Abstract

An accurate numerical simulation study of a polarization conversion phenomenon in deeply etched semiconductor electro-optic waveguide modulators is presented. Based on a powerful and versatile finite element package, the effect of various imperfect fabrication conditions on unwanted and unexpected polarization conversion in electro-optic semiconductor modulators is, for the first time to our knowledge reported and explained in terms of its origin.

© 2005 Optical Society of America

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References

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  1. C. M. Gee, G. D. Thurmond, H. W. Yen, “17-GHz bandwidth electro-optic modulator,” Appl. Phys. Lett. 43, 998–1000 (1983).
    [CrossRef]
  2. K. Kubota, J. Noda, O. Mikami, “Traveling wave optical modulator using a directional coupler LiNbO3waveguide,” IEEE J. Quantum Electron. QE-16, 754–760 (1980).
    [CrossRef]
  3. R. C. Alferness, N. P. Economou, L. L. Buhl, “Fast compact optical waveguide switch modulator,” Appl. Phys. Lett. 38, 214–217 (1981).
    [CrossRef]
  4. S. S. A. Obayya, S. Haxha, B. M. A. Rahman, C. Themistos, K. T. V. Grattan, “Optimization of the optical properties of a deeply etched semiconductor electrooptic modulator,” J. Light-wave Technol. 21, 1813–1819 (2003).
    [CrossRef]
  5. R. G. Walker, “High-speed III–V semiconductor intensity modulators,” IEEE J. Quantum Electron. 27, 654–667 (1991).
    [CrossRef]
  6. L. Eldada, “Advances in telecom and datacom optical components,” Opt. Eng. 40, 1165–1178 (2001).
    [CrossRef]
  7. R. Spickermann, M. G. Peters, N. Dagli, “A polarization independent GaAs–AlGaAs electrooptic modulator,” IEEE J. Quantum Electron. 32, 764–769 (1996).
    [CrossRef]
  8. N. Somasiri, B. M. A. Rahman, “Polarization crosstalk in high index contrast planar silica waveguides with slanted sidewalls,” J. Lightwave Technol. 21, 54–60 (2003).
    [CrossRef]
  9. A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley Interscience, New York, 1984).
  10. B. M. A. Rahman, J. B. Davies, “Finite-element solution of integrated optical waveguides,” J. Lightwave Technol. LT-2, 682–688 (1984).
    [CrossRef]
  11. B. M. A. Rahman, J. B. Davies, “Analysis of optical waveguide discontinuities,” J. Lightwave Technol. LT-6, 52–57 (1988).
    [CrossRef]
  12. J. M. Heaton, QinetiQ, St. Andrews Road, Malvern, Worchestershire WR14 3PS, UK (personal communication, 2003).

2003 (2)

S. S. A. Obayya, S. Haxha, B. M. A. Rahman, C. Themistos, K. T. V. Grattan, “Optimization of the optical properties of a deeply etched semiconductor electrooptic modulator,” J. Light-wave Technol. 21, 1813–1819 (2003).
[CrossRef]

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

2001 (1)

L. Eldada, “Advances in telecom and datacom optical components,” Opt. Eng. 40, 1165–1178 (2001).
[CrossRef]

1996 (1)

R. Spickermann, M. G. Peters, N. Dagli, “A polarization independent GaAs–AlGaAs electrooptic modulator,” IEEE J. Quantum Electron. 32, 764–769 (1996).
[CrossRef]

1991 (1)

R. G. Walker, “High-speed III–V semiconductor intensity modulators,” IEEE J. Quantum Electron. 27, 654–667 (1991).
[CrossRef]

1988 (1)

B. M. A. Rahman, J. B. Davies, “Analysis of optical waveguide discontinuities,” J. Lightwave Technol. LT-6, 52–57 (1988).
[CrossRef]

1984 (1)

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

1983 (1)

C. M. Gee, G. D. Thurmond, H. W. Yen, “17-GHz bandwidth electro-optic modulator,” Appl. Phys. Lett. 43, 998–1000 (1983).
[CrossRef]

1981 (1)

R. C. Alferness, N. P. Economou, L. L. Buhl, “Fast compact optical waveguide switch modulator,” Appl. Phys. Lett. 38, 214–217 (1981).
[CrossRef]

1980 (1)

K. Kubota, J. Noda, O. Mikami, “Traveling wave optical modulator using a directional coupler LiNbO3waveguide,” IEEE J. Quantum Electron. QE-16, 754–760 (1980).
[CrossRef]

Alferness, R. C.

R. C. Alferness, N. P. Economou, L. L. Buhl, “Fast compact optical waveguide switch modulator,” Appl. Phys. Lett. 38, 214–217 (1981).
[CrossRef]

Buhl, L. L.

R. C. Alferness, N. P. Economou, L. L. Buhl, “Fast compact optical waveguide switch modulator,” Appl. Phys. Lett. 38, 214–217 (1981).
[CrossRef]

Dagli, N.

R. Spickermann, M. G. Peters, N. Dagli, “A polarization independent GaAs–AlGaAs electrooptic modulator,” IEEE J. Quantum Electron. 32, 764–769 (1996).
[CrossRef]

Davies, J. B.

B. M. A. Rahman, J. B. Davies, “Analysis of optical waveguide discontinuities,” J. Lightwave Technol. LT-6, 52–57 (1988).
[CrossRef]

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

Economou, N. P.

R. C. Alferness, N. P. Economou, L. L. Buhl, “Fast compact optical waveguide switch modulator,” Appl. Phys. Lett. 38, 214–217 (1981).
[CrossRef]

Eldada, L.

L. Eldada, “Advances in telecom and datacom optical components,” Opt. Eng. 40, 1165–1178 (2001).
[CrossRef]

Gee, C. M.

C. M. Gee, G. D. Thurmond, H. W. Yen, “17-GHz bandwidth electro-optic modulator,” Appl. Phys. Lett. 43, 998–1000 (1983).
[CrossRef]

Grattan, K. T. V.

S. S. A. Obayya, S. Haxha, B. M. A. Rahman, C. Themistos, K. T. V. Grattan, “Optimization of the optical properties of a deeply etched semiconductor electrooptic modulator,” J. Light-wave Technol. 21, 1813–1819 (2003).
[CrossRef]

Haxha, S.

S. S. A. Obayya, S. Haxha, B. M. A. Rahman, C. Themistos, K. T. V. Grattan, “Optimization of the optical properties of a deeply etched semiconductor electrooptic modulator,” J. Light-wave Technol. 21, 1813–1819 (2003).
[CrossRef]

Heaton, J. M.

J. M. Heaton, QinetiQ, St. Andrews Road, Malvern, Worchestershire WR14 3PS, UK (personal communication, 2003).

Kubota, K.

K. Kubota, J. Noda, O. Mikami, “Traveling wave optical modulator using a directional coupler LiNbO3waveguide,” IEEE J. Quantum Electron. QE-16, 754–760 (1980).
[CrossRef]

Mikami, O.

K. Kubota, J. Noda, O. Mikami, “Traveling wave optical modulator using a directional coupler LiNbO3waveguide,” IEEE J. Quantum Electron. QE-16, 754–760 (1980).
[CrossRef]

Noda, J.

K. Kubota, J. Noda, O. Mikami, “Traveling wave optical modulator using a directional coupler LiNbO3waveguide,” IEEE J. Quantum Electron. QE-16, 754–760 (1980).
[CrossRef]

Obayya, S. S. A.

S. S. A. Obayya, S. Haxha, B. M. A. Rahman, C. Themistos, K. T. V. Grattan, “Optimization of the optical properties of a deeply etched semiconductor electrooptic modulator,” J. Light-wave Technol. 21, 1813–1819 (2003).
[CrossRef]

Peters, M. G.

R. Spickermann, M. G. Peters, N. Dagli, “A polarization independent GaAs–AlGaAs electrooptic modulator,” IEEE J. Quantum Electron. 32, 764–769 (1996).
[CrossRef]

Rahman, B. M. A.

S. S. A. Obayya, S. Haxha, B. M. A. Rahman, C. Themistos, K. T. V. Grattan, “Optimization of the optical properties of a deeply etched semiconductor electrooptic modulator,” J. Light-wave Technol. 21, 1813–1819 (2003).
[CrossRef]

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

B. M. A. Rahman, J. B. Davies, “Analysis of optical waveguide discontinuities,” J. Lightwave Technol. LT-6, 52–57 (1988).
[CrossRef]

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

Somasiri, N.

Spickermann, R.

R. Spickermann, M. G. Peters, N. Dagli, “A polarization independent GaAs–AlGaAs electrooptic modulator,” IEEE J. Quantum Electron. 32, 764–769 (1996).
[CrossRef]

Themistos, C.

S. S. A. Obayya, S. Haxha, B. M. A. Rahman, C. Themistos, K. T. V. Grattan, “Optimization of the optical properties of a deeply etched semiconductor electrooptic modulator,” J. Light-wave Technol. 21, 1813–1819 (2003).
[CrossRef]

Thurmond, G. D.

C. M. Gee, G. D. Thurmond, H. W. Yen, “17-GHz bandwidth electro-optic modulator,” Appl. Phys. Lett. 43, 998–1000 (1983).
[CrossRef]

Walker, R. G.

R. G. Walker, “High-speed III–V semiconductor intensity modulators,” IEEE J. Quantum Electron. 27, 654–667 (1991).
[CrossRef]

Yariv, A.

A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley Interscience, New York, 1984).

Yeh, P.

A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley Interscience, New York, 1984).

Yen, H. W.

C. M. Gee, G. D. Thurmond, H. W. Yen, “17-GHz bandwidth electro-optic modulator,” Appl. Phys. Lett. 43, 998–1000 (1983).
[CrossRef]

Appl. Phys. Lett. (2)

C. M. Gee, G. D. Thurmond, H. W. Yen, “17-GHz bandwidth electro-optic modulator,” Appl. Phys. Lett. 43, 998–1000 (1983).
[CrossRef]

R. C. Alferness, N. P. Economou, L. L. Buhl, “Fast compact optical waveguide switch modulator,” Appl. Phys. Lett. 38, 214–217 (1981).
[CrossRef]

IEEE J. Quantum Electron. (3)

K. Kubota, J. Noda, O. Mikami, “Traveling wave optical modulator using a directional coupler LiNbO3waveguide,” IEEE J. Quantum Electron. QE-16, 754–760 (1980).
[CrossRef]

R. G. Walker, “High-speed III–V semiconductor intensity modulators,” IEEE J. Quantum Electron. 27, 654–667 (1991).
[CrossRef]

R. Spickermann, M. G. Peters, N. Dagli, “A polarization independent GaAs–AlGaAs electrooptic modulator,” IEEE J. Quantum Electron. 32, 764–769 (1996).
[CrossRef]

J. Light-wave Technol. (1)

S. S. A. Obayya, S. Haxha, B. M. A. Rahman, C. Themistos, K. T. V. Grattan, “Optimization of the optical properties of a deeply etched semiconductor electrooptic modulator,” J. Light-wave Technol. 21, 1813–1819 (2003).
[CrossRef]

J. Lightwave Technol. (3)

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

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

B. M. A. Rahman, J. B. Davies, “Analysis of optical waveguide discontinuities,” J. Lightwave Technol. LT-6, 52–57 (1988).
[CrossRef]

Opt. Eng. (1)

L. Eldada, “Advances in telecom and datacom optical components,” Opt. Eng. 40, 1165–1178 (2001).
[CrossRef]

Other (2)

A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley Interscience, New York, 1984).

J. M. Heaton, QinetiQ, St. Andrews Road, Malvern, Worchestershire WR14 3PS, UK (personal communication, 2003).

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Figures (11)

Fig. 1
Fig. 1

Schematic diagram of a deeply etched AlGaAs/GaAs semiconductor EO modulator.

Fig. 2
Fig. 2

Variation of the propagation constants of the fundamental TE and TM modes with a modulating voltage for different slant angle values.

Fig. 3
Fig. 3

Contour plots of the (a) major Hx and (b) minor Hy field components of the fundamental TM mode for zero modulating voltage.

Fig. 4
Fig. 4

Contour plots of the minor Hy field component of the fundamental TM mode when the modulating voltage was (a) −10 V and (b) −24.2 V.

Fig. 5
Fig. 5

Variation of the beat length with a modulating voltage for different slant angle values.

Fig. 6
Fig. 6

Variation of modal transmission coefficients of both the fundamental TE and the TM modes with a modulating voltage for different slant angle values.

Fig. 7
Fig. 7

Variation of the TM power with propagation distance Z for different modulating voltage values.

Fig. 8
Fig. 8

Variation of the maximum polarization conversion ratio with a modulating voltage for different slant angle values.

Fig. 9
Fig. 9

Variation of the polarization conversion ratio with a modulating voltage for different slant angle values at a 4-cm device length.

Fig. 10
Fig. 10

Variation of the beat length with a modulating voltage for different Al concentration values of buffer layer x1.

Fig. 11
Fig. 11

Variation of the polarization conversion ratio with a modulating voltage for different Al concentration values of buffer layer x1 at a 2-cm device length.

Equations (8)

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L = ɛ [ ( d ϕ d x ) 2 + ( d ϕ d y ) 2 ] d x d y ,
E = - ϕ ( x ,     y ) .
n ¯ ( x , y ) = [ n ( x , y ) + Δ n x x ( x , y ) Δ n x y ( x , y ) 0 Δ n y x ( x , y ) n ( x , y ) + Δ n y y ( x , y ) 0 0 0 n ( x , y ) + Δ n z z ( x , y ) ] ,
Δ n x x = - Δ n z z = n 3 ( x , y ) 2 r 41 E y ( x , y ) ,             Δ n y y = 0 ,
Δ n x y = Δ n y x = n 3 ( x , y ) 2 r 41 E x ( x , y ) ,
ω 2 = [ ( × H ) * · ɛ ¯ ¯ - 1 ( × H ) + p ( · H ) * ( · H ) ] d Ω H * · μ ¯ ¯ H d Ω ,
J = E t I - E t II 2 + α Z 0 2 H t I - H t II 2 d Ω ;
L π = π ( β TE - β TM ) .

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