Abstract

We analyze slow light propagation in a coupled semiconductor quantum wells system exhibiting tunneling induced transparency. A group index as high as 85, for simple applicable GaAs/AlGaAs quantum wells structures, is predicted. Using DC voltage, the resonant tunneling rate can be altered and the related group index can be controlled over a broad range.

© 2006 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. P. W. Milonni, Fast Light, Slow light and Left-Handed Light, (Bristol, England: Institute of Physics, c2005).
  2. S. E. Harris, "Electromagnetically induced transparency," Phys. Today 50, 36-42 (1997).
    [CrossRef]
  3. Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, "Tunable all-optical delays via Brillouin slow light in an optical fiber," Phys. Rev. Lett. 94, 153902 (2005).
    [CrossRef] [PubMed]
  4. S. Sarkar, Y. Guo, and H. Wang, "Tunable optical delay via carrier induced exciton dephasing in semiconductor quantum wells," Opt. Express 14, 2845-2850 (2006).
    [CrossRef] [PubMed]
  5. J. E. Heebner, R. W. Boyd, and Q-Han Park, "Slow light, induced dispersion, enhanced nonlinearity, and optical solitons in a resonator-array waveguide," Phys. Rev. E 65, 036619 (2002).
    [CrossRef]
  6. H. Altuga and J. Vuèkoviæb "Experimental demonstration of the slow group velocity of light in two-dimensional coupled photonic crystal microcavity arrays," Appl. Phys. Lett. 86, 111102 (2005).
    [CrossRef]
  7. D. Budker, D. F. Kimball, S. M. Rochester, and V. V. Yashchuk, "Nonlinear magneto-optics and reduced group velocity of light in atomic vapor with slow ground state relaxatoin," Phys. Rev. Lett. 83, 1767 (1999).
    [CrossRef]
  8. A. V. Turukhin, V. S. Sudarshanam, M. S. Shahriar, J. A. Musser, B. S. Ham, P. R. Hemmer, "Observation of ultraslow and stored light pulses in a solid," Phys. Rev. Lett. 88, 023602 (2002).
    [CrossRef] [PubMed]
  9. P. -C. Ku, F. Sedgwick, C. J. Chang-Hasnain, P. Palinginis, T. Li, H. Wang, S. -W. Chang, and S. -L. Chuang, "Slow light in semiconductor quantum wells," Opt. Lett. 29, 2291-2293 (2004).
    [CrossRef] [PubMed]
  10. J Kim, S L Chuang, P. C. Ku, C J Chang-Hasnain, "Slow light using semiconductor quantum dots," J. Phys. Condens. Matter 16, S3727 - S3735 (2004).
    [CrossRef]
  11. P. Palinginis, F. Sedgwick, S. Crankshaw, M. Moewe, and C. Chang-Hasnain, "Room temperature slow light in a quantum-well waveguide via coherent population oscillation," Opt. Express 13, 9909-9915 (2005).
    [CrossRef] [PubMed]
  12. H. Schmidt and A. Imamoglu, "Nonlinear optical devices based on a transparency in semiconductor intersubband transitions," Opt. Commun. 131, 333 (1996).
    [CrossRef]
  13. H. Mizuta and T. Tanoue, The Physics and Applications of Resonant Tunnelling Diodes (Cambridge, MA: Cambridge, 1995).
    [CrossRef]
  14. H. Kang, G. Hernandez, and Y. Zhu, "Resonant four-wave mixing with slow light," Phys. Rev. A 70, 061804(R) (2004).
    [CrossRef]
  15. H. Schmidt, K. L. Campman, A. C. Gossard, and A. Imamoglu, "Tunneling induced transparency: Fano interference in intersubband transitions," Appl. Phys. Lett. 70, 3455-3457 (1997).
    [CrossRef]
  16. P. Ginzburg and M. Orenstein, "Visible -Near IR controllable slow light by interband transitions in coupled quantum well structures," in preparation.
  17. L. Allen and J. H. Eberly, Optical resonance and two-level atoms, (New York, Wiley-Interscience, c1975).
  18. A. M. Fox, D. A. B. Miller, G. Livescu, J. E. Cunningham, and W. Y. Jan, "Excitonic effects in coupled quantum wells," Phys. Rev. B 44, 6231-6242 (1991).
    [CrossRef]
  19. D. E. Nikonov, A. Imamoğlu, L. V. Butov, and H. Schmidt, "Collective Intersubband Excitations in Quantum Wells: Coulomb Interaction versus Subband Dispersion," Phys. Rev. Lett. 79, 4633-4636 (1997).
    [CrossRef]
  20. P. Basu, Theory of optical processes in semiconductors: bulk and microstructures, (Oxford: Clarendon Press, c1997).
  21. J. Li, and C. Ning, "Collective excitations in InAs quantum well intersubband transitions," Physica E 22, 628-631 (2004).
    [CrossRef]

2006 (1)

2005 (3)

H. Altuga and J. Vuèkoviæb "Experimental demonstration of the slow group velocity of light in two-dimensional coupled photonic crystal microcavity arrays," Appl. Phys. Lett. 86, 111102 (2005).
[CrossRef]

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, "Tunable all-optical delays via Brillouin slow light in an optical fiber," Phys. Rev. Lett. 94, 153902 (2005).
[CrossRef] [PubMed]

P. Palinginis, F. Sedgwick, S. Crankshaw, M. Moewe, and C. Chang-Hasnain, "Room temperature slow light in a quantum-well waveguide via coherent population oscillation," Opt. Express 13, 9909-9915 (2005).
[CrossRef] [PubMed]

2004 (3)

P. -C. Ku, F. Sedgwick, C. J. Chang-Hasnain, P. Palinginis, T. Li, H. Wang, S. -W. Chang, and S. -L. Chuang, "Slow light in semiconductor quantum wells," Opt. Lett. 29, 2291-2293 (2004).
[CrossRef] [PubMed]

J Kim, S L Chuang, P. C. Ku, C J Chang-Hasnain, "Slow light using semiconductor quantum dots," J. Phys. Condens. Matter 16, S3727 - S3735 (2004).
[CrossRef]

J. Li, and C. Ning, "Collective excitations in InAs quantum well intersubband transitions," Physica E 22, 628-631 (2004).
[CrossRef]

2002 (1)

A. V. Turukhin, V. S. Sudarshanam, M. S. Shahriar, J. A. Musser, B. S. Ham, P. R. Hemmer, "Observation of ultraslow and stored light pulses in a solid," Phys. Rev. Lett. 88, 023602 (2002).
[CrossRef] [PubMed]

1999 (1)

D. Budker, D. F. Kimball, S. M. Rochester, and V. V. Yashchuk, "Nonlinear magneto-optics and reduced group velocity of light in atomic vapor with slow ground state relaxatoin," Phys. Rev. Lett. 83, 1767 (1999).
[CrossRef]

1997 (3)

S. E. Harris, "Electromagnetically induced transparency," Phys. Today 50, 36-42 (1997).
[CrossRef]

D. E. Nikonov, A. Imamoğlu, L. V. Butov, and H. Schmidt, "Collective Intersubband Excitations in Quantum Wells: Coulomb Interaction versus Subband Dispersion," Phys. Rev. Lett. 79, 4633-4636 (1997).
[CrossRef]

H. Schmidt, K. L. Campman, A. C. Gossard, and A. Imamoglu, "Tunneling induced transparency: Fano interference in intersubband transitions," Appl. Phys. Lett. 70, 3455-3457 (1997).
[CrossRef]

1996 (1)

H. Schmidt and A. Imamoglu, "Nonlinear optical devices based on a transparency in semiconductor intersubband transitions," Opt. Commun. 131, 333 (1996).
[CrossRef]

1991 (1)

A. M. Fox, D. A. B. Miller, G. Livescu, J. E. Cunningham, and W. Y. Jan, "Excitonic effects in coupled quantum wells," Phys. Rev. B 44, 6231-6242 (1991).
[CrossRef]

Altuga, H.

H. Altuga and J. Vuèkoviæb "Experimental demonstration of the slow group velocity of light in two-dimensional coupled photonic crystal microcavity arrays," Appl. Phys. Lett. 86, 111102 (2005).
[CrossRef]

Bigelow, M. S.

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, "Tunable all-optical delays via Brillouin slow light in an optical fiber," Phys. Rev. Lett. 94, 153902 (2005).
[CrossRef] [PubMed]

Boyd, R. W.

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, "Tunable all-optical delays via Brillouin slow light in an optical fiber," Phys. Rev. Lett. 94, 153902 (2005).
[CrossRef] [PubMed]

Budker, D.

D. Budker, D. F. Kimball, S. M. Rochester, and V. V. Yashchuk, "Nonlinear magneto-optics and reduced group velocity of light in atomic vapor with slow ground state relaxatoin," Phys. Rev. Lett. 83, 1767 (1999).
[CrossRef]

Butov, L. V.

D. E. Nikonov, A. Imamoğlu, L. V. Butov, and H. Schmidt, "Collective Intersubband Excitations in Quantum Wells: Coulomb Interaction versus Subband Dispersion," Phys. Rev. Lett. 79, 4633-4636 (1997).
[CrossRef]

Campman, K. L.

H. Schmidt, K. L. Campman, A. C. Gossard, and A. Imamoglu, "Tunneling induced transparency: Fano interference in intersubband transitions," Appl. Phys. Lett. 70, 3455-3457 (1997).
[CrossRef]

Chang, S. -W.

Chang-Hasnain, C J

J Kim, S L Chuang, P. C. Ku, C J Chang-Hasnain, "Slow light using semiconductor quantum dots," J. Phys. Condens. Matter 16, S3727 - S3735 (2004).
[CrossRef]

Chang-Hasnain, C.

Chang-Hasnain, C. J.

Chuang, S L

J Kim, S L Chuang, P. C. Ku, C J Chang-Hasnain, "Slow light using semiconductor quantum dots," J. Phys. Condens. Matter 16, S3727 - S3735 (2004).
[CrossRef]

Chuang, S. -L.

Crankshaw, S.

Cunningham, J. E.

A. M. Fox, D. A. B. Miller, G. Livescu, J. E. Cunningham, and W. Y. Jan, "Excitonic effects in coupled quantum wells," Phys. Rev. B 44, 6231-6242 (1991).
[CrossRef]

Fox, A. M.

A. M. Fox, D. A. B. Miller, G. Livescu, J. E. Cunningham, and W. Y. Jan, "Excitonic effects in coupled quantum wells," Phys. Rev. B 44, 6231-6242 (1991).
[CrossRef]

Gaeta, A. L.

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, "Tunable all-optical delays via Brillouin slow light in an optical fiber," Phys. Rev. Lett. 94, 153902 (2005).
[CrossRef] [PubMed]

Gauthier, D. J.

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, "Tunable all-optical delays via Brillouin slow light in an optical fiber," Phys. Rev. Lett. 94, 153902 (2005).
[CrossRef] [PubMed]

Gossard, A. C.

H. Schmidt, K. L. Campman, A. C. Gossard, and A. Imamoglu, "Tunneling induced transparency: Fano interference in intersubband transitions," Appl. Phys. Lett. 70, 3455-3457 (1997).
[CrossRef]

Guo, Y.

Ham, B. S.

A. V. Turukhin, V. S. Sudarshanam, M. S. Shahriar, J. A. Musser, B. S. Ham, P. R. Hemmer, "Observation of ultraslow and stored light pulses in a solid," Phys. Rev. Lett. 88, 023602 (2002).
[CrossRef] [PubMed]

Harris, S. E.

S. E. Harris, "Electromagnetically induced transparency," Phys. Today 50, 36-42 (1997).
[CrossRef]

Hemmer, P. R.

A. V. Turukhin, V. S. Sudarshanam, M. S. Shahriar, J. A. Musser, B. S. Ham, P. R. Hemmer, "Observation of ultraslow and stored light pulses in a solid," Phys. Rev. Lett. 88, 023602 (2002).
[CrossRef] [PubMed]

Imamoglu, A.

H. Schmidt, K. L. Campman, A. C. Gossard, and A. Imamoglu, "Tunneling induced transparency: Fano interference in intersubband transitions," Appl. Phys. Lett. 70, 3455-3457 (1997).
[CrossRef]

D. E. Nikonov, A. Imamoğlu, L. V. Butov, and H. Schmidt, "Collective Intersubband Excitations in Quantum Wells: Coulomb Interaction versus Subband Dispersion," Phys. Rev. Lett. 79, 4633-4636 (1997).
[CrossRef]

H. Schmidt and A. Imamoglu, "Nonlinear optical devices based on a transparency in semiconductor intersubband transitions," Opt. Commun. 131, 333 (1996).
[CrossRef]

Jan, W. Y.

A. M. Fox, D. A. B. Miller, G. Livescu, J. E. Cunningham, and W. Y. Jan, "Excitonic effects in coupled quantum wells," Phys. Rev. B 44, 6231-6242 (1991).
[CrossRef]

Kim, J

J Kim, S L Chuang, P. C. Ku, C J Chang-Hasnain, "Slow light using semiconductor quantum dots," J. Phys. Condens. Matter 16, S3727 - S3735 (2004).
[CrossRef]

Kimball, D. F.

D. Budker, D. F. Kimball, S. M. Rochester, and V. V. Yashchuk, "Nonlinear magneto-optics and reduced group velocity of light in atomic vapor with slow ground state relaxatoin," Phys. Rev. Lett. 83, 1767 (1999).
[CrossRef]

Ku, P. C.

J Kim, S L Chuang, P. C. Ku, C J Chang-Hasnain, "Slow light using semiconductor quantum dots," J. Phys. Condens. Matter 16, S3727 - S3735 (2004).
[CrossRef]

Ku, P. -C.

Li, J.

J. Li, and C. Ning, "Collective excitations in InAs quantum well intersubband transitions," Physica E 22, 628-631 (2004).
[CrossRef]

Li, T.

Livescu, G.

A. M. Fox, D. A. B. Miller, G. Livescu, J. E. Cunningham, and W. Y. Jan, "Excitonic effects in coupled quantum wells," Phys. Rev. B 44, 6231-6242 (1991).
[CrossRef]

Miller, D. A. B.

A. M. Fox, D. A. B. Miller, G. Livescu, J. E. Cunningham, and W. Y. Jan, "Excitonic effects in coupled quantum wells," Phys. Rev. B 44, 6231-6242 (1991).
[CrossRef]

Moewe, M.

Musser, J. A.

A. V. Turukhin, V. S. Sudarshanam, M. S. Shahriar, J. A. Musser, B. S. Ham, P. R. Hemmer, "Observation of ultraslow and stored light pulses in a solid," Phys. Rev. Lett. 88, 023602 (2002).
[CrossRef] [PubMed]

Nikonov, D. E.

D. E. Nikonov, A. Imamoğlu, L. V. Butov, and H. Schmidt, "Collective Intersubband Excitations in Quantum Wells: Coulomb Interaction versus Subband Dispersion," Phys. Rev. Lett. 79, 4633-4636 (1997).
[CrossRef]

Ning, C.

J. Li, and C. Ning, "Collective excitations in InAs quantum well intersubband transitions," Physica E 22, 628-631 (2004).
[CrossRef]

Okawachi, Y.

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, "Tunable all-optical delays via Brillouin slow light in an optical fiber," Phys. Rev. Lett. 94, 153902 (2005).
[CrossRef] [PubMed]

Palinginis, P.

Rochester, S. M.

D. Budker, D. F. Kimball, S. M. Rochester, and V. V. Yashchuk, "Nonlinear magneto-optics and reduced group velocity of light in atomic vapor with slow ground state relaxatoin," Phys. Rev. Lett. 83, 1767 (1999).
[CrossRef]

Sarkar, S.

Schmidt, H.

H. Schmidt, K. L. Campman, A. C. Gossard, and A. Imamoglu, "Tunneling induced transparency: Fano interference in intersubband transitions," Appl. Phys. Lett. 70, 3455-3457 (1997).
[CrossRef]

D. E. Nikonov, A. Imamoğlu, L. V. Butov, and H. Schmidt, "Collective Intersubband Excitations in Quantum Wells: Coulomb Interaction versus Subband Dispersion," Phys. Rev. Lett. 79, 4633-4636 (1997).
[CrossRef]

H. Schmidt and A. Imamoglu, "Nonlinear optical devices based on a transparency in semiconductor intersubband transitions," Opt. Commun. 131, 333 (1996).
[CrossRef]

Schweinsberg, A.

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, "Tunable all-optical delays via Brillouin slow light in an optical fiber," Phys. Rev. Lett. 94, 153902 (2005).
[CrossRef] [PubMed]

Sedgwick, F.

Shahriar, M. S.

A. V. Turukhin, V. S. Sudarshanam, M. S. Shahriar, J. A. Musser, B. S. Ham, P. R. Hemmer, "Observation of ultraslow and stored light pulses in a solid," Phys. Rev. Lett. 88, 023602 (2002).
[CrossRef] [PubMed]

Sharping, J. E.

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, "Tunable all-optical delays via Brillouin slow light in an optical fiber," Phys. Rev. Lett. 94, 153902 (2005).
[CrossRef] [PubMed]

Sudarshanam, V. S.

A. V. Turukhin, V. S. Sudarshanam, M. S. Shahriar, J. A. Musser, B. S. Ham, P. R. Hemmer, "Observation of ultraslow and stored light pulses in a solid," Phys. Rev. Lett. 88, 023602 (2002).
[CrossRef] [PubMed]

Turukhin, A. V.

A. V. Turukhin, V. S. Sudarshanam, M. S. Shahriar, J. A. Musser, B. S. Ham, P. R. Hemmer, "Observation of ultraslow and stored light pulses in a solid," Phys. Rev. Lett. 88, 023602 (2002).
[CrossRef] [PubMed]

Vuèkoviæb, J.

H. Altuga and J. Vuèkoviæb "Experimental demonstration of the slow group velocity of light in two-dimensional coupled photonic crystal microcavity arrays," Appl. Phys. Lett. 86, 111102 (2005).
[CrossRef]

Wang, H.

Yashchuk, V. V.

D. Budker, D. F. Kimball, S. M. Rochester, and V. V. Yashchuk, "Nonlinear magneto-optics and reduced group velocity of light in atomic vapor with slow ground state relaxatoin," Phys. Rev. Lett. 83, 1767 (1999).
[CrossRef]

Zhu, Z.

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, "Tunable all-optical delays via Brillouin slow light in an optical fiber," Phys. Rev. Lett. 94, 153902 (2005).
[CrossRef] [PubMed]

Appl. Phys. Lett. (2)

H. Altuga and J. Vuèkoviæb "Experimental demonstration of the slow group velocity of light in two-dimensional coupled photonic crystal microcavity arrays," Appl. Phys. Lett. 86, 111102 (2005).
[CrossRef]

H. Schmidt, K. L. Campman, A. C. Gossard, and A. Imamoglu, "Tunneling induced transparency: Fano interference in intersubband transitions," Appl. Phys. Lett. 70, 3455-3457 (1997).
[CrossRef]

J. Phys. Condens. Matter (1)

J Kim, S L Chuang, P. C. Ku, C J Chang-Hasnain, "Slow light using semiconductor quantum dots," J. Phys. Condens. Matter 16, S3727 - S3735 (2004).
[CrossRef]

Opt. Commun. (1)

H. Schmidt and A. Imamoglu, "Nonlinear optical devices based on a transparency in semiconductor intersubband transitions," Opt. Commun. 131, 333 (1996).
[CrossRef]

Opt. Express (2)

Opt. Lett. (1)

Phys. Rev. B (1)

A. M. Fox, D. A. B. Miller, G. Livescu, J. E. Cunningham, and W. Y. Jan, "Excitonic effects in coupled quantum wells," Phys. Rev. B 44, 6231-6242 (1991).
[CrossRef]

Phys. Rev. Lett. (4)

D. E. Nikonov, A. Imamoğlu, L. V. Butov, and H. Schmidt, "Collective Intersubband Excitations in Quantum Wells: Coulomb Interaction versus Subband Dispersion," Phys. Rev. Lett. 79, 4633-4636 (1997).
[CrossRef]

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, "Tunable all-optical delays via Brillouin slow light in an optical fiber," Phys. Rev. Lett. 94, 153902 (2005).
[CrossRef] [PubMed]

D. Budker, D. F. Kimball, S. M. Rochester, and V. V. Yashchuk, "Nonlinear magneto-optics and reduced group velocity of light in atomic vapor with slow ground state relaxatoin," Phys. Rev. Lett. 83, 1767 (1999).
[CrossRef]

A. V. Turukhin, V. S. Sudarshanam, M. S. Shahriar, J. A. Musser, B. S. Ham, P. R. Hemmer, "Observation of ultraslow and stored light pulses in a solid," Phys. Rev. Lett. 88, 023602 (2002).
[CrossRef] [PubMed]

Phys. Today (1)

S. E. Harris, "Electromagnetically induced transparency," Phys. Today 50, 36-42 (1997).
[CrossRef]

Physica E (1)

J. Li, and C. Ning, "Collective excitations in InAs quantum well intersubband transitions," Physica E 22, 628-631 (2004).
[CrossRef]

Other (7)

P. W. Milonni, Fast Light, Slow light and Left-Handed Light, (Bristol, England: Institute of Physics, c2005).

J. E. Heebner, R. W. Boyd, and Q-Han Park, "Slow light, induced dispersion, enhanced nonlinearity, and optical solitons in a resonator-array waveguide," Phys. Rev. E 65, 036619 (2002).
[CrossRef]

P. Basu, Theory of optical processes in semiconductors: bulk and microstructures, (Oxford: Clarendon Press, c1997).

P. Ginzburg and M. Orenstein, "Visible -Near IR controllable slow light by interband transitions in coupled quantum well structures," in preparation.

L. Allen and J. H. Eberly, Optical resonance and two-level atoms, (New York, Wiley-Interscience, c1975).

H. Mizuta and T. Tanoue, The Physics and Applications of Resonant Tunnelling Diodes (Cambridge, MA: Cambridge, 1995).
[CrossRef]

H. Kang, G. Hernandez, and Y. Zhu, "Resonant four-wave mixing with slow light," Phys. Rev. A 70, 061804(R) (2004).
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1.
Fig. 1.

The coupled quantum wells configuration (a) Energy-level diagram. (b) In plane electronic wave functions

Fig. 2.
Fig. 2.

The permeability (0 bias voltage) (a) Dispersion curve (b) Group index

Fig. 3.
Fig. 3.

Applying 106 eV DC field (a) Energy-level diagram tilting (dashed line: original energy levels) (b) In plane electronic wave functions tilting (dashed line: original wavefunctions)

Fig. 4.
Fig. 4.

Applying 104 eV DC field (a) Dispersion curve (b) Group index

Fig. 5.
Fig. 5.

Applying 105 eV DC field (a) Dispersion curve (b) Group index

Fig. 6.
Fig. 6.

Group index as a function of applied DC field (a) Zoomed at positive group indices (b) Extended voltage region

Equations (5)

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

H 0 = ћ ( ω 1 0 0 0 0 ω 2 0 0 0 0 ω 3 0 0 0 0 ω 4 ) V pert = ( 0 μ 12 E 0 0 μ 12 * E * 0 α 0 0 α * 0 μ 43 E 0 0 μ 43 * E * 0 )
( i ( ω ω 21 ) γ 21 i α 2 ћ 0 0 i α 1 ћ i ( ω ω 41 ) γ 41 0 0 0 0 i ( ω ω 23 ) γ 23 i α 2 ћ 0 0 i α 1 ћ i ( ω ω 43 ) γ 43 ) ×
× ( σ 12 σ 14 σ 32 σ 34 ) = i ћ ( μ 12 E ( ρ 11 ρ 22 ) 0 0 μ 34 E ( ρ 33 ρ 44 ) )
χ = χ bac i N ( μ 12 2 ( ρ 11 ρ 22 ) ћ 1 α 1 α 2 ћ 2 ( i ( ω ω 41 ) γ 41 ) + i ( ω ω 21 ) γ 21 + + μ 34 2 ( ρ 44 ρ 33 ) ћ 1 α 1 α 2 ћ 2 ( i ( ω ω 23 ) γ 23 ) + i ( ω ω 43 ) γ 43 )
n group ( ω s ) = n r ( ω s ) + ω s ( d n r d ω ) ω = ω s v group = c n group

Metrics