Optical computers and photonic integrated circuits in high capacity optical networks are hot topics, attracting the attention of expert researchers and commercial technology companies. Optical packet switching and routing technologies promise to provide a more efficient source of power, and footprint scaling with increased router capacity; integrating more optical processing elements into the same chip to increase on-chip processing capability and system intelligence has become a priority.

This book is an in-depth look at modelling techniques and the simulation of a wide range of liquid crystal based modern photonic devices with enhanced high levels of flexible integration and enhanced power processing. It covers the physics of liquid crystal materials; techniques required for modelling liquid crystal based devices; the state-of-the art liquid crystal photonic based applications for telecommunications such as couplers, polarization rotators, polarization splitters and multiplexer-demultiplexers; liquid core photonic crystal fiber (LC-PCF) sensors including biomedical and temperature sensors; and liquid crystal photonic crystal based encryption systems for security applications.

Key features

* Offers a unique source of in-depth learning on the fundamental principles of computational liquid crystal photonics.

* Explains complex concepts such as photonic crystals, liquid crystals, waveguides and modes, and frequency- and time-domain techniques used in the design of liquid crystal photonic crystal photonic devices in terms that are easy to understand.

* Demonstrates the useful properties of liquid crystals in a diverse and ever-growing list of technological applications.

* Requires only a foundational knowledge of mathematics and physics.

Salah S. A. Obayya, Zewail City of Science and Technology, Giza, Egypt
Professor Salah Obayya developed for his PhD a novel finite element-based full-vectorial-beam-propagation algorithm for the analysis of various photonic devices. He worked as a Senior Research Fellow at the School of Engineering, City University London. From June 2003 until Sept. 2006, he joined the School of Engineering and Design, Brunel University, West London, U.K., to work as a Senior Lecturer, followed by a Readership at The School of Electronic and Electrical Engineering, University of Leeds. Professor Obayya is now Full Professorial Chair of Photonics and led the establishment of the "Nano-Photonics Research Centre" at The University of Glamorgan, UK, while he is now Full Professor of Photonics and Director of Centre for Photonics and Smart Materials at Zewail City of Science and Technology.

Mohamed Farahat O. Hameed, Zerwail City of Science and Technology, Giza, Egypt
Dr Mohamed Farahat O. Hameed was a member of Prof. Obayya photonics group at Leeds University, South Wales University, UK, and now Zewail City, contributing in the design and analysis of a wide range of liquid crystal based photonic devices such as polarization splitter, polarization rotators, couplers, multiplexer-demultiplexers, and sensors.

Nihal F. F. Areed, Zerwail City of Science and Technology, Giza, Egypt
Associate Professor Nihal Areed is a lecturer at Electronics and Communications Dept., Faculty of Engineering, Mansoura University, Mansoura, Egypt. She obtained her PhD degrees in Electronics and Communications Engineering from Mansoura University, Egypt. Her main research interests are focused on the fields of electromagnetics and photonics, in particular in the area of modelling, design and numerical simulation of nanophotonic devices.

Preface xv

Part I Basic Principles 1

1 Principles of Waveguides 3

1.1 Introduction 3

1.2 Basic Optical Waveguides 4

1.3 Maxwell's Equations 6

1.4 The Wave Equation and Its Solutions 7

1.5 Boundary Conditions 9

1.6 Phase and Group Velocity 10

1.6.1 Phase Velocity 10

1.6.2 Group Velocity 11

1.7 Modes in Planar Optical Waveguide 12

1.7.1 Radiation Modes 13

1.7.2 Confinement Modes 13

1.8 Dispersion in Planar Waveguide 13

1.8.1 lntermodal Dispersion 14

1.8.2 lntramodal Dispersion 14

1.9 Summary 15

References 15

2 Fundamentals of Photonic Crystals 17

2.1 Introduction 17

2.2 Types of PhCs 18

2.2.1 1D PhCs 18

2.2.2 2D PhCs 19

2.2.3 3D PhCs 21

2.3 Photonic Band Calculations 21

2.3.1 Maxwell's Equations and the PhC 22

2.3.2 Floquet-Bloch Theorem, Reciprocal Lattice, and Brillouin Zones 23

2.3.3 Plane Wave Expansion Method 26

2.3.4 FDTD Method 29

2.3.4.1 Band Structure 29

2.3.4.2 Transmission Diagram 30

2.3.5 Photonic Band for Square Lattice 30

2.4 Defects in PhCs 31

2.5 Fabrication Techniques of PhCs 32

2.5.1 Electron-Beam Lithography 32

2.5.2 Interference Lithography 33

2.5.3 Nano-Imprint Lithography 33

2.5.4 Colloidal Self-Assembly 34

2.6 Applications of PhCs 34

2.7 Photonic Crystal Fiber 35

2.7.1 Construction 35

2.7.2 Modes of Operation 36

2.7.2.1 High Index Guiding Fiber 36

2.7.2.2 PBG Fibers 36

2.7.3 Fabrication of PCF 37

2.7.4 Applications of PCF 37

2.8 Summary 37

References 37

3 Fundamentals of Liquid Crystals 41

3.1 Introduction 41

3.2 Molecular Structure and Chemical Composition of an LC Cell 42

3.3 LC Phases 42

3.3.1 Thermotropic LCs 44

3.3.1.1 Nematic Phase 44

3.3.1.2 Smectic Phase 44

3.3.1.3 Chiral Phases 45

3.3.1.4 Blue Phases 46

3.3.1.5 Discotic Phases 46

3.3.2 Lyotropic LCs 47

3.3.3 Metallotropic LCs 48

3.4 LC Physical Properties in External Fields 48

3.4.1 Electric Field Effect 48

3.4.2 Magnetic Field Effect 49

3.4.2.1 Frederiks Transition 49

3.5 Theortitcal Tratment of LC 50

3.5.1 LC Parameters 50

3.5.1.1 Director 50

3.5.1.2 Order Parameter 50

3.5.2 LC Models 51

3.5.2.1 Onsager Hard-Rod Model 51

3.5.2.2 Maier-Saupe Mean Field Theory 52

3.5.2.3 McMillan's Model 52

3.6 LC Sample Preparation 52

3.7 LCs for Display Applications 53

3.8 LC Thermometers 54

3.9 Optical Imaging 54

3.10 LC into Fiber Optics and LC Planar Photonic Crystal 54

3.11 LC Solar Cell 55

References 55

Part II N umerical Techniques 57

4 Full-Vectorial Finite-Difference Method 59

4.1 Introduction 59

4.2 Overview of Modeling Methods 59

4.3 Formulation of the FVFDM 60

4.3.1 Maxwell's Equations 60

4.3.2 Wave Equation 61

4.3.3 Boundary Conditions 63

4.3.4 Maxwell's Equations in Complex Coordinate 64

4.3.5 Matrix Solution 65

4.3.5.1 Power Method 65

4.3.5.2 Inverse Power Method 66

4.3.5.3 Shifted Inverse Power Method 66

4.4 Summary 66

References 66

5 Assessment of the Full-Vectorial Finite-Difference Method 69

5.1 Introduction 69

5.2 Overview of the LC-PCF 69

5.3 Soft Glass 70

5.4 Design of Soft Glass PCF with LC Core 71

5.5 Numerical Results 73

5.5.1 FVFDM Validation 73

5.5.2 Modal Hybridness 74

5.5.3 Effective Index 75

5.5.4 Effective Mode Area 76

5.5.5 Nonlinearity 76

5.5.6 Birefringence 77

5.5.7 Effect of the NLC Rotation Angle 80

5.5.8 Effect of the Temperature 81

5.5.9 Elliptical SGLC-PCF 83

5.6 Experimental Results of LC-PCF 84

5.6.1 Filling Temperature 84

5.6.2 Filling Time 84

5.7 Summary 85

References 85

6 Full-Vectorial Beam Propagation Method …