Abstract

The 3D finite-difference time-domain (FDTD) method is used to analyze the polarization effects in two kinds of linearly tapered optical waveguides: slab waveguides with only lateral tapers and rectangular cross section waveguides with both lateral and vertical tapers. For the slab waveguides, each guided mode of both the back reflected and output powers are determined and compared. For rectangular cross section waveguides, the output power of TE and TM modes with respect to taper length are computed and compared.

© 2003 Optical Society of America

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References

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  1. Thomas Dillion, Anita Balcha, Dr.Janusz Murakowski and Dr. Dennis Prather, �??Process development and application of grayscale lithography for efficient three-dimensionally profiled fiber-to-waveguide couplers,�?? SPIE�??s 48th annual meeting, (to be published).
  2. G.Agrawal, Fiber-Optic Communication Systems (Wiley, New York, 1992).
  3. M.Wu, P.Fan and C.Lee, �??Completely adiabatic s-shaped bent tapers in optical waveguides,�?? IEEE Photon. Tech. Lett. 9, 212-214 (1997).
    [CrossRef]
  4. C.Lee, M.Wu, L.Sheu, P.Fan and J.Hsu, �??Design and analysis of completely adiabatic tapered waveguides by conformal mapping,�?? IEEE J. Lightwave Technol. 15, 403-410 (1993).
  5. J.Sakai and E.Marcatili, �??Lossless dielectric tapers with three-dimensional geometry,�?? IEEE J. Lightwave Technol. 9, 386-393 (1991).
    [CrossRef]
  6. R.Weder, �??Dielectric three-dimensional electromagnetic tapers with no loss,�?? IEEE J. Quantum Electron. 24, 775-779 (1988).
    [CrossRef]
  7. E.Marcatili, �??Dielectric tapers with curved axes and no loss,�?? IEEE J.Quantum Electron., QE 21, 307-314 (1985).
    [CrossRef]
  8. I.Lu, �??Intrinsic modes in wedge-shaped taper above an anisotropic substrate,�?? IEEE J.Quantum Electron., 27, 2373-2377 (1991).
    [CrossRef]
  9. S. El Yumin, K. Komori, S. Arai and G. Bendelli, �??Taper-shape dependence of tapered-waveguide traveling wave semiconductor laser amplifier (TTW-SLA),�?? IEICE Tran. Electron., E77-C 4, 624-632 (1994).
  10. A. Milton and W. Burns, �??Mode coupling in optical waveguide horns,�?? IEEE J. Quantum Electron., QE-13 10, 828-834 (1977).
    [CrossRef]
  11. C.Vassallo, �??Analysis of tapered mode transformers for semiconductor optical amplifiers,�?? Opt. Quantum Electron. 26, 1025-1026 (1996).
  12. Z.N.Lu and R.Bansal, �??A finite-difference third-order simplified wave equation method: an assessment and application,�?? IEEE Microwave Theory Technol. 42, 132-136 (1994).
    [CrossRef]
  13. Z.N.Lu, R.Bansal and Peter K.Cheo, �??Radiation losses of tapered dielectric waveguides: a finite difference analysis with ridge waveguide applications,�?? IEEE J. Lightwave Technol., 12, 1373-1377 (1994).
    [CrossRef]
  14. G. R. Hadley, �??Design of tapered waveguides for improved output coupling,�?? IEEE Photon. Technol. Lett. 5, 1068-1070 (1993).
    [CrossRef]
  15. R. K. Winn and J. H. Harris, �??Coupling from multimode to single mode linear waveguides using horn-shaped strctures,�?? IEEE Microwave Theory Tech., 23, 3012-3015 (1975).
    [CrossRef]
  16. E. A. J. Marcatilli, �??Dielectric rectangular waveguide and directional coupler for integrated optics,�?? Bell System Tech. 48, 2071 (1969).
  17. D. P. Rodohan and S. R. Saunders, �??Parallel implementations of the finite difference time domain (FDTD) method,�?? Computation in Electromagnetics, Second International Conference, 367-370 (1994).
  18. C. Guiffaut and K. Mahdjoubi, �??A parallel FDTD algorithm using the MPI library,�?? IEEE Antennas and Propagation Magazine, 43, 94-103 (2001).
    [CrossRef]

Bell System Tech.

E. A. J. Marcatilli, �??Dielectric rectangular waveguide and directional coupler for integrated optics,�?? Bell System Tech. 48, 2071 (1969).

IEEE Antennas and Propagation Magazine

C. Guiffaut and K. Mahdjoubi, �??A parallel FDTD algorithm using the MPI library,�?? IEEE Antennas and Propagation Magazine, 43, 94-103 (2001).
[CrossRef]

IEEE J. Lightwave Technol.

Z.N.Lu, R.Bansal and Peter K.Cheo, �??Radiation losses of tapered dielectric waveguides: a finite difference analysis with ridge waveguide applications,�?? IEEE J. Lightwave Technol., 12, 1373-1377 (1994).
[CrossRef]

C.Lee, M.Wu, L.Sheu, P.Fan and J.Hsu, �??Design and analysis of completely adiabatic tapered waveguides by conformal mapping,�?? IEEE J. Lightwave Technol. 15, 403-410 (1993).

J.Sakai and E.Marcatili, �??Lossless dielectric tapers with three-dimensional geometry,�?? IEEE J. Lightwave Technol. 9, 386-393 (1991).
[CrossRef]

IEEE J. Quantum Electron.

R.Weder, �??Dielectric three-dimensional electromagnetic tapers with no loss,�?? IEEE J. Quantum Electron. 24, 775-779 (1988).
[CrossRef]

A. Milton and W. Burns, �??Mode coupling in optical waveguide horns,�?? IEEE J. Quantum Electron., QE-13 10, 828-834 (1977).
[CrossRef]

IEEE J.Quantum Electron.

E.Marcatili, �??Dielectric tapers with curved axes and no loss,�?? IEEE J.Quantum Electron., QE 21, 307-314 (1985).
[CrossRef]

I.Lu, �??Intrinsic modes in wedge-shaped taper above an anisotropic substrate,�?? IEEE J.Quantum Electron., 27, 2373-2377 (1991).
[CrossRef]

IEEE Microwave Theory Tech.

R. K. Winn and J. H. Harris, �??Coupling from multimode to single mode linear waveguides using horn-shaped strctures,�?? IEEE Microwave Theory Tech., 23, 3012-3015 (1975).
[CrossRef]

IEEE Microwave Theory Technol.

Z.N.Lu and R.Bansal, �??A finite-difference third-order simplified wave equation method: an assessment and application,�?? IEEE Microwave Theory Technol. 42, 132-136 (1994).
[CrossRef]

IEEE Photon. Tech. Lett.

M.Wu, P.Fan and C.Lee, �??Completely adiabatic s-shaped bent tapers in optical waveguides,�?? IEEE Photon. Tech. Lett. 9, 212-214 (1997).
[CrossRef]

IEEE Photon. Technol. Lett.

G. R. Hadley, �??Design of tapered waveguides for improved output coupling,�?? IEEE Photon. Technol. Lett. 5, 1068-1070 (1993).
[CrossRef]

IEICE Tran. Electron.

S. El Yumin, K. Komori, S. Arai and G. Bendelli, �??Taper-shape dependence of tapered-waveguide traveling wave semiconductor laser amplifier (TTW-SLA),�?? IEICE Tran. Electron., E77-C 4, 624-632 (1994).

Opt. Quantum Electron.

C.Vassallo, �??Analysis of tapered mode transformers for semiconductor optical amplifiers,�?? Opt. Quantum Electron. 26, 1025-1026 (1996).

Other

Thomas Dillion, Anita Balcha, Dr.Janusz Murakowski and Dr. Dennis Prather, �??Process development and application of grayscale lithography for efficient three-dimensionally profiled fiber-to-waveguide couplers,�?? SPIE�??s 48th annual meeting, (to be published).

G.Agrawal, Fiber-Optic Communication Systems (Wiley, New York, 1992).

D. P. Rodohan and S. R. Saunders, �??Parallel implementations of the finite difference time domain (FDTD) method,�?? Computation in Electromagnetics, Second International Conference, 367-370 (1994).

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Figures (12)

Fig. 1.
Fig. 1.

Tapered Slab Waveguide.

Fig. 2 (a)
Fig. 2 (a)

Top view of the waveguide

Fig. 2 (b)
Fig. 2 (b)

Side view of the waveguide.

Fig. 3.
Fig. 3.

Tapered Rectangular Waveguide.

Fig. 4.
Fig. 4.

Side view of the tapered rectangular waveguide.

Fig. 5
Fig. 5

The cross section of the 3D rectangular waveguide

Fig. 6.
Fig. 6.

The diagram of the computation region.

Fig. 7.
Fig. 7.

Steady state field in the middle xy plane.

Fig. 8.
Fig. 8.

(a) Normalized field amplitude of the output field. (b) Power distribution of output field

Fig. 9.
Fig. 9.

(a) Normalized field amplitude of back reflected field. (b) Power distribution of back-reflected field

Fig. 10.
Fig. 10.

(a) Radiation loss comparison. (b) Back reflection loss comparison.

Fig. 11.
Fig. 11.

(a) Output power percentage versus taper length, TM source. (b) Output power percentage versus taper length, TE source.

Equations (6)

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

H z = { A cos ( k y y Φ ) cos ( k z z Ψ ) Region 1 A cos ( k y a Φ ) e γ y ( y a ) cos ( k z z Ψ ) Region 2 A cos ( k y y Φ ) e γ z ( z d ) cos ( k z d Ψ ) Region 3
H mn z = A mn B mn ( y , z )
B mn ( y , z ) B mn ¯ ( y , z ) dy dz = { C mn m = m ¯ , n = n ¯ 0 else
H total z = m = 1 n = 1 I H mn z = m = 1 n = 1 I A mn B mn ( y , z )
A mn C mn = H total z B mn ( y , z ) dy dz
A mn = H total z B mn ( y , z ) dy dz C mn

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