T. Kaiser

Structural resonances in a dielectric sphere illuminated by an evanescent wave

Mie scattering of an evanescent wave by a dielectric sphere has been theoretically treated by Chew et al. [Appl. Optics 18 (1979) 2679]. We found some discrepancies between our expansion coefficients and that of Chew. The correct analytic expressions are given by reviewing the theory shortly. Furthermore, we investigate the resonance structure and the source function for different decay rates of the evanescent wave. Numerical results are given for the differential scattering cross section and the source function. Source functions for resonant and nonresonant cases are presented for different penetration depths of the evanescent wave.

Enhancement of the Raman spectrum of optically levitated microspheres by seeded nanoparticles

Optical levitation experiments were performed with diethyl sebacate and diethyl hexylsebacate particles with a diameter range of 20–30 μm. The particles were seeded with polystyrene–latex particles with a diameter of 90 nm. Elastically and inelastically scattered light was recorded simultaneously. Although no change in the Mie scattering could be observed, the nonresonant part of the Raman spectrum was raised by a factor of 2. The C–H stretching region between 2800 and 3100 cm−1 was investigated, and the time dependence of the Raman intensity was measured at a fixed wave number of Δν = 2920 cm−1.

INVESTIGATION OF COATED DROPLETS IN AN OPTICAL TRAP : RAMAN-SCATTERING, ELASTIC-LIGHT-SCATTERING, AND EVAPORATION CHARACTERISTICS

Single optically levitated microparticles were investigated by Raman spectroscopy. The particles were composed of di-octyl-phthalate (DOP) and glycerol; these substances are not mixable and form a two-phase droplet. Measurements of the Raman spectrum confirm the formation of droplets containing both chemical species. The spectra show strong input and output structural resonances as expected. If the particle is in resonance, the field inside the particle is enhanced, and most of the inelastically scattered light is emitted from molecules close to the droplet rim. If the particle does not fulfill the resonance condition, the contribution of an individual molecule to the Raman scattering does not depend strongly on the radial position of this molecule. On this basis, the radial distribution of the two components inside the evaporating droplet was determined by time-dependent measurements of the Raman spectrum. Furthermore, elastic-light scattering and the evaporation characteristics of the particles were investigated.

Computation of the internal field of a large spherical particle by use of the geometrical-optics approximation

We obtain the internal electric field of an illuminated liquid droplet using geometrical optics. The approximation includes the phase effects of various components. We compare the geometrical-optics solution with the Mie theory solution for a nonabsorbing particle with a size parameter of alpha = 500 and an index of refraction of n = 1.332.

Ray interpretation of multipole fields in spherical dielectric cavities

We present a caustic model of morphology-dependent resonances based on geometrical optics, which describes the electromagnetic field in cylinders or spheres by families of ray congruences. A ray congruence in this model is basically a family of rays that osculate in phase on a common circle, the caustic. The circumference of this circle is in the plane case an integer multiple of the wavelength. This integer number corresponds to the mode number in the multipole expansion. In the spherical case two families of caustics exist. The mode numbers l, m of the multipole expansion for spherical particles define the corresponding radii of the caustics of the two ray families. The localization principle follows in this model simply by conservation of angular momentum. The condition for narrow modes caused by total internal reflection and the leaking of these modes is explained. The excitation of narrow resonances can also be explained in a straightforward manner by requiring that rays propagating from the caustic to the surface couple in phase to the caustic after reflection. Comparison with the exact solution shows excellent agreement.

Structural resonances in a coated sphere: investigation of the volume-averaged source function and resonance positions.

Morphology-dependent resonances in a coated sphere are investigated by computation of the volumeaveraged source function obtained from Lorenz-Mie theory. Analytic expressions for the source function in absorbing and nonabsorbing spheres are given in a suitable form for computations. An advantage of the investigation of the source function is that core and shell contributions can be computed and examined independently. Furthermore the influences of the refractive index and the thickness of the outer layer on resonance positions and height are studied in detail. These influences are presented for the α(104) partial-wave example.

Optical trap sedimentation cell—a new technique for the sizing of microparticles

Abstract In this paper a new technique for the sizing of optically levitated particles is reported. It is based upon the analysis of the dynamical behavior of the investigated particle during a transient interruption of the supporting laser beam. A mathematical model to describe the movement of the particle was developed and experiments with various samples were performed. The evaporation of single- and two-component droplets were monitored on-line. To allow a verification of the obtained results, the intensity of the light scattered by the particle was recorded simultaneously during the experiments. Comparison of measured data and computations according to Lorenz-Mie theory showed that the reported technique enables the determination of particle size with an accuracy better than 1% in less than 1 min without knowledge of its optical properties.

Controlled modification of the expansion order as a tool in mie computations.

In the framework of Mie theory the involved electromagnetic fields are expanded in an infinite series of multipoles. In numerical computations the summation has to be terminated after a finite number of terms (the expansion order N), which unavoidably produces errors. On the other hand, it is known that the contributions of terms of order l with x <l < N, where x is the dimensionless size parameter, are highly localized, i.e., these contributions appear as sharp peaks in resonance spectra. We show that it is possible to specify the expansion order in a controlled manner to extract certain features from Mie spectra. This controlled modification of the expansion order can be used as a high-pass, low-pass or bandpass filter. Formulas that serve as linewidth (frequency) and resonance-order filters are given, and their usage is demonstrated.

Eigenmodes of spherical dielectric cavities: coupling of internal and external rays

Eigenmodes of spherical dielectric cavities are investigated within the framework of geometrical optics. A model for the coupling of internal and external rays is presented. Approximate expressions for the expansion coefficients of Mie theory are derived. Formulas for the modulus and the phase are given. The systematic behavior of the phase angle is investigated. All expressions are explicit equations and may be used to calculate the expansion coefficients as a function of order l or size parameter x. All features of the presented results are understandable in terms of light rays. A plane interface analog is presented. The so-called resonance regime (Λ/n<x<Λ), where n is the relative refractive index and Λ=l+1/2, is considered especially. An implicit equation for these resonance positions is rederived, and explicit relations for their strengths and widths are given. All findings are in agreement with results derived from Mie theory.