OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 16, Iss. 5 — Mar. 3, 2008
  • pp: 3299–3304

Bloch oscillations in chirped layered structures with metamaterials

Arthur R. Davoyan, Ilya V. Shadrivov, Andrey A. Sukhorukov, and Yuri S. Kivshar  »View Author Affiliations


Optics Express, Vol. 16, Issue 5, pp. 3299-3304 (2008)
http://dx.doi.org/10.1364/OE.16.003299


View Full Text Article

Enhanced HTML    Acrobat PDF (395 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

We analyze the Bloch oscillations of electromagnetic waves in chirped layered structures with alternating layers of negative-index metamaterial and conventional dielectric under the condition of the zero average refractive index. We consider the case when the chirp is introduced by varying the thickness of the layers linearly across the structure. We demonstrate that such structures can support three different types of the Bloch oscillations for electromagnetic waves associated with either propagating or evanescent guided modes. In particular, we predict a novel type of the Bloch oscillations associated with coupling between surface waves excited at the interfaces separating the layers of negative-index metamaterial and the layers of the conventional dielectric.

© 2008 Optical Society of America

OCIS Codes
(050.2770) Diffraction and gratings : Gratings
(350.5500) Other areas of optics : Propagation
(350.3618) Other areas of optics : Left-handed materials

ToC Category:
Metamaterials

History
Original Manuscript: December 18, 2007
Revised Manuscript: February 18, 2008
Manuscript Accepted: February 20, 2008
Published: February 26, 2008

Citation
Arthur R. Davoyan, Ilya V. Shadrivov, Andrey A. Sukhorukov, and Yuri S. Kivshar, "Bloch oscillations in chirped layered structures with metamaterials," Opt. Express 16, 3299-3304 (2008)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-5-3299


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. F. Bloch, "Uber die Quantenmechanik der Elektronen in Kristallgittern," Z. Phys. A: Hadrons Nucl. 52, 555-600 (1928).
  2. G. H. Wannier, "Wave functions and effective Hamiltonian for Bloch electrons in an electric field," Phys. Rev. 117, 432-439 (1960). [CrossRef]
  3. C. Waschke, H. G. Roskos, R. Schwedler, K. Leo, H. Kurz, and K. Kohler, "Coherent submillimeter-wave emission from Bloch oscillations in a semiconductor superlattice," Phys. Rev. Lett. 70, 3319-3322 (1993). [CrossRef] [PubMed]
  4. C. M. de Sterke, J. N. Bright, P. A. Krug, and T. E. Hammon, "Observation of an optical Wannier-Stark ladder," Phys. Rev. E 57, 2365-2370 (1998). [CrossRef]
  5. R. Morandotti, U. Peschel, J. S. Aitchinson, H. S. Eisenberg, Y. Silberberg, "Experimental observation of linear and nonlinear optical Bloch oscillations," Phys. Rev. Lett. 83, 4756-4759 (1999) [CrossRef]
  6. T. Pertsch, P. Dannberg, W. Elflein, A. Brauer, and F. Lederer, "Optical Bloch Oscillations in Temperature Tuned Waveguide Arrays," Phys. Rev. Lett. 83, 4752-4755 (1999). [CrossRef]
  7. V. Agarwal, J. A. del Rio, G. Malpuech, M. Zamfirescu, A. Kavokin, D. Coquillat, D. Scalbert, M. Vladimirova, and B. Gil, "Photon Bloch Oscillations in Porous Silicon Optical Superlattices," Phys. Rev. Lett. 92, 097401 (2004). [CrossRef] [PubMed]
  8. P. B. Wilkinson, "Photonic Bloch oscillations and Wannier-Stark ladders in exponentially chirped Bragg gratings," Phys. Rev. E 65, 056616 (2002). [CrossRef]
  9. R. Sapienza, P. Costantino, D. Wiersma, M. Ghulinyan, C. J. Oton, and L. Pavesi, "Optical Analogue of Electronic Bloch Oscillations," Phys. Rev. Lett. 91, 263902 (2003). [CrossRef]
  10. G. Lenz, I. Talanina, and C. M. de Sterke, "Bloch Oscillations in an Array of Curved Optical Waveguides," Phys. Rev. Lett. 83, 963-966 (1999). [CrossRef]
  11. D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, "Metamaterials and Negative Refractive Index," Science 305, 788-792 (2004). [CrossRef] [PubMed]
  12. J. Li, L. Zhou, C. T. Chan, and P. Sheng, "Photonic Band Gap from a Stack of Positive and Negative Index Materials," Phys. Rev. Lett. 90, 083901 (2003). [CrossRef] [PubMed]
  13. I. V. Shadrivov, A. A. Sukhorukov, and Yu. S. Kivshar, "Beam shaping by a periodic structure with negative refraction," Appl. Phys. Lett. 82, 3820-3822 (2003). [CrossRef]
  14. P. Yeh, Optical Waves in Layered Media (John Wiley & Sons, New York, 1988).
  15. I. V. Shadrivov, A. A. Sukhorukov, Yu. S. Kivshar, A. A. Zharov, A. D. Boardman, and P. Egan, "Nonlinear surface waves in left-handed materials," Phys. Rev. E 69, 016617 (2004). [CrossRef]
  16. A. A. Sukhorukov, I. V. Shadrivov, and Yu. S. Kivshar, "Wave scattering by metamaterial wedges and interfaces," Int. J. Num. Model. 19, 105-117 (2006). [CrossRef]
  17. V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of epsilon and mu," Usp. Fiz. Nauk 92, 517-526 (1967) (in Russian) [English translation: Sov. Phys. Usp. 10, 509 (1968)].

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited