Abstract

Random surface scattering in a one-mode waveguide is studied for a surface profile that has long-range correlations along the waveguide. Analytical treatment of this scattering shows that, with the proper choice of surface, one can arrange any desired combination of transparent and nontransparent frequency windows. We suggest a method for finding such profiles and demonstrate its effectiveness by making use of direct numerical simulations.

© 2001 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. F. M. Izrailev and A. Krokhin, Phys. Rev. Lett. 82, 4062 (1999).
    [CrossRef]
  2. A. A. Krokhin and F. M. Izrailev, Ann. Phys. (Leipzig) 8, 153 (1999).
    [CrossRef]
  3. F. M. Izrailev, A. A. Krokhin, and S. E. Ulloa, Phys. Rev. B 63, 041102(R)1-4 (2001).
    [CrossRef]
  4. U. Kuhl, F. M. Izrailev, A. A. Krokhin, and H.-J. Stoeckmann, Appl. Phys. Lett. 77, 633 (2000).
    [CrossRef]
  5. P. Sheng, ed., Scattering and Localization of Classical Waves in Random Media (World Scientific, Singapore, 1990).
  6. V. Freilikher and S. Gredeskul, in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1992), Vol. 30, p. 137.
    [CrossRef]
  7. J. A. Sánchez-Gil, V. Freilikher, I. V. Yurkevich, and A. A. Maradudin, Phys. Rev. Lett. 80, 948 (1998).
    [CrossRef]
  8. J. A. Sánchez-Gil, V. Freilikher, A. A. Maradudin, and I. V. Yurkevich, Phys. Rev. B 59, 5915–5925 (1999).
    [CrossRef]
  9. Y. F. Fyodorov and A. D. Mirlin, Int. J. Mod. Phys. 8, 3795 (1994).
    [CrossRef]
  10. N. M. Makarov and I. V. Yurkevich, Zh. Eskp. Teor. Fiz. 96, 1106 (1989)Sov. Phys. JETP 69, 628 (1989).
  11. V. Freilikher, N. M. Makarov, and I. V. Yurkevich, Phys. Rev. B 41, 8033 (1990).
    [CrossRef]
  12. I. M. Lifshits, S. A. Gredeskul, and L. A. Pastur, Introduction to the Theory of Disordered Systems (Wiley, New York, 1988).
  13. I. Simonsen, T. A. Leskova, and A. A. Maradudin, Phys. Rev. B 64, 035425 (2001).
    [CrossRef]
  14. A. A. Maradudin, I. Simonsen, T. A. Leskova, and E. R. Méndez, Physica B 296, 85 (2001).
    [CrossRef]
  15. C. S. West and K. A. O’Donnell, J. Opt. Soc. Am. A 12, 390 (1995).
    [CrossRef]

2001

F. M. Izrailev, A. A. Krokhin, and S. E. Ulloa, Phys. Rev. B 63, 041102(R)1-4 (2001).
[CrossRef]

I. Simonsen, T. A. Leskova, and A. A. Maradudin, Phys. Rev. B 64, 035425 (2001).
[CrossRef]

A. A. Maradudin, I. Simonsen, T. A. Leskova, and E. R. Méndez, Physica B 296, 85 (2001).
[CrossRef]

2000

U. Kuhl, F. M. Izrailev, A. A. Krokhin, and H.-J. Stoeckmann, Appl. Phys. Lett. 77, 633 (2000).
[CrossRef]

1999

F. M. Izrailev and A. Krokhin, Phys. Rev. Lett. 82, 4062 (1999).
[CrossRef]

A. A. Krokhin and F. M. Izrailev, Ann. Phys. (Leipzig) 8, 153 (1999).
[CrossRef]

J. A. Sánchez-Gil, V. Freilikher, A. A. Maradudin, and I. V. Yurkevich, Phys. Rev. B 59, 5915–5925 (1999).
[CrossRef]

1998

J. A. Sánchez-Gil, V. Freilikher, I. V. Yurkevich, and A. A. Maradudin, Phys. Rev. Lett. 80, 948 (1998).
[CrossRef]

1995

1994

Y. F. Fyodorov and A. D. Mirlin, Int. J. Mod. Phys. 8, 3795 (1994).
[CrossRef]

1990

V. Freilikher, N. M. Makarov, and I. V. Yurkevich, Phys. Rev. B 41, 8033 (1990).
[CrossRef]

1989

N. M. Makarov and I. V. Yurkevich, Zh. Eskp. Teor. Fiz. 96, 1106 (1989)Sov. Phys. JETP 69, 628 (1989).

Freilikher, V.

J. A. Sánchez-Gil, V. Freilikher, A. A. Maradudin, and I. V. Yurkevich, Phys. Rev. B 59, 5915–5925 (1999).
[CrossRef]

J. A. Sánchez-Gil, V. Freilikher, I. V. Yurkevich, and A. A. Maradudin, Phys. Rev. Lett. 80, 948 (1998).
[CrossRef]

V. Freilikher, N. M. Makarov, and I. V. Yurkevich, Phys. Rev. B 41, 8033 (1990).
[CrossRef]

V. Freilikher and S. Gredeskul, in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1992), Vol. 30, p. 137.
[CrossRef]

Fyodorov, Y. F.

Y. F. Fyodorov and A. D. Mirlin, Int. J. Mod. Phys. 8, 3795 (1994).
[CrossRef]

Gredeskul, S.

V. Freilikher and S. Gredeskul, in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1992), Vol. 30, p. 137.
[CrossRef]

Gredeskul, S. A.

I. M. Lifshits, S. A. Gredeskul, and L. A. Pastur, Introduction to the Theory of Disordered Systems (Wiley, New York, 1988).

Izrailev, F. M.

F. M. Izrailev, A. A. Krokhin, and S. E. Ulloa, Phys. Rev. B 63, 041102(R)1-4 (2001).
[CrossRef]

U. Kuhl, F. M. Izrailev, A. A. Krokhin, and H.-J. Stoeckmann, Appl. Phys. Lett. 77, 633 (2000).
[CrossRef]

A. A. Krokhin and F. M. Izrailev, Ann. Phys. (Leipzig) 8, 153 (1999).
[CrossRef]

F. M. Izrailev and A. Krokhin, Phys. Rev. Lett. 82, 4062 (1999).
[CrossRef]

Krokhin, A.

F. M. Izrailev and A. Krokhin, Phys. Rev. Lett. 82, 4062 (1999).
[CrossRef]

Krokhin, A. A.

F. M. Izrailev, A. A. Krokhin, and S. E. Ulloa, Phys. Rev. B 63, 041102(R)1-4 (2001).
[CrossRef]

U. Kuhl, F. M. Izrailev, A. A. Krokhin, and H.-J. Stoeckmann, Appl. Phys. Lett. 77, 633 (2000).
[CrossRef]

A. A. Krokhin and F. M. Izrailev, Ann. Phys. (Leipzig) 8, 153 (1999).
[CrossRef]

Kuhl, U.

U. Kuhl, F. M. Izrailev, A. A. Krokhin, and H.-J. Stoeckmann, Appl. Phys. Lett. 77, 633 (2000).
[CrossRef]

Leskova, T. A.

A. A. Maradudin, I. Simonsen, T. A. Leskova, and E. R. Méndez, Physica B 296, 85 (2001).
[CrossRef]

I. Simonsen, T. A. Leskova, and A. A. Maradudin, Phys. Rev. B 64, 035425 (2001).
[CrossRef]

Lifshits, I. M.

I. M. Lifshits, S. A. Gredeskul, and L. A. Pastur, Introduction to the Theory of Disordered Systems (Wiley, New York, 1988).

Makarov, N. M.

V. Freilikher, N. M. Makarov, and I. V. Yurkevich, Phys. Rev. B 41, 8033 (1990).
[CrossRef]

N. M. Makarov and I. V. Yurkevich, Zh. Eskp. Teor. Fiz. 96, 1106 (1989)Sov. Phys. JETP 69, 628 (1989).

Maradudin, A. A.

I. Simonsen, T. A. Leskova, and A. A. Maradudin, Phys. Rev. B 64, 035425 (2001).
[CrossRef]

A. A. Maradudin, I. Simonsen, T. A. Leskova, and E. R. Méndez, Physica B 296, 85 (2001).
[CrossRef]

J. A. Sánchez-Gil, V. Freilikher, A. A. Maradudin, and I. V. Yurkevich, Phys. Rev. B 59, 5915–5925 (1999).
[CrossRef]

J. A. Sánchez-Gil, V. Freilikher, I. V. Yurkevich, and A. A. Maradudin, Phys. Rev. Lett. 80, 948 (1998).
[CrossRef]

Méndez, E. R.

A. A. Maradudin, I. Simonsen, T. A. Leskova, and E. R. Méndez, Physica B 296, 85 (2001).
[CrossRef]

Mirlin, A. D.

Y. F. Fyodorov and A. D. Mirlin, Int. J. Mod. Phys. 8, 3795 (1994).
[CrossRef]

O’Donnell, K. A.

Pastur, L. A.

I. M. Lifshits, S. A. Gredeskul, and L. A. Pastur, Introduction to the Theory of Disordered Systems (Wiley, New York, 1988).

Sánchez-Gil, J. A.

J. A. Sánchez-Gil, V. Freilikher, A. A. Maradudin, and I. V. Yurkevich, Phys. Rev. B 59, 5915–5925 (1999).
[CrossRef]

J. A. Sánchez-Gil, V. Freilikher, I. V. Yurkevich, and A. A. Maradudin, Phys. Rev. Lett. 80, 948 (1998).
[CrossRef]

Simonsen, I.

A. A. Maradudin, I. Simonsen, T. A. Leskova, and E. R. Méndez, Physica B 296, 85 (2001).
[CrossRef]

I. Simonsen, T. A. Leskova, and A. A. Maradudin, Phys. Rev. B 64, 035425 (2001).
[CrossRef]

Stoeckmann, H.-J.

U. Kuhl, F. M. Izrailev, A. A. Krokhin, and H.-J. Stoeckmann, Appl. Phys. Lett. 77, 633 (2000).
[CrossRef]

Ulloa, S. E.

F. M. Izrailev, A. A. Krokhin, and S. E. Ulloa, Phys. Rev. B 63, 041102(R)1-4 (2001).
[CrossRef]

West, C. S.

Yurkevich, I. V.

J. A. Sánchez-Gil, V. Freilikher, A. A. Maradudin, and I. V. Yurkevich, Phys. Rev. B 59, 5915–5925 (1999).
[CrossRef]

J. A. Sánchez-Gil, V. Freilikher, I. V. Yurkevich, and A. A. Maradudin, Phys. Rev. Lett. 80, 948 (1998).
[CrossRef]

V. Freilikher, N. M. Makarov, and I. V. Yurkevich, Phys. Rev. B 41, 8033 (1990).
[CrossRef]

N. M. Makarov and I. V. Yurkevich, Zh. Eskp. Teor. Fiz. 96, 1106 (1989)Sov. Phys. JETP 69, 628 (1989).

Ann. Phys. (Leipzig)

A. A. Krokhin and F. M. Izrailev, Ann. Phys. (Leipzig) 8, 153 (1999).
[CrossRef]

Appl. Phys. Lett.

U. Kuhl, F. M. Izrailev, A. A. Krokhin, and H.-J. Stoeckmann, Appl. Phys. Lett. 77, 633 (2000).
[CrossRef]

Int. J. Mod. Phys.

Y. F. Fyodorov and A. D. Mirlin, Int. J. Mod. Phys. 8, 3795 (1994).
[CrossRef]

J. Opt. Soc. Am. A

Phys. Rev. B

J. A. Sánchez-Gil, V. Freilikher, A. A. Maradudin, and I. V. Yurkevich, Phys. Rev. B 59, 5915–5925 (1999).
[CrossRef]

V. Freilikher, N. M. Makarov, and I. V. Yurkevich, Phys. Rev. B 41, 8033 (1990).
[CrossRef]

I. Simonsen, T. A. Leskova, and A. A. Maradudin, Phys. Rev. B 64, 035425 (2001).
[CrossRef]

F. M. Izrailev, A. A. Krokhin, and S. E. Ulloa, Phys. Rev. B 63, 041102(R)1-4 (2001).
[CrossRef]

Phys. Rev. Lett.

F. M. Izrailev and A. Krokhin, Phys. Rev. Lett. 82, 4062 (1999).
[CrossRef]

J. A. Sánchez-Gil, V. Freilikher, I. V. Yurkevich, and A. A. Maradudin, Phys. Rev. Lett. 80, 948 (1998).
[CrossRef]

Physica B

A. A. Maradudin, I. Simonsen, T. A. Leskova, and E. R. Méndez, Physica B 296, 85 (2001).
[CrossRef]

Zh. Eskp. Teor. Fiz.

N. M. Makarov and I. V. Yurkevich, Zh. Eskp. Teor. Fiz. 96, 1106 (1989)Sov. Phys. JETP 69, 628 (1989).

Other

P. Sheng, ed., Scattering and Localization of Classical Waves in Random Media (World Scientific, Singapore, 1990).

V. Freilikher and S. Gredeskul, in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1992), Vol. 30, p. 137.
[CrossRef]

I. M. Lifshits, S. A. Gredeskul, and L. A. Pastur, Introduction to the Theory of Disordered Systems (Wiley, New York, 1988).

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 (1)

Fig. 1
Fig. 1

Selective dependence of the rescaled localization length on the normalized wave vector for two realizations of a random surface with long-range correlations. Inset, enlarged view of the transition region about point K=1.

Equations (15)

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

ξx=0,ξxξx=σ2Wx-x.
d2dt2+k1Rc2Ψt=2πσRcπRcd3φtΨt,
Lloc-1=σ2π2πd6W2k12k12,
φt=-dtZt-tβt,
βt=Rc-dkx2πexpikxRctW1/2kx.
W1x=sinx/Rcx/Rc,
W1kx=πRcΘ1-kxRc,
φ1t=1π-dtZt-tsint/t.
1Lloc1k1=1πRcσRc2πRcd6Θ1-2k1Rc2k1Rc2.
LLloc11/2Rc12πσRc2πRcd6LRc1.
W2x=πδx/Rc-sinx/Rcx/Rc,
W2kx=πRcΘkxRc-1.
φ2t=πZt-1π-dtZt-tsint/t.
1Lloc2k1=1πRcσRc2πRcd6Θ2k1Rc-12k1Rc2.
LLloc2π3/d112πσRc2πRcd4LRc1.

Metrics