arXiv subjects
Publications and source records attributed to S. Chavez-Cerda.
In this paper we present a detailed physical analysis of the formation of the propagation transverse modes in planar dielectric waveguides using a mathematical-physics approach. We demonstrate physically that, at the wavelength scale, the pure stationary mode inside planar waveguide is described by the cosine function. Meanwhile, the sine function yields a quasi-stationary periodic mode.
In this paper we demonstrate that using a mathematical physics approach (focusing the attention to the physics and using mathematics as a tool) it is possible to visualize the formation of the transverse modes inside a cylindrical waveguide. In opposition, the physical mathematics solutions (looking at the mathematical problem and then trying to impose a physical interpretation), when studying cylindrical waveguides yields to the Bessel differential equation and then it is argued that in the core are only the Bessel functions of the first kind those who describe the transverse modes. And the Neumann functions are deemed non physical due to its singularity at the origin and eliminated from the final description of the solution. In this paper we show, using a geometrical-wave optics approach, that the inclusion of this function is physically necessary to describe fully and properly the formation of the propagating transverse modes. Also, the field in the outside of a dielectric waveguide arises in a natural way.
It is shown that three-dimensional nonparaxial beams are described by the oblate spheroidal exact solutions of the Helmholtz equation. For the first time, their beam behaviour is investigated and their corresponding parameters are defined. Using the fact that the beam width of the family of paraxial Gaussian beams is described by an hyperbola, the connection between the physical parameters of nonparaxial spheroidal beam solutions and those of paraxial beams is formally stablished. These results are also helpful to investigate the exact vector nonparaxial beams.
In a simple picture, a Bessel beam is viewed as a transverse standing wave formed in the interference region between incoming and outgoing conical waves. Based on this interpretation we propose an optical resonator that supports modes that are approximations to Bessel-Gauss beams. The Fox-Li algorithm in two transverse dimension is applied to confirm the conlcusion