טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentAnatoly Patsyk
SubjectAccelerating Beams in Curved Space
DepartmentDepartment of Physics
Supervisor ? 18? Segev Mordechai
Full Thesis textFull thesis text - English Version


Abstract

This work focuses on theoretical and experimental aspects of light propagtion on curved surfaces. Specifically, I was interested in accelerating beams that propagate in a nondiffracting self-similar fashion. Accelerating beams were introduced into optics in 2007 as beams whose structure corresponds to the Airy function. Such Airy beams were paraxial and accelerating only to small angles. Later, additional kinds of accelerating beams were discovered, for example, non-paraxial accelerating beams that bend to large angles. Those beams preserve their structure and accelerate in the direction transverse to their propagation.

Today, accelerating beams already offer a variety of applications: for example, they are used to manipulate micro particles or in laser micromachining where curved features in the material are generated by a predesigned laser beam that moves on a curved trajectory. More recently, the concept of accelerating beams was introduced into curved-space optics, but to date no experiments have ever been carried out on accelerating beams in any curved-space system.

In my work, I study accelerating beams propagating on a 2D spherical surface.  I found the structure of these beams analytically and simulated their propagation on a spherical surface numerically, by means of beam propagation code specifically designed for a spherical surface. These accelerating beams have lobes that propagate on non-geodesic trajectories. Moreover, these beams can accelerate toward the center of mass if their transverse scale is changed. This property and several others are unique to accelerating beams in curved space.

Finally, I demonstrate these accelerating beams experimentally. The beam’s wavefront is created by reflecting a laser beam off a SLM (spatial light modulator). Then, the beam is launched into a thin glass hemishpere forming a spherical surface. The accelerating properties of the beams are observed when one compares the transverse location of the main lobe of the beam with the location of a beam constructed from only a single lobe. The single lobe follows the geodesic trajectory whereas the main lobe of the whole beam follows a non-geodesic trajectory. Such beams greatly manifest the interplay between the curvature of space and the wave properties of light.

The glass samples had a thickness of 500 microns, they act like multimode waveguides in the radial direction. In order to see the wave propagation properties clearer, it is better to use thinner waveguides, ideally those that support a single bound mode. A good candidate for this is a soap bubble that has a thickness of several microns, which in principle can be reduced to several molecular layers. Therefore, we also studied experimentally light propagation in a thin liquid soap-water surface, soap bubbles. In those experiments the light exhibits no diffraction broadening at all, which is unexpected according to previous literature. This effect is independent of the curvature of a film, so it probably occurs due to the local interaction of the light and the molecules of the surface. While there are some earlier works related to those effects, the mechanism of creation of these nondiffracting channels in liquid thin films is an open question.