Abstract

This paper presents the implementation of a parallelized Finite-Difference Time-Domain method, based on the Message Passing Interface (i.e. MPI), which is used to study the modal properties of three-dimensional (3D) dielectric waveguide structures. To this end, we also use the least-square method to obtain the wave vector, β, along the axis of propagation. Lastly, bending losses in arbitrary-angle waveguides are also discussed.

© 2004 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |

  1. T. Tamir, Integrated Optics (Berlin: Springer-Verlag, 1975), Chap.2.
  2. A. Asi, and L. Shafai, �??Dispersion analysis of anisotropic inhomogeneous waveguides using compact 2DFDTD,�?? Electron. Lett., vol. 28, pp. 1451-1452 (1992).
    [CrossRef]
  3. K.S. Yee, �??Numerical solution of initial boundary value problems involving Maxwell�??s equations in isotropic media,�?? IEEE Trans. Antennas Propag. 14, 302 (1966).
    [CrossRef]
  4. G. Mur, �??Absrobing boundary conditions for the finite-difference approximation of the time-domain electromagnetic-filed equations,�?? IEEE Trans Electromagn. Compat. EMC-23, pp.377-382 (1981).
    [CrossRef]
  5. J.P. Berenger, �??A perfectly matched layer for the absorption of electromagnetic waves,�?? J. Comp. Physics 114, 185-200 (1994).
    [CrossRef]
  6. A. Taflove and S.C. Hagness, Computational Electromagnetics: The Finite-Difference Time Domain Method, 2nd ed. (Artech House, Norwood MA, 2000).
  7. E.A.J. Marcatili, �??Dielectric rectangular waveguide and directional coupler for integrated optics,�?? Bell Syst. Tech. J. 48, 2071-2102 (1969).
  8. Willam Gropp, Ewing Lusk, and Anthony Skjellum, Using MPI: Portable Parallel Programming with the Message-Passing Interface (The MIT Press, Cambridge MA, 1994).
  9. M.A. Hernandez-Lopez and M. Quintillan, �??Propagation characteristics of modes in some rectangular waveguides using the finite-difference time-domain method,�?? J. Electromagnetic Waves and Applications 14,1707-1722 (2000).
    [CrossRef]
  10. W.H. Press, S.A. Teulcoolsky, W.T. Vetterling, and B.P. Flannery, Numerical Recipes in FORTRAN(Cambridge University Press, 1992).
  11. J.E. Goell, �??A circular harmonic computer analysis of rectangular dielectric waveguides,�?? Bell Syst. Tech.J. 48, 2133-2160 (1969).
  12. A. Kumar, K. Thyagarajan, and A.K. Ghatak, �??Analysis of rectangular �??core dielectric waveguides �?? A accurate perturbation approach,�?? Opt. Lett. 8, 63-65 (1983).
    [CrossRef] [PubMed]
  13. J.H. Greene and A. Taflove, "Initial three-dimensional finite-difference time-domain phenomenology study of the transient response of a large vertically coupled photonic racetrack," Opt. Lett. 28, 1733-1735 (2003).
    [CrossRef] [PubMed]
  14. Ao Jiang, Finite �??Difference Time Domain Method on Paralle Architecture using Message Passing Interface,�?? M.S. Thesis, Dept. of Ece, University of Delaware (2003).
  15. V. Varadarajan and R. Mittra, �??Finite-Difference Time Domain (FDTD), Analysis Using Distributed Computing,�?? IEEE Microwave and Guided Wave Letters, 4, 144-145 (1994).
    [CrossRef]
  16. A.M. Liu, A.S. Mohan, T. A. Aubrey, and W.R. Belcher, �??Techniques for Implementation of FDTD Method on CM-5 Parallel Computer,�?? IEEE Antennas and Propagation Magazine 37, 64-71 (1995).
    [CrossRef]
  17. S.M. Lee, W.C. Chew, S.L. Chuang, and J.J. Coleman, �??Bending loss in optical waveguides for nonplanar laser array applications,�?? J. Appl. Phys. 71, 2513-2520 (1992).
    [CrossRef]

Bell Syst. Tech. J.

E.A.J. Marcatili, �??Dielectric rectangular waveguide and directional coupler for integrated optics,�?? Bell Syst. Tech. J. 48, 2071-2102 (1969).

J.E. Goell, �??A circular harmonic computer analysis of rectangular dielectric waveguides,�?? Bell Syst. Tech.J. 48, 2133-2160 (1969).

Electron. Lett.

A. Asi, and L. Shafai, �??Dispersion analysis of anisotropic inhomogeneous waveguides using compact 2DFDTD,�?? Electron. Lett., vol. 28, pp. 1451-1452 (1992).
[CrossRef]

IEEE Antennas and Propagation Magazine

A.M. Liu, A.S. Mohan, T. A. Aubrey, and W.R. Belcher, �??Techniques for Implementation of FDTD Method on CM-5 Parallel Computer,�?? IEEE Antennas and Propagation Magazine 37, 64-71 (1995).
[CrossRef]

IEEE Microwave and Guided Wave Letters

V. Varadarajan and R. Mittra, �??Finite-Difference Time Domain (FDTD), Analysis Using Distributed Computing,�?? IEEE Microwave and Guided Wave Letters, 4, 144-145 (1994).
[CrossRef]

IEEE Trans Electromagn. Compat.

G. Mur, �??Absrobing boundary conditions for the finite-difference approximation of the time-domain electromagnetic-filed equations,�?? IEEE Trans Electromagn. Compat. EMC-23, pp.377-382 (1981).
[CrossRef]

IEEE Trans. Antennas Propag.

K.S. Yee, �??Numerical solution of initial boundary value problems involving Maxwell�??s equations in isotropic media,�?? IEEE Trans. Antennas Propag. 14, 302 (1966).
[CrossRef]

J. Appl. Phys.

S.M. Lee, W.C. Chew, S.L. Chuang, and J.J. Coleman, �??Bending loss in optical waveguides for nonplanar laser array applications,�?? J. Appl. Phys. 71, 2513-2520 (1992).
[CrossRef]

J. Comp. Physics

J.P. Berenger, �??A perfectly matched layer for the absorption of electromagnetic waves,�?? J. Comp. Physics 114, 185-200 (1994).
[CrossRef]

J. Electromagnetic Waves and Application

M.A. Hernandez-Lopez and M. Quintillan, �??Propagation characteristics of modes in some rectangular waveguides using the finite-difference time-domain method,�?? J. Electromagnetic Waves and Applications 14,1707-1722 (2000).
[CrossRef]

Opt. Lett.

Other

T. Tamir, Integrated Optics (Berlin: Springer-Verlag, 1975), Chap.2.

Ao Jiang, Finite �??Difference Time Domain Method on Paralle Architecture using Message Passing Interface,�?? M.S. Thesis, Dept. of Ece, University of Delaware (2003).

W.H. Press, S.A. Teulcoolsky, W.T. Vetterling, and B.P. Flannery, Numerical Recipes in FORTRAN(Cambridge University Press, 1992).

Willam Gropp, Ewing Lusk, and Anthony Skjellum, Using MPI: Portable Parallel Programming with the Message-Passing Interface (The MIT Press, Cambridge MA, 1994).

A. Taflove and S.C. Hagness, Computational Electromagnetics: The Finite-Difference Time Domain Method, 2nd ed. (Artech House, Norwood MA, 2000).

Supplementary Material (2)

» Media 1: AVI (858 KB)     
» Media 2: AVI (1138 KB)     

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1.
Fig. 1.

(a) The top-down view of a typical optical waveguide structure. (b) The side view of a three-dimensional waveguide bend.

Fig. 2.
Fig. 2.

The division of the waveguide structure.

Fig. 3.
Fig. 3.

The absolute speedup curve for 3D waveguide structures, measured using a Beowulf cluster.

Fig. 4.
Fig. 4.

Loss (dB) vs. the length of the diagonal waveguide (λ)

Fig. 5.
Fig. 5.

Loss (dB) vs. θ of diagonal waveguide (degree). The circle points are the loss using sharp corner, the star point is the loss using curved corner.

Fig. 6.
Fig. 6.

2D plot of the steady state field of Hz component in the middle plane

Fig. 7.
Fig. 7.

Movies of the wave propagation of Hz component in the middle plane through waveguide bends (a) (858 KB) sharp bends (b) (1.14 MB) curved bends

Tables (2)

Tables Icon

Table 1. The propagation constant β 1 of single mode in waveguide structure with dimensions of 0.1789λ×0.1789λ×6λ, calculated by three different methods.

Tables Icon

Table 2. The wave vector (β 1, β 2) in waveguide structure with dimensions of 0.257λ×0.257λ×10λ, calculated by three different methods.

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

E M ( z i , A k , β k ) = k = 1 M A k exp ( j β k z i ) ,
min A k , β k i E z ( z i ) E M ( z i , A k , β k ) 2 ,
E z ( a i ) = E 0 sin ( 2 π ft ) ,
S a ( p ) = Execution time using single processor system Execution time using a multipleprocessor system with p processors .
P x = 1 2 Re ( E × H * ) = 1 2 s Re ( E y H z * E z H y * ) d S .
loss = 10 × log ( P out P in ) ,

Metrics