Self-collimation in planar photonic crystals

We analyze, in three dimensions, the dispersion properties of dielectric slabs perforated with two-dimensional photonic crystals (PCs) of square symmetry. The band diagrams are calculated for all k-vectors in the first Brillouin zone, and not only along the characteristic high-symmetry directions. We have analyzed the equal-frequency contours of the first two bands, and we found that the square lattice planar photonic crystal is a good candidate for the self-collimation of light beams. We map out the group velocities for the second band of a square lattice planar PC and show that the group velocity is the highest in the region of maximum self-collimation. Such a self-collimated beam is predicted to show beating patterns due to the specific shape of the equal-frequency contours. A geometrical transformation maps the region of the first and second photonic bands where self-collimation takes place one onto the other and gives additional insights on the structural similarities of self-collimation in those two bands.

[1]  A. Scherer,et al.  Waveguiding in Planar Photonic Crystals , 2000 .

[2]  Steven G. Johnson,et al.  Guided modes in photonic crystal slabs , 1999 .

[3]  Susumu Noda,et al.  Trapping and emission of photons by a single defect in a photonic bandgap structure , 2000, Nature.

[4]  Masaya Notomi,et al.  Theory of light propagation in strongly modulated photonic crystals: Refractionlike behavior in the vicinity of the photonic band gap , 2000 .

[5]  Toshihiko Baba,et al.  Photonic crystal light deflection devices using the superprism effect , 2002 .

[6]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[7]  Thomas P. Pearsall,et al.  Experimental and theoretical confirmation of Bloch-mode light propagation in planar photonic crystal waveguides , 2002 .

[8]  Henri Benisty,et al.  Coupled guide and cavity in a two-dimensional photonic crystal , 2001 .

[9]  O. Painter,et al.  Two-dimensional photonic bandgap defect laser , 1999, 1999 Digest of the LEOS Summer Topical Meetings: Nanostructures and Quantum Dots/WDM Components/VCSELs and Microcavaties/RF Photonics for CATV and HFC Systems (Cat. No.99TH8455).

[10]  Shojiro Kawakami,et al.  Fabrication of submicrometre 3D periodic structures composed of Si/SiO2 , 1997 .

[11]  Thomas F. Krauss,et al.  Two-dimensional photonic-bandgap structures operating at near-infrared wavelengths , 1996, Nature.

[12]  T. Krauss,et al.  Superprism phenomena in planar photonic crystals , 2002 .

[13]  Henri Benisty,et al.  Quantitative measurement of transmission, reflection and diffraction of two-dimensional photonic band gap structures at near-infrared wavelengths , 1997 .

[14]  P. Roberts,et al.  Design of thin-film photonic crystal waveguides , 2000, QELS 2000.

[15]  Masaya Notomi,et al.  Superprism Phenomena in Photonic Crystals , 1998 .

[16]  G. Tayeb,et al.  Anomalous refractive properties of photonic crystals , 2000, Journal of the Optical Society of America. A, Optics, image science, and vision.

[17]  Pierre Benech,et al.  Propagation losses of the fundamental mode in a single line-defect photonic crystal waveguide on an InP membrane , 2002 .

[18]  Allen Taflove,et al.  Computational Electrodynamics the Finite-Difference Time-Domain Method , 1995 .

[19]  Eli Yablonovitch,et al.  Inhibited spontaneous emission in solid-state electronics , 1987 .

[20]  Masaya Notomi,et al.  Self-collimating phenomena in photonic crystals , 1999 .