At the exit surface of a photonic crystal, the intensity of the diffracted wave can be periodically modulated, showing a maximum in the “positive” (forward diffracted) or in the “negative” (diffracted) direction, depending on the slab thickness. This thickness dependence is a direct result of the so-called Pendellösung phenomenon, consisting of the periodic exchange inside the crystal of the energy between direct and diffracted beams. We report the experimental observation of this effect in the microwave region at about 14GHz by irradiating 2D photonic crystal slabs of different thickness and detecting the intensity distribution of the electromagnetic field at the exit surface and inside the crystal itself.

© 2008 Optical Society of America

1. P. P. Ewald, "Zur Theorie der Interferenzen der R¨ontgenstrahlen," Physik Z. 14, 465 (1913).
2. P. P. Ewald, "Crystal optics for visible light and X rays," Rev. Mod. Phys. 37, 46 (1965). [CrossRef]
3. A. Authier, Dynamical Theory of X-ray Diffraction (Oxford University Press,Oxford, 2001).
4. N. Kato and A. R. Lang, "The projection topograph: a new method in X-ray diffraction microradiography," Acta Cryst. 12, 249 (1959). [CrossRef]
5. D. Sippel, K. Kleinstu, and G. E. R. Schulze, "Pendellösungs-interferenzen mit thermischen neutronen an Sieinkristallen," Phys. Lett. 14, 174 (1965). [CrossRef]
6. C. G. Shull, "Observation of Pendellösung Fringe Structure in Neutron Diffraction," Phys. Rev. Lett. 21, 1585 (1968). [CrossRef]
7. V. Mocella, J. Hrtwig, J. Baruchel, and A. Mazuelas, "Influence of the transverse and longitudinal coherence in dynamical theory of X-ray diffraction," J. Phys. D: Appl. Phys. 32, A88 (1999). [CrossRef]
8. M. Born, Athomtheorie des festen Zustandes (Springer, Berlin, 1923).
9. V. Mocella, "Negative refraction in Photonic Crystals: thickness dependence and Pendell¨osung phenomenon," Opt. Express 13, 1361 (2005). [CrossRef] [PubMed]
10. A. Balestreri, L. C. Andreani, and M. Agio, "Optical properties and diffraction effects in opal photonic crystals," Phys. Rev. E 74, 036.603 (2006). [CrossRef]
11. O. Francescangeli, S. Melone, and R. D. Leo, "Dynamical diffraction of microwaves by periodic dielectric media," Phys. Rev. A 40, 4988 (1989). [CrossRef] [PubMed]
12. M. L. Calvo, P. Cheben, O. Martnez-Matos, F. del Monte, and J. A. Rodrigo, "Experimental Detection of the Optical Pendell¨osung Effect," Phys. Rev. Lett. 97, 084,801 (2006). [CrossRef]
13. V. Mocella, P. Dardano, L. Moretti, and I. Rendina, "A polarizing beam splitter using negative refraction of photonic crystals," Opt. Express 13, 7699 (2005). [CrossRef] [PubMed]
14. N. Kato, "The determination of structure factors by means of Pendell¨osung fringes," Acta Cryst. A 25, 119 (1969)

Acta Cryst.

• N. Kato and A. R. Lang, "The projection topograph: a new method in X-ray diffraction microradiography," Acta Cryst. 12, 249 (1959). [CrossRef]

Acta Cryst. A

• N. Kato, "The determination of structure factors by means of Pendell¨osung fringes," Acta Cryst. A 25, 119 (1969)

J. Phys. D: Appl. Phys.

• V. Mocella, J. Hrtwig, J. Baruchel, and A. Mazuelas, "Influence of the transverse and longitudinal coherence in dynamical theory of X-ray diffraction," J. Phys. D: Appl. Phys. 32, A88 (1999). [CrossRef]

Opt. Express

• V. Mocella, "Negative refraction in Photonic Crystals: thickness dependence and Pendell¨osung phenomenon," Opt. Express 13, 1361 (2005). [CrossRef] [PubMed]
• V. Mocella, P. Dardano, L. Moretti, and I. Rendina, "A polarizing beam splitter using negative refraction of photonic crystals," Opt. Express 13, 7699 (2005). [CrossRef] [PubMed]

Phys. Lett.

• D. Sippel, K. Kleinstu, and G. E. R. Schulze, "Pendellösungs-interferenzen mit thermischen neutronen an Sieinkristallen," Phys. Lett. 14, 174 (1965). [CrossRef]

Phys. Rev. A

• O. Francescangeli, S. Melone, and R. D. Leo, "Dynamical diffraction of microwaves by periodic dielectric media," Phys. Rev. A 40, 4988 (1989). [CrossRef] [PubMed]

Phys. Rev. Lett.

• M. L. Calvo, P. Cheben, O. Martnez-Matos, F. del Monte, and J. A. Rodrigo, "Experimental Detection of the Optical Pendell¨osung Effect," Phys. Rev. Lett. 97, 084,801 (2006). [CrossRef]
• C. G. Shull, "Observation of Pendellösung Fringe Structure in Neutron Diffraction," Phys. Rev. Lett. 21, 1585 (1968). [CrossRef]

Physik Z.

• P. P. Ewald, "Zur Theorie der Interferenzen der R¨ontgenstrahlen," Physik Z. 14, 465 (1913).

Rev. Mod. Phys.

• P. P. Ewald, "Crystal optics for visible light and X rays," Rev. Mod. Phys. 37, 46 (1965). [CrossRef]

Other

• A. Authier, Dynamical Theory of X-ray Diffraction (Oxford University Press,Oxford, 2001).
• A. Balestreri, L. C. Andreani, and M. Agio, "Optical properties and diffraction effects in opal photonic crystals," Phys. Rev. E 74, 036.603 (2006). [CrossRef]
• M. Born, Athomtheorie des festen Zustandes (Springer, Berlin, 1923).

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