Discrete modulation continuous variable quantum key distribution (DM-CV-QKD) is highly considered in real implementations to avoid the complexity of Gaussian modulation (GM), which is optimum in terms of the key rate. DM-CV-QKD systems usually consider M-symbol phase shift keying (M-PSK) constellations. However, this type of constellation cannot reach transmission distances and key rates as high as GM, limiting the practical implementation of CV-QKD systems. Here, by considering M-symbol amplitude and phase shift keying (M-APSK) constellations, we can approximate GM. Indeed, considering finite-size effects, 4 ring 64-APSK can reach 52.0 km, only 7.2 km less than GM and 282% the maximum achievable transmission distance for 8-PSK.

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New types of finite energy Airy beams are proposed. We consider two different types of beams, namely, beams that are obtained as blocked and exponentially attenuated versions of Airy functions Ai and Bi, and beams of finite width but having the Airy functions typical phase. All of them show very interesting properties, such as parabolic trajectories for longer propagation distances, profile evolution exhibiting less diffraction, or better definiteness of the main peak, when compared with other finite energy Airy beams studied before.

Normal mode stability of both rectilinear and self-bending photorefractive screening solitons is considered. In each case, the Evans function procedure is used to investigate stability and to search for internal modes. For the rectilinear case, a standard Evans function procedure is applied. However, in the self-bending case the asymptotic form of the eigenvalue problem is a system of Airy equations, instead of the usual system of constant coefficient differential equations. To overcome this difference, a modified version of the Evans function method, using Airy functions rather than exponentials, is implemented and applied. The results confirm stability and give an internal mode pattern in good agreement with full numerical integration.

We obtained a propagation equation for an optical pulse at an electromagnetically induced transparency window guided on a gas-filled hollow-core photonic crystal fiber. This equation admits dissipative solitons whose analytical expression was also obtained. Depending on the parameter region, they may be stable or unstable. We simulated a typical experimental arrangement and found some cases for which the equation parameters are such that it admits stable solitons.