Abstract

Simple and accurate analytic expressions are provided for the maximum reflectivity and tolerances of an impedance-matched asymmetric Fabry-Perot used as a high-contrast spatial light modulator when electroabsorptive quantum wells provide loss modulation. When the device geometry is optimized, these expressions depend only on material properties. The maximum reflectivity depends only on the fractional absorption change and is independent of the front-mirror reflectivity. The most important tolerance is on the flatness of crystal growth; the fractional-length tolerance is proportional to the absorption coefficient. These formulas agree with experimentally reported results from multiple-quantum-well modulators and previous numerical analyses; they are useful for quickly predicting optimized performance of possible new materials. The normally on and normally off geometries are compared. The effect of finite back-mirror reflectivity is clarified. Deviations from impedance match enable increased reflectance difference at the expense of contrast ratio, an approach which is evaluated as a function of material parameters.

© 2002 Optical Society of America

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  1. P. Zouganeli, P. J. Stevens, D. Atkinson, G. Parry, “Design trade-offs and evaluation of the performance attainable by GaAs-Al0.3Ga0.7As asymmetric Fabry-Perot modulators,” IEEE J. Quantum Electron. 31, 927–943 (1995).
    [CrossRef]
  2. P. Zouganeli, G. Parry, “Evaluation of the tolerance of asymmetric Fabry-Perot modulators with respect to realistic operating conditions,” IEEE J. Quantum Electron. 31, 1140–1151 (1995).
    [CrossRef]
  3. K.-K. Law, J. L. Merz, L. A. Coldren, “The effect of layer thickness variations on the performance of asymmetric Fabry-Perot reflection modulators,” J. Appl. Phys. 72, 855–869 (1992).
    [CrossRef]
  4. B. Pezeshki, J. S. Harris, “Optimization of modulation ratio and insertion loss in reflective electroabsorption modulators,” Appl. Phys. Lett. 57, 1491–1493 (1990).
    [CrossRef]
  5. B. Pezeshki, D. Thomas, J. S. Harris, “Optimization of reflection electroabsorption modulators,” in Physical concepts of materials for novel optoelectronic device applications II: Device physics and applications, M. Razeghi, ed., Proc. SPIE1362, 559–565 (1991).
    [CrossRef]
  6. M. G. Xu, B. D. Nener, J. M. Dell, “Design of externally tuned asymmetric fibre Fabry-Perot electroabsorption optical modulators,” IEE Proc. Optoelectron. 145, 344–352 (1998).
    [CrossRef]
  7. C. C. Barron, C. J. Mahon, B. J. Thibeault, L. A. Coldren, “Design, fabrication and characterization of high-speed asymmetric Fabry-Perot modulators for optical interconnect applications,” Opt. Quantum Electron. 25, S885–S898 (1993).
    [CrossRef]
  8. R. I. Killey, M. Whitehead, P. N. Stavrinou, G. Parry, C. C. Button, “Design of InGaAsP multiple quantum-well Fabry-Perot modulators for soliton control,” J. Lightwave Technol. 17, 1408–1413 (1999).
    [CrossRef]
  9. See, for example, E. Garmire, “Criteria for optical bistability in lossy saturating Fabry-Perots,” IEEE J. Quantum Electron. 25, 289–295 (1989).
  10. K. W. Jelley, R. W. H. Englemann, K. Alavi, H. Lee, “Well size related limitations on maximum electroabsorption in GaAs/AlGaAs MQW Structures,” Appl. Phys. Lett. 55, 70–72 (1989).
    [CrossRef]
  11. G. Parry, M. Whitehead, P. Stevens, A. Rivers, P. Bartnes, D. Atkinson, “The design and application of III-V MQW optical modulators,” Phys. Scr. T35, 210 (1991).
    [CrossRef]
  12. B. Pezeshki, S. M. Lord, J. S. Harris, “Electroabsorptive modulators in InGaAs/AlGaAs,” Appl. Phys. Lett. 59, 888–890 (1991).
    [CrossRef]
  13. B. Pezeshki, S. M. Lord, T. B. Boykin, J. S. Harris, “GaAs/AlAs quantum wells for electroabsorption modulators,” Appl. Phys. Lett. 60, 2779–2781 (1992).
    [CrossRef]
  14. H. Q. Hou, A. N. Cheng, H. H. Wieder, W. S. C. Chang, C. W. Tu, “Electroabsorption of InAlAs/InP strained MQW for 1.3 µm waveguide modulators,” Appl. Phys. Lett. 63, 1833–1835 (1993).
    [CrossRef]
  15. R. P. Leavitt, J. L. Bradshaw, J. T. Pham, “Superlattice-equivalent (In,Ga)As/(In,Al)As quantum wells with large Stark shifts in the 1.3 µm spectral region,” Appl. Phys. Lett. 66, 1803–1805 (1995).
    [CrossRef]
  16. M. K. Chin, W. S. C. Chang, “Electroabsorption properties of InGaAs/InAlAs MQW structures at 1.5 µm,” IEEE Photon. Technol. Lett. 6, 502–504 (1994).
    [CrossRef]
  17. M. G. Xu, T. A. Fisher, J. M. Dell, A. Clark, “Wide optical bandwidth asymmetric Fabry-Perot reflection modulator using the quantum confined Stark effect,” J. Appl. Phys. 84, 5761–5765 (1998).
    [CrossRef]
  18. K. Bacher, B. Pezeshki, S. M. Lord, J. S. Harris, “Molecular beam epitaxy growth of vertical cavity optical devices with in situ corrections,” Appl. Phys. Lett. 61, 1387–1391 (1992).
    [CrossRef]
  19. M. R. Ramadas, E. Garmire, A. K. Ghatak, K. Thygarajan, M. R. Shenoy, “Analysis of absorbing and leaky planar waveguides: a novel method,” Opt. Lett. 14, 376–378 (1989).
    [CrossRef] [PubMed]
  20. B. G. Kim, E. Garmire, “Comparison between the matrix method and the coupled-wave method in the analysis of Bragg reflector structures,” J. Opt. Soc. Am. A. 9, 132–136 (1992).
    [CrossRef]

1999

1998

M. G. Xu, B. D. Nener, J. M. Dell, “Design of externally tuned asymmetric fibre Fabry-Perot electroabsorption optical modulators,” IEE Proc. Optoelectron. 145, 344–352 (1998).
[CrossRef]

M. G. Xu, T. A. Fisher, J. M. Dell, A. Clark, “Wide optical bandwidth asymmetric Fabry-Perot reflection modulator using the quantum confined Stark effect,” J. Appl. Phys. 84, 5761–5765 (1998).
[CrossRef]

1995

R. P. Leavitt, J. L. Bradshaw, J. T. Pham, “Superlattice-equivalent (In,Ga)As/(In,Al)As quantum wells with large Stark shifts in the 1.3 µm spectral region,” Appl. Phys. Lett. 66, 1803–1805 (1995).
[CrossRef]

P. Zouganeli, P. J. Stevens, D. Atkinson, G. Parry, “Design trade-offs and evaluation of the performance attainable by GaAs-Al0.3Ga0.7As asymmetric Fabry-Perot modulators,” IEEE J. Quantum Electron. 31, 927–943 (1995).
[CrossRef]

P. Zouganeli, G. Parry, “Evaluation of the tolerance of asymmetric Fabry-Perot modulators with respect to realistic operating conditions,” IEEE J. Quantum Electron. 31, 1140–1151 (1995).
[CrossRef]

1994

M. K. Chin, W. S. C. Chang, “Electroabsorption properties of InGaAs/InAlAs MQW structures at 1.5 µm,” IEEE Photon. Technol. Lett. 6, 502–504 (1994).
[CrossRef]

1993

H. Q. Hou, A. N. Cheng, H. H. Wieder, W. S. C. Chang, C. W. Tu, “Electroabsorption of InAlAs/InP strained MQW for 1.3 µm waveguide modulators,” Appl. Phys. Lett. 63, 1833–1835 (1993).
[CrossRef]

C. C. Barron, C. J. Mahon, B. J. Thibeault, L. A. Coldren, “Design, fabrication and characterization of high-speed asymmetric Fabry-Perot modulators for optical interconnect applications,” Opt. Quantum Electron. 25, S885–S898 (1993).
[CrossRef]

1992

K.-K. Law, J. L. Merz, L. A. Coldren, “The effect of layer thickness variations on the performance of asymmetric Fabry-Perot reflection modulators,” J. Appl. Phys. 72, 855–869 (1992).
[CrossRef]

B. Pezeshki, S. M. Lord, T. B. Boykin, J. S. Harris, “GaAs/AlAs quantum wells for electroabsorption modulators,” Appl. Phys. Lett. 60, 2779–2781 (1992).
[CrossRef]

K. Bacher, B. Pezeshki, S. M. Lord, J. S. Harris, “Molecular beam epitaxy growth of vertical cavity optical devices with in situ corrections,” Appl. Phys. Lett. 61, 1387–1391 (1992).
[CrossRef]

B. G. Kim, E. Garmire, “Comparison between the matrix method and the coupled-wave method in the analysis of Bragg reflector structures,” J. Opt. Soc. Am. A. 9, 132–136 (1992).
[CrossRef]

1991

G. Parry, M. Whitehead, P. Stevens, A. Rivers, P. Bartnes, D. Atkinson, “The design and application of III-V MQW optical modulators,” Phys. Scr. T35, 210 (1991).
[CrossRef]

B. Pezeshki, S. M. Lord, J. S. Harris, “Electroabsorptive modulators in InGaAs/AlGaAs,” Appl. Phys. Lett. 59, 888–890 (1991).
[CrossRef]

1990

B. Pezeshki, J. S. Harris, “Optimization of modulation ratio and insertion loss in reflective electroabsorption modulators,” Appl. Phys. Lett. 57, 1491–1493 (1990).
[CrossRef]

1989

See, for example, E. Garmire, “Criteria for optical bistability in lossy saturating Fabry-Perots,” IEEE J. Quantum Electron. 25, 289–295 (1989).

K. W. Jelley, R. W. H. Englemann, K. Alavi, H. Lee, “Well size related limitations on maximum electroabsorption in GaAs/AlGaAs MQW Structures,” Appl. Phys. Lett. 55, 70–72 (1989).
[CrossRef]

M. R. Ramadas, E. Garmire, A. K. Ghatak, K. Thygarajan, M. R. Shenoy, “Analysis of absorbing and leaky planar waveguides: a novel method,” Opt. Lett. 14, 376–378 (1989).
[CrossRef] [PubMed]

Alavi, K.

K. W. Jelley, R. W. H. Englemann, K. Alavi, H. Lee, “Well size related limitations on maximum electroabsorption in GaAs/AlGaAs MQW Structures,” Appl. Phys. Lett. 55, 70–72 (1989).
[CrossRef]

Atkinson, D.

P. Zouganeli, P. J. Stevens, D. Atkinson, G. Parry, “Design trade-offs and evaluation of the performance attainable by GaAs-Al0.3Ga0.7As asymmetric Fabry-Perot modulators,” IEEE J. Quantum Electron. 31, 927–943 (1995).
[CrossRef]

G. Parry, M. Whitehead, P. Stevens, A. Rivers, P. Bartnes, D. Atkinson, “The design and application of III-V MQW optical modulators,” Phys. Scr. T35, 210 (1991).
[CrossRef]

Bacher, K.

K. Bacher, B. Pezeshki, S. M. Lord, J. S. Harris, “Molecular beam epitaxy growth of vertical cavity optical devices with in situ corrections,” Appl. Phys. Lett. 61, 1387–1391 (1992).
[CrossRef]

Barron, C. C.

C. C. Barron, C. J. Mahon, B. J. Thibeault, L. A. Coldren, “Design, fabrication and characterization of high-speed asymmetric Fabry-Perot modulators for optical interconnect applications,” Opt. Quantum Electron. 25, S885–S898 (1993).
[CrossRef]

Bartnes, P.

G. Parry, M. Whitehead, P. Stevens, A. Rivers, P. Bartnes, D. Atkinson, “The design and application of III-V MQW optical modulators,” Phys. Scr. T35, 210 (1991).
[CrossRef]

Boykin, T. B.

B. Pezeshki, S. M. Lord, T. B. Boykin, J. S. Harris, “GaAs/AlAs quantum wells for electroabsorption modulators,” Appl. Phys. Lett. 60, 2779–2781 (1992).
[CrossRef]

Bradshaw, J. L.

R. P. Leavitt, J. L. Bradshaw, J. T. Pham, “Superlattice-equivalent (In,Ga)As/(In,Al)As quantum wells with large Stark shifts in the 1.3 µm spectral region,” Appl. Phys. Lett. 66, 1803–1805 (1995).
[CrossRef]

Button, C. C.

Chang, W. S. C.

M. K. Chin, W. S. C. Chang, “Electroabsorption properties of InGaAs/InAlAs MQW structures at 1.5 µm,” IEEE Photon. Technol. Lett. 6, 502–504 (1994).
[CrossRef]

H. Q. Hou, A. N. Cheng, H. H. Wieder, W. S. C. Chang, C. W. Tu, “Electroabsorption of InAlAs/InP strained MQW for 1.3 µm waveguide modulators,” Appl. Phys. Lett. 63, 1833–1835 (1993).
[CrossRef]

Cheng, A. N.

H. Q. Hou, A. N. Cheng, H. H. Wieder, W. S. C. Chang, C. W. Tu, “Electroabsorption of InAlAs/InP strained MQW for 1.3 µm waveguide modulators,” Appl. Phys. Lett. 63, 1833–1835 (1993).
[CrossRef]

Chin, M. K.

M. K. Chin, W. S. C. Chang, “Electroabsorption properties of InGaAs/InAlAs MQW structures at 1.5 µm,” IEEE Photon. Technol. Lett. 6, 502–504 (1994).
[CrossRef]

Clark, A.

M. G. Xu, T. A. Fisher, J. M. Dell, A. Clark, “Wide optical bandwidth asymmetric Fabry-Perot reflection modulator using the quantum confined Stark effect,” J. Appl. Phys. 84, 5761–5765 (1998).
[CrossRef]

Coldren, L. A.

C. C. Barron, C. J. Mahon, B. J. Thibeault, L. A. Coldren, “Design, fabrication and characterization of high-speed asymmetric Fabry-Perot modulators for optical interconnect applications,” Opt. Quantum Electron. 25, S885–S898 (1993).
[CrossRef]

K.-K. Law, J. L. Merz, L. A. Coldren, “The effect of layer thickness variations on the performance of asymmetric Fabry-Perot reflection modulators,” J. Appl. Phys. 72, 855–869 (1992).
[CrossRef]

Dell, J. M.

M. G. Xu, B. D. Nener, J. M. Dell, “Design of externally tuned asymmetric fibre Fabry-Perot electroabsorption optical modulators,” IEE Proc. Optoelectron. 145, 344–352 (1998).
[CrossRef]

M. G. Xu, T. A. Fisher, J. M. Dell, A. Clark, “Wide optical bandwidth asymmetric Fabry-Perot reflection modulator using the quantum confined Stark effect,” J. Appl. Phys. 84, 5761–5765 (1998).
[CrossRef]

Englemann, R. W. H.

K. W. Jelley, R. W. H. Englemann, K. Alavi, H. Lee, “Well size related limitations on maximum electroabsorption in GaAs/AlGaAs MQW Structures,” Appl. Phys. Lett. 55, 70–72 (1989).
[CrossRef]

Fisher, T. A.

M. G. Xu, T. A. Fisher, J. M. Dell, A. Clark, “Wide optical bandwidth asymmetric Fabry-Perot reflection modulator using the quantum confined Stark effect,” J. Appl. Phys. 84, 5761–5765 (1998).
[CrossRef]

Garmire, E.

B. G. Kim, E. Garmire, “Comparison between the matrix method and the coupled-wave method in the analysis of Bragg reflector structures,” J. Opt. Soc. Am. A. 9, 132–136 (1992).
[CrossRef]

M. R. Ramadas, E. Garmire, A. K. Ghatak, K. Thygarajan, M. R. Shenoy, “Analysis of absorbing and leaky planar waveguides: a novel method,” Opt. Lett. 14, 376–378 (1989).
[CrossRef] [PubMed]

See, for example, E. Garmire, “Criteria for optical bistability in lossy saturating Fabry-Perots,” IEEE J. Quantum Electron. 25, 289–295 (1989).

Ghatak, A. K.

Harris, J. S.

K. Bacher, B. Pezeshki, S. M. Lord, J. S. Harris, “Molecular beam epitaxy growth of vertical cavity optical devices with in situ corrections,” Appl. Phys. Lett. 61, 1387–1391 (1992).
[CrossRef]

B. Pezeshki, S. M. Lord, T. B. Boykin, J. S. Harris, “GaAs/AlAs quantum wells for electroabsorption modulators,” Appl. Phys. Lett. 60, 2779–2781 (1992).
[CrossRef]

B. Pezeshki, S. M. Lord, J. S. Harris, “Electroabsorptive modulators in InGaAs/AlGaAs,” Appl. Phys. Lett. 59, 888–890 (1991).
[CrossRef]

B. Pezeshki, J. S. Harris, “Optimization of modulation ratio and insertion loss in reflective electroabsorption modulators,” Appl. Phys. Lett. 57, 1491–1493 (1990).
[CrossRef]

B. Pezeshki, D. Thomas, J. S. Harris, “Optimization of reflection electroabsorption modulators,” in Physical concepts of materials for novel optoelectronic device applications II: Device physics and applications, M. Razeghi, ed., Proc. SPIE1362, 559–565 (1991).
[CrossRef]

Hou, H. Q.

H. Q. Hou, A. N. Cheng, H. H. Wieder, W. S. C. Chang, C. W. Tu, “Electroabsorption of InAlAs/InP strained MQW for 1.3 µm waveguide modulators,” Appl. Phys. Lett. 63, 1833–1835 (1993).
[CrossRef]

Jelley, K. W.

K. W. Jelley, R. W. H. Englemann, K. Alavi, H. Lee, “Well size related limitations on maximum electroabsorption in GaAs/AlGaAs MQW Structures,” Appl. Phys. Lett. 55, 70–72 (1989).
[CrossRef]

Killey, R. I.

Kim, B. G.

B. G. Kim, E. Garmire, “Comparison between the matrix method and the coupled-wave method in the analysis of Bragg reflector structures,” J. Opt. Soc. Am. A. 9, 132–136 (1992).
[CrossRef]

Law, K.-K.

K.-K. Law, J. L. Merz, L. A. Coldren, “The effect of layer thickness variations on the performance of asymmetric Fabry-Perot reflection modulators,” J. Appl. Phys. 72, 855–869 (1992).
[CrossRef]

Leavitt, R. P.

R. P. Leavitt, J. L. Bradshaw, J. T. Pham, “Superlattice-equivalent (In,Ga)As/(In,Al)As quantum wells with large Stark shifts in the 1.3 µm spectral region,” Appl. Phys. Lett. 66, 1803–1805 (1995).
[CrossRef]

Lee, H.

K. W. Jelley, R. W. H. Englemann, K. Alavi, H. Lee, “Well size related limitations on maximum electroabsorption in GaAs/AlGaAs MQW Structures,” Appl. Phys. Lett. 55, 70–72 (1989).
[CrossRef]

Lord, S. M.

B. Pezeshki, S. M. Lord, T. B. Boykin, J. S. Harris, “GaAs/AlAs quantum wells for electroabsorption modulators,” Appl. Phys. Lett. 60, 2779–2781 (1992).
[CrossRef]

K. Bacher, B. Pezeshki, S. M. Lord, J. S. Harris, “Molecular beam epitaxy growth of vertical cavity optical devices with in situ corrections,” Appl. Phys. Lett. 61, 1387–1391 (1992).
[CrossRef]

B. Pezeshki, S. M. Lord, J. S. Harris, “Electroabsorptive modulators in InGaAs/AlGaAs,” Appl. Phys. Lett. 59, 888–890 (1991).
[CrossRef]

Mahon, C. J.

C. C. Barron, C. J. Mahon, B. J. Thibeault, L. A. Coldren, “Design, fabrication and characterization of high-speed asymmetric Fabry-Perot modulators for optical interconnect applications,” Opt. Quantum Electron. 25, S885–S898 (1993).
[CrossRef]

Merz, J. L.

K.-K. Law, J. L. Merz, L. A. Coldren, “The effect of layer thickness variations on the performance of asymmetric Fabry-Perot reflection modulators,” J. Appl. Phys. 72, 855–869 (1992).
[CrossRef]

Nener, B. D.

M. G. Xu, B. D. Nener, J. M. Dell, “Design of externally tuned asymmetric fibre Fabry-Perot electroabsorption optical modulators,” IEE Proc. Optoelectron. 145, 344–352 (1998).
[CrossRef]

Parry, G.

R. I. Killey, M. Whitehead, P. N. Stavrinou, G. Parry, C. C. Button, “Design of InGaAsP multiple quantum-well Fabry-Perot modulators for soliton control,” J. Lightwave Technol. 17, 1408–1413 (1999).
[CrossRef]

P. Zouganeli, G. Parry, “Evaluation of the tolerance of asymmetric Fabry-Perot modulators with respect to realistic operating conditions,” IEEE J. Quantum Electron. 31, 1140–1151 (1995).
[CrossRef]

P. Zouganeli, P. J. Stevens, D. Atkinson, G. Parry, “Design trade-offs and evaluation of the performance attainable by GaAs-Al0.3Ga0.7As asymmetric Fabry-Perot modulators,” IEEE J. Quantum Electron. 31, 927–943 (1995).
[CrossRef]

G. Parry, M. Whitehead, P. Stevens, A. Rivers, P. Bartnes, D. Atkinson, “The design and application of III-V MQW optical modulators,” Phys. Scr. T35, 210 (1991).
[CrossRef]

Pezeshki, B.

B. Pezeshki, S. M. Lord, T. B. Boykin, J. S. Harris, “GaAs/AlAs quantum wells for electroabsorption modulators,” Appl. Phys. Lett. 60, 2779–2781 (1992).
[CrossRef]

K. Bacher, B. Pezeshki, S. M. Lord, J. S. Harris, “Molecular beam epitaxy growth of vertical cavity optical devices with in situ corrections,” Appl. Phys. Lett. 61, 1387–1391 (1992).
[CrossRef]

B. Pezeshki, S. M. Lord, J. S. Harris, “Electroabsorptive modulators in InGaAs/AlGaAs,” Appl. Phys. Lett. 59, 888–890 (1991).
[CrossRef]

B. Pezeshki, J. S. Harris, “Optimization of modulation ratio and insertion loss in reflective electroabsorption modulators,” Appl. Phys. Lett. 57, 1491–1493 (1990).
[CrossRef]

B. Pezeshki, D. Thomas, J. S. Harris, “Optimization of reflection electroabsorption modulators,” in Physical concepts of materials for novel optoelectronic device applications II: Device physics and applications, M. Razeghi, ed., Proc. SPIE1362, 559–565 (1991).
[CrossRef]

Pham, J. T.

R. P. Leavitt, J. L. Bradshaw, J. T. Pham, “Superlattice-equivalent (In,Ga)As/(In,Al)As quantum wells with large Stark shifts in the 1.3 µm spectral region,” Appl. Phys. Lett. 66, 1803–1805 (1995).
[CrossRef]

Ramadas, M. R.

Rivers, A.

G. Parry, M. Whitehead, P. Stevens, A. Rivers, P. Bartnes, D. Atkinson, “The design and application of III-V MQW optical modulators,” Phys. Scr. T35, 210 (1991).
[CrossRef]

Shenoy, M. R.

Stavrinou, P. N.

Stevens, P.

G. Parry, M. Whitehead, P. Stevens, A. Rivers, P. Bartnes, D. Atkinson, “The design and application of III-V MQW optical modulators,” Phys. Scr. T35, 210 (1991).
[CrossRef]

Stevens, P. J.

P. Zouganeli, P. J. Stevens, D. Atkinson, G. Parry, “Design trade-offs and evaluation of the performance attainable by GaAs-Al0.3Ga0.7As asymmetric Fabry-Perot modulators,” IEEE J. Quantum Electron. 31, 927–943 (1995).
[CrossRef]

Thibeault, B. J.

C. C. Barron, C. J. Mahon, B. J. Thibeault, L. A. Coldren, “Design, fabrication and characterization of high-speed asymmetric Fabry-Perot modulators for optical interconnect applications,” Opt. Quantum Electron. 25, S885–S898 (1993).
[CrossRef]

Thomas, D.

B. Pezeshki, D. Thomas, J. S. Harris, “Optimization of reflection electroabsorption modulators,” in Physical concepts of materials for novel optoelectronic device applications II: Device physics and applications, M. Razeghi, ed., Proc. SPIE1362, 559–565 (1991).
[CrossRef]

Thygarajan, K.

Tu, C. W.

H. Q. Hou, A. N. Cheng, H. H. Wieder, W. S. C. Chang, C. W. Tu, “Electroabsorption of InAlAs/InP strained MQW for 1.3 µm waveguide modulators,” Appl. Phys. Lett. 63, 1833–1835 (1993).
[CrossRef]

Whitehead, M.

R. I. Killey, M. Whitehead, P. N. Stavrinou, G. Parry, C. C. Button, “Design of InGaAsP multiple quantum-well Fabry-Perot modulators for soliton control,” J. Lightwave Technol. 17, 1408–1413 (1999).
[CrossRef]

G. Parry, M. Whitehead, P. Stevens, A. Rivers, P. Bartnes, D. Atkinson, “The design and application of III-V MQW optical modulators,” Phys. Scr. T35, 210 (1991).
[CrossRef]

Wieder, H. H.

H. Q. Hou, A. N. Cheng, H. H. Wieder, W. S. C. Chang, C. W. Tu, “Electroabsorption of InAlAs/InP strained MQW for 1.3 µm waveguide modulators,” Appl. Phys. Lett. 63, 1833–1835 (1993).
[CrossRef]

Xu, M. G.

M. G. Xu, T. A. Fisher, J. M. Dell, A. Clark, “Wide optical bandwidth asymmetric Fabry-Perot reflection modulator using the quantum confined Stark effect,” J. Appl. Phys. 84, 5761–5765 (1998).
[CrossRef]

M. G. Xu, B. D. Nener, J. M. Dell, “Design of externally tuned asymmetric fibre Fabry-Perot electroabsorption optical modulators,” IEE Proc. Optoelectron. 145, 344–352 (1998).
[CrossRef]

Zouganeli, P.

P. Zouganeli, P. J. Stevens, D. Atkinson, G. Parry, “Design trade-offs and evaluation of the performance attainable by GaAs-Al0.3Ga0.7As asymmetric Fabry-Perot modulators,” IEEE J. Quantum Electron. 31, 927–943 (1995).
[CrossRef]

P. Zouganeli, G. Parry, “Evaluation of the tolerance of asymmetric Fabry-Perot modulators with respect to realistic operating conditions,” IEEE J. Quantum Electron. 31, 1140–1151 (1995).
[CrossRef]

Appl. Phys. Lett.

B. Pezeshki, J. S. Harris, “Optimization of modulation ratio and insertion loss in reflective electroabsorption modulators,” Appl. Phys. Lett. 57, 1491–1493 (1990).
[CrossRef]

B. Pezeshki, S. M. Lord, J. S. Harris, “Electroabsorptive modulators in InGaAs/AlGaAs,” Appl. Phys. Lett. 59, 888–890 (1991).
[CrossRef]

B. Pezeshki, S. M. Lord, T. B. Boykin, J. S. Harris, “GaAs/AlAs quantum wells for electroabsorption modulators,” Appl. Phys. Lett. 60, 2779–2781 (1992).
[CrossRef]

H. Q. Hou, A. N. Cheng, H. H. Wieder, W. S. C. Chang, C. W. Tu, “Electroabsorption of InAlAs/InP strained MQW for 1.3 µm waveguide modulators,” Appl. Phys. Lett. 63, 1833–1835 (1993).
[CrossRef]

R. P. Leavitt, J. L. Bradshaw, J. T. Pham, “Superlattice-equivalent (In,Ga)As/(In,Al)As quantum wells with large Stark shifts in the 1.3 µm spectral region,” Appl. Phys. Lett. 66, 1803–1805 (1995).
[CrossRef]

K. W. Jelley, R. W. H. Englemann, K. Alavi, H. Lee, “Well size related limitations on maximum electroabsorption in GaAs/AlGaAs MQW Structures,” Appl. Phys. Lett. 55, 70–72 (1989).
[CrossRef]

K. Bacher, B. Pezeshki, S. M. Lord, J. S. Harris, “Molecular beam epitaxy growth of vertical cavity optical devices with in situ corrections,” Appl. Phys. Lett. 61, 1387–1391 (1992).
[CrossRef]

IEE Proc. Optoelectron.

M. G. Xu, B. D. Nener, J. M. Dell, “Design of externally tuned asymmetric fibre Fabry-Perot electroabsorption optical modulators,” IEE Proc. Optoelectron. 145, 344–352 (1998).
[CrossRef]

IEEE J. Quantum Electron.

See, for example, E. Garmire, “Criteria for optical bistability in lossy saturating Fabry-Perots,” IEEE J. Quantum Electron. 25, 289–295 (1989).

P. Zouganeli, P. J. Stevens, D. Atkinson, G. Parry, “Design trade-offs and evaluation of the performance attainable by GaAs-Al0.3Ga0.7As asymmetric Fabry-Perot modulators,” IEEE J. Quantum Electron. 31, 927–943 (1995).
[CrossRef]

P. Zouganeli, G. Parry, “Evaluation of the tolerance of asymmetric Fabry-Perot modulators with respect to realistic operating conditions,” IEEE J. Quantum Electron. 31, 1140–1151 (1995).
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[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Reflectivity of an electroabsorptive asymmetric Fabry-Perot (AFP) modulator in the on state, as a function of the front-mirror reflectivity R f , for various values of back-mirror reflectivity R b , at two different material figures of merit β = Δα/α+. The lower set of curves have the same values of R b as the upper set.

Fig. 2
Fig. 2

Reflectivity of an AFP electroabsorption modulator in the on state when back-mirror reflectivity R b = 1, as a function of the fractional absorption change β. The material figure of merit f is also shown. Four curves overlap each other, corresponding to different front-mirror reflectivities R f . The triangles represent the simplified model: R on = β2/(2 - β)2.

Fig. 3
Fig. 3

Reflectivity as a function of half round-trip phase ϕ = 2πnL/λ for an AFP electroabsorption modulator using the quantum confined Stark effect in GaAs/AlGaAs quantum wells. Two loss values are assumed with β = 0.9: α+L = 0.6 and α-L = 0.06. (a) The normally on configuration in which impedance match (and zero AFP reflectivity) take place under high QW loss at V = V o . (b) The normally off configuration in which impedance match and zero AFP reflectivity take place under low QW loss, at V = 0. Both modulators have the same reflectivity in the on state.

Fig. 4
Fig. 4

Difference between on-state and off-state AFP reflectivities, DRR on - R off, as a function of the parameter describing deviation from impedance match ζ ≡ δα/α+ for various values of material parameter β.

Fig. 5
Fig. 5

Maximum AFP reflectivity change DRR on - R off determined from the data of Fig. 4, as a function of β, along with the corresponding AFP reflectivities R on,max and R off,max, as well as the impedance-matched value R o . Also shown are the log of the corresponding contrast ratio CR = R on/R off (dashed curve) as well as the values of ζ at which the maximum occurred, ζmax. The magnitude of the last two parameters is denoted on the right-hand side scale.

Tables (1)

Tables Icon

Table 1 Operating Loss Conditions at Impedance Match for Different Modulator Designs

Equations (30)

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RFP=R0+F sin2 ϕ1+F sin2 ϕ,
R0=Rf1-Re/Rf21-Re2,
ReRfRb1/2 exp-αL.
Rf=Rb exp-2αiL,
Ron=Rf1-Rb/Rfβ/221-RfRb/Rfβ/22,
Ron=Rb exp-2αiL×1-expΔαL21-Rb exp-2αiLexpΔαL2,
Ro=β2-β2=f2+f2=X-1X+12,
Rb=exp-2αcL.
Ron=β22-β+2γ2.
Ron=Ro1-4γ/2-β,
1-Rb<xαiL/2.
Ronδϕ=Ron0+Fδϕ21-Ron0.
F=1/αsL2,
δRonRonδϕ-Ron01-RonδϕαsL2.
δRon=4π21-Ronδnαsλ2.
δRoff=4Rf1-Rf2 δϕ2.
δRoff=δϕαTL2,
δRoff=2πδnαTλ2,
δRoff=2πnαTλ2δλλ2.
Re=Rf expδαL.
δRoff=δαL2Rf1-Rf2.
δRoff=δα/2αT2.
Ron=1/Rf1-1-Rf1-Re2.
δRoff,ϕ=2πnα+λ2δLL2.
δRoff,α=α+δL2Rf1-Rf2=α+δL22α+L2=δL2L2.
δRoff=2πnα+λ2+14δLL2.
Ron=Rf1-expδαLexpΔαL21-Rf expδαLexpΔαL2,
Ron=Δα+δα22αo-Δα-δα2.
Ron=β+ζ22-β+ζ2.
DRRon-Roff=β+ζ22-β+ζ2-ζ22+ζ2.

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