Artificial Materials

This book addresses artificial materials including photonic crystals (PC) and metamaterials (MM).

The first part is devoted to design concepts: negative permeability and permittivity for negative refraction, periodic structures, transformation optics.

The second part concerns PC and MM in stop band regime: from cavities, guides to high impedance surfaces. Abnormal refraction, less than one and negative, in PC and MM are studied in a third part, addressing super-focusing and cloaking.

Applications for telecommunications, lasers and imaging systems are also explored.

Introduction xi

PART 1. A FEW FUNDAMENTAL CONCEPTS 1

Chapter 1. Definitions and Concepts 3

1.1. Effective parameters of materials 3

1.2. Terminology of artificial materials 6

1.3. Negative refraction: stakes and consequences 8

1.4. Bibliography 11

Chapter 2. The Metamaterial Approach – Permeability and Permittivity Engineering 13

2.1. Background history 13

2.2. An imbricated lattice approach 17

2.3. Cell approach 23

2.4. Alternative approach: Mie resonances 31

2.5. Bibliography 33

Chapter 3. Photonic Crystal Approach – Band Gap Engineering 37

3.1. Historical background 37

3.2. Study tool: band structure 39

3.3. 2D ½ photonic crystals 44

3.4. A few words on three-dimensional photonic crystals 53

3.5. Conclusion: metamaterials or photonic crystals? 55

3.6. Bibliography 56

Chapter 4. Transformation Optics 59

4.1. Context 59

4.2. Method description 60

4.3. Bibliography 69

PART 2. MATERIALS USED IN A BAND GAP REGIME 71

Chapter 5. Point and Extended Defects in Photonic Crystals 73

5.1. Context 73

5.2. Defect zoology 74

5.3. Selectivity of photonic crystal microcavities 77

5.4. Waveguiding in photonic crystals 82

5.5. Slowing down light 90

5.6. Bibliography 92

Chapter 6. Routing Devices made from Photonic Crystals 95

6.1. The building brick: the add/drop filter 95

6.2. A few photonic crystal approaches 98

6.3. Interference-based couplers 100

6.4. Conclusion 117

6.5. Bibliography 117

Chapter 7. Single Negative Metamaterials 121

7.1. Context 121

7.2. ENGs: negative permittivity materials 122

7.3. MNGs: negative permeability materials 128

7.4. What of frequency-selective surfaces? 132

7.5. Bibliographyc 135

PART 3. MATERIALS IN AN ABNORMAL REFRACTION REGIME (N < 1 AND N < 0) 137

Chapter 8. Two-dimensional Microwave Balanced Composite Prism 139

8.1. Why use a microwave prism? 139

8.2. Conception and sizing of a balanced composite lattice 140

8.3. Two-dimensional prism 147

8.4. Bibliography 154

Chapter 9. Metal-dielectric Materials – from the Terahertz to the Visible 157

9.1. From the terahertz to the infrared 157

9.2. A backward propagation line at terahertz frequency 158

9.3. From “nano”-resonators to “fishnets” 163

9.4. Three-dimensional metamaterials 172

9.5. Bibliography 174

Chapter 10. Abnormal Refraction in Photonic Crystals 177

10.1. Context 177

10.2. (An)isotropy in photonic crystals 178

10.3. Exploiting anisotropy 185

10.4. Focalization and negative refraction: looking for isotropy 189

10.5. Bibliography 194

Chapter 11. A Photonic Crystal Flat Lens at Optical Wavelength 197

11.1. A bit of background 197

11.2. How to define a typical prototype at optical wavelengths 198

11.3. Lens optimization: impedance and resolution 201

11.4. Experiments 213

11.5. Reverse engineering: from a two-dimensional prototype to three-dimensional reality 218

11.6. Conclusion 221

11.7. Bibliography 222

Chapter 12. Wave-controlling Systems – Towards Bypass and Invisibility 225

12.1. “Transformation optics” or “dispersion engineering” 225

12.2. Component approaches for controlling waves 226

12.3. Invisibility at terahertz frequencies: Mie resonances 241

12.4. An alternative with the photonic crystal: the butterfly 246

12.5. Perspectives 250

12.6. Bibliography 250

PART 4. MOVING TOWARD APPLICATIONS 253

Chapter 13. Guiding, Filtering and Routing Electromagnetic Waves 255

13.1. Context 255

13.2. Guiding: propagation lines and tunable phase shifters 256

13.3. Filtering 266

13.4. Metamaterial-based routing 273

13.5. Conclusion 276

13.6. Bibliography 276

Chapter 14. Antennas 279

14.1. Towards the miniaturization of transmission/reception systems 279

14.2. Directivity engineering 280

14.3. Subwavelength sizing 293

14.4. Conclusion 298

14.5. Bibliography 299

Chapter 15. Optics: Fibers and Cavities 301

15.1. Optical issues: the privileged domain of photonic crystals 301

15.2. Microstructured optical fibers 302

15.3. Toward zero threshold lasers 310

15.4. Bibliography 318

Chapter 16. Detection, Imaging and Tomography Systems 321

16.1. From detection to imaging 321

16.2. Terahertz sensors 322

16.3. Direct approach for imaging 326

16.4. Detection and image reconstruction 328

16.5. A vast field to explore 337

16.6. Bibliography 339

Conclusion 341

Index 345

Olivier VANBéSIEN is Professor, IEMN, at Lille University, France.