Tight focusing properties of a circular partially coherent Gaussian beam

Multi-focused electric and magnetic field sourcing from an azimuthally polarized vortex circular hyperbolic umbilic beam

In this paper, one kind of multi-focusing electric and magnetic field which is sourced from an azimuthally polarized vortex circular hyperbolic umbilic beam (APVCHUB) is presented. After passing through a high NA objective, both the electric and magnetic fields of the APVCHUBs will focus multiple times, and a high-purity longitudinal magnetic field (p q =80%) will be generated. Besides, the mutual induction of the vortex phase and azimuthal polarization changes the electric and magnetic fields' vibration state and intensity distribution, making the longitudinal magnetic field carry an m-order concentric vortex. Our findings suggest that the APVCHUB could have potential applications in magnetic particle manipulation, extremely weak magnetic detection, data storage, semiconductor quantum dot excitation, etc.

Nonparaxial Propagation of Bessel Correlated Vortex Beams in Free Space

The nonparaxial propagation of partially coherent beams carrying vortices in free space is investigated using the method of decomposition of the incident field into coherent diffraction-free modes. Modified Bessel correlated vortex beams with the wavefront curvature are introduced. Analytical expressions are presented to describe the intensity distribution and the degree of coherence at different distances. The evolution of the intensity distribution during beam propagation for various source parameters is analyzed. The effects of nonparaxiality in the propagation of tightly focused coherent vortex beams are analyzed.

Minimal Focal Spot Size Measured Based on Intensity and Power Flow

It is shown, theoretically and numerically, that the distributions of the longitudinal energy flow for tightly focused light with circular and linear polarization are the same, and that the spot has circular symmetry. It is also shown that the longitudinal energy flows are equal for optical vortices with unit topological charge and with radial or azimuthal polarization. The focal spot has a minimum diameter (all other characteristics being equal), which is measured based on the intensity of an optical vortex with azimuthal polarization. The diameter of the focal spot calculated from the energy flow for light with circular or linear polarization is slightly larger (by a fraction of a percentage). The magnitude of the diameter based on the intensity plays a role in the interaction of light with matter, and the magnitude of the diameter based on the energy flux affects the resolution in optical microscopy which is crucial in sensorial applications.

Linear canonical transform as a tool to analyze coherence properties of electromagnetic beams propagating in a quadratic phase system

Linear canonical transformation (LCT) provides a generalized and elegant mathematical framework for analyzing the coherence properties of an electromagnetic (EM) beam propagating in quadratic phase systems (QPSs). It is shown that LCT may be used to analyze coherence properties such as generalized Stokes parameters and EM degree of coherence of a partially coherent EM beam propagating through a QPS. We present simulation results of a Gaussian Schell model beam propagating through a Fourier system, fractional Fourier system, and 4f imaging system with an aperture and beam relay system.

Tunable degree of polarization of an unpolarized, partially coherent beam with circular coherence in a high numerical aperture system

The polarization properties of a strongly focused, unpolarized, partially coherent beam with circular coherence are studied in this Letter. It is found that the degree of polarization (DoP) in the focal plane can be adjusted, not only by the initial coherence and the semi-aperture angle, but also through an annular pupil due to the unusual coherence of the source. Our results show that for an unpolarized, partially coherent incident beam, the field in the focal plane can go from almost an unpolarized state to almost a fully polarized state along a radial distance, although the initial coherence length is very short. Through adjusting the width of the annular pupil, the DoP on average can be significantly reduced or enhanced. Especially for the very narrow annulus, the approximation expression of the DoP is derived, from which the accurate positions of the peak values of the DoP can be easily calculated. Our findings provide an alternative way to tailor the DoP in three-dimensional optical fields.

Spatial-Temporal Self-Focusing of Partially Coherent Pulsed Beams in Dispersive Medium

Partially coherent pulsed beams have many applications in pulse shaping, fiber optics, ghost imaging, etc. In this paper, a novel class of partially coherent pulsed (PCP) sources with circular spatial coherence distribution and sinc temporal coherence distribution is introduced. The analytic formula for the spatial-temporal intensity of pulsed beams generated by this kind of source in dispersive media is derived. The evolution behavior of spatial-temporal intensity of the pulsed beams in water and air is investigated, respectively. It is found that the pulsed beams exhibit spatial-temporal self-focusing behavior upon propagation. Furthermore, a physical interpretation of the spatial-temporal self-focusing phenomenon is given. This is a phenomenon of optical nonlinearity, which may have potential application in laser micromachining and laser filamentation.