Abstract

A full-vectorial H-field Finite Element Method has been used for the rigorous modal analysis of silicon strip waveguides. The spatial variation of the full-vectorial H and E-fields are also discussed in details and further, the Poynting vector is also presented. The modal area, hybridness, single mode operation and birefringence are also described for such silicon strip waveguides.

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References

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  1. M. Lipson, “Guiding, Modulating, and Emitting Light on Silicon-Challenges and Opportunities,” J. Lightwave Technol. 23(12), 4222–4238 (2005).
    [CrossRef]
  2. Y. Vlasov and S. J. McNab, “Losses in single-mode silicon-on-insulator strip waveguides and bends,” Opt. Express 12(8), 1622–1631 (2004).
    [CrossRef] [PubMed]
  3. D. Dai and S. He, “Ultrasmall overlapped arrayed-waveguide grating based on Si nanowire waveguides for dense wavelength division multiplexing,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1301–1305 (2006).
    [CrossRef]
  4. L. Liao, D. Samara-Rubio, M. Morse, A. Liu, D. Hodge, D. Rubin, U. D. Keil, and T. Franck, “High speed silicon Mach-Zehnder modulator,” Opt. Express 13(8), 3129–3135 (2005).
    [CrossRef] [PubMed]
  5. O. Boyraz and B. Jalali, “Demonstration of a silicon Raman laser,” Opt. Express 12(21), 5269–5273 (2004).
    [CrossRef] [PubMed]
  6. L. Yin, Q. Lin, and G. P. Agrawal, “Soliton fission and supercontinuum generation in silicon waveguides,” Opt. Lett. 32(4), 391–393 (2007).
    [CrossRef] [PubMed]
  7. B. M. A. Rahman and J. B. Davies, “Finite element solution of integrated optical waveguides,” J. Lightwave Technol. 2(5), 682–688 (1984).
    [CrossRef]
  8. B. M. A. Rahman and J. B. Davies, “Penalty Function Improvement of Waveguide Solution by Finite Elements,” IEEE Trans. Microw. Theory Tech. 32(8), 922–928 (1984).
    [CrossRef]
  9. B. M. A. Rahman and J. B. Davies, “Vector-H finite element solution of GaAs/GaAlAs rib waveguides,” Optoelectronics, IEE Proceedings J 132, 349–353 (1985).
    [CrossRef]
  10. ISO 11146, Laser and laser related equipment – Test methods for laser beam widths, divergence and beam propagation ratios, International Organization for Standardization, Geneva, Switzerland, 2005.
  11. N. Somasiri and B. M. A. Rahman, “Polarization crosstalk in high index contrast planar silica waveguides with slanted sidewalls,” J. Lightwave Technol. 21(1), 54–60 (2003).
    [CrossRef]
  12. B. M. A. Rahman, S. S. A. Obayya, N. Somasiri, M. Rajarajan, K. T. V. Grattan, and H. A. El-Mikathi, “Design and characterization of compact single-section passive polarization rotator,” J. Lightwave Technol. 19(4), 512–519 (2001).
    [CrossRef]

2007

2006

D. Dai and S. He, “Ultrasmall overlapped arrayed-waveguide grating based on Si nanowire waveguides for dense wavelength division multiplexing,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1301–1305 (2006).
[CrossRef]

2005

2004

2003

2001

1985

B. M. A. Rahman and J. B. Davies, “Vector-H finite element solution of GaAs/GaAlAs rib waveguides,” Optoelectronics, IEE Proceedings J 132, 349–353 (1985).
[CrossRef]

1984

B. M. A. Rahman and J. B. Davies, “Finite element solution of integrated optical waveguides,” J. Lightwave Technol. 2(5), 682–688 (1984).
[CrossRef]

B. M. A. Rahman and J. B. Davies, “Penalty Function Improvement of Waveguide Solution by Finite Elements,” IEEE Trans. Microw. Theory Tech. 32(8), 922–928 (1984).
[CrossRef]

Agrawal, G. P.

Boyraz, O.

Dai, D.

D. Dai and S. He, “Ultrasmall overlapped arrayed-waveguide grating based on Si nanowire waveguides for dense wavelength division multiplexing,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1301–1305 (2006).
[CrossRef]

Davies, J. B.

B. M. A. Rahman and J. B. Davies, “Vector-H finite element solution of GaAs/GaAlAs rib waveguides,” Optoelectronics, IEE Proceedings J 132, 349–353 (1985).
[CrossRef]

B. M. A. Rahman and J. B. Davies, “Penalty Function Improvement of Waveguide Solution by Finite Elements,” IEEE Trans. Microw. Theory Tech. 32(8), 922–928 (1984).
[CrossRef]

B. M. A. Rahman and J. B. Davies, “Finite element solution of integrated optical waveguides,” J. Lightwave Technol. 2(5), 682–688 (1984).
[CrossRef]

El-Mikathi, H. A.

Franck, T.

Grattan, K. T. V.

He, S.

D. Dai and S. He, “Ultrasmall overlapped arrayed-waveguide grating based on Si nanowire waveguides for dense wavelength division multiplexing,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1301–1305 (2006).
[CrossRef]

Hodge, D.

Jalali, B.

Keil, U. D.

Liao, L.

Lin, Q.

Lipson, M.

Liu, A.

McNab, S. J.

Morse, M.

Obayya, S. S. A.

Rahman, B. M. A.

N. Somasiri and B. M. A. Rahman, “Polarization crosstalk in high index contrast planar silica waveguides with slanted sidewalls,” J. Lightwave Technol. 21(1), 54–60 (2003).
[CrossRef]

B. M. A. Rahman, S. S. A. Obayya, N. Somasiri, M. Rajarajan, K. T. V. Grattan, and H. A. El-Mikathi, “Design and characterization of compact single-section passive polarization rotator,” J. Lightwave Technol. 19(4), 512–519 (2001).
[CrossRef]

B. M. A. Rahman and J. B. Davies, “Vector-H finite element solution of GaAs/GaAlAs rib waveguides,” Optoelectronics, IEE Proceedings J 132, 349–353 (1985).
[CrossRef]

B. M. A. Rahman and J. B. Davies, “Penalty Function Improvement of Waveguide Solution by Finite Elements,” IEEE Trans. Microw. Theory Tech. 32(8), 922–928 (1984).
[CrossRef]

B. M. A. Rahman and J. B. Davies, “Finite element solution of integrated optical waveguides,” J. Lightwave Technol. 2(5), 682–688 (1984).
[CrossRef]

Rajarajan, M.

Rubin, D.

Samara-Rubio, D.

Somasiri, N.

Vlasov, Y.

Yin, L.

IEEE J. Sel. Top. Quantum Electron.

D. Dai and S. He, “Ultrasmall overlapped arrayed-waveguide grating based on Si nanowire waveguides for dense wavelength division multiplexing,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1301–1305 (2006).
[CrossRef]

IEEE Trans. Microw. Theory Tech.

B. M. A. Rahman and J. B. Davies, “Penalty Function Improvement of Waveguide Solution by Finite Elements,” IEEE Trans. Microw. Theory Tech. 32(8), 922–928 (1984).
[CrossRef]

J. Lightwave Technol.

Opt. Express

Opt. Lett.

Optoelectronics, IEE Proceedings J

B. M. A. Rahman and J. B. Davies, “Vector-H finite element solution of GaAs/GaAlAs rib waveguides,” Optoelectronics, IEE Proceedings J 132, 349–353 (1985).
[CrossRef]

Other

ISO 11146, Laser and laser related equipment – Test methods for laser beam widths, divergence and beam propagation ratios, International Organization for Standardization, Geneva, Switzerland, 2005.

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Figures (16)

Fig. 1
Fig. 1

Variations of the effective index, ne with the waveguide width, W, for different quasi-TE modes.

Fig. 2
Fig. 2

Variations of effective area, Aeff, with the width for different quasi-TE modes.

Fig. 3
Fig. 3

Variations of power confinement factor in silicon, ΓSi, with the waveguide width, W, for different quasi-TE modes.

Fig. 4
Fig. 4

Variations of ne, Aeff and ΓSiO2 with the waveguide width for the Hy11 mode.

Fig. 5
Fig. 5

Variations of Hy along X-axis and Y-axis for the Hy11 mode

Fig. 6
Fig. 6

Non-dominant Hx field profile of the Hy11 mode.

Fig. 7
Fig. 7

Variations of the Hz field along the Y-axis for the Hy11 mode.

Fig. 8
Fig. 8

Variations of Hy hybridness with the width for the Hy11, Hy21, Hy31 and Hy41 modes.

Fig. 9
Fig. 9

Variations of Hz hybridness with the width for the Hy11, Hy21, Hy31 and Hy41 modes.

Fig. 10
Fig. 10

Variations of the Ex field along the X and Y-axes for the Hy11 mode.

Fig. 11
Fig. 11

Variations of the Ey field along the X and Y-axes for the Hy11 mode.

Fig. 12
Fig. 12

Variations of the Ez field along the X-axis for the Hy11 mode.

Fig. 13
Fig. 13

Variations of the Sz intensity along the X and Y-axes for the Hy11 mode.

Fig. 14
Fig. 14

Variations of the ne and Aeff with the width for the Hy11 and Hx11 modes.

Fig. 15
Fig. 15

Variations of the ne and Aeff with SiO2 or Air cladding for the Hy11 mode

Fig. 16
Fig. 16

Variations of the modal birefringence with the width for the fundamental modes with silica or air cladding.

Equations (3)

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ω 2 = [ ( × H ) * ε 1 ( × H ) + p ( H ) * ( H ) ]   d x d y H * μ   H  d x d y
A eff = ( Ω | E t | 2 d x d y ) 2 Ω | E t | 4 d x d y
S z = Ω { E * × H   } z d x d y

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