Exact Equivalent Straight Waveguide Model for Bent and Twisted Waveguides

Exact equivalent straight waveguide representation is given for a waveguide of arbitrary curvature and torsion. No assumptions regarding refractive index contrast, isotropy of materials, or particular morphology in the waveguide cross section are made. This enables rigorous full-vector modeling of in-plane curved or helically wound waveguides with use of available simulators for straight waveguides without the restrictions of the known approximate equivalent-index formulas.

[1]  E. J. Post,et al.  Formal Structure of Electromagnetics , 1963 .

[2]  D. Marcuse,et al.  Influence of curvature on the losses of doubly clad fibers. , 1982, Applied optics.

[3]  H. Bastiaansen,et al.  Source-type integral equation analysis of circularly curved channel waveguides in a multilayered background , 1995 .

[4]  G. Rodrigue,et al.  Vector finite-element modeling of the full-wave Maxwell equations to evaluate power loss in bent optical fibers , 2005, Journal of Lightwave Technology.

[5]  Sébastien Guenneau,et al.  Modelling of twisted optical waveguides with edge elements , 2004 .

[6]  H. Bastiaansen,et al.  Rigorous, full-vectorial source-type integral equation analysis of circularly curved channel waveguides , 1995 .

[7]  R. Stoffer,et al.  Analytic approach to dielectric optical bent slab waveguides , 2005 .

[8]  Dietrich Marcuse,et al.  Field deformation and loss caused by curvature of optical fibers , 1976 .

[9]  J. Harris,et al.  Analysis of curved optical waveguides by conformal transformation , 1975, IEEE Journal of Quantum Electronics.

[10]  John R. Marciante,et al.  Mode-area scaling of helical-core, dual-clad fiber lasers and amplifiers using an improved bend-loss model , 2006 .

[11]  R. Pregla The method of lines for the analysis of dielectric waveguide bends , 1996 .

[12]  Radiation loss and mode field distribution in curved holey fibers , 2005 .

[13]  S. Gedney,et al.  Numerical stability of nonorthogonal FDTD methods , 2000 .

[14]  M. Germano,et al.  On the effect of torsion on a helical pipe flow , 1982, Journal of Fluid Mechanics.

[15]  W. Pascher Modelling of rib waveguide bends for sensor applications , 2001 .

[16]  Andrei V. Lavrinenko,et al.  Perfectly matched layer method in the finite‐difference time‐domain and frequency‐domain calculations , 2007 .

[17]  Wei-Ping Huang,et al.  Polarization rotation in semiconductor bending waveguides: a coupled-mode theory formulation , 1998 .

[18]  Kunimasa Saitoh,et al.  Full-vectorial finite element method in a cylindrical coordinate system for loss analysis of photonic wire bends. , 2006, Optics express.

[19]  J. Ritter,et al.  Efficient FDTD/matrix-pencil method for the full-wave scattering parameter analysis of waveguiding structures , 1996 .

[20]  Wei-Ping Huang,et al.  Full-vectorial wave propagation in semiconductor optical bending waveguides and equivalent straight waveguide approximations , 1998 .

[21]  Yen Liu,et al.  Fourier Analysis of Numerical Algorithms for the Maxwell Equations , 1993 .

[22]  Anand Gopinath,et al.  Vector analysis of optical dielectric waveguide bends using finite-difference method , 1996 .

[23]  N. Feng,et al.  Computation of full-vector modes for bending waveguide using cylindrical perfectly matched layers , 2002 .

[24]  G. Rodrigue,et al.  Study of optically induced effects due to bending and twisting using the vector finite-element method , 2006 .

[25]  R. J. Joseph,et al.  Advances in Computational Electrodynamics: The Finite - Di erence Time - Domain Method , 1998 .

[26]  Sébastien Guenneau,et al.  Asymptotic modelling of weakly twisted electrostatic problems , 2006 .

[27]  K. Yee Numerical solution of initial boundary value problems involving maxwell's equations in isotropic media , 1966 .

[28]  D. Shyroki,et al.  Efficient Cartesian-Grid-Based Modeling of Rotationally Symmetric Bodies , 2007, IEEE Transactions on Microwave Theory and Techniques.

[29]  Ian J Craddock,et al.  Simple and accurate hybrid FDTD model of uniform waveguide bends , 2004 .