Focusing of a femtosecond vortex light pulse through a high numerical aperture objective

Abstract

We investigate the focusing properties of a femtosecond vortex light pulse focused by a high numerical aperture objective. By using the Richards-Wolf vectorial diffraction method, the intensity distribution, the velocity variation and the orbital angular momentum near the focus are studied in great detail. We have discovered that the femtosecond vortex light pulse can travel at various speeds, that is, slower or faster than light with a tight focusing system. Moreover, we have found that the numerical aperture of the focusing objective and the duration of the vortex light pulse will influence the orbital angular momentum distribution in the focused field.

Ultrafast multi-target control of tightly focused light fields

“…where (r,  , t) is the incoming time-dependent polar coordinate; σ 0 and m stand for the beam waist and the topological charge of the incident beam; A(t) = exp[-(a g t/T) 2 ]exp(-iω 0 t) is the temporal pulse having a Gaussian shape envelope, in which a g = (2ln2) 1/2 , T denotes the pulse duration, as well as ω 0 is its central angular frequency. According to the time-dependent vectorial diffraction theory [16][17]18 , we can garner the focal light fields in the Fourier domain,…”

“…f represents the focal length of the objective lens. Here the pupil apodization function of a single spectral component can be expressed as 16,17 :…”

“…Despite of significant progresses, these approaches still suffer from several possible limitations in practice, such as two-level quantum systems, paraxial optical configurations as well as restricted near-field regions. To cope with these issues, approaches exploring the ultrafast optical fields by tightly focusing linearly/radially polarized (vortex) beams based on the time-dependent vectorial diffraction theory have been proposed [16][17]18 . In addition, Zhan et al recently demonstrated that transverse spatial-time optical vortex beams are achievable through a controllable linear pulse shaping method 19 .…”

Ultrafast Spin‐to‐Orbit and Orbit‐to‐Local‐Spin Conversions of Tightly Focused Hybridly Polarized Light Pulses

“…One the other hand, the same hybridly polarized counterpart in the presence of vortex phases is also focused by the same objective lens, enabling the locally induced circular polarization at the focus of the total light field, therefore allowing access to the ultrafast OTLS conversion. In this connection, we start from an incident hybridly polarized light field with the vortex-dressed Laguerre-Gaussian (LG) femtosecond pulse envelope, which in the pupil plane can be featured by, [34][35][36] Eðr, φ, tÞ…”

“…We then introduce the incident light fields charactered by Equation ( 1) into a high NA objective lens, after which a 3D-polarized tightly focused light fields can be well-established. In this way, according to the time-dependent vectorial diffraction theory, [34,35] such 3D light fields in optical spectrum domain near the focus point can be formulized as…”