Theoretical Investigation And Research On Several Special Beams

Non-diffracting and self-accelerating beams have been a hot topic since the Airy wave packet was introduced to optics domain from quantum mechanics in 2007. Great efforts have been made on this theme in recent years. As exact solutions of the paraxial wave equation (which is equivalent to the Schrodinger equation), Airy beams propagate along parabolic trajectories and are endowed with non-diffracting and self-healing properties. Possible applications, including guiding micro-particles, producing curved plasma channels, and dynamically routing surface plasmon polaritons, have also been proposed and demonstrated. To break the paraxial limitation of Airy beam, the following research focus varies from paraxial regime to non-paraxial regime and a series of new non-diffracting beams have been discovered. However, most of these beams are obtained under the time harmonic condition.To break this limitation, we propose the concept of time-dependent Bessel beam, which generalizes the non-diffracting beams to non-time-harmonic regime. We start from Maxwell’s equations in vacuum under non-paraxial condition using the method borrowed from the half-Bessel beam.We use two different assumptions to study the diffraction properties and space-time characters of two kinds of time-dependent Bessel beams. For the plane wave assumption, we calculate and discuss the transverse intensity and the intensity distribution in detail. We have also deduced the critical condition of the beam’s space-time characters, and the result agrees well with the concept of the light cone in the theory of special relativity. For the damping wave assumption, we have got another kind of time-dependent Bessel beam. Similar properties have been found with the first kind of time-dependent Bessel beam. We have also found the similarities of the Bessel beam and the skin effect of electromagnetic wave in electrodynamics.The first chapter is the general introduction of this thesis, which introduces several special beams including Airy beams, half-Bessel beams and Mathieu beams.In chapter two, we introduce the time-dependent Bessel beams without damping. We calculate the transverse intensity, and it can exhibit non-diffraction in four dimensional space-time. Furthermore, the result agrees well with the concept of the light cone in the theory of special relativity.In chapter three, we introduce the time-dependent Bessel beams with damping. We find similar properties with the first kind of time-dependent Bessel beam. We also find the similarities of the Bessel beam and the skin effect of electromagnetic wave in electrodynamics.In chapter four, we make the summary and forecast about the research work in this thesis.