Preface ........................................................ XV
List of Contributors ......................................... XVII
I. Linear and Non-linear Properties of Photonic Crystals ........ 1
1. Solitary Wave Formation in One-dimensional Photonic
Crystals ..................................................... 3
Sabine Essig, Jens Niegemann, Lasha Tkeshelashvili, and
Kurt Busch
1.1. Introduction ............................................ 3
1.2. Variational Approach to the NLCME ....................... 5
1.3. Radiation Losses ........................................ 9
1.4. Results ................................................ 11
1.5. Conclusions and Outlook ................................ 12
References .................................................. 13
2. Microscopic Analysis of the Optical and Electronic
Properties of Semiconductor Photonic-Crystal Structures ..... 15
Bemhard Pasenow, Matthias Reichelt, Tineke Stroucken,
Torsten Meier, and Stephan W. Koch
2.1. I ntroduction .......................................... 15
2.2. Theoretical Approach ................................... 16
2.2.1. Spatially-Inhomogeneous Maxwell Equations
in Semiconductor Photonic-Crystal Structures .... 17
2.2.1.1. Transverse Part: Self-Consistent
Solution of the Maxwell Semiconductor
Bloch Equations ........................ 18
2.2.1.2. Longitudinal Part: The Generalized
Coulomb Interaction .................... 18
2.2.2. Hamiltonian Describing the Material Dynamics .... 19
2.2.3. Semiconductor Bloch Equations in Real Space ..... 21
2.2.3.1. Low-Intensity Limit .................... 22
2.3. Numerical Results ...................................... 24
2.3.1. Semiconductor Photonic-Crystal Structure ........ 24
2.3.2. Linear Excitonic Absorption ..................... 26
2.3.3. Coherent Wave Packet Dynamics ................... 29
2.3.4. Wave Packet Dynamics with Dephasing and
Relaxation ...................................... 31
2.3.5. Quasi-Equilibrium Absorption and Gain Spectra ... 33
2.4. Summary ................................................ 35
References .................................................. 36
3. Functional 3D Photonic Films from Polymer Beads ............. 39
Birger Lange, Friederike Fleischhaker, and Rudolf
Zentel
3.1. I ntroduction .......................................... 39
3.2. Opals as Coloring Agents ............................... 43
3.2.1. Opal Flakes as Effect Pigments in Clear
Coatings ........................................ 44
3.2.2. Opaline Effect Pigments by Spray Induced
Self-Assembly ................................... 44
3.3. Loading of Opals with Highly Fluorescent Dyes .......... 46
3.4. New Properties Through Replication ..................... 47
3.4.1. Increase of Refractive Index .................... 47
3.4.2. Robust Replica .................................. 48
3.4.3. Inert Replica for Chemistry and Catalysis
at High Temperatures ............................ 49
3.5. Defect Incorporation into Opals ........................ 50
3.5.1. Patterning of the Opal Itself ................... 51
3.5.2. Patterning of an Infiltrated Material ........... 53
3.5.3. Chemistry in Defect Layers ...................... 55
References ...................................... 58
4. Bloch Modes and Group Velocity Delay in Coupled
Resonator Chains ............................................ 63
Bjbrn M. Möller, Mikhail V. Artemyev, and Ulrike
Woggon
4.1. Introduction ........................................... 63
4.2. Experiment ............................................. 64
4.3. Coherent Cavity Field Coupling in One-Dimensional
CROWs .................................................. 65
4.4. Mode Structure in Finite CROWs ......................... 67
4.5. Slowing Down Light in CROWs ............................ 70
4.6. Disorder and Detuning in CROWs ......................... 72
4.7. Summary ................................................ 74
References .................................................. 74
5. Coupled Nanopillar Waveguides: Optical Properties and
Applications ................................................ 77
Dmitry N. Chigrin, Sergei V. Zhukovsky, Andrei V.
Lavrinenko, and Johann Kroha
5.1. Introduction ........................................... 77
5.2. Dispersion Engineering ................................. 79
5.2.1. Dispersion Tuning ............................... 79
5.2.2. Coupled Mode Model .............................. 82
5.3. Transmission Efficiency ................................ 85
5.4. Aperiodic Nanopillar Waveguides ........................ 88
5.5. Applications ........................................... 89
5.5.1. Directional Coupler ............................. 89
5.5.2. Laser Resonators ................................ 90
5.6. Conclusion ............................................. 94
References .................................................. 95
6. Investigations on the Generation of Photonic Crystals
using Two-Photon Polymerization (2PP) of Inorganic-
Organic Hybrid Polymers with Ultra-Short Laser Pulses ....... 97
R. Houbertz, P. Declerck, S. Passinger, A. Ovsianikov,
J. Serbin, and B.N. Chichkov
6.1. Introduction ........................................... 97
6.2. High-Refractive Index Inorganic-Organic Hybrid
Polymers ............................................... 98
6.3. Multi-Photon Fabrication .............................. 104
6.3.1. Experimental Setup ............................. 204
6.3.2. Fabrication of PhC in Standard ORMOCER® ........ 105
6.3.3. 2PP of High Refractive Index Materials ......... 107
6.3.4. Patterning and PhC Fabrication in Positive
Resist Material S1813 .......................... 111
6.4. Summary and Outlook ................................... 112
References ................................................. 113
7. Ultra-low Refractive Index Mesoporous Substrates for
Wavegu ide Structu res ..................................... 115
D. Konjhodzic, S. Schröter, and F. Marlow
7.1. Introduction .......................................... 115
7.2. Mesoporous Films ...................................... 116
7.2.1. Fabrication of Mesoporous Silica Films ......... 116
7.2.1.1. General Remarks ....................... 116
7.2.1.2. Preparation Details ................... 117
7.2.2. Characterization and Structure Determination
of MSFs ........................................ 118
7.2.3. Optical Properties of MSFs ..................... 121
7.2.4. Synthesis Mechanism ............................ 123
7.3. MSFs as Substrates for Waveguide Structures ........... 124
7.3.1. Polymer Waveguides ............................. 124
7.3.2. Ta2O5 Waveguides and 2D PhC Structures ......... 126
7.3.3. PZT Films ...................................... 127
7.4. Conclusions ........................................... 129
References ................................................. 130
8. Linear and Nonlinear Effects of Light Propagation in
Low-index Photonic Crystal Slabs ........................... 131
R. Iliew, C. Etrich, M. Augustin, E.-B. Kley, S.
Nolte, A. Tünnermann, and F. Lederer
8.1. Introduction .......................................... 131
8.2. Fabrication of Photonic Crystal Slabs ................. 132
8.3. Linear Properties of Photonic Crystal Slabs ........... 133
8.3.1. Transmission and High Dispersion of Line-
Defect Waveguides .............................. 134
8.3.2. High-Quality Factor Microcavities in a Low-
Index Photonic Crystal Membrane ................ 138
8.3.3. Unusual Diffraction and Refraction Phenomena
in Photonic Crystal Slabs ...................... 141
8.3.3.1. Self-Collimated Light at Infrared
and Visible Wavelengths ............... 142
8.3.3.2. Negative Refraction of Light .......... 143
8.4. Light Propagation in Nonlinear Photonic Crystals ...... 145
8.4.1. An Optical Parametric Oscillator in
a Photonic Crystal Microcavity ................. 145
8.4.2. Discrete Solitons in Coupled Defects in
Photonic Crystals .............................. 147
8.5. Conclusion ............................................ 152
References ................................................. 152
9. Linear and Non-linear Optical Experiments Based on
Macroporous Silicon Photonic Crystals ...................... 157
Ralf B. Wehrspohn, Stefan L Schweizer, and Vahid
Sandoghdar
9.1. Introduction .......................................... 157
9.2. Fabrication of 2D Photonic Crystals ................... 158
9.2.1. Macroporous Silicon Growth Model ............... 158
9.2.2. Extension of the Pore Formation Modelto
Trench Formation ............................... 162
9.2.3. Fabrication of Trenches and More Complex
Geometries ..................................... 162
9.2.4. Current Limits of Silicon Macropore Etching .... 164
9.3. Defects in 2D Macroporous Silicon Photonic Crystals ... 264
9.3.1. Waveguides ..................................... 165
9.3.2. Beaming ........................................ 166
9.3.3. Microcavities .................................. 168
9.4. Internal Emitter ...................................... 170
9.4.1. Internal Emitter in Bulk 2D Silicon Photonic
Crystals ....................................... 170
9.4.2. Internal Emitter in Microcavities of 2D
Silicon Photonic Crystals ...................... 172
9.4.3. Modified Thermal Emission ...................... 174
9.5. Tunability of Silicon Photonic Crystals ............... 175
9.5.1. Liquid Crystals Tuning ......................... 175
9.5.2. Free-carrier Tuning ............................ 176
9.5.3. Nonlinear Optical Tuning ....................... 177
9.6. Summary ............................................... 179
References ................................................. 180
10.Dispersive Properties of Photonic Crystal Waveguide
Resonators ................................................. 183
T. Sunner, M. Cellner, M. Scholz, A. Löffler, M. Kamp,
and A. Forchel
10.1.Introduction .......................................... 183
10.2.Design and Fabrication ................................ 184
10.2.1.Resonator Design ............................... 184
10.2.2.Fabrication .................................... 186
10.3.Transmission Measurements ............................. 187
10.4.Dispersion Measurements ............................... 189
10.5.Analysis .............................................. 192
10.5.1.Hubert Transformation .......................... 192
10.5.2.Fabry-Perot Model .............................. 194
10.6.Postfabrication Tuning ................................ 195
10.7.Conclusion ............................................ 196
References ................................................. 197
II.Tuneable Photonic Crystals ................................. 199
11.Polymer Based Tuneable Photonic Crystals ................... 202
J.H. Wülbern, M. Schmidt, U. Hübner, R. Boucher,
W. Volksen, Y. Lu, R. Zentel, and M. Eich
11.1.Introduction .......................................... 202
11.2.Preparation of Photonic Crystal Structures in
Polymer Waveguide Material ............................ 202
11.2.1.Materials ...................................... 202
11.2.2.Fabrication .................................... 203
11.3.Realization and Characterization of Electro-
Optically Tuneable Photonic Crystals .................. 208
11.3.1.Characterization ............................... 208
11.3.2.Experimental Results ........................... 220
11.4.Synthesis of Electro-Optically Active Polymers ........ 223
11.5.Conclusions and Outlook ............................... 227
References ................................................. 228
12.Tuneable Photonic Crystals obtained by Liquid Crystal
Infiltration ............................................... 222
H.-S. Kitzerow, A. Lorenz, and H. Matthias
12.1.Introduction .......................................... 222
12.2.Experimental Results .................................. 223
12.2.1.Colloidal Crystals ............................. 223
12.2.2.Photonic Crystals Made of Macroporous
Silicon ........................................ 226
12.2.3.Photonic Crystal Fibres ........................ 231
12.3.Discussion ............................................ 232
12.4.Conclusions ........................................... 233
References ................................................. 234
13.Lasing in Dye-doped Chiral Liquid Crystals: Influence of
Defect Modes ............................................... 239
Wolfgang Haase, Fedor Podgornou, Yuko Matsuhisa, and
Masanori Ozaki
13.1.Introduction .......................................... 239
13.2.Experiment ............................................ 240
13.2.1.Lasing in Cholesterics with Structural
Defects ........................................ 241
13.2.1.1.Preparation of Cholesterics ........... 241
13.2.1.2.Cell Fabrication ...................... 241
13.2.1.3.Preparation of СLC/TiO2 Dispersion .... 242
13.2.1.4.The Experimental Setup ................ 242
13.2.1.5.Experimental Results .................. 243
13.2.2.Lasing in Ferroelectric Liquid Crystals ........ 243
13.2.2.1.Sample Preparation .................... 244
13.2.2.2.The Experimental Setup ................ 245
13.2.2.3.Experimental Results .................. 245
13.2.3.Conclusion ..................................... 248
References ................................................. 248
14.Photonic Crystals based on Chiral Liquid Crystal ........... 251
M. Ozaki, Y. Matsuhisa, H. Yoshida, R. Ozaki,
and A. Fujii
14.1.Introduction .......................................... 251
14.2.Photonic Band Gap and Band Edge Lasing in Chiral
Liquid Crystal ........................................ 252
14.2.1.Laser Action in Cholesteric Liquid Crystal ..... 252
14.2.2.Low-Threshold Lasing Based on Band-Edge
Excitation in CLC .............................. 254
14.2.3.Laser Action in Polymerized Cholesteric
Liquid Crystal Film ............................ 255
14.2.4.Electrically Tunable Laser Action in Chiral
Smectic Liquid Crystal ......................... 256
14.3.Twist Defect Mode in Cholesteric Liquid Crystal ....... 258
14.4.Chiral Defect Mode Induced by Partial Deformation
of Helix .............................................. 259
14.5.Tunable Defect Mode Lasing in a Periodic Structure
Containing CLC Layer as a Defect ...................... 262
14.6.Summary ............................................... 265
References ................................................. 266
15.Tunable Superprism Effect in Photonic Crystals ............. 269
F. Clockler, S. Peters, U. Lemmer, and M. Cerken
15.1.Introduction .......................................... 269
15.2.The Superprism Effect ................................. 270
15.2.1.Origin of the Superprism Effect ................ 270
15.2.2.Performance Considerations for Superprsim
Devices ........................................ 271
15.2.3.Bragg-Stacks and Other ID Superprisms .......... 272
15.2.4.Current State in Superprism Structures ......... 272
15.3.Tunable Photonic Crystals ............................. 273
15.3.1.Liquid Crystals ................................ 274
15.3.2.Tuning by Pockels Effect ....................... 275
15.3.3.All-Optical Tuning ............................. 276
15.3.4.Other Tuning Mechanisms ........................ 278
15.4.Tunable Superprism Structures ......................... 278
15.5.ID Hybrid Organic-Anorganic Structures ................ 279
15.5.1.Survey of Optically Nonlinear Organic
Materials ...................................... 279
15.5.1.1.Thermo-Optic Organic Materials ........ 280
15.5.1.2.Electro-optic Organic Materials ....... 280
15.5.1.3.All-optical Organic Materials ......... 281
15.5.2.Numerical Simulation of a Doubly Resonant
Structures for All-Optical Spatial Beam
Switching ...................................... 282
15.5.2.1.Beam Shifting for Two Active
Cavities .............................. 284
15.5.2.2.Beam Shifting for One Active Cavity ... 284
15.5.2.3.Beam Shifting for Active Coupling
Layers ................................ 284
15.6.Conclusions and Outlook ............................... 286
References ................................................. 286
III.Photonic Crystal Fibres ................................... 289
16.Preparation and Application of Functionalized Photonic
Crystal Fibres ............................................. 291
H. Bartelt,J. Kirchhof, J. Kobeike, K. Chuster,
A. Schwuchow, K. Mörl, U. Röpke, J. Leppert,
H. Lehmann, S. Smolka, M. Barth, O. Benson, S. Taccheo,
and C.D. Andrea
16.1.Introduction .......................................... 291
16.2.General Preparation Techniques for PCFs ............... 292
16.3.Silica-Based PCFs with Index Guiding .................. 292
16.3.1.Specific Properties of Pure Silica PCFs ........ 293
16.3.2.PCF with Very Large Mode Field Parameter
(VLMA-PCF) ..................................... 295
16.3.3.Doped Silica PCF with Germanium-Doped Holey
Core ........................................... 297
16.3.4.Highly Germanium-Doped Index Guiding PCF ....... 299
16.4.Photonic Band Gap Fibres .............................. 302
16.5.Non-Silica PCF ........................................ 305
16.6.Selected Linear and Nonlinear Applications ............ 307
16.6.1.Spectral Sensing ............................... 307
16.6.2.Supercontinuum Generation ...................... 308
16.7.Conclusions ........................................... 310
References ................................................. 310
17.Finite Element Simulation of Radiation Losses in
Photonic Crystal Fibers .................................... 313
Jan Pomplun, Lin Zschiedrich, Roland Klose, Frank
Schmidt, and Sven Burger
17.1.I ntroduction ......................................... 313
17.2.Formulation of Propagation Mode Problem ............... 314
17.3.Discretization of Maxwell's Equations with the
Finite Element Method ................................. 315
17.4.Computation of Leaky Modes in Hollow Core Photonic
Crystal Fibers ........................................ 328
17.5.Goal Oriented Error Estimator ......................... 319
17.6.Convergence of Eigenvalues Using Different Error
Estimators ............................................ 321
17.7.Optimization of HCPCF Design .......................... 324
17.8.Kagome-Structured Fibers .............................. 325
17.9.Conclusion ............................................ 329
References ................................................. 330
IV.Plasmonic and Metamaterials ................................ 333
18.Optical Properties of Photonic/Plasmonic Structures
in Nanocomposite Glass ..................................... 335
H. Graener, A. Abdolvand, S. Wackerow, O. Kiriyenko,
and W. Hergert
18.1.Introduction .......................................... 335
18.2.Experimental Investigations ........................... 335
18.3.Calculation of Effective Permittivity ................. 339
18.3.1.Extensions of the Method ....................... 344
18.4.Summary ............................................... 345
References ................................................. 346
19.Optical Properties of Disordered Metallic Photonic
Crystal Slabs .............................................. 349
D. Nau, A. Schönhardt, A. Christ, T. Zentgraf, Ch.
Bauer, J. Kuhl, and H. Giessen
19.1.Introduction .......................................... 349
19.2.Sample Description and Disorder Models ................ 350
19.3.Transmission Properties ............................... 357
19.4.Bandstructure ......................................... 361
19.5.Conclusion ............................................ 366
References ................................................. 366
20.Superfocusing of Optical Beams Below the Diffraction
Limit by Media with Negative Refraction .................... 369
A. Husakou and J. Herrmann
20.1.Introduction .......................................... 369
20.2.Superfocusing of a Non-Moving Beam by the Combined
Action of an Aperture and a Negative-Index Layer ...... 371
20.2.1.Effective-Medium Approach ...................... 371
20.2.2.Direct Numerical Solution of Maxwell
Equations for Photonic Crystals ................ 373
20.3.Focusing of Scanning Light Beams Below the
Diffraction Limit Using a Saturable Absorber and
a Negative-Refraction Material ........................ 376
20.3.1.Effective-Medium Approach ...................... 377
20.3.2.Direct Numerical Solution of Maxwell
Equations for Photonic Crystals ................ 379
20.4.Subdiffraction Focusing of Scanning Beams by a
Negative-Refraction Layer Combined with a Nonlinear
Kerr-Туре Layer ....................................... 381
20.4.1.Effective-Medium Approach ...................... 381
20.4.2.Direct Numerical Solution of Maxwell
Equations for Photonic Crystals ................ 385
20.5.Conclusion ............................................ 386
References ................................................. 387
21.Negative Refraction in 2D Photonic Crystal Super-
Lattice: Towards Devices in the IR and Visible Ranges ...... 389
Y. Neve-Oz, M. Golosovsky, A. Frenkel, and D. Davidov
21.1.Introduction .......................................... 389
21.2.Design ................................................ 390
21.3.Simulations, Results and Discussion ................... 392
21.3.1.Wave Transmission Through the Superlattice
Slab: Evidence for Negative Phase Velocity ..... 392
21.3.2.Refraction Through a Superlattice Prism ........ 393
21.3.3.Determination of the Refractive Indices
Using the Equal Frequency Contours ............. 395
21.4.Conclusions and Future Directions ..................... 397
References ................................................. 398
22.Negative Permeability around 630 nm in Nanofabricated
Vertical Meander Metamaterials ............................. 399
Heinz Schweizer, Liwei Fu, Hedwig Gräbeldinger,
Hongcang Guo, Na Liu, Stefan Kaiser, and Harald
Giessen
22.1.Introduction .......................................... 399
22.2.Theoretical Approach .................................. 401
22.2.1.Transmission Line Analysis ..................... 401
22.2.1.1.Three Basic TL Circuits ............... 402
22.2.1.2.Role of the S eries Capacitance ....... 403
22.2.2.Numerical Simulations and Syntheses with TL
Analysis ....................................... 404
22.2.2.1.Metamaterials with Different Unit
Cells ................................. 404
22.2.2.2.Numerical Simulation of Meander
Structures ............................ 408
22.3.Experimental Approaches ............................... 410
22.3.1.Fabrication Technologies ....................... 410
22.3.1.1.Plane Metallic Matrices ............... 410
22.3.1.2.Novel Meander Structure ............... 411
22.3.2.Characterization of Fabricated Structures ........... 412
22.3.2.1.Experimental Results of Meander
Strips ................................ 413
22.3.2.2.Experimental Results of Meander
Plates ................................ 414
22.4.Conclusion ............................................ 415
References .................................................... 425
Index ......................................................... 417
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