Abstract

Rabi splitting in quantum well (QW) embedded in microcavities under strong coupling condition is modeled by a time-dependent transfer matrix model. The spectral response of QW under the influence of excitonic effects is simulated by infinite impulse digital filters. It is shown that the splitting energy obtained from the proposed model match well with that deduced from the reflection spectrum analysis. The lasing spectra observed from different transmission angles of the QW microcavity can also be calculated. Hence, it is proved that the proposed model can be used to design and analyze the lasing characteristics of QW microcavities under strong coupling condition.

© 2008 Optical Society of America

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  1. S. Sato, "Liquid-crystal lens-cells with variable focal length," Jpn. J. Appl. Phys. 18, 1679-1684 (1979).
  2. H. Ren and S. T. Wu, "Inhomogeneous polymer-dispersed liquid crystals with gradient refractive index," Appl. Phys. Lett. 81, 3537-3539 (2002).
    [CrossRef]
  3. H. Ren, Y. H. Fan, and S. T. Wu, "Tunable Fresnel lens using nanoscale polymer-dispersed liquid crystals," Appl. Phys. Lett. 83, 1515-1517 (2003).
    [CrossRef] [PubMed]
  4. H. Ren, D. W. Fox, B. Wu, and S. T. Wu, "Liquid crystal lens with large focal length tunability and low operating voltage," Opt. Express 15, 11328-11335 (2007).
    [CrossRef]
  5. M. Ye, B. Wang, and S. Sato, "Liquid crystal lens with focal length variable from negative to positive values," IEEE Photon. Technol. Lett. 18, 78-81 (2006).
    [CrossRef] [PubMed]
  6. H. Ren, Y.-H. Fan, S. Gauza, and S. T. Wu, "Tunable-focus flat liquid crystal spherical lens," Appl. Phys. Lett. 84, 4789-4791 (2004).
    [CrossRef]
  7. T. Nose and S. Sato, "A liquid crystal microlens obtained with a nonuniform electric field," Liq. Cryst. 5, 1425-1433 (1989).
    [CrossRef]
  8. B. Wang, M. Ye, and S. Sato, "Experimental and numerical studies on liquid crystal lens with spherical electrode," Mol. Cryst. Liq. Cryst. 433, 217-227 (2005).
    [CrossRef]
  9. B. Wang, M. Ye, M. Honma, T. Nose, and S. Sato, "Liquid crystal lens with spherical electrode," Jpn. J. Appl. Phys. 41, L1232-L1233 (2002).
  10. H. Ren and S. T. Wu, "Adaptive liquid crystal lens with large focal length tenability," Opt. Express 14, 11292-11298 (2006)
    [CrossRef]
  11. P. J. W. Hands, A. K. Kirby, and G. D. Love, "Adaptive modally addressed liquid crystal lenses," Proc. SPIE 5518, 136-143 (2004).
    [CrossRef] [PubMed]
  12. M. Ye, S. Hayasaka, and S. Sato, "Liquid Crystal Lens Array with Hexagonal-Hole-Patterned Electrodes," Jpn. J. of Appl. Phys. 43, 6108-6111 (2004).
    [CrossRef]
  13. B. Wang, M. Ye, and S. Sato, "Liquid crystal lens with stacked structure of liquid-crystal layers," Opt. Commun. 250, 266-273 (2005)
  14. M. Ye, B. Wang, and S. Sato, "Liquid crystal lens with focus movable in focal plane," Opt. Commun. 259, 710-722 (2006)
  15. N. A. Clark, M. A. Handschy, and S. T. Lagerwall, "Ferroelectric Liquid Crystal Electro-optic using The Surface Stabilized Structure," Mol. Cryst. Liq. Cryst. 94, 213-234 (1983).
  16. Y. H. Fan, H. Ren, and S. T. Wu, "Electrically switchable Fresnel lens using a polymer-separated composite film," Opt. Express 13, 4141-4147 (2005).
  17. V. Y. Reshetnyak, S. L. Subota, and T. V. Galstian, "Theoretical analyses of the electric field control of focal length in a gradient polymer stabilized liquid crystal lens," Mol. Cryst. Liq. Cryst. 454, 187-200 (2006).
  18. M. Honma, T. Nose, and S. Sato, "Improvement of aberration properties of liquid crystal microlenses using the stacked electrode structure," Jpn. J. of Appl. Phys. 40, 1322-1327 (2001).
  19. M. Ye and S. Sato, "Optical Properties of Liquid Crystal Lens of Any Size," Jpn. J. Appl. Phys. 41, 571-573 (2002).
  20. M. Ye, B. Wang, M. Kawamura, and S. Sato, "Image Formation using Liquid Crystal Lens," Jpn. J. Appl. Phys. 46, 6776-6777 (2007).
  21. M. Ye and S. Sato, "Enhancement of focusing power of liquid crystal lens by new cell structure," Mol. Cryst. Liq. Cryst. 413, 417-421 (2004).
  22. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1968).

2007

H. Ren, D. W. Fox, B. Wu, and S. T. Wu, "Liquid crystal lens with large focal length tunability and low operating voltage," Opt. Express 15, 11328-11335 (2007).
[CrossRef]

M. Ye, B. Wang, M. Kawamura, and S. Sato, "Image Formation using Liquid Crystal Lens," Jpn. J. Appl. Phys. 46, 6776-6777 (2007).

2006

M. Ye, B. Wang, and S. Sato, "Liquid crystal lens with focal length variable from negative to positive values," IEEE Photon. Technol. Lett. 18, 78-81 (2006).
[CrossRef] [PubMed]

H. Ren and S. T. Wu, "Adaptive liquid crystal lens with large focal length tenability," Opt. Express 14, 11292-11298 (2006)
[CrossRef]

M. Ye, B. Wang, and S. Sato, "Liquid crystal lens with focus movable in focal plane," Opt. Commun. 259, 710-722 (2006)

V. Y. Reshetnyak, S. L. Subota, and T. V. Galstian, "Theoretical analyses of the electric field control of focal length in a gradient polymer stabilized liquid crystal lens," Mol. Cryst. Liq. Cryst. 454, 187-200 (2006).

2005

B. Wang, M. Ye, and S. Sato, "Liquid crystal lens with stacked structure of liquid-crystal layers," Opt. Commun. 250, 266-273 (2005)

B. Wang, M. Ye, and S. Sato, "Experimental and numerical studies on liquid crystal lens with spherical electrode," Mol. Cryst. Liq. Cryst. 433, 217-227 (2005).
[CrossRef]

Y. H. Fan, H. Ren, and S. T. Wu, "Electrically switchable Fresnel lens using a polymer-separated composite film," Opt. Express 13, 4141-4147 (2005).

2004

M. Ye and S. Sato, "Enhancement of focusing power of liquid crystal lens by new cell structure," Mol. Cryst. Liq. Cryst. 413, 417-421 (2004).

H. Ren, Y.-H. Fan, S. Gauza, and S. T. Wu, "Tunable-focus flat liquid crystal spherical lens," Appl. Phys. Lett. 84, 4789-4791 (2004).
[CrossRef]

P. J. W. Hands, A. K. Kirby, and G. D. Love, "Adaptive modally addressed liquid crystal lenses," Proc. SPIE 5518, 136-143 (2004).
[CrossRef] [PubMed]

M. Ye, S. Hayasaka, and S. Sato, "Liquid Crystal Lens Array with Hexagonal-Hole-Patterned Electrodes," Jpn. J. of Appl. Phys. 43, 6108-6111 (2004).
[CrossRef]

2003

H. Ren, Y. H. Fan, and S. T. Wu, "Tunable Fresnel lens using nanoscale polymer-dispersed liquid crystals," Appl. Phys. Lett. 83, 1515-1517 (2003).
[CrossRef] [PubMed]

2002

B. Wang, M. Ye, M. Honma, T. Nose, and S. Sato, "Liquid crystal lens with spherical electrode," Jpn. J. Appl. Phys. 41, L1232-L1233 (2002).

H. Ren and S. T. Wu, "Inhomogeneous polymer-dispersed liquid crystals with gradient refractive index," Appl. Phys. Lett. 81, 3537-3539 (2002).
[CrossRef]

M. Ye and S. Sato, "Optical Properties of Liquid Crystal Lens of Any Size," Jpn. J. Appl. Phys. 41, 571-573 (2002).

2001

M. Honma, T. Nose, and S. Sato, "Improvement of aberration properties of liquid crystal microlenses using the stacked electrode structure," Jpn. J. of Appl. Phys. 40, 1322-1327 (2001).

1989

T. Nose and S. Sato, "A liquid crystal microlens obtained with a nonuniform electric field," Liq. Cryst. 5, 1425-1433 (1989).
[CrossRef]

1983

N. A. Clark, M. A. Handschy, and S. T. Lagerwall, "Ferroelectric Liquid Crystal Electro-optic using The Surface Stabilized Structure," Mol. Cryst. Liq. Cryst. 94, 213-234 (1983).

1979

S. Sato, "Liquid-crystal lens-cells with variable focal length," Jpn. J. Appl. Phys. 18, 1679-1684 (1979).

Clark, N. A.

N. A. Clark, M. A. Handschy, and S. T. Lagerwall, "Ferroelectric Liquid Crystal Electro-optic using The Surface Stabilized Structure," Mol. Cryst. Liq. Cryst. 94, 213-234 (1983).

Fan, Y. H.

Y. H. Fan, H. Ren, and S. T. Wu, "Electrically switchable Fresnel lens using a polymer-separated composite film," Opt. Express 13, 4141-4147 (2005).

H. Ren, Y. H. Fan, and S. T. Wu, "Tunable Fresnel lens using nanoscale polymer-dispersed liquid crystals," Appl. Phys. Lett. 83, 1515-1517 (2003).
[CrossRef] [PubMed]

Fan, Y.-H.

H. Ren, Y.-H. Fan, S. Gauza, and S. T. Wu, "Tunable-focus flat liquid crystal spherical lens," Appl. Phys. Lett. 84, 4789-4791 (2004).
[CrossRef]

Fox, D. W.

Galstian, T. V.

V. Y. Reshetnyak, S. L. Subota, and T. V. Galstian, "Theoretical analyses of the electric field control of focal length in a gradient polymer stabilized liquid crystal lens," Mol. Cryst. Liq. Cryst. 454, 187-200 (2006).

Gauza, S.

H. Ren, Y.-H. Fan, S. Gauza, and S. T. Wu, "Tunable-focus flat liquid crystal spherical lens," Appl. Phys. Lett. 84, 4789-4791 (2004).
[CrossRef]

Hands, P. J. W.

P. J. W. Hands, A. K. Kirby, and G. D. Love, "Adaptive modally addressed liquid crystal lenses," Proc. SPIE 5518, 136-143 (2004).
[CrossRef] [PubMed]

Handschy, M. A.

N. A. Clark, M. A. Handschy, and S. T. Lagerwall, "Ferroelectric Liquid Crystal Electro-optic using The Surface Stabilized Structure," Mol. Cryst. Liq. Cryst. 94, 213-234 (1983).

Hayasaka, S.

M. Ye, S. Hayasaka, and S. Sato, "Liquid Crystal Lens Array with Hexagonal-Hole-Patterned Electrodes," Jpn. J. of Appl. Phys. 43, 6108-6111 (2004).
[CrossRef]

Honma, M.

B. Wang, M. Ye, M. Honma, T. Nose, and S. Sato, "Liquid crystal lens with spherical electrode," Jpn. J. Appl. Phys. 41, L1232-L1233 (2002).

M. Honma, T. Nose, and S. Sato, "Improvement of aberration properties of liquid crystal microlenses using the stacked electrode structure," Jpn. J. of Appl. Phys. 40, 1322-1327 (2001).

Kawamura, M.

M. Ye, B. Wang, M. Kawamura, and S. Sato, "Image Formation using Liquid Crystal Lens," Jpn. J. Appl. Phys. 46, 6776-6777 (2007).

Kirby, A. K.

P. J. W. Hands, A. K. Kirby, and G. D. Love, "Adaptive modally addressed liquid crystal lenses," Proc. SPIE 5518, 136-143 (2004).
[CrossRef] [PubMed]

Lagerwall, S. T.

N. A. Clark, M. A. Handschy, and S. T. Lagerwall, "Ferroelectric Liquid Crystal Electro-optic using The Surface Stabilized Structure," Mol. Cryst. Liq. Cryst. 94, 213-234 (1983).

Love, G. D.

P. J. W. Hands, A. K. Kirby, and G. D. Love, "Adaptive modally addressed liquid crystal lenses," Proc. SPIE 5518, 136-143 (2004).
[CrossRef] [PubMed]

Nose, T.

B. Wang, M. Ye, M. Honma, T. Nose, and S. Sato, "Liquid crystal lens with spherical electrode," Jpn. J. Appl. Phys. 41, L1232-L1233 (2002).

M. Honma, T. Nose, and S. Sato, "Improvement of aberration properties of liquid crystal microlenses using the stacked electrode structure," Jpn. J. of Appl. Phys. 40, 1322-1327 (2001).

T. Nose and S. Sato, "A liquid crystal microlens obtained with a nonuniform electric field," Liq. Cryst. 5, 1425-1433 (1989).
[CrossRef]

Ren, H.

H. Ren, D. W. Fox, B. Wu, and S. T. Wu, "Liquid crystal lens with large focal length tunability and low operating voltage," Opt. Express 15, 11328-11335 (2007).
[CrossRef]

H. Ren and S. T. Wu, "Adaptive liquid crystal lens with large focal length tenability," Opt. Express 14, 11292-11298 (2006)
[CrossRef]

Y. H. Fan, H. Ren, and S. T. Wu, "Electrically switchable Fresnel lens using a polymer-separated composite film," Opt. Express 13, 4141-4147 (2005).

H. Ren, Y.-H. Fan, S. Gauza, and S. T. Wu, "Tunable-focus flat liquid crystal spherical lens," Appl. Phys. Lett. 84, 4789-4791 (2004).
[CrossRef]

H. Ren, Y. H. Fan, and S. T. Wu, "Tunable Fresnel lens using nanoscale polymer-dispersed liquid crystals," Appl. Phys. Lett. 83, 1515-1517 (2003).
[CrossRef] [PubMed]

H. Ren and S. T. Wu, "Inhomogeneous polymer-dispersed liquid crystals with gradient refractive index," Appl. Phys. Lett. 81, 3537-3539 (2002).
[CrossRef]

Reshetnyak, V. Y.

V. Y. Reshetnyak, S. L. Subota, and T. V. Galstian, "Theoretical analyses of the electric field control of focal length in a gradient polymer stabilized liquid crystal lens," Mol. Cryst. Liq. Cryst. 454, 187-200 (2006).

Sato, S.

M. Ye, B. Wang, M. Kawamura, and S. Sato, "Image Formation using Liquid Crystal Lens," Jpn. J. Appl. Phys. 46, 6776-6777 (2007).

M. Ye, B. Wang, and S. Sato, "Liquid crystal lens with focus movable in focal plane," Opt. Commun. 259, 710-722 (2006)

M. Ye, B. Wang, and S. Sato, "Liquid crystal lens with focal length variable from negative to positive values," IEEE Photon. Technol. Lett. 18, 78-81 (2006).
[CrossRef] [PubMed]

B. Wang, M. Ye, and S. Sato, "Experimental and numerical studies on liquid crystal lens with spherical electrode," Mol. Cryst. Liq. Cryst. 433, 217-227 (2005).
[CrossRef]

B. Wang, M. Ye, and S. Sato, "Liquid crystal lens with stacked structure of liquid-crystal layers," Opt. Commun. 250, 266-273 (2005)

M. Ye and S. Sato, "Enhancement of focusing power of liquid crystal lens by new cell structure," Mol. Cryst. Liq. Cryst. 413, 417-421 (2004).

M. Ye, S. Hayasaka, and S. Sato, "Liquid Crystal Lens Array with Hexagonal-Hole-Patterned Electrodes," Jpn. J. of Appl. Phys. 43, 6108-6111 (2004).
[CrossRef]

B. Wang, M. Ye, M. Honma, T. Nose, and S. Sato, "Liquid crystal lens with spherical electrode," Jpn. J. Appl. Phys. 41, L1232-L1233 (2002).

M. Ye and S. Sato, "Optical Properties of Liquid Crystal Lens of Any Size," Jpn. J. Appl. Phys. 41, 571-573 (2002).

M. Honma, T. Nose, and S. Sato, "Improvement of aberration properties of liquid crystal microlenses using the stacked electrode structure," Jpn. J. of Appl. Phys. 40, 1322-1327 (2001).

T. Nose and S. Sato, "A liquid crystal microlens obtained with a nonuniform electric field," Liq. Cryst. 5, 1425-1433 (1989).
[CrossRef]

S. Sato, "Liquid-crystal lens-cells with variable focal length," Jpn. J. Appl. Phys. 18, 1679-1684 (1979).

Subota, S. L.

V. Y. Reshetnyak, S. L. Subota, and T. V. Galstian, "Theoretical analyses of the electric field control of focal length in a gradient polymer stabilized liquid crystal lens," Mol. Cryst. Liq. Cryst. 454, 187-200 (2006).

Wang, B.

M. Ye, B. Wang, M. Kawamura, and S. Sato, "Image Formation using Liquid Crystal Lens," Jpn. J. Appl. Phys. 46, 6776-6777 (2007).

M. Ye, B. Wang, and S. Sato, "Liquid crystal lens with focus movable in focal plane," Opt. Commun. 259, 710-722 (2006)

M. Ye, B. Wang, and S. Sato, "Liquid crystal lens with focal length variable from negative to positive values," IEEE Photon. Technol. Lett. 18, 78-81 (2006).
[CrossRef] [PubMed]

B. Wang, M. Ye, and S. Sato, "Experimental and numerical studies on liquid crystal lens with spherical electrode," Mol. Cryst. Liq. Cryst. 433, 217-227 (2005).
[CrossRef]

B. Wang, M. Ye, and S. Sato, "Liquid crystal lens with stacked structure of liquid-crystal layers," Opt. Commun. 250, 266-273 (2005)

B. Wang, M. Ye, M. Honma, T. Nose, and S. Sato, "Liquid crystal lens with spherical electrode," Jpn. J. Appl. Phys. 41, L1232-L1233 (2002).

Wu, B.

Wu, S. T.

H. Ren, D. W. Fox, B. Wu, and S. T. Wu, "Liquid crystal lens with large focal length tunability and low operating voltage," Opt. Express 15, 11328-11335 (2007).
[CrossRef]

H. Ren and S. T. Wu, "Adaptive liquid crystal lens with large focal length tenability," Opt. Express 14, 11292-11298 (2006)
[CrossRef]

Y. H. Fan, H. Ren, and S. T. Wu, "Electrically switchable Fresnel lens using a polymer-separated composite film," Opt. Express 13, 4141-4147 (2005).

H. Ren, Y.-H. Fan, S. Gauza, and S. T. Wu, "Tunable-focus flat liquid crystal spherical lens," Appl. Phys. Lett. 84, 4789-4791 (2004).
[CrossRef]

H. Ren, Y. H. Fan, and S. T. Wu, "Tunable Fresnel lens using nanoscale polymer-dispersed liquid crystals," Appl. Phys. Lett. 83, 1515-1517 (2003).
[CrossRef] [PubMed]

H. Ren and S. T. Wu, "Inhomogeneous polymer-dispersed liquid crystals with gradient refractive index," Appl. Phys. Lett. 81, 3537-3539 (2002).
[CrossRef]

Ye, M.

M. Ye, B. Wang, M. Kawamura, and S. Sato, "Image Formation using Liquid Crystal Lens," Jpn. J. Appl. Phys. 46, 6776-6777 (2007).

M. Ye, B. Wang, and S. Sato, "Liquid crystal lens with focus movable in focal plane," Opt. Commun. 259, 710-722 (2006)

M. Ye, B. Wang, and S. Sato, "Liquid crystal lens with focal length variable from negative to positive values," IEEE Photon. Technol. Lett. 18, 78-81 (2006).
[CrossRef] [PubMed]

B. Wang, M. Ye, and S. Sato, "Experimental and numerical studies on liquid crystal lens with spherical electrode," Mol. Cryst. Liq. Cryst. 433, 217-227 (2005).
[CrossRef]

B. Wang, M. Ye, and S. Sato, "Liquid crystal lens with stacked structure of liquid-crystal layers," Opt. Commun. 250, 266-273 (2005)

M. Ye, S. Hayasaka, and S. Sato, "Liquid Crystal Lens Array with Hexagonal-Hole-Patterned Electrodes," Jpn. J. of Appl. Phys. 43, 6108-6111 (2004).
[CrossRef]

M. Ye and S. Sato, "Enhancement of focusing power of liquid crystal lens by new cell structure," Mol. Cryst. Liq. Cryst. 413, 417-421 (2004).

M. Ye and S. Sato, "Optical Properties of Liquid Crystal Lens of Any Size," Jpn. J. Appl. Phys. 41, 571-573 (2002).

B. Wang, M. Ye, M. Honma, T. Nose, and S. Sato, "Liquid crystal lens with spherical electrode," Jpn. J. Appl. Phys. 41, L1232-L1233 (2002).

Appl. Phys. Lett.

H. Ren and S. T. Wu, "Inhomogeneous polymer-dispersed liquid crystals with gradient refractive index," Appl. Phys. Lett. 81, 3537-3539 (2002).
[CrossRef]

H. Ren, Y. H. Fan, and S. T. Wu, "Tunable Fresnel lens using nanoscale polymer-dispersed liquid crystals," Appl. Phys. Lett. 83, 1515-1517 (2003).
[CrossRef] [PubMed]

H. Ren, Y.-H. Fan, S. Gauza, and S. T. Wu, "Tunable-focus flat liquid crystal spherical lens," Appl. Phys. Lett. 84, 4789-4791 (2004).
[CrossRef]

IEEE Photon. Technol. Lett.

M. Ye, B. Wang, and S. Sato, "Liquid crystal lens with focal length variable from negative to positive values," IEEE Photon. Technol. Lett. 18, 78-81 (2006).
[CrossRef] [PubMed]

Jpn. J. Appl. Phys.

S. Sato, "Liquid-crystal lens-cells with variable focal length," Jpn. J. Appl. Phys. 18, 1679-1684 (1979).

B. Wang, M. Ye, M. Honma, T. Nose, and S. Sato, "Liquid crystal lens with spherical electrode," Jpn. J. Appl. Phys. 41, L1232-L1233 (2002).

M. Ye and S. Sato, "Optical Properties of Liquid Crystal Lens of Any Size," Jpn. J. Appl. Phys. 41, 571-573 (2002).

M. Ye, B. Wang, M. Kawamura, and S. Sato, "Image Formation using Liquid Crystal Lens," Jpn. J. Appl. Phys. 46, 6776-6777 (2007).

Jpn. J. of Appl. Phys.

M. Ye, S. Hayasaka, and S. Sato, "Liquid Crystal Lens Array with Hexagonal-Hole-Patterned Electrodes," Jpn. J. of Appl. Phys. 43, 6108-6111 (2004).
[CrossRef]

M. Honma, T. Nose, and S. Sato, "Improvement of aberration properties of liquid crystal microlenses using the stacked electrode structure," Jpn. J. of Appl. Phys. 40, 1322-1327 (2001).

Liq. Cryst.

T. Nose and S. Sato, "A liquid crystal microlens obtained with a nonuniform electric field," Liq. Cryst. 5, 1425-1433 (1989).
[CrossRef]

Mol. Cryst. Liq. Cryst.

B. Wang, M. Ye, and S. Sato, "Experimental and numerical studies on liquid crystal lens with spherical electrode," Mol. Cryst. Liq. Cryst. 433, 217-227 (2005).
[CrossRef]

N. A. Clark, M. A. Handschy, and S. T. Lagerwall, "Ferroelectric Liquid Crystal Electro-optic using The Surface Stabilized Structure," Mol. Cryst. Liq. Cryst. 94, 213-234 (1983).

M. Ye and S. Sato, "Enhancement of focusing power of liquid crystal lens by new cell structure," Mol. Cryst. Liq. Cryst. 413, 417-421 (2004).

V. Y. Reshetnyak, S. L. Subota, and T. V. Galstian, "Theoretical analyses of the electric field control of focal length in a gradient polymer stabilized liquid crystal lens," Mol. Cryst. Liq. Cryst. 454, 187-200 (2006).

Opt. Commun.

B. Wang, M. Ye, and S. Sato, "Liquid crystal lens with stacked structure of liquid-crystal layers," Opt. Commun. 250, 266-273 (2005)

M. Ye, B. Wang, and S. Sato, "Liquid crystal lens with focus movable in focal plane," Opt. Commun. 259, 710-722 (2006)

Opt. Express

Proc. SPIE

P. J. W. Hands, A. K. Kirby, and G. D. Love, "Adaptive modally addressed liquid crystal lenses," Proc. SPIE 5518, 136-143 (2004).
[CrossRef] [PubMed]

Other

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1968).

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Figures (4)

Fig. 1.
Fig. 1.

(a) Schematic of field transmission in a microcavity, where n is the refractive index of dielectric layer and z is the interface position; (b) digital filter treatment of reflection and transmission of active region, where RDF and TDF (i.e., reflection and transmission digital filters) are reflection and transmission digital filters, respectively.

Fig. 2.
Fig. 2.

Reproductions of r QW and t QW using RDF and TDF.

Fig. 3.
Fig. 3.

Normalized lasing spectra [(a) & (c)] and reflection [(b)] of the QW-embedded microcavity. The function of splitting energy with digital filter sampling time is given in (d).

Fig. 4.
Fig. 4.

Reflection [(a)] and, lasing [(b)] spectra with different transmission angles θ. In (b), arrows indicate the positions of the suppressed LPB modes.

Equations (11)

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

E j ( z , t ) = E j + ( z , t ) + E j ( z , t ) , z j 1 z z j ,
[ E j + ( z j , t ) E j ( z j 1 , t ) ] = [ exp ( i k j d j ) 0 0 exp ( i k j d j ) ] [ E j + ( z j 1 , t Δ t ) E j ( z j , t Δ t ) ] ,
[ E j + 1 + ( z j , t ) E j ( z j , t ) ] = M j [ E j + ( z j , t ) E j + 1 ( z j , t ) ] ,
M j = 1 n j cos ( θ j ) + n j + 1 cos ( θ j + 1 ) [ 2 n j cos ( θ j ) n j + 1 cos ( θ j + 1 ) n j cos ( θ j ) n j cos ( θ j ) n j + 1 cos ( θ j + 1 ) 2 n j + 1 cos ( θ j + 1 ) ] .
E 1 + ( z 0 , t ) = r 1 E 1 ( z 0 , t ) , E N + ( z N , t ) = r N E N ( z N , t ) ,
r QW = i Γ o ω o + ω i ( Γ o + γ ) , t QW = 1 + r QW ,
E s 2 + ( t , z QW 2 ) = t QW [ exp ( i k QW d QW ) E s 1 + ( t 2 Δ t , z QW 1 ) + S + ] + r QW E s 2 ( t , z QW 2 ) ,
E s 1 ( t , z QW 1 ) = t QW [ exp ( i k QW d QW ) E s 2 ( t 2 Δ t , z QW 2 ) + S ] + r QW E s 1 + ( t , z QW 1 ) ,
H r ( w ) = A 1 B exp ( j ω Δ T ) , H t ( w ) = 1 + H r ( w ) ,
y r ( t ) = A x r ( t ) + B y r ( t Δ T ) ,
y t ( t ) = ( 1 A ) x t ( t ) B x t ( t Δ T ) + B y t ( t Δ T ) ,

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