Free-space quantum key distribution (QKD) presents significant opportunities for advancing quantum communication systems by enabling the deployment of quantum networks across geographically challenging or inaccessible regions and expansive terrains without reliance on optical fiber infrastructure. This methodology addresses the constraints of traditional cabling and establishes a more adaptable framework for transmitting quantum information. When combined with continuous-variable QKD (CV-QKD) protocols, this approach facilitates the establishment of secure communication channels through scalable systems optimized to mitigate environmental disturbances. In this paper, we examine recent advancements and technical considerations in implementing CV-QKD within atmospheric channels, with a focus on addressing atmospheric phenomena such as turbulence, scattering, and beam wandering. We review the current state of practical free-space CV-QKD systems, including successful experimental demonstrations and prototype designs. Furthermore, we discuss prospects for enhancing this technology, particularly its integration with conventional telecommunications infrastructure and potential applications in future quantum networks.
A method for calculating diffractive optical elements for solving classification problems that are robust to positioning errors is proposed. In the method, the classification error is represented as a functional depending on the phase function of the element being designed and a random vector representing the positioning error as lateral displacement of the element relative to the optical axis. The mathematical expectation of this functional is then used as the error functional in the gradient method for diffractive optical element calculation. Explicit expressions for the derivatives of the error functional are derived. Using this method, a diffractive optical element for classifying handwritten digits is calculated. Numerical simulations show good performance of the designed element (classification accuracy exceeds 96% while relative contrast between energy focused in the classified class and target class exceeds 13%) with lateral displacements of 2 pixels in lateral direction, which corresponds to the center of the element shifting up to 17 wavelengths.
In this paper, we consider the behavior of the phase and local wave vector of a tightly focused optical vortex with linear polarization. It is shown that the regions of phase singularity correspond to giant values of the local wave vector. In contrast to the scalar approximation, when the theory predicts that when focusing an optical vortex with a large topological charge at the focus, the optical vortex is preserved with the same topological charge, the non--paraxial vector approximation shows that a vortex with a large topological charge at the focus always splits into several vortices. That is, several points of phase singularity arise (and, as a consequence, several regions with a giant wave vector). In particular, if the topological charge is equal to two, then two optical vortices with unit topological charges shifted from the optical axis are observed in the focal plane. If the topological charge exceeds two (i.e. three or more), then three optical vortices are always formed in the focal plane, two of which have a single topological charge and are shifted from the optical axis, and the third vortex remains on the optical axis and has a topological charge two less than the initial topological charge of the focused optical vortex. In this case, the centers of the vortices shifted from the optical axis approximately correspond to the boundaries of the zones of reverse energy flow.
A method for generating light curves with high efficiency using sector generalized spiral phase plates with a non-monotonic angular dependence of the phase is proposed. The proposed method is based on piecewise linear approximation of the phase function derivative and segmentation of a generalized spiral phase plate. The presented results demonstrate the possibility of forming light curves with a fairly arbitrary geometry, which expands the range of approaches to effectively forming light curves with a given intensity distribution.
The topological charge of a finite superposition of optical vortices with a Gaussian envelope is considered in this work. In the initial plane of such a superposition, the topological charge is shown theoretically and numerically to be equal to the number of zeros of a complex polynomial of degree n, where n is the maximum topological charge of the optical vortices in the superposition, located in a circle of unit radius together with the boundary. And during propagation in free space, the topological charge of such a superposition is always equal to n. If the modulus of the coefficient of the superposition term with topological charge equal to k is greater than the sum of the moduli of all other superposition coefficients, then there are k zeros in the unit radius circle and the topological charge of the entire superposition in the initial plane is equal to k (k <= n). If all superposition coefficients are equal in modulus, then the topological charge is equal to half (n / 2) in the initial plane, but during propagation the topological charge is again equal to n. In this case, additional zeros of the optical vortices superposition are formed almost immediately, at a distance much smaller than the wavelength from the initial plane, and at a distance from the optical axis greater than the radius of the limiting aperture of the initial field.
