טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
Ph.D Thesis
Ph.D StudentYoav Berlatzky
SubjectScattering from Non-Continuous 2D Potentials:
Theory and Applications
DepartmentDepartment of Physics
Supervisors Professor Emeritus Moiseyev Nimrod
Professor Emeritus Fishman Shmuel (Deceased)
Full Thesis textFull thesis text - English Version


Abstract

Initially this work was motivated by finding a semi-classical method used to drastically reduce the bending losses in curved optical waveguides. The method consists of creating a quasi-periodic structure by placing additional waveguides in parallel and in close proximity to the original waveguide, creating a reflective chirped Bragg grating. For a specific set of structure parameters the leaky mode's outward radiating tail is confined, decreasing the mode's decay rate by about two orders of magnitude. Although lacking proper justification, the semi-classical method is based on employing the Born Oppenheimer (BO) adiabatic approximation for the waveguide structure.


Finding the reason why the BO adiabatic approximation works so well in this scenario is the main thrust of this work. We show that the usual Lippmann-Schwinger Equation and Born Series treatment for finding the beyond-adiabatic corrections fails when applied to discontinuous structures such as waveguides with sharply delineated edges. Bypassing these difficulties requires the development of a novel general formalism for treating scattering in the Born-Oppenheimer expansion with a discontinuous transverse basis. This results in a novel Lippmann-Schwinger Equation and Born series with an exotic non-adiabatic coupling term applicable to such cases.


Finally, the novel formalism is used to analytically calculate corrections beyond the Born Oppenheimer adiabatic approximation used in the semi-classical method. The leading order corrections are in good agreement with the numerically exact results. They also provide a qualitative explanation of the coherent quasi-cancellations between the non-adiabatic terms from adjacent scattering centers in the 2D Bragg grating. This accounts for non-adiabatic corrections that are much smaller than those initially expected.