A general approach to the numerical determination of modal propagation constants and field distributions of optical fibres

Meunier, J.-P.; Pigeon, Jérôme; Massot, Jean

doi:10.1007/bf00620032

Cited by 55 publications

(31 citation statements)

References 14 publications

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“…The application of the Galerkin method to a weakly-guiding optical fiber model is described in full detail in [25] by Meunier et al Here we recall that the method results in a matrix eigenvalue problem…”

Section: The Proposed Method: Calculation Of Single-mode Fiber Dispermentioning

confidence: 99%

“…The integrals J m ij can be expressed analytically [25] where only V is frequency-dependent, and are also easy to differentiate.…”

Section: Derivatives Of the Matrix Amentioning

confidence: 99%

“…Appendix B provides the short description of the theory developed by Meunier et al [25] that applies the Galerkin method to optical fiber model and shows how the symmetric matrix A in Equation (6) is obtained. The matrix has terms…”

Section: Derivatives Of the Matrix Amentioning

confidence: 99%

“…One of the most powerful, accurate, yet simple techniques to find the solution of the scalar wave equation is the Galerkin method which in this case coincides with the Rayleigh-Ritz variational method [24]. The Galerkin method [25][26][27][28][29][30][31][32][33][34] has been used to calculate the propagation coefficients and modal fields of optical fibers and rectangular and slab dielectric-waveguides, with the aid of different sets of entire basis functions such as Bessel functions, Laguerre-Gauss or Hermite-Gauss polynomial functions. These have the advantages that: a) they form complete sets of orthonormal functions which satisfy the boundary conditions (the fields are finite at the waveguide axis and decay to zero at an infinite lateral distance from the axis), b) they represent the solutions of a problem with a similar geometry: Bessel functions are the eigensolutions of the scalar wave equations for step-index circular core fibers while Laguerre-Gauss and Hermite-Gauss polynomials are the eigenmodes of an infinitely extended parabolic refractive index profile in circular and rectangular waveguide geometries respectively (see Figure 1(a)).…”

Section: Introductionmentioning

confidence: 99%

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A Rapid Accurate Technique to Calculate the Group Delay, Dispersion and Dispersion Slope of Arbitrary Radial Refractive Index Profile Weakly-Guiding Optical Fibers

Mussina¹,

Selviah²,

Fernández³

et al. 2014

PIER

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Abstract-This paper introduces a new numerical method to calculate the group delay, chromatic dispersion and dispersion slope of weakly-guiding optical fibers with arbitrary radial refractive index profiles. It is based on the analytical differentiation of the propagation coefficient up to the third order. The simulation results are compared to experimental data, with those calculated by other approaches and exact data where possible. Due to the analytical differentiation of the matrix equation, the method is more accurate compared to other approaches, it is also much faster than numerical differentiation as allows avoiding repeated solution of the eigenvalue problem to calculate the derivatives of the propagation coefficient. The precision of the method is limited only by the approximation errors of the mode solver. The Galerkin method with Laguerre-Gauss basis functions is used to determine the propagation coefficients of weakly-guiding structures. The new method enables fiber manufacturers to rapidly design dispersion characteristics of graded index, step index, single-and multiple-clad fibers, as well as few-mode and bend insensitive fibers.

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Section: The Proposed Method: Calculation Of Single-mode Fiber Dispermentioning

confidence: 99%

“…The integrals J m ij can be expressed analytically [25] where only V is frequency-dependent, and are also easy to differentiate.…”

Section: Derivatives Of the Matrix Amentioning

confidence: 99%

Section: Derivatives Of the Matrix Amentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A Rapid Accurate Technique to Calculate the Group Delay, Dispersion and Dispersion Slope of Arbitrary Radial Refractive Index Profile Weakly-Guiding Optical Fibers

Mussina¹,

Selviah²,

Fernández³

et al. 2014

PIER

View full text Add to dashboard Cite

show abstract

“…Though numerical methods are exact methods, they usually are cumbersome and take more computation time. The Ritz-Galerkin method [16] or variational method [17], using Laguerre-Gaussian basis function, seem to have both merits of simplicity and accuracy. Because these basis functions approximate the electromagnetic field very well, only a few terms are needed.…”

Section: Introductionmentioning

confidence: 99%