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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  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 (Weily, 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]

2001 (1)

C. Guiffaut and K. Mahdjoubi, “A parallel FDTD algorithm using the MPI library,” IEEE Antennas and Propagation Magazine,  43, 94–103 (2001).
[Crossref]

1997 (1)

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]

1996 (1)

C. Vassallo, “Analysis of tapered mode transformers for semiconductor optical amplifiers,” Opt. Quantum Electron. 26, 1025–1026 (1996).

1994 (3)

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]

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]

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).

1993 (2)

G.R. Hadley, “Design of tapered waveguides for improved output coupling,” IEEE Photon. Technol. Lett. 5, 1068–1070 (1993).
[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).

1991 (2)

J. Sakai and E. Marcatili, “Lossless dielectric tapers with three-dimensional geometry,” IEEE J. Lightwave Technol. 9, 386–393 (1991).
[Crossref]

I. Lu, “Intrinsic modes in wedge-shaped taper above an anisotropic substrate,” IEEE J.Quantum Electron,  27, 2373–2377 (1991).
[Crossref]

1988 (1)

R. Weder, “Dielectric three-dimensional electromagnetic tapers with no loss,” IEEE J. Quantum Electron. 24, 775–779 (1988).
[Crossref]

1985 (1)

E. Marcatili, “Dielectric tapers with curved axes and no loss,” IEEE J.Quantum Electron, QE 21, 307–314 (1985).
[Crossref]

1977 (1)

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

1975 (1)

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]

1969 (1)

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

Agrawal, G.

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

Arai, S.

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).

Balcha, Anita

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).

Bansal, R.

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]

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]

Bendelli, G.

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).

Burns, W.

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

Cheo, Peter K.

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]

Dillion, Thomas

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).

Fan, P.

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]

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).

Guiffaut, C.

C. Guiffaut and K. Mahdjoubi, “A parallel FDTD algorithm using the MPI library,” IEEE Antennas and Propagation Magazine,  43, 94–103 (2001).
[Crossref]

Hadley, G.R.

G.R. Hadley, “Design of tapered waveguides for improved output coupling,” IEEE Photon. Technol. Lett. 5, 1068–1070 (1993).
[Crossref]

Harris, J.H.

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]

Hsu, J.

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).

Komori, K.

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).

Lee, C.

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]

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).

Lu, I.

I. Lu, “Intrinsic modes in wedge-shaped taper above an anisotropic substrate,” IEEE J.Quantum Electron,  27, 2373–2377 (1991).
[Crossref]

Lu, Z.N.

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]

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]

Mahdjoubi, K.

C. Guiffaut and K. Mahdjoubi, “A parallel FDTD algorithm using the MPI library,” IEEE Antennas and Propagation Magazine,  43, 94–103 (2001).
[Crossref]

Marcatili, E.

J. Sakai and E. Marcatili, “Lossless dielectric tapers with three-dimensional geometry,” IEEE J. Lightwave Technol. 9, 386–393 (1991).
[Crossref]

E. Marcatili, “Dielectric tapers with curved axes and no loss,” IEEE J.Quantum Electron, QE 21, 307–314 (1985).
[Crossref]

Marcatilli, E.A.J.

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

Milton, A.

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

Murakowski, Dr.Janusz

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).

Prather, Dr. Dennis

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).

Rodohan, D.P.

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).

Sakai, J.

J. Sakai and E. Marcatili, “Lossless dielectric tapers with three-dimensional geometry,” IEEE J. Lightwave Technol. 9, 386–393 (1991).
[Crossref]

Saunders, S.R

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).

Sheu, L.

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).

Vassallo, C.

C. Vassallo, “Analysis of tapered mode transformers for semiconductor optical amplifiers,” Opt. Quantum Electron. 26, 1025–1026 (1996).

Weder, R.

R. Weder, “Dielectric three-dimensional electromagnetic tapers with no loss,” IEEE J. Quantum Electron. 24, 775–779 (1988).
[Crossref]

Winn, R.K.

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]

Wu, M.

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]

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).

Yumin, S.El

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).

Bell System Tech. (1)

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

IEEE Antennas and Propagation Magazine (1)

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. (3)

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. (1)

R. Weder, “Dielectric three-dimensional electromagnetic tapers with no loss,” IEEE J. Quantum Electron. 24, 775–779 (1988).
[Crossref]

IEEE J.Quantum Electron (1)

I. Lu, “Intrinsic modes in wedge-shaped taper above an anisotropic substrate,” IEEE J.Quantum Electron,  27, 2373–2377 (1991).
[Crossref]

IEEE J.Quantum Electron, QE (1)

E. Marcatili, “Dielectric tapers with curved axes and no loss,” IEEE J.Quantum Electron, QE 21, 307–314 (1985).
[Crossref]

IEEE J.Quantum Electron, QE-13 (1)

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

IEEE Microwave Theory Tech. (1)

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. (1)

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. (1)

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. (1)

G.R. Hadley, “Design of tapered waveguides for improved output coupling,” IEEE Photon. Technol. Lett. 5, 1068–1070 (1993).
[Crossref]

IEICE Tran. Electron, E77-C (1)

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. (1)

C. Vassallo, “Analysis of tapered mode transformers for semiconductor optical amplifiers,” Opt. Quantum Electron. 26, 1025–1026 (1996).

Other (3)

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).

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 (Weily, New York, 1992).

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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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