2021-03-262012-05-070277786X1996756XWOS;000305692300022SCOPUS;2-s2.0-84862700952http://hdl.handle.net/10784/27392Some special functions of the Mathematical Physics are a very helpful resource in problems involving the propagation of coherent light beams, which will suffer dispersion in a turbulent media such as the Earth's ionosphere waveguide. Unfortunately, these tools are difficult to use because it involves very complex mathematical developments. For this reason it is interesting to find a friendly method to make the implementation of these special functions possible. Using Maple I will be able to overcome the mathematical difficulty of solving these equations and get to the understanding of these phenomena. Specifically I will consider the excitation of the Earth's ionosphere as a cavity or a waveguide by satellite borne current sources in the form of satellite-based antennas when the medium inside the waveguide is turbulent. As a result, three kinds of coherent light beams will be derived: Bessel beams, for relatively low turbulence, Whittaker beams, for moderate turbulence, and Heun beams, for strong or fully developed turbulence. These beams are represented by the corresponding electric fields but the associated magnetic fields can be derived as well. It is verified that Maple is a very powerful tool in the study of the propagation of an input field through axially symmetric systems using the methods of the Mathematical Physics. It is expected that Maple will have important applications for more general models concerning propagation trough turbulent environments. © 2012 Copyright Society of Photo-Optical Instrumentation Engineers (SPIE).enghttps://v2.sherpa.ac.uk/id/publication/issn/0277-786Xinfo:eu-repo/semantics/conferencePaperBessel beamCoherent beamsComputer algebraEarth ionosphere waveguideHeun beamsLegendre functionMapleMathematical physicsWhittaker beamsBessel functionsElectric fieldsIonosphereIonospheric measurementLaser beamsMagnetic fieldsMechanicsSatellite antennasSatellitesWaveguidesAtmospheric thermodynamics2021-03-26Montoya Isaza, SebastianOspina Giraldo, Juan Fernando10.1117/12.919446