Size-dependent optical forces on dielectric microspheres in hollow core photonic crystal fibers.

Optical forces on microspheres inside hollow core photonic crystal fibers (HC-PCFs) are often predicted using a ray optics model, which constrains its validity based on wavelength and microsphere sizes. Here, we introduce a rigorous treatment of the electromagnetic forces based on the Lorenz-Mie theory, which involves analytical determination of beam shape coefficients for the optical modes of a HC-PCF. The method is more practicable than numerical approaches and, in contrast with ray optics models, it is not limited by system size parameters. Time of flight measurements of microspheres flying through the HC-PCF lead to results consistent with the Lorenz-Mie predictions.

Changes in fertilization medium viscosity using hyaluronic acid impact bull sperm motility and acrosome status.

The female reproductive tract, in particular the composition of the uterine and oviduct fluids, is responsible, at least in part, for triggering sperm cell modifications, essential for the acquisition of fertilization ability. Hyaluronic acid (HA) is a glycosaminoglycan present in these fluids, and its role in the fertilization process and sperm functionality is still barely understood. This work was designed to (a) determine the rheological characteristics of the fertilization medium by the addition of HA and (b) determine the HA influence on sperm motility and functional status. To that end, the in vitro fertilization medium was supplemented with 4 doses of HA (6, 60, 600 and 6,000 µg/ml) and analysed for viscosity and adhesion strength characteristics. Then, thawed semen from 6 bulls were incubated in these media and assessed at 4 different moments for morphological and functional parameters (plasma and acrosomal membrane integrities, mitochondrial membrane potential, capacitation, acrosomal reaction, and motility). The rheological evaluation showed that the addition of HA was able to increase both the viscosity and the adhesion strength of the fertilization medium, especially in the 6,000 µg/ml group in which the effect was more pronounced. No influence of HA could be observed on mitochondrial potential, and acrosomal and plasma membrane integrities. However, HA supplementation, at lower doses, led to an increase in the number of reacted sperm, as well as changes in motility parameters, with increase in the number of motile, rapid and progressive spermatozoa. In conclusion, the addition of HA alters the rheological properties of the fertilization medium and leads to the improvement of the properties related to sperm motility and capacitation, without compromising other functional aspects of the cell.

Expansion of arbitrary electromagnetic fields in terms of vector spherical wave functions.

Since 1908, when Mie reported analytical expressions for the fields scattered by a spherical particle upon incidence of plane-waves, generalizing his analysis for the case of an arbitrary incident wave has been an open question because of the cancellation of the prefactor radial spherical Bessel function. This cancellation was obtained before by our own group for a highly focused beam centered in the objective. In this work, however, we show for the first time how these terms can be canceled out for any arbitrary incident field that satisfies Maxwells equations, and obtain analytical expressions for the beam shape coefficients. We show several examples on how to use our method to obtain analytical beam shape coefficients for: Bessel beams, general hollow waveguide modes and specific geometries such as cylindrical and rectangular. Our method uses the vector potential, which shows the interesting characteristic of being gauge invariant. These results are highly relevant for speeding up numerical calculation of light scattering applications such as the radiation forces acting on spherical particles placed in an arbitrary electromagnetic field, as in an optical tweezers system.

Effect of finite terms on the truncation error of Mie series.

The finite sum of the squares of the Mie coefficients is very useful for addressing problems of classical light scattering. An approximate formula available in the literature, and still in use today, has been developed to determine a priori the number of the most significant terms needed to evaluate the scattering cross section. Here, we obtain an improved formula, which includes the number of terms needed for determining the scattering cross section within a prescribed relative error. This is accomplished using extended precision computation for a wide range of commonly used size parameters and indices of refraction. The revised formula for the finite number of terms can be a promising and valuable approach for efficient modeling light scattering phenomena.

Rotational dynamics of optically trapped nanofibers.

We report on the experimental evidence of tilted polymer nanofiber rotation, using a highly focused linear polarized Gaussian beam. Torque is controlled by varying trapping power or fiber tilt angle. This suggests an alternative strategy to previously reported approaches for the rotation of nano-objects, to test fundamental theoretical aspects. We compare experimental rotation frequencies to calculations based on T-Matrix formalism, which accurately reproduces measured data, thus providing a comprehensive description of trapping and rotation dynamics of the linear nanostructures.

Axial optical trapping efficiency through a dielectric interface.

Axial trapping through a dielectric interface is investigated in the framework of the angular spectrum representation and of the generalized Lorenz-Mie theory. We determine the optical force for an arbitrarily polarized non-paraxial, strongly aberrated, axially symmetric focusing beam and apply this description to the case of an arbitrarily positioned dielectric microsphere, commonly employed in optical tweezers, not taking into account the contribution of evanescent waves at the interface. We derive the analytical expression of the force profile, finding that the incident polarization does not affect the axial optical force. In addition, we derive an approximated expression for the axial force as a function of beam displacement just outside the microsphere and we show how the information provided by the ripple structure of the optical trapping efficiency versus sphere displacement curve, due to the aberration effect, could be exploited to calibrate the bead axial position versus the experimental beam positioning controls.

Exact partial wave expansion of optical beams with respect to an arbitrary origin.

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.