Using an analytical expression for an integral involving Bessel and Legendre functions, we succeed in obtaining the partial wave decomposition of a general optical beam at an arbitrary location relative to the origin. We also showed that solid angle integration will eliminate the radial dependence of the expansion coefficients. The beam shape coefficients obtained are given by an exact expression in terms of single or double integrals. These integrals can be evaluated numerically on a short time scale. We present the results for the case of a linear-polarized Gaussian beam.

A double tweezers setup was employed to perform ultra sensitive force measurements and to obtain the full optical force curve as a function of radial position and wavelength. The light polarization was used to select either the transverse electric (TE), or transverse magnetic (TM), or both, modes excitation. Analytical solution for optical trapping force on a spherical dielectric particle for an arbitrary positioned focused beam is presented in a generalized Lorenz-Mie diffraction theory. The theoretical prediction of the theory agrees well with the experimental results. The algorithm presented here can be easily extended to other beam geometries and scattering particles.

Ge nanocrystallites (Ge-nc) embedded in a SiO(2) matrix are investigated using Raman spectroscopy, photoluminescence and Fourier transform infrared spectroscopy. The samples were prepared by ion implantation with different implantation doses (0.5, 0.8, 1, 2, 3 and 4) × 10(16) cm(-2) using 250 keV energy. After implantation, the samples were annealed at 1000 °C in a forming gas atmosphere for 1 h. All samples show a broad Raman spectrum centred at w≈304 cm(-1) with a slight shift depending on the implantation doses. The Raman intensity also depends on the Ge(74+) dose. A maximum photoluminescence intensity is observed for the sample implanted at room temperature with a dose of 2 × 10(16) cm(-2) at 3.2 eV. Infrared spectroscopy shows that the SiO(2) films moved off stoichiometry due to Ge(74+) ion implantation, and Ge oxides are formed in it. This result is shown as a reduction of GeO(x) at exactly the dose corresponding to the maximum blue-violet PL emission and the largest Raman emission at 304 cm(-1). Finally, the Raman spectra were fitted with a theoretical expression to evaluate the average size, full-width at half-maximum (FWHM) and dispersion of Ge-nc size.