This book provides a set of theoretical and numerical tools useful for the study of wave propagation in metamaterials and photonic crystals. While concentrating on electromagnetic waves, most of the material can be used for acoustic (or quantum) waves. For each presented numerical method, numerical code written in MATLAB® is presented. The codes are limited to 2D problems and can be easily translated in Python or Scilab, and used directly with Octave as well.
| Foreword |
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| Author biography |
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1.1 Macroscopic Maxwell equations |
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1 | (2) |
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1.2.2 Fields decomposition for z invariant media |
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3 | (1) |
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1.3 Harmonic scattering by a bounded obstacle |
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3 | (2) |
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1.4 Covariant formulation |
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5 | (7) |
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1.4.1 The definition of differential forms |
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6 | (3) |
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9 | (1) |
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1.4.3 The exterior derivative |
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10 | (1) |
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11 | (1) |
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1.5 Maxwell equations using forms |
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2.1 The periodic structure |
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1 | (5) |
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2.1.1 Waves in a homogeneous space |
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1 | (1) |
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2 | (4) |
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2.2 Computation of band structures |
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6 | (5) |
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2.3 Topological aspects of Bloch theory |
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11 | (8) |
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2.3.2 Bloch waves revisited |
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19 | (3) |
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1 | (1) |
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3.1 Multiple scattering theory |
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1 | (16) |
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3.1.1 Scattering matrix of a single obstacle |
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1 | (2) |
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3.1.2 Multiple scattering for a finite collection of objects |
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3 | (2) |
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3.1.3 Multiple scattering for a periodic collection of objects |
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3.1.4 Numerical implementation for a finite set of circular cylinders |
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9 | (8) |
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3.2.1 Mathematical formulation of the problem |
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17 | (9) |
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3.2.2 Numerical implementation |
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26 | (5) |
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4 Direct space discretization |
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1 | (1) |
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4.2 Differentiation matrices |
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1 | (8) |
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4.2.1 Chebyshev differentiation matrices |
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1 | (2) |
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3 | (3) |
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4.2.3 Differentiating in higher dimensions: the Kronecker product |
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6 | (1) |
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4.2.4 Perfectly matched layers |
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7 | (2) |
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4.3 Finite differences in frequency domain |
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9 | (5) |
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4.4 Time-dependent problems |
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4.4.1 Time discretization of the equation |
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16 | (1) |
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4.4.2 Finite differences in time domain |
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17 | (7) |
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5 Homogenization and transformation optics |
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1 | (25) |
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1 | (16) |
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5.1.1 Soft problems: a two-scale approach |
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1 | (6) |
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7 | (2) |
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9 | (8) |
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5.2 Transformation optics |
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17 | (9) |
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5.2.1 The geometry of Maxwell equations |
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17 | (3) |
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20 | (6) |
| References |
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Didier Felbacq was born in June 1969 in Cambrai, France. He graduated in mathematics (agregation, 1993) and physics (Ecole Centrale Marseille, 1992). His PhD thesis was on the theoretical and numerical modeling of photonic crystals (1994). Since 2002, he has been a full professor of physics at University of Montpellier. He is involved in theoretical and numerical research in close collaboration with experimentalists. His current activities cover electron transport in transistors for TeraHertz emission and detection, second harmonic emission in photonic crystals, excitons in 2D materials, quantum metamaterials, thermal metamaterials, acoustic metamaterials and biophysics. Didier Felbacq is a former member of the Institut Universitaire de France.
