Abstract

We identify nondiffracting beams in two-dimensional periodic systems, exhibiting symmetry properties and phase structure characteristic of the band(s) they are associated with.

© 2005 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. A. Stratton, Electromagnetic Theory (McGraw-Hill, 1941), Chap. VI.
  2. J. Durnin, J. Opt. Soc. Am. A 4, 651 (1987).
    [CrossRef]
  3. J. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
    [CrossRef] [PubMed]
  4. J. Lu and J. F. Greenleaf, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 39, 19 (1992).
    [CrossRef]
  5. T. Wulle and S. Herminghaus, Phys. Rev. Lett. 70, 1401 (1993).
    [CrossRef] [PubMed]
  6. P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, Phys. Rev. Lett. 91, 093904 (2003).
    [CrossRef]
  7. Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Phys. Rev. Lett. 93, 093904 (2004).
    [CrossRef]
  8. J. Salo, J. Fagerholm, A. T. Friberg, and M. M. Salomaa, Phys. Rev. Lett. 83, 1171 (1999).
    [CrossRef]
  9. D. N. Christodoulides, N. K. Efremidis, P. Di Trapani, and B. A. Malomed, Opt. Lett. 29, 1446 (2004).
    [CrossRef] [PubMed]
  10. S. Longhi and D. Janner, Phys. Rev. B 70, 235123 (2004).
    [CrossRef]
  11. C. Conti and S. Trillo, Phys. Rev. Lett. 92, 120404 (2004).
    [CrossRef]
  12. G. Indebetouw, J. Opt. Soc. Am. A 6, 150 (1989).
    [CrossRef]
  13. J. C. Gutiérrez-Vega, M. D. Iturbe-Castillo, and S. Chávez-Cerda, Opt. Lett. 25, 1493 (2000).
    [CrossRef]
  14. N. W. Ashcroft and N. D. Mermin, Solid State Physics (Saunders, 1976).
  15. O. Manela, O. Cohen, G. Bartal, J. W. Fleischer, and M. Segev, Opt. Lett. 29, 2049 (2004).
    [CrossRef] [PubMed]
  16. G. Bartal, O. Manela, O. Cohen, J. W. Fleischer, and M. SegevPhys. Rev. Lett. 95, 053904 (2005).
    [CrossRef]

2005 (1)

G. Bartal, O. Manela, O. Cohen, J. W. Fleischer, and M. SegevPhys. Rev. Lett. 95, 053904 (2005).
[CrossRef]

2004 (5)

O. Manela, O. Cohen, G. Bartal, J. W. Fleischer, and M. Segev, Opt. Lett. 29, 2049 (2004).
[CrossRef] [PubMed]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Phys. Rev. Lett. 93, 093904 (2004).
[CrossRef]

D. N. Christodoulides, N. K. Efremidis, P. Di Trapani, and B. A. Malomed, Opt. Lett. 29, 1446 (2004).
[CrossRef] [PubMed]

S. Longhi and D. Janner, Phys. Rev. B 70, 235123 (2004).
[CrossRef]

C. Conti and S. Trillo, Phys. Rev. Lett. 92, 120404 (2004).
[CrossRef]

2003 (1)

P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, Phys. Rev. Lett. 91, 093904 (2003).
[CrossRef]

2000 (1)

1999 (1)

J. Salo, J. Fagerholm, A. T. Friberg, and M. M. Salomaa, Phys. Rev. Lett. 83, 1171 (1999).
[CrossRef]

1993 (1)

T. Wulle and S. Herminghaus, Phys. Rev. Lett. 70, 1401 (1993).
[CrossRef] [PubMed]

1992 (1)

J. Lu and J. F. Greenleaf, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 39, 19 (1992).
[CrossRef]

1989 (1)

1987 (2)

J. Durnin, J. Opt. Soc. Am. A 4, 651 (1987).
[CrossRef]

J. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef] [PubMed]

Ashcroft, N. W.

N. W. Ashcroft and N. D. Mermin, Solid State Physics (Saunders, 1976).

Bartal, G.

G. Bartal, O. Manela, O. Cohen, J. W. Fleischer, and M. SegevPhys. Rev. Lett. 95, 053904 (2005).
[CrossRef]

O. Manela, O. Cohen, G. Bartal, J. W. Fleischer, and M. Segev, Opt. Lett. 29, 2049 (2004).
[CrossRef] [PubMed]

Chávez-Cerda, S.

Christodoulides, D. N.

Cohen, O.

G. Bartal, O. Manela, O. Cohen, J. W. Fleischer, and M. SegevPhys. Rev. Lett. 95, 053904 (2005).
[CrossRef]

O. Manela, O. Cohen, G. Bartal, J. W. Fleischer, and M. Segev, Opt. Lett. 29, 2049 (2004).
[CrossRef] [PubMed]

Conti, C.

C. Conti and S. Trillo, Phys. Rev. Lett. 92, 120404 (2004).
[CrossRef]

P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, Phys. Rev. Lett. 91, 093904 (2003).
[CrossRef]

Di Trapani, P.

D. N. Christodoulides, N. K. Efremidis, P. Di Trapani, and B. A. Malomed, Opt. Lett. 29, 1446 (2004).
[CrossRef] [PubMed]

P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, Phys. Rev. Lett. 91, 093904 (2003).
[CrossRef]

Durnin, J.

J. Durnin, J. Opt. Soc. Am. A 4, 651 (1987).
[CrossRef]

J. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef] [PubMed]

Eberly, J. H.

J. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef] [PubMed]

Efremidis, N. K.

Fagerholm, J.

J. Salo, J. Fagerholm, A. T. Friberg, and M. M. Salomaa, Phys. Rev. Lett. 83, 1171 (1999).
[CrossRef]

Fleischer, J. W.

G. Bartal, O. Manela, O. Cohen, J. W. Fleischer, and M. SegevPhys. Rev. Lett. 95, 053904 (2005).
[CrossRef]

O. Manela, O. Cohen, G. Bartal, J. W. Fleischer, and M. Segev, Opt. Lett. 29, 2049 (2004).
[CrossRef] [PubMed]

Friberg, A. T.

J. Salo, J. Fagerholm, A. T. Friberg, and M. M. Salomaa, Phys. Rev. Lett. 83, 1171 (1999).
[CrossRef]

Greenleaf, J. F.

J. Lu and J. F. Greenleaf, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 39, 19 (1992).
[CrossRef]

Gutiérrez-Vega, J. C.

Herminghaus, S.

T. Wulle and S. Herminghaus, Phys. Rev. Lett. 70, 1401 (1993).
[CrossRef] [PubMed]

Indebetouw, G.

Iturbe-Castillo, M. D.

Janner, D.

S. Longhi and D. Janner, Phys. Rev. B 70, 235123 (2004).
[CrossRef]

Jedrkiewicz, O.

P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, Phys. Rev. Lett. 91, 093904 (2003).
[CrossRef]

Kartashov, Y. V.

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Phys. Rev. Lett. 93, 093904 (2004).
[CrossRef]

Longhi, S.

S. Longhi and D. Janner, Phys. Rev. B 70, 235123 (2004).
[CrossRef]

Lu, J.

J. Lu and J. F. Greenleaf, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 39, 19 (1992).
[CrossRef]

Malomed, B. A.

Manela, O.

G. Bartal, O. Manela, O. Cohen, J. W. Fleischer, and M. SegevPhys. Rev. Lett. 95, 053904 (2005).
[CrossRef]

O. Manela, O. Cohen, G. Bartal, J. W. Fleischer, and M. Segev, Opt. Lett. 29, 2049 (2004).
[CrossRef] [PubMed]

Mermin, N. D.

N. W. Ashcroft and N. D. Mermin, Solid State Physics (Saunders, 1976).

Miceli, J. J.

J. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef] [PubMed]

Piskarskas, A.

P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, Phys. Rev. Lett. 91, 093904 (2003).
[CrossRef]

Salo, J.

J. Salo, J. Fagerholm, A. T. Friberg, and M. M. Salomaa, Phys. Rev. Lett. 83, 1171 (1999).
[CrossRef]

Salomaa, M. M.

J. Salo, J. Fagerholm, A. T. Friberg, and M. M. Salomaa, Phys. Rev. Lett. 83, 1171 (1999).
[CrossRef]

Segev, M.

G. Bartal, O. Manela, O. Cohen, J. W. Fleischer, and M. SegevPhys. Rev. Lett. 95, 053904 (2005).
[CrossRef]

O. Manela, O. Cohen, G. Bartal, J. W. Fleischer, and M. Segev, Opt. Lett. 29, 2049 (2004).
[CrossRef] [PubMed]

Stratton, J. A.

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, 1941), Chap. VI.

Torner, L.

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Phys. Rev. Lett. 93, 093904 (2004).
[CrossRef]

Trillo, S.

C. Conti and S. Trillo, Phys. Rev. Lett. 92, 120404 (2004).
[CrossRef]

P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, Phys. Rev. Lett. 91, 093904 (2003).
[CrossRef]

Trull, J.

P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, Phys. Rev. Lett. 91, 093904 (2003).
[CrossRef]

Valiulis, G.

P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, Phys. Rev. Lett. 91, 093904 (2003).
[CrossRef]

Vysloukh, V. A.

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Phys. Rev. Lett. 93, 093904 (2004).
[CrossRef]

Wulle, T.

T. Wulle and S. Herminghaus, Phys. Rev. Lett. 70, 1401 (1993).
[CrossRef] [PubMed]

IEEE Trans. Ultrason. Ferroelectr. Freq. Control (1)

J. Lu and J. F. Greenleaf, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 39, 19 (1992).
[CrossRef]

J. Opt. Soc. Am. A (2)

Opt. Lett. (3)

Phys. Rev. B (1)

S. Longhi and D. Janner, Phys. Rev. B 70, 235123 (2004).
[CrossRef]

Phys. Rev. Lett. (7)

C. Conti and S. Trillo, Phys. Rev. Lett. 92, 120404 (2004).
[CrossRef]

J. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef] [PubMed]

T. Wulle and S. Herminghaus, Phys. Rev. Lett. 70, 1401 (1993).
[CrossRef] [PubMed]

P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, Phys. Rev. Lett. 91, 093904 (2003).
[CrossRef]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Phys. Rev. Lett. 93, 093904 (2004).
[CrossRef]

J. Salo, J. Fagerholm, A. T. Friberg, and M. M. Salomaa, Phys. Rev. Lett. 83, 1171 (1999).
[CrossRef]

G. Bartal, O. Manela, O. Cohen, J. W. Fleischer, and M. SegevPhys. Rev. Lett. 95, 053904 (2005).
[CrossRef]

Other (2)

N. W. Ashcroft and N. D. Mermin, Solid State Physics (Saunders, 1976).

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, 1941), Chap. VI.

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 (4)

Fig. 1
Fig. 1

(a) First two bands in the band structure of a 2D square lattice with D = 5.5 . Inset, high symmetry points of the reciprocal lattice. (b), (c) Curves of equal propagation constant of the first band (b) and the second band (c).

Fig. 2
Fig. 2

Absolute value (a), (c), (e) and phase (b), (d), (f) of first-band NDBs, with the wavenumber (a), (b) encircling the Γ point, (c), (d) passing through the X points, (e), (f) encircling the M points. The insets show the loci of the FB modes in the first BZ from which the NDBs were constructed. The gray circles in (b) indicate the boundaries of the waveguides.

Fig. 3
Fig. 3

Absolute value (a), (c), (e) and phase (b), (d), (f) of the second-band NDB, with the wavenumber (a), (b) encircling the Γ point, (c), (d) encircling the Γ point with greater distance, (e), (f) encircling the X points. The insets show the loci of the FB modes in the second BZ from which the NDBs were constructed. The gray circles in (b) indicate the boundaries of the waveguides.

Fig. 4
Fig. 4

Absolute value (a), (c), (e) and phase (b), (d), (f) of NDBs. (a), (b) Combination of second-band Γ-point NDB and third-band M-point NDB phase retarded by π rad , with both NDBs sharing the same β; (c), (d) first-band vortex NDB encircling the Γ point, (e), (f) second-band vortex NDB encircling the X points. The insets show the loci of the FB modes in the corresponding BZs from which the NDBs were constructed. The gray circles in (b) indicate the boundaries of the waveguides.

Equations (1)

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

i A z + 2 A + V ( r ) A = 0 ,

Metrics