Abstract

The performance of a polarization splitter based on vertically coupled microring resonator is rigorously investigated by a combination of a 3D full vectorial film mode matching method with a 3D full vectorial coupled mode theory. The spectral responses of the structure for TE and TM mode are calculated, together with eigenmodes of uncoupled waveguides and scattering matrix of coupling region. The result shows that the response of microring resonator is indeed strongly polarization dependent and the resonance wavelengths are different for TE and TM mode. Such property allows for the design of wavelength-sensitive integrated polarization splitter. The influence of geometrical parameters on splitting ratio is investigated and the results indicate that the structure can have a splitting ratio greater than 20dB at 1.55µm.

© 2006 Optical Society of America

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References

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  1. T. Hayakawa, S. Asakawa, and Y. Kokubun, "ARROW-B type polarization splitter with asymmetric Y-branch fabricated by a self-alignment process," J. Lightwave Technol. 15, 1165-1170 (1997).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  4. B. E. Little and S. T. Chu, "Toward very large-scale integrated photonics," Opt. Photonics News 11, 24-29 (2000).
    [CrossRef]
  5. D. J. W. Klunder, C. G. H. Roeloffzen, and A. Driessen, "A novel polarization- independent wavelength-division-multiplexing filter based on cylindrical microresonators," IEEE J. Sel. Tops. Quantum Electron. 8, 1294-1299 (2002).
    [CrossRef]
  6. L. Prkna, M. Hubalek, and J. Ctyroky, "Field modeling of circular microresonators by film mode matching," IEEE J. Sel. Tops. Quantum Electron. 11, 217-223 (2005).
    [CrossRef]
  7. L. Prkna, M. Hubalek, and J. Ctyroky, "Vectorial eigenmode solver for bent waveguides based on mode matching," IEEE Photon. Technol. Lett. 15, 1249-1251 (2003).
  8. R. Stoffer, K. R. Hiremath, M. Hammer, L. Prkna, and J. Ctyroky, "Cylindrical integrated optical microresonators: modeling by 3-D vectorial coupled mode theory," Opt. Commun. 256,46-67 (2005).
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    [CrossRef]
  10. K. R. Hiremath, "Modling of circular integrated optical microresonators by 2-D frequency domain coupled mode theory," Opt. Commun. 257, 277-297 (2006).
    [CrossRef]
  11. K. R. Hiremath, "Coupled mode theory based modeling and analysis of circular optical microresonators," Ph.D. dissertation, University of Twente, the Netherlands, 2005, http://wwwhome.math.utwente.nl/~hiremathkr/research/thesis.pdf

2006

K. R. Hiremath, "Modling of circular integrated optical microresonators by 2-D frequency domain coupled mode theory," Opt. Commun. 257, 277-297 (2006).
[CrossRef]

2005

R. Stoffer, K. R. Hiremath, M. Hammer, L. Prkna, and J. Ctyroky, "Cylindrical integrated optical microresonators: modeling by 3-D vectorial coupled mode theory," Opt. Commun. 256,46-67 (2005).
[CrossRef]

L. Prkna, M. Hubalek, and J. Ctyroky, "Field modeling of circular microresonators by film mode matching," IEEE J. Sel. Tops. Quantum Electron. 11, 217-223 (2005).
[CrossRef]

2004

2003

E. Simova and I. Golub, "Polarization splitter/combiner in high index contrast Bragg reflector waveguides," Opt. Express 11, 3425-3430 (2003).
[CrossRef] [PubMed]

L. Prkna, M. Hubalek, and J. Ctyroky, "Vectorial eigenmode solver for bent waveguides based on mode matching," IEEE Photon. Technol. Lett. 15, 1249-1251 (2003).

2002

D. J. W. Klunder, C. G. H. Roeloffzen, and A. Driessen, "A novel polarization- independent wavelength-division-multiplexing filter based on cylindrical microresonators," IEEE J. Sel. Tops. Quantum Electron. 8, 1294-1299 (2002).
[CrossRef]

2000

B. E. Little and S. T. Chu, "Toward very large-scale integrated photonics," Opt. Photonics News 11, 24-29 (2000).
[CrossRef]

1997

T. Hayakawa, S. Asakawa, and Y. Kokubun, "ARROW-B type polarization splitter with asymmetric Y-branch fabricated by a self-alignment process," J. Lightwave Technol. 15, 1165-1170 (1997).
[CrossRef]

1994

Asakawa, S.

T. Hayakawa, S. Asakawa, and Y. Kokubun, "ARROW-B type polarization splitter with asymmetric Y-branch fabricated by a self-alignment process," J. Lightwave Technol. 15, 1165-1170 (1997).
[CrossRef]

Chu, S. T.

B. E. Little and S. T. Chu, "Toward very large-scale integrated photonics," Opt. Photonics News 11, 24-29 (2000).
[CrossRef]

Ctyroky, J.

L. Prkna, M. Hubalek, and J. Ctyroky, "Field modeling of circular microresonators by film mode matching," IEEE J. Sel. Tops. Quantum Electron. 11, 217-223 (2005).
[CrossRef]

R. Stoffer, K. R. Hiremath, M. Hammer, L. Prkna, and J. Ctyroky, "Cylindrical integrated optical microresonators: modeling by 3-D vectorial coupled mode theory," Opt. Commun. 256,46-67 (2005).
[CrossRef]

L. Prkna, M. Hubalek, and J. Ctyroky, "Vectorial eigenmode solver for bent waveguides based on mode matching," IEEE Photon. Technol. Lett. 15, 1249-1251 (2003).

Driessen, A.

D. J. W. Klunder, C. G. H. Roeloffzen, and A. Driessen, "A novel polarization- independent wavelength-division-multiplexing filter based on cylindrical microresonators," IEEE J. Sel. Tops. Quantum Electron. 8, 1294-1299 (2002).
[CrossRef]

Golub, I.

Hammer, M.

R. Stoffer, K. R. Hiremath, M. Hammer, L. Prkna, and J. Ctyroky, "Cylindrical integrated optical microresonators: modeling by 3-D vectorial coupled mode theory," Opt. Commun. 256,46-67 (2005).
[CrossRef]

Hayakawa, T.

T. Hayakawa, S. Asakawa, and Y. Kokubun, "ARROW-B type polarization splitter with asymmetric Y-branch fabricated by a self-alignment process," J. Lightwave Technol. 15, 1165-1170 (1997).
[CrossRef]

Hiremath, K. R.

K. R. Hiremath, "Modling of circular integrated optical microresonators by 2-D frequency domain coupled mode theory," Opt. Commun. 257, 277-297 (2006).
[CrossRef]

R. Stoffer, K. R. Hiremath, M. Hammer, L. Prkna, and J. Ctyroky, "Cylindrical integrated optical microresonators: modeling by 3-D vectorial coupled mode theory," Opt. Commun. 256,46-67 (2005).
[CrossRef]

Huang, W. P.

Hubalek, M.

L. Prkna, M. Hubalek, and J. Ctyroky, "Field modeling of circular microresonators by film mode matching," IEEE J. Sel. Tops. Quantum Electron. 11, 217-223 (2005).
[CrossRef]

L. Prkna, M. Hubalek, and J. Ctyroky, "Vectorial eigenmode solver for bent waveguides based on mode matching," IEEE Photon. Technol. Lett. 15, 1249-1251 (2003).

Klunder, D. J. W.

D. J. W. Klunder, C. G. H. Roeloffzen, and A. Driessen, "A novel polarization- independent wavelength-division-multiplexing filter based on cylindrical microresonators," IEEE J. Sel. Tops. Quantum Electron. 8, 1294-1299 (2002).
[CrossRef]

Kokubun, Y.

T. Hayakawa, S. Asakawa, and Y. Kokubun, "ARROW-B type polarization splitter with asymmetric Y-branch fabricated by a self-alignment process," J. Lightwave Technol. 15, 1165-1170 (1997).
[CrossRef]

Koshiba, M.

Little, B. E.

B. E. Little and S. T. Chu, "Toward very large-scale integrated photonics," Opt. Photonics News 11, 24-29 (2000).
[CrossRef]

Prkna, L.

L. Prkna, M. Hubalek, and J. Ctyroky, "Field modeling of circular microresonators by film mode matching," IEEE J. Sel. Tops. Quantum Electron. 11, 217-223 (2005).
[CrossRef]

R. Stoffer, K. R. Hiremath, M. Hammer, L. Prkna, and J. Ctyroky, "Cylindrical integrated optical microresonators: modeling by 3-D vectorial coupled mode theory," Opt. Commun. 256,46-67 (2005).
[CrossRef]

L. Prkna, M. Hubalek, and J. Ctyroky, "Vectorial eigenmode solver for bent waveguides based on mode matching," IEEE Photon. Technol. Lett. 15, 1249-1251 (2003).

Roeloffzen, C. G. H.

D. J. W. Klunder, C. G. H. Roeloffzen, and A. Driessen, "A novel polarization- independent wavelength-division-multiplexing filter based on cylindrical microresonators," IEEE J. Sel. Tops. Quantum Electron. 8, 1294-1299 (2002).
[CrossRef]

Saitoh, K.

Sato, Y.

Simova, E.

Stoffer, R.

R. Stoffer, K. R. Hiremath, M. Hammer, L. Prkna, and J. Ctyroky, "Cylindrical integrated optical microresonators: modeling by 3-D vectorial coupled mode theory," Opt. Commun. 256,46-67 (2005).
[CrossRef]

IEEE J. Sel. Tops. Quantum Electron.

D. J. W. Klunder, C. G. H. Roeloffzen, and A. Driessen, "A novel polarization- independent wavelength-division-multiplexing filter based on cylindrical microresonators," IEEE J. Sel. Tops. Quantum Electron. 8, 1294-1299 (2002).
[CrossRef]

L. Prkna, M. Hubalek, and J. Ctyroky, "Field modeling of circular microresonators by film mode matching," IEEE J. Sel. Tops. Quantum Electron. 11, 217-223 (2005).
[CrossRef]

IEEE Photon. Technol. Lett.

L. Prkna, M. Hubalek, and J. Ctyroky, "Vectorial eigenmode solver for bent waveguides based on mode matching," IEEE Photon. Technol. Lett. 15, 1249-1251 (2003).

J. Lightwave Technol.

T. Hayakawa, S. Asakawa, and Y. Kokubun, "ARROW-B type polarization splitter with asymmetric Y-branch fabricated by a self-alignment process," J. Lightwave Technol. 15, 1165-1170 (1997).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Commun.

K. R. Hiremath, "Modling of circular integrated optical microresonators by 2-D frequency domain coupled mode theory," Opt. Commun. 257, 277-297 (2006).
[CrossRef]

R. Stoffer, K. R. Hiremath, M. Hammer, L. Prkna, and J. Ctyroky, "Cylindrical integrated optical microresonators: modeling by 3-D vectorial coupled mode theory," Opt. Commun. 256,46-67 (2005).
[CrossRef]

Opt. Express

Opt. Photonics News

B. E. Little and S. T. Chu, "Toward very large-scale integrated photonics," Opt. Photonics News 11, 24-29 (2000).
[CrossRef]

Other

K. R. Hiremath, "Coupled mode theory based modeling and analysis of circular optical microresonators," Ph.D. dissertation, University of Twente, the Netherlands, 2005, http://wwwhome.math.utwente.nl/~hiremathkr/research/thesis.pdf

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Figures (10)

Fig. 1.
Fig. 1.

Vertically coupled microring resonator. The blue and orange arrows represent two orthogonal polarization states, and they are transferred to different output ports

Fig. 2.
Fig. 2.

Cross section view and top view of the microresonator structure

Fig. 3.
Fig. 3.

The cross section of uncoupled straight waveguide and corresponding field distributions of the transverse components of the electric intensity of the fundamental TE and TM mode.

Fig. 4.
Fig. 4.

The cross section of uncoupled bent waveguide and corresponding field distributions of the transverse components of the electric intensity of the fundamental TE and TM mode.

Fig. 5.
Fig. 5.

Top view and cross section of coupling region. The dashed lines indicate the boundary of computational region [xb , xt ]×[yi , yo ]×[zi , zo ].

Fig. 6.
Fig. 6.

The evolution of the elements of scattering matrix for TE and TM mode as a function of output plan position of coupling region

Fig. 7.
Fig. 7.

The cross section of both straight and bent waveguides with field distribution of the horizontal component of the magnetic intensity for a sequence of longitudinal distances. Coupling between the fundamental TM modes of the two waveguides is shown.

Fig. 9.
Fig. 9.

Spectral responses of the entire structure for both TE and TM mode

Fig. 10.
Fig. 10.

Splitting ratios at 1.55µm of the resonator as a function of horizontal gap d

Fig. 11.
Fig. 11.

Splitting ratios of the resonator as a function of wavelength

Tables (2)

Tables Icon

Table 1. Propagation constants of modes related to Fig. 3 and Fig. 4

Tables Icon

Table 2. Splitting ratios of drop and through port

Equations (5)

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

( E , H ) = A b ( z ) ( E b , H b ) + A s ( z ) ( E s , H s )
d d z [ A b ( z ) A s ( z ) ] = i C 1 K [ A b ( z ) A s ( z ) ]
( A b ( z o ) A s ( z o ) ) = S ( A b ( z i ) A s ( z i ) ) = ( S bb S bs S sb S ss ) ( A b ( z i ) A s ( z i ) )
P drop = P in S bs 2 S sb 2 exp ( α L ) 1 + S bb 4 exp ( 2 α L ) 2 S bb 2 exp ( α L ) cos ( β L 2 φ )
P through = P in S ss 2 ( 1 + S bb 2 d 2 exp ( α L ) 2 S bb d exp ( α L ) cos ( β L 2 φ ϕ ) ) 1 + S bb 4 exp ( 2 α L ) 2 S bb 2 exp ( α L ) cos ( β L 2 φ )

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