Refraction and Dispersion in Nonlinear Photonic Crystal Superlattices

Transcription

1 Refraction and Dispersion in Nonlinear Photonic Crystal Superlattices LEOS 18 th Annual Meeting Sydney, Australia Monday, 24 October 2005 Curtis W. Neff, Tsuyoshi Yamashita and Christopher J. Summers Presented by: Davy P. Gaillot School of Materials Science & Engineering, Georgia Institute of Technology Atlanta, GA 30332

2 Outline Introduction to superlattice structure Experimental methods Fabrication Optical characterization Results Reflectivity spectrum Band structure: Measured and calculated Tunable SL PC structures Consequences of index tuning Refraction effects: FDTD and wavevector analyses Conclusion 2005 Neff 2

3 Motivation Fabrication of 2D PCs not as complicated as 3D 2D PC offers integration onto opto-electronic systems directly on common substrate Superlattice PC structures of this type have not been fabricated or characterized Observe band folding effects in PCs Improvement of large refraction effects (superprism) for beam steering, signal processing, demultiplexing Investigate methods to electro-optically tune these effects, such as tunable refraction 2005 Neff 3

4 Two Dimensional PC: Triangular Lattice Simpler structure than 3D Top-down fabrication Integration with planar circuits Simpler analysis of optical properties than 3D Can have full PBG (light in plane of PC) Giant refraction effects Superprism effects y x Hz Ey Ex TE polarization Real Space Band diagram: Plot of dispersion relationship, ω(k), along irreducible BZ boundary Reciprocal Space Band Diagram 2005 Neff 4

5 Superlattice: Real & Reciprocal Space b 1 a 1 row i row j a a 2 b 2 Υ Γ Μ Χ Real Space Alternating rows posses different property ( r, n, or both) Unit cell definition with two holes per lattice point Reciprocal Space New BZ representation: hexagonal becomes rectangular BZ folding Symmetry reduction: six-fold to two-fold 2005 Neff 5

6 Fabrication E-beam lithography ICP dry etching with Chlorine/C 4 F 6 recipe 1 mm 2 area written using smaller unit patterns Lattice constant: a=358 nm Silicon slab waveguide (SWG) ~300 nm 1 µm Si SiO 2 Si 2005 Neff 6

7 Optical Characterization Resonant band coupling technique (Astratov et al. PRB 99) Light with in-plane wavevector matching wavevector of a band in PC couples with SWG, causing dip in reflectivity spectrum Effective for bands outside of guiding regime of SWG (light cone). Incident beam In-plane wavevector Γ Y W lamp k 0 X θ M Signal chopper θ Sample stage φ Spectrometer InGaAs detector Lock-in analyzer Preamplifier 2005 Neff 7

8 Reflectivity: Unpatterned vs. Thin Film Interference Patterned SoI Gradual dips thin film interference Sharp dips coupling of light with band of PC Repeat measurement for multiple angles, θ, and multiple lattice directions 2005 Neff 8

9 Superlattice: Measured and Calculated Bands Measured bands FDTD calculated bands Dips in spectrum filtered and plotted as ω vs. k Full 3D FDTD calculations to match structure 400 nm X M Γ Y 2005 Neff 9

10 Tunable Photonic Crystal Superlattices Triangular Lattice Dynamic SL Dynamic Hybrid Dynamic : Row addressing scheme to modulate n (Park et al., Static SL PECS IV 2002) Static : Modulation in hole radius Static E/O SL allows tunability of optical properties (Neff et al., SPIE 2004) Static Infiltrated Static E/O 2005 Neff 10

11 Static Infiltrated SL Band Structure Biased ε = 2.25 Unbiased ε = 2.89 Dispersion Contours Refraction Changing bias/unbias state changes alignment of LC director Æ changes ε Changes band structure Changes dispersion contours Changes refraction response 2005 Neff 11

12 Beam Visualization and Wavevector Analysis Interface line θr~85 Construction line εh=2.25 θr~8 θi=6 θi=6 θ ~70 r Γ M θr~8 εh=3.61 Si Region εh=2.25 εh=3.61 Y ωn=0.260 Beam steering over 60 Discrepancies between FDTD and wavevector calculations caused by: Finite beam size in FDTD and inaccurate measurements due to beam spreading 2005 Neff 12

13 Conclusion Successfully developed new concept of SL PC Experimentally observed band folding effect Demonstrated that SL offers enhancement in tunable refraction effects SL introduces unique optical properties to PCs and creates new regimes for beam propagation effects 2005 Neff 13

14 Acknowledgements Group members: Dr. Jeffrey S. King Dr. Elton Graugnard Faculty & Staff of MiRC Supported under MURI project funded by Army Research Office under contract DAAD Contact information: Dr. Neff: Dr. Summers: 2005 Neff 14