, the tangential force is greater than (or comparable with) the normal force. The strong tangential force can be useful for rotating submicrometer-sized rotors at a metal boundary and the normal force can keep the rotors close to the metal boundary.

Optical force on a sphere caused by the evanescent field of a Gaussian beam; effects of multiple scattering

Abstract We examine theoretically the optical force exerted on a dielectric sphere by the evanescent field of a Gaussian beam, where multiple scattering of light between the sphere and the prism substrate is considered. We derive first an expression of the n th order field ( n ≥ 1) that is scattered by the sphere and we then formulate the optical force due to the scattered fields up to n th order. Numerical results show that the effect of multiple scattering up to third order exerted on the optical force is within the extent of ∼ 10% in resonance regions but it is negligible in off-resonance regions.

Moiré patterns of two different elongated circular gratings for the fine visual measurement of linear displacements

An elongated circular grating having the shape of an athletic track was proposed to determine both the moving displacement and its direction within an accuracy of ten times that of conventional circular gratings. The properties of moire´ fringes from two complementary elongated circular gratings were investigated for fine visual measurement of linear displacements. Moire patterns formed by superposition of two different elongated circular gratings were demonstrated to ´ provide a simple fringe-counting method for determining both the relative linear displacement and its direction within the accuracy of 1r10 pitch of the grating. The measurement of the refractive indices of C H and CCl and the thermal 61 2 4 expansion coefficient of aluminium, using elongated circular gratings, are presented. q 1998 Elsevier Science B.V. All rights reserved.

Use of a phase type elongated circular grating in Talbot moiré deflectometry

Summary We analyze theoretically and experimentally the self-image of a phase type elongated circular (EC) grating which has a periodic structure of rectangular type, so that it can be employed in Talbot moire deflectometry. We examine the visibility of a self-imaged phase EC grating while the optical phase difference of the grating is varied. We show that the self-image of a phase EC grating of rectangular type is slightly aberrated around the center of the interface of linear and semicircular parts but moire fringes by self-imaging a phase EC grating on a reference EC grating are little influenced by the image aberration. We conclude that a phase EC grating as well as an amplitude EC grating in our earlier work [Optik 113 (2002) 285] can be effectively applied to a Talbot interferometer when the phase difference of the grating is prepared close to 90°.

Optical torque exerted on a sphere in the evanescent field of a circularly-polarized Gaussian laser beam

Abstract We analyze theoretically the optical torque for rotating a sphere in the evanescent field that is formed at the plane interface by total internal reflection of a circularly polarized Gaussian laser beam. For the incidence of a Gaussian beam in the x – z plane we examine analytically and numerically the Cartesian components of the optical torque T x , T y and T z about the center of the sphere, in comparison with plane wave results. We show that T x and T z rely on the transport of angular momentum to the sphere by a circularly polarized light but the existence of T y does not require any circularly-polarized component of the incident light.

Radiation force and torque exerted on a stratified sphere in the circularly polarized TEM 01 *-mode laser beam

An expression of the circularly polarized TEM01*-mode laser beam is obtained from the vector potential A, of which the scalar part becomes a linear combination of the complex multipole fields with the orders of (1, 0) and (0, 1). A light-scattering theory of the TEM01*-mode laser beam by a stratified sphere is developed, and the analytic formulas are derived for the radiation force and torque on a stratified particulate sphere located anywhere in the TEM01*-mode laser beam. Numerical calculations of the radiation force and torque are presented for a single-layered sphere case. The z-components of radiation force Fz and radiation torque Trot,z on a transparent hollow sphere with r1 = 0.5λ, r2 = 2.0λ in radii and N2 = 1.5 + i0.001 in refractive index are found to be 2 × 10−9 (dyne) and 0.75 × 10−14 (dyne cm), respectively, for a 1-W TEM01*-mode laser beam.

Characterization of Fresnel images of an elongated circular grating

Summary We characterize theoretically and experimentally Fresnel images (or self-images) of an elongated circular (EC) grating which could be employed for the visual measurement of linear displacements in Talbot moire deflectometry. Based on a Fresnel diffraction integral, we estimate the shape of the Fresnel image formed at a specific distance from the EC grating in which both parallel lines and semicircles are illuminated by a coherent plane wave. For a square type transmittance of the grating, we also compare the theoretical estimates with its self-images captured by an array of charge-coupled devices (CCD). We show that self-images of the EC grating are substantially aberrated near the center of the interface between the linear and semicircular parts but not in its off-central region. Moire patterns by two self-imaged EC gratings are found not much affected by the central aberration.

Determination of the absolute order of shadow moiré fringes by using two differently colored light sources

We present a simple method of determining the absolute order of shadow moiré fringes by using two differently colored light sources. This technique is based on the periodic color structures generated by superimposing two moiré patterns with different colors.

OPTICALLY INDUCED ROTATION OF COMBINED MIE PARTICLES WITHIN AN EVANESCENT FIELD OF A GAUSSIAN BEAM

We demonstrate a windmill type rotation of combined Mie particles caused by optical forces of the evanescent field generated at the surface of a Gadolinium Gallium Garnet prism where a linearly polarized Nd:YAG laser beam (of wavelength 532 nm and power 100 mW) is totally reflected. The combined particles such as doublets (or triplets) consisting of polystyrene latex (or yeast) spheres with diameters of 3–5 µm are reported to rotate with angular velocities of 1 rpm in water when the particles are slightly displaced from the center of the Gaussian evanescent spot. The particle rotation in the inhomogeneous evanescent fields can be useful for a potential application to micromotors or microaccelerometers.