Abstract

We study the lasing eigenvalue problems for a periodic open optical resonator made of an infinite grating of circular dielectric cylinders standing in free space, in the E- and H-polarization modes. If possessing a “negative-absorption” refractive index, such cylinders model a chain of quantum wires made of the gain material under pumping. The initial-guess values for the lasing frequencies are provided by the plane-wave scattering problems. We demonstrate a new effect: the existence of specific grating eigenmodes that have a low threshold of lasing even if the wires are optically very thin.

© 2010 Optical Society of America

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References

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  1. V. Twersky, IRE Trans. Antennas Propagat. 10, 737(1962).
    [CrossRef]
  2. C. M. Linton, J. Eng. Math. 33, 377 (1998).
    [CrossRef]
  3. K. Yasumoto, H. Toyama, and T. Kushta, IEEE Trans. Antennas Propagat. 52, 2603 (2004).
    [CrossRef]
  4. A. I. Nosich, E. I. Smotrova, S. V. Boriskina, T. M. Benson, and P. Sewell, Opt. Quantum Electron. 39, 1253(2007).
    [CrossRef]
  5. A. I. Nosich, J. Electromagn. Waves Appl. 8, 329 (1994).
    [CrossRef]
  6. E. I. Smotrova and A. I. Nosich, Opt. Quantum Electron. 36, 213 (2004).
    [CrossRef]
  7. E. I. Smotrova, A. I. Nosich, T. M. Benson, and P. Sewell, IEEE J. Sel. Top. Quantum Electron. 11, 1135 (2005).
    [CrossRef]
  8. V. O. Byelobrov and A. I. Nosich, Opt. Quantum Electron. 39, 927 (2007).
    [CrossRef]
  9. E. I. Smotrova, A. I. Nosich, T. M. Benson, and P. Sewell, IEEE J. Sel. Top. Quantum Electron. 12, 78 (2006).
    [CrossRef]
  10. E. I. Smotrova, A. I. Nosich, T. M. Benson, and P. Sewell, IEEE Photonics Technol. Lett. 18, 1993 (2006).
    [CrossRef]
  11. E. I. Smotrova, T. M. Benson, P. Sewell, J. Ctyroky, and A. I. Nosich, J. Opt. Soc. Am. A 25, 2884 (2008).
    [CrossRef]
  12. R. Gomez-Medina, M. Laroche, and J. J. Saenz, Opt. Express 14, 3730 (2006).
    [CrossRef] [PubMed]
  13. M. Laroche, S. Albaladejo, R. Gomez-Medina, and J. J. Saenz, Phys. Rev. B 74, 245422 (2006).
    [CrossRef]
  14. M. Laroche, S. Albaladejo, R. Carminati, and J. J. Saenz, Opt. Lett. 32, 2762 (2007).
    [CrossRef] [PubMed]

2008 (1)

2007 (3)

M. Laroche, S. Albaladejo, R. Carminati, and J. J. Saenz, Opt. Lett. 32, 2762 (2007).
[CrossRef] [PubMed]

A. I. Nosich, E. I. Smotrova, S. V. Boriskina, T. M. Benson, and P. Sewell, Opt. Quantum Electron. 39, 1253(2007).
[CrossRef]

V. O. Byelobrov and A. I. Nosich, Opt. Quantum Electron. 39, 927 (2007).
[CrossRef]

2006 (4)

E. I. Smotrova, A. I. Nosich, T. M. Benson, and P. Sewell, IEEE J. Sel. Top. Quantum Electron. 12, 78 (2006).
[CrossRef]

E. I. Smotrova, A. I. Nosich, T. M. Benson, and P. Sewell, IEEE Photonics Technol. Lett. 18, 1993 (2006).
[CrossRef]

R. Gomez-Medina, M. Laroche, and J. J. Saenz, Opt. Express 14, 3730 (2006).
[CrossRef] [PubMed]

M. Laroche, S. Albaladejo, R. Gomez-Medina, and J. J. Saenz, Phys. Rev. B 74, 245422 (2006).
[CrossRef]

2005 (1)

E. I. Smotrova, A. I. Nosich, T. M. Benson, and P. Sewell, IEEE J. Sel. Top. Quantum Electron. 11, 1135 (2005).
[CrossRef]

2004 (2)

K. Yasumoto, H. Toyama, and T. Kushta, IEEE Trans. Antennas Propagat. 52, 2603 (2004).
[CrossRef]

E. I. Smotrova and A. I. Nosich, Opt. Quantum Electron. 36, 213 (2004).
[CrossRef]

1998 (1)

C. M. Linton, J. Eng. Math. 33, 377 (1998).
[CrossRef]

1994 (1)

A. I. Nosich, J. Electromagn. Waves Appl. 8, 329 (1994).
[CrossRef]

1962 (1)

V. Twersky, IRE Trans. Antennas Propagat. 10, 737(1962).
[CrossRef]

Albaladejo, S.

M. Laroche, S. Albaladejo, R. Carminati, and J. J. Saenz, Opt. Lett. 32, 2762 (2007).
[CrossRef] [PubMed]

M. Laroche, S. Albaladejo, R. Gomez-Medina, and J. J. Saenz, Phys. Rev. B 74, 245422 (2006).
[CrossRef]

Benson, T. M.

E. I. Smotrova, T. M. Benson, P. Sewell, J. Ctyroky, and A. I. Nosich, J. Opt. Soc. Am. A 25, 2884 (2008).
[CrossRef]

A. I. Nosich, E. I. Smotrova, S. V. Boriskina, T. M. Benson, and P. Sewell, Opt. Quantum Electron. 39, 1253(2007).
[CrossRef]

E. I. Smotrova, A. I. Nosich, T. M. Benson, and P. Sewell, IEEE J. Sel. Top. Quantum Electron. 12, 78 (2006).
[CrossRef]

E. I. Smotrova, A. I. Nosich, T. M. Benson, and P. Sewell, IEEE Photonics Technol. Lett. 18, 1993 (2006).
[CrossRef]

E. I. Smotrova, A. I. Nosich, T. M. Benson, and P. Sewell, IEEE J. Sel. Top. Quantum Electron. 11, 1135 (2005).
[CrossRef]

Boriskina, S. V.

A. I. Nosich, E. I. Smotrova, S. V. Boriskina, T. M. Benson, and P. Sewell, Opt. Quantum Electron. 39, 1253(2007).
[CrossRef]

Byelobrov, V. O.

V. O. Byelobrov and A. I. Nosich, Opt. Quantum Electron. 39, 927 (2007).
[CrossRef]

Carminati, R.

Ctyroky, J.

Gomez-Medina, R.

M. Laroche, S. Albaladejo, R. Gomez-Medina, and J. J. Saenz, Phys. Rev. B 74, 245422 (2006).
[CrossRef]

R. Gomez-Medina, M. Laroche, and J. J. Saenz, Opt. Express 14, 3730 (2006).
[CrossRef] [PubMed]

Kushta, T.

K. Yasumoto, H. Toyama, and T. Kushta, IEEE Trans. Antennas Propagat. 52, 2603 (2004).
[CrossRef]

Laroche, M.

Linton, C. M.

C. M. Linton, J. Eng. Math. 33, 377 (1998).
[CrossRef]

Nosich, A. I.

E. I. Smotrova, T. M. Benson, P. Sewell, J. Ctyroky, and A. I. Nosich, J. Opt. Soc. Am. A 25, 2884 (2008).
[CrossRef]

V. O. Byelobrov and A. I. Nosich, Opt. Quantum Electron. 39, 927 (2007).
[CrossRef]

A. I. Nosich, E. I. Smotrova, S. V. Boriskina, T. M. Benson, and P. Sewell, Opt. Quantum Electron. 39, 1253(2007).
[CrossRef]

E. I. Smotrova, A. I. Nosich, T. M. Benson, and P. Sewell, IEEE J. Sel. Top. Quantum Electron. 12, 78 (2006).
[CrossRef]

E. I. Smotrova, A. I. Nosich, T. M. Benson, and P. Sewell, IEEE Photonics Technol. Lett. 18, 1993 (2006).
[CrossRef]

E. I. Smotrova, A. I. Nosich, T. M. Benson, and P. Sewell, IEEE J. Sel. Top. Quantum Electron. 11, 1135 (2005).
[CrossRef]

E. I. Smotrova and A. I. Nosich, Opt. Quantum Electron. 36, 213 (2004).
[CrossRef]

A. I. Nosich, J. Electromagn. Waves Appl. 8, 329 (1994).
[CrossRef]

Saenz, J. J.

Sewell, P.

E. I. Smotrova, T. M. Benson, P. Sewell, J. Ctyroky, and A. I. Nosich, J. Opt. Soc. Am. A 25, 2884 (2008).
[CrossRef]

A. I. Nosich, E. I. Smotrova, S. V. Boriskina, T. M. Benson, and P. Sewell, Opt. Quantum Electron. 39, 1253(2007).
[CrossRef]

E. I. Smotrova, A. I. Nosich, T. M. Benson, and P. Sewell, IEEE Photonics Technol. Lett. 18, 1993 (2006).
[CrossRef]

E. I. Smotrova, A. I. Nosich, T. M. Benson, and P. Sewell, IEEE J. Sel. Top. Quantum Electron. 12, 78 (2006).
[CrossRef]

E. I. Smotrova, A. I. Nosich, T. M. Benson, and P. Sewell, IEEE J. Sel. Top. Quantum Electron. 11, 1135 (2005).
[CrossRef]

Smotrova, E. I.

E. I. Smotrova, T. M. Benson, P. Sewell, J. Ctyroky, and A. I. Nosich, J. Opt. Soc. Am. A 25, 2884 (2008).
[CrossRef]

A. I. Nosich, E. I. Smotrova, S. V. Boriskina, T. M. Benson, and P. Sewell, Opt. Quantum Electron. 39, 1253(2007).
[CrossRef]

E. I. Smotrova, A. I. Nosich, T. M. Benson, and P. Sewell, IEEE Photonics Technol. Lett. 18, 1993 (2006).
[CrossRef]

E. I. Smotrova, A. I. Nosich, T. M. Benson, and P. Sewell, IEEE J. Sel. Top. Quantum Electron. 12, 78 (2006).
[CrossRef]

E. I. Smotrova, A. I. Nosich, T. M. Benson, and P. Sewell, IEEE J. Sel. Top. Quantum Electron. 11, 1135 (2005).
[CrossRef]

E. I. Smotrova and A. I. Nosich, Opt. Quantum Electron. 36, 213 (2004).
[CrossRef]

Toyama, H.

K. Yasumoto, H. Toyama, and T. Kushta, IEEE Trans. Antennas Propagat. 52, 2603 (2004).
[CrossRef]

Twersky, V.

V. Twersky, IRE Trans. Antennas Propagat. 10, 737(1962).
[CrossRef]

Yasumoto, K.

K. Yasumoto, H. Toyama, and T. Kushta, IEEE Trans. Antennas Propagat. 52, 2603 (2004).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (2)

E. I. Smotrova, A. I. Nosich, T. M. Benson, and P. Sewell, IEEE J. Sel. Top. Quantum Electron. 11, 1135 (2005).
[CrossRef]

E. I. Smotrova, A. I. Nosich, T. M. Benson, and P. Sewell, IEEE J. Sel. Top. Quantum Electron. 12, 78 (2006).
[CrossRef]

IEEE Photonics Technol. Lett. (1)

E. I. Smotrova, A. I. Nosich, T. M. Benson, and P. Sewell, IEEE Photonics Technol. Lett. 18, 1993 (2006).
[CrossRef]

IEEE Trans. Antennas Propagat. (1)

K. Yasumoto, H. Toyama, and T. Kushta, IEEE Trans. Antennas Propagat. 52, 2603 (2004).
[CrossRef]

IRE Trans. Antennas Propagat. (1)

V. Twersky, IRE Trans. Antennas Propagat. 10, 737(1962).
[CrossRef]

J. Electromagn. Waves Appl. (1)

A. I. Nosich, J. Electromagn. Waves Appl. 8, 329 (1994).
[CrossRef]

J. Eng. Math. (1)

C. M. Linton, J. Eng. Math. 33, 377 (1998).
[CrossRef]

J. Opt. Soc. Am. A (1)

Opt. Express (1)

Opt. Lett. (1)

Opt. Quantum Electron. (3)

A. I. Nosich, E. I. Smotrova, S. V. Boriskina, T. M. Benson, and P. Sewell, Opt. Quantum Electron. 39, 1253(2007).
[CrossRef]

E. I. Smotrova and A. I. Nosich, Opt. Quantum Electron. 36, 213 (2004).
[CrossRef]

V. O. Byelobrov and A. I. Nosich, Opt. Quantum Electron. 39, 927 (2007).
[CrossRef]

Phys. Rev. B (1)

M. Laroche, S. Albaladejo, R. Gomez-Medina, and J. J. Saenz, Phys. Rev. B 74, 245422 (2006).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Cross section of the periodic cavity of active dielectric circular cylinders or quantum wires.

Fig. 2
Fig. 2

Reflectance of the circular-wire grating in the (a) H-polarization and (b) E-polarization cases as a function of the normalized frequency σ and relative distance ξ between the wires of refractive index α = 1.4142 .

Fig. 3
Fig. 3

Dependences of the (a) frequencies and (b) thresholds of lasing for the H-polarized grating modes H 1 + and H 1 from the relative distance between the wires at α = 1.4142 .

Fig. 4
Fig. 4

Same as in Fig. 3 for the E-polarized grating modes E 1 + and E 1 .

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