No Arabic abstract
Numerical simulation is used to analyze statistical characteristics of vortex beams propagating in the atmosphere. The cumulative distribution function and the probability density function of intensity fluctuations are compared for Gaussian beams and vortex beams. It is shown that for propagation conditions in the turbulent atmosphere corresponding to weak fluctuations (Rytov parameter much smaller than unity), intensity fluctuations at the axis of the Gaussian beam have the lognormal distribution, whereas the probability density distribution of the radiation intensity fluctuations at the axis of the vortex beams is well approximated by the exponential distribution characteristic of conditions of saturated fluctuations (Rytov parameter much larger than unity)
Vortex beams with orbital angular momentum has been attracting tremendous attention due to their considerable applications ranging from optical tweezers to quantum information processing. Metalens, an ultra-compact and multifunctional device, provide a desired platform for designing vortex beams. A spin-dependent metalens can boost the freedom to further satisfy practical applications. By combining geometric phase and propagation phase, we propose and demonstrate an approach to design a spin-dependent metalens generating dual-focused vortex beams along longitudinal or transverse direction, i.e., metalenses with predesigned spin-dependent phase profiles. Under the illumination of an elliptical polarization incident beam, two spin-dependent focused vortex beams can be observed, and the relative focal intensity of them can be easily adjusted by modulating the ellipticity of the incident beam. Moreover, we also demonstrated that the separate distance between these dual-focused beams and their topological charges could be simultaneously tailored at will, which may have a profound impact on optical trapping and manipulation in photonics.
A large distance propagation in turbulent atmosphere results in disintegration of laser beam into speckles. We find that the most intense speckle approximately preserves both the Gaussian shape and the diameter of the initial collimated beam while loosing energy during propagation. One per 1000 of atmospheric realizations produces at 7km distance an intense speckle above 20% of the initial power. Such optimal realizations create effective extended lenses focusing the intense speckle beyond the diffraction limit of vacuum propagation. Atmospheric realizations change every several milliseconds. We propose to use intense speckles to greatly increase the time-averaged power delivery to the target plane by triggering the pulsed laser operations only at times of optimal realizations. Resulting power delivery and laser irradiance at the intense speckles well exceeds both intensity of diffraction-limited beam and intensity averaged over typical realizations.
We study density fluctuations in supersonic turbulence using both theoretical methods and numerical simulations. A theoretical formulation is developed for the probability distribution function (PDF) of the density at steady state, connecting it to the conditional statistics of the velocity divergence. Two sets of numerical simulations are carried out, using either a Riemann solver to evolve the Euler equations or a finite-difference method to evolve the Navier-Stokes (N-S) equations. After confirming the validity of our theoretical formulation with the N-S simulations, we examine the effects of dynamical processes on the PDF, showing that the nonlinear term in the divergence equation amplifies the right tail of the PDF and reduces the left one, the pressure term reduces both the right and left tails, and the viscosity term, counter-intuitively, broadens the right tail of the PDF. Despite the inaccuracy of the velocity divergence from the Riemann runs, as found in our previous work, we show that the density PDF from the Riemann runs is consistent with that from the N-S runs. Taking advantage of their much higher effective resolution, we then use the Riemann runs to study the dependence of the PDF on the Mach number, $mathcal{M}$, up to $mathcal{M}sim30$. The PDF width, $sigma_{s}$, follows the relation $sigma_{s}^2 = ln (1+b^2 {mathcal M}^2)$, with $bapprox0.38$. However, the PDF exhibits a negative skewness that increases with increasing $mathcal{M}$, so much of the growth of $sigma_{s}$ is accounted for by the growth of the left PDF tail, while the growth of the right tail tends to saturate. Thus, the usual prescription that combines a lognormal shape with the standard variance-Mach number relation greatly overestimates the right PDF tail at large $mathcal{M}$, which may have a significant impact on theoretical models of star formation.
Harnessing the spontaneous emission of incoherent quantum emitters is one of the hallmarks of nano-optics. Yet, an enduring challenge remains-making them emit vector beams, which are complex forms of light associated with fruitful developments in fluorescence imaging, optical trapping and high-speed telecommunications. Vector beams are characterized by spatially varying polarization states whose construction requires coherence properties that are typically possessed by lasers-but not by photons produced by spontaneous emission. Here, we show a route to weave the spontaneous emission of an ensemble of colloidal quantum dots into vector beams. To this end, we use holographic nanostructures that impart the necessary spatial coherence, polarization and topological properties to the light originating from the emitters. We focus our demonstration on vector vortex beams, which are chiral vector beams carrying non-zero orbital angular momentum, and argue that our approach can be extended to other forms of vectorial light.
We study the properties of the Fraunhofer diffraction patterns produced by Gaussian beams crossing spiral phase plates. We show, both analytically and numerically, that off-axis displacements of the input beam produce asymmetric diffraction patterns. The intensity profile along the direction of maximum asymmetry shows two different peaks. We find that the intensity ratio between these two peaks decreases exponentially with the off-axis displacement of the incident beam, the decay being steeper for higher strengths of the optical singularity of the spiral phase plate. We analyze how this intensity ratio can be used to measure small misalignments of the input beam with a very high precision.