Fundamental (HE 11 ) modes of graded optical fibers

The HE11 fields of weakly guiding fibers with graded refractive-index profiles are nearly identical to the fields of a step-index fiber with dimensionless frequency V¯ and radius ρ¯, where V¯ and ρ¯ are found by an elementary variational method. The results are remarkably accurate, with errors of a fraction of a percent at most, so that a simple, closed-form expression for the HE11 fields of graded fibers is now available. The step-fiber approximation is more widely applicable than the Gaussian field approximation which is inadequate for small V and for describing the evanescent field. However, the variational procedure also complements the Gaussian field approximation by providing analytical expressions for the spot size and propagation constant in several profiles of interest.

[1]  A. Snyder,et al.  Attenuation coefficient for tunnelling leaky rays in graded fibres , 1976 .

[2]  J. Love.  Power series solutions of the scalar wave equation for cladded, power-law profiles of arbitrary exponent , 1979 .

[3]  A. Snyder.  Asymptotic Expressions for Eigenfunctions and Eigenvalues of a Dielectric or Optical Waveguide , 1969 .

[4]  D. Marcuse.  Loss analysis of single-mode fiber splices , 1977, The Bell System Technical Journal.

[5]  T. Okoshi,et al.  Vectorial Wave Analysis of Inhomogeneous Optical Fibers Using Finite Element Method , 1978 .

[6]  E. A. J. Marcatili,et al.  Multimode theory of graded-core fibers , 1973 .

[7]  S. Miller,et al.  Light propagation in generalized lens-like media , 1965 .

[8]  Dietrich Marcuse,et al.  Gaussian approximation of the fundamental modes of graded-index fibers , 1978 .

[9]  A. Ankiewicz,et al.  Geometric optics approach to light acceptance and propagation in graded index fibres , 1977 .

[10]  C. N. Kurtz,et al.  Scalar Analysis of Radially Inhomogeneous Guiding Media , 1967 .

[11]  A. Snyder.  Mode-propagation in optical waveguides , 1970 .

[12]  W. A. Gambling,et al.  Simple characterisation factor for practical single-mode fibres , 1977 .

[13]  M. Matsuhara,et al.  Analysis of TEM modes in dielectric waveguides, by a variational method , 1973 .

[14]  K. Okamoto,et al.  Analysis of Wave Propagation in Inhomogeneous Optical Fibers Using a Variational Method , 1974 .

[15]  M. Vassell.  Calculation of propagating modes in a graded-index optical fibre , 1974 .

[16]  N. Okamoto,et al.  Guided waves along an optical fiber with parabolic index profile , 1977 .

[17]  Allan W. Snyder,et al.  Modes of optical waveguides , 1978 .

[18]  W. A. Gambling,et al.  Propagation in radially-inhomogeneous single-mode fibre , 1978 .