Generation of dark hollow femtosecond pulsed beam by phase-only liquid crystal spatial light modulator

Two-photon microscopy with enhanced resolution and signal-to-background ratio using hollow Gaussian beam excitation

Two-photon microscopy (TPM) offers deeper imaging depth inside the scattering medium, however, it suffers from limited resolution owing to the longer excitation wavelength. We demonstrate the use of a hollow Gaussian beam (HGB) at the therapeutic window to improve the resolution and signal-to-background ratio (SBR). The HGB was produced by omitting the azimuthal phase term from the vortex mode, and the excitation point spread function (PSF) can be readily tuned by the mode order. The performance of the TPM with HGB was evaluated by experimentally imaging 100 nm fluorescent beads to estimate the PSF. The HGB improved the lateral resolution of the TPM by 36% in contrast to the conventional TPM. The HGB also furnishes an improvement of SBR by eliminating the out-of-focus light owing to its ring shape. Furthermore, we have used a translating lens-based module for additional lateral resolution tuning and reduced the resolution further down to 44% with respect to conventional TPM. Finally, we have performed imaging with merely two-dimensional scanning of a 50 µm thick mouse brain slice (Thy-YFP H-line) using the developed TPM with HGB. Our compact, robust, and low-cost design of the HGB generation scheme can easily be integrated into the commercial TPM to accommodate the improvements.

Beam propagation factor and kurtosis parameter of hollow vortex Gaussian beams: an alternative method

Based on the second-order moments, an analytical and concise expression of the beam propagation factor of a hollow vortex Gaussian beam has been derived, which is applicable for an arbitrary topological charge $m$m. The beam propagation factor is determined by the beam order $n$n and the topological charge $m$m. With increasing the topological charge $m$m, the beam propagation factor increases. However, the effect of the beam order $n$n on the beam propagation factor is associated with the topological charge $m$m. By using the transformation formula of higher-order intensity moments, an analytical expression of the kurtosis parameter of a hollow vortex Gaussian beam passing through a paraxial and real $ABCD$ABCD optical system has been presented. The kurtosis parameter is determined by the beam order $n$n, the topological charge $m$m, and the position of observation plane $ \eta $η. The influence of the beam order $n$n on the kurtosis parameter is related with the topological charge $m$m and the position parameter $ \eta $η. When the beam order $n$n is larger than 1, the kurtosis parameter in different observation $\eta$η-planes decreases and tends to a stable value with increasing the topological charge $m$m. When $m = \pm {2}n$m=±2n, the kurtosis parameter is independent of the position parameter $ \eta $η and keeps unvaried during the beam propagation. Regardless of the values of $n$n and $m$m, the kurtosis parameter must tend to a saturated value or a stable value as the position parameter $ \eta $η increases to a sufficiently large value. This research is beneficial to the practical application of a hollow vortex Gaussian beam.

Hollow Gaussian beam generation through nonlinear interaction of photons with orbital angular momentum

Hollow Gaussian beams (HGB) are a special class of doughnut shaped beams that do not carry orbital angular momentum (OAM). Such beams have a wide range of applications in many fields including atomic optics, bio-photonics, atmospheric science, and plasma physics. Till date, these beams have been generated using linear optical elements. Here, we show a new way of generating HGBs by three-wave mixing in a nonlinear crystal. Based on nonlinear interaction of photons having OAM and conservation of OAM in nonlinear processes, we experimentally generated ultrafast HGBs of order as high as 6 and power >180 mW at 355 nm. This generic concept can be extended to any wavelength, timescales (continuous-wave and ultrafast) and any orders. We show that the removal of azimuthal phase of vortices does not produce Gaussian beam. We also propose a new and only method to characterize the order of the HGBs.

Nonparaxial propagation properties of a vector partially coherent dark hollow beam

Based on the generalized Raleigh-Sommerfeld diffraction integrals, analytical nonparaxial propagation formulas for the elements of the cross-spectral density matrix of a vector partially coherent dark hollow beam (DHB) in free space are derived. The effect of spatial coherence and beam waist sizes on the statistical properties of a nonparaxial vector DHB is studied numerically. It is found that one can modulate the statistical properties of a nonparaxial vector DHB by varying its initial spatial coherence, which will be useful in some applications where nonparaxial beams are commonly encountered.

Propagation of a partially coherent hollow vortex Gaussian beam through a paraxial ABCD optical system in turbulent atmosphere

The propagation of a partially coherent hollow vortex Gaussian beam through a paraxial ABCD optical system in turbulent atmosphere has been investigated. The analytical expressions for the average intensity and the degree of the polarization of a partially coherent hollow vortex Gaussian beam through a paraxial ABCD optical system are derived in turbulent atmosphere, respectively. The average intensity distribution and the degree of the polarization of a partially coherent hollow vortex Gaussian beam in turbulent atmosphere are numerically demonstrated. The influences of the beam parameters, the topological charge, the transverse coherent lengths, and the structure constant of the atmospheric turbulence on the propagation of a partially coherent hollow vortex Gaussian beam in turbulent atmosphere are also examined in detail. This research is beneficial to the practical applications in free-space optical communications and the remote sensing of the dark hollow beams.