Analysis of Beam Properties of Lorentz-Gauss and Hermite- Gaussian beams for Unstable Resonator through Paraxial ABCD Optical System

Abstract

Light can take the form of beams that are an approximate version of waves which are spatially localized and non-divergent. Waves with wave front normal making small angles with z-axis are called paraxial waves. These waves must satisfy the Helmholtz equation. This equation has important applications in the science of optics, where it provides solutions that describe the propagation of electromagnetic waves (light) in the form of either paraboloidal waves or Gaussian beams. Most lasers emit beams that take this form. The solution of this equation shows the characteristics of an optical beam called as Gaussian beam. Our focus is on the beams which have the wave front similar to Gaussian beam i.e. paraboloidal wave front but with different intensity distribution. Beams with paraboloidal wave front match the curvatures of spherical mirror with large radius. Advances in nanometer technology have triggered a broad activity in low-dimensional quantum systems. It started with two-dimensional (2D) electron systems at the interface of two materials several decades ago, and recently it has shifted to 2D materials, for example, 2D topological insulators, and graphene. The most interesting feature of these systems is their similarity to ultrarelativistic electrons and positrons which obey the Dirac equation. In photonics an intermediate approach has been widely used which is based on beam optics, in particular, in laser physics. Ray optics with the inclusion of essential phenomena such as diffraction and interference gives the base for Beam optics. Compared to mechanics it corresponds to the quasi-classical approach. For the case of electromagnetic phenomena, the meta-material properties of p-n junctions in graphene can be understood by inspecting classical trajectories or using ray optics. In this work we have compared the characteristics of Effective beam size and Spatial complex degree of coherence of Lorentz-Gauss beam and Hermite-Gaussian beams. The mathematical model of Lorentz-Gauss beam and Hermite-Gaussian beam is analyzed in terms of ABCD parameters. The dependence of Effective beam size and Spatial complex degree of coherence on beam parameters and coherence length is shown and the role of ABCD parameters is widely discussed. We have found out in this work that for effective beam size of Lorentz-Gauss beams there exists a threshold point between coherence length value of 0.1 mm to 2 mm. In contrast to Lorentz-Gauss beams where there is a threshold point after which effective beam size is asymptotically increasing for Hermite-Gaussian beams there exists a threshold point after which effective beam size diminishes. The Spatial complex degree of coherence is found out to be same for both the beams. In this work the effect of beam parameters on effective beam size is shown for unstable resonator. The results obtained will be useful in long-distance Optical communication. The approach used in this work can be extended in the field of photonics.