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Identifier 000430640
Title Controlling the dynamics of optical beams
Author Γκουτσούλας, Μιχαήλ
Thesis advisor Εφραιμίδης, Νικόλαος
Abstract Since the theoretical prediction and experimental demonstration of optical Airy beams [Opt. Lett., 32(8):979–981,(2007), Phys. Rev. Lett., 99:213901,(2007)], accelerating waves have been established as a very important tool in the field of optics. The last dozen of years accelerating beams have attracted a lot of interest due to their intriguing properties, and were extensively studied both from a theoretical and an experimental perspective. Originally, Airy beams were proposed in quantum mechanics in the seminal work of Berry and Balazs [Am. J. Phys. 47(3):264–267, (1979)], showing that the potential-free Schrödinger equation admits propagation-invariant solutions in the form of accelerating Airy wavepackets. Beyond Airy beams, another family of diffraction-free waves was proposed and experimentally observed by Durnin, the well-known Bessel beams [J. Opt.Soc. Am. A, 4(4):651–654, (1987), Phys. Rev. Lett., 58:1499–1501, (1987)]. Due to their resilience to diffraction-spreading and the uniformity of their amplitude, such beams were also exploited in many applications. Furthermore, in the nonparaxial domain where rays and thus beams can bend at large angles, diffraction free beams accelerating along circular, elliptical, exponential and general power-law trajectories were demonstrated. In another concept, abruptly autofocusing waves mainly represented by Airy beams with radial symmetry, propagate along parabolic trajectories while focusing most of their energy right before a target. In this dissertation, we focus on engineering the properties of optical waves. We focus in the case of propagation-invariant fields of the Airy and Bessel type and on different classes of accelerating waves. We engineer their fundamental properties such as their amplitude, their width and their trajectory. Furthermore, we examine the focusing characteristics of abruptly autofocusing waves. The possibility of optimizing their focusing features is of our particular interest. To begin with, we study the generation of accelerating waves in the paraxial domain, whose propagation defining properties such as trajectory, maximum amplitude and beam-width will be predesigned. In the case of the power-law trajectories, the propagation of such beams is described by Airy-type solutions which are directly expressed in terms of the geometric properties of the preselected path. Additionally, we investigate the propagation of accelerating beams in the nonparaxial domain. In this case we study accelerating beams along circular, elliptic and power-law curves. Our solutions indicate that independently of the trajectory assumed, the dynamics of the beam near the caustic are described by Airy-type functions. Our formulas are expressed in an elegant and practical way and highlight the dependence to the curvature of the predesigned trajectory, among other geometrical features. In particular, we show that the generation of accelerating beams along nonparaxial trajectories with pre-engineered amplitude and beam-width, is possible. Moreover, we consider the propagation of abruptly autofocusing waves in the paraxial domain. Specifically, we emphasize on the propagation of such beams along convex but otherwise arbitrary predefined trajectories. Furthermore, in order to optimize their focusing characteristics, we properly modulate the important parameters such as the initial amplitude, the curvature of the trajectory, and the distance from the optical axis on the input plane, in order to achieve higher intensity contrast at the focus along with damped oscillatory behavior after the focal point. Beyond accelerating beams, we also study the case of Bessel beams of zeroth order and higher-order optical vortices of the Bessel-type. We propose a method for generating such beams, exhibiting pre-engineered maximum amplitude and beam-width or hollowcore radius along the propagation distance. In both cases, numerical results agree well with the theoretical model developed.
Language English
Subject Accelerating beams
Airy beams
Amplitude engineering
Beam-width engineering
Bessel beams
Diffraction -free
Power-law beams
Self -healing
Trajectory engineering
Έλεγχος πλάτους
Επιταχυνόμενα κύματα
Κύματα airy
Issue date 2020-07-24
Collection   School/Department--School of Sciences and Engineering--Department of Mathematics and Applied Mathematics--Doctoral theses
  Type of Work--Doctoral theses
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