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E-raamat: Computational Methods for Electromagnetic and Optical Systems

(University of Dayton, Ohio, USA), (University of Alabama, Huntsville, USA)
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Computational Methods for Electromagnetic and Optical SystemsSuurem pilt
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The current rapid and complex advancement applications of electromagnetic (EM) and optical systems calls for a much needed update on the computational methods currently in use. Completely revised and reflecting ten years of develoments, this second edition of the bestselling Computational Methods for Electromagnetic and Optical Systems provides the update so desperately needed in this field.

Offering a wealth of new material, this second edition begins with scalar wave propagation and analysis techniques, chiral and metamaterials, and photonic band gap structures. It examines Pontying vector and stored energy, as well as energy, group, and phase velocities; reviews k-space state variable formation with applications to anistropic planar systems; and presents full-field rigorous coupled wave analysis of planar diffraction gratings with applications to H-mode, E-mode, crossed gratings, single and multilayered diffraction grating analysis, and diffraction from anistropic gratings.

Later chapters highlight spectral techniques and RCWA as applied to the analysis of dynamic wave-mixing in PR materials with induced transmission and reflection gratings and demonstrate the RCWA algorithm to analyze cylindrical and spherical systems using circular, bipolar cylindrical, and spherical coordinates. The book concludes with several RCWA computational case studies involving scattering from spatially inhomogeneous eccentric circular cylinders, solved in bipolar coordinates. Many of these examples apply the complex Poynting theorem or the forwardscattering (optical) theorem to validate numerical solutions by verifying power conservation.

Using common computational tools such as Fortran, MATLAB, COMSOL, and RSOFT, the text offers numerous examples to illuminate the material, many of which employ a full-field vector approach to analyze and solve Maxwells equations in anisotropic media where a standard wave equation approach is intractable. Designed to introduce novel spectral computational techniques, the book demonstrates the application of these methods to analyze a variety of EM and optical systems.

Arvustused

Praise for the First Edition

"...a small but formidable book which rigorously sets out the basic theory, provides useful illustrative problems and directs the reader to relevant further reading from the excellent reference lists. The book is directed towards graduate students and researchers but selected sections would provide valuable undergraduate teaching material. It is the type of wide-ranging reference book that will find its way onto many bookshelves and, over the years, will become well-worn from frequent use." ProfBooks.com, 2001

Preface xiii
Authors xv
Chapter 1 Mathematical Preliminaries 1(10)
1.1 Introduction
1(1)
1.2 Fourier Series and Its Properties
1(2)
1.3 Fourier Transform
3(1)
1.4 Hankel Transform
4(1)
1.5 Discrete Fourier Transform
4(1)
1.6 Review of Eigenanalysis
5(5)
Problems
10(1)
References
10(1)
Chapter 2 Scalar EM Beam Propagation in Inhomogeneous Media 11(40)
2.1 Introduction
11(1)
2.2 Transfer Function for Propagation
11(1)
2.3 Split-Step Beam Propagation Method
12(2)
2.4 Beam Propagation in Linear Media
14(4)
2.4.1 Linear Free-Space Beam Propagation
14(2)
2.4.2 Propagation of Gaussian Beam through Graded Index Medium
16(2)
2.5 Beam Propagation through Diffraction Gratings: Acoustooptic Diffraction
18(1)
2.6 Beam Propagation in Kerr-Type Nonlinear Media
19(9)
2.6.1 Nonlinear Schrodinger Equation
19(3)
2.6.2 Simulation of Self-Focusing Using Adaptive Fourier and Fourier-Hankel Transform Methods
22(6)
2.7 Beam Propagation and Coupling in Photorefractive Media
28(11)
2.7.1 Basic Photorefractive Physics
28(1)
2.7.2 Induced Transmission Gratings
29(6)
2.7.3 Induced Reflection Gratings and Bidirectional Beam Propagation Method
35(4)
2.8 z-Scan Method
39(7)
2.8.1 Model for Beam Propagation through PR Lithium Niobate
41(2)
2.8.2 z-Scan: Analytical Results, Simulations, and Sample Experiments
43(3)
Problems
46(1)
References
47(4)
Chapter 3 EM Wave Propagation in Linear Media 51(32)
3.1 Introduction
51(1)
3.2 Maxwell's Equations
51(2)
3.3 Constitutive Relations: Frequency Dependence and Chirality
53(3)
3.3.1 Constitutive Relations and Frequency Dependence
53(2)
3.3.2 Constitutive Relations for Chiral Media
55(1)
3.4 Plane Wave Propagation through Linear Homogeneous Isotropic Media
56(6)
3.4.1 Dispersive Media
57(4)
3.4.2 Chiral Media
61(1)
3.5 Power Flow, Stored Energy, Energy Velocity, Group Velocity, and Phase Velocity
62(3)
3.6 Metamaterials and Negative Index Media
65(6)
3.6.1 Beam Propagation in NIMs
68(3)
3.7 Propagation through Photonic Band Gap Structures: The Transfer Matrix Method
71(7)
3.7.1 Periodic PIM-NIM Structures
75(1)
3.7.2 EM Propagation in Complex Structures
75(3)
Problems
78(2)
References
80(3)
Chapter 4 Spectral State Variable Formulation for Planar Systems 83(46)
4.1 Introduction
83(3)
4.2 State Variable Analysis of an Isotropic Layer
86(18)
4.2.1 Introduction
86(1)
4.2.2 Analysis
87(3)
4.2.3 Complex Poynting Theorem
90(3)
4.2.4 State Variable Analysis of an Isotropic Layer in Free Space
93(5)
4.2.5 State Variable Analysis of a Radar Absorbing Layer
98(2)
4.2.6 State Variable Analysis of a Source in Isotropic Layered Media
100(4)
4.3 State Variable Analysis of an Anisotropic Layer
104(8)
4.3.1 Introduction
104(1)
4.3.2 Basic Equations
104(4)
4.3.3 Numerical Results
108(4)
4.4 One-Dimensional k-Space State Variable Solution
112(10)
4.4.1 Introduction
112(1)
4.4.2 k-Space Formulation
112(1)
4.4.3 Ground Plane Slot Waveguide System
113(7)
4.4.4 Ground Plane Slot Waveguide System, Numerical Results
120(2)
Problems
122(4)
References
126(3)
Chapter 5 Planar Diffraction Gratings 129(80)
5.1 Introduction
129(3)
5.2 H-Mode Planar Diffraction Grating Analysis
132(21)
5.2.1 Full-Field Formulation
133(6)
5.2.2 Differential Equation Method
139(6)
5.2.3 Numerical Results
145(5)
5.2.4 Diffraction Grating Mirror
150(3)
5.3 Application of RCWA and the Complex Poynting Theorem to E-Mode Planar Diffraction Grating Analysis
153(19)
5.3.1 E-Mode RCWA Formulation
155(3)
5.3.2 Complex Poynting Theorem
158(7)
5.3.2.1 Sample Calculation of PuWE
159(1)
5.3.2.2 Other Poynting Theorem Integrals
160(1)
5.3.2.3 Simplification of Results and Normalization
160(5)
5.3.3 Numerical Results
165(7)
5.4 Multilayer Analysis of E-Mode Diffraction Gratings
172(8)
5.4.1 E-Mode Formulation
173(5)
5.4.2 Numerical Results
178(2)
5.5 Crossed Diffraction Grating
180(22)
5.5.1 Crossed Diffraction Grating Formulation
180(14)
5.5.2 Numerical Results
194(8)
Problems
202(3)
References
205(4)
Chapter 6 Application of RCWA to Analysis of Induced Photorefractive Gratings 209(44)
6.1 Introduction to Photorefractive Materials
209(2)
6.2 Dynamic Nonlinear Model for Diffusion-Controlled PR Materials
211(1)
6.3 Approximate Analysis
212(15)
6.3.1 Numerical Algorithm
215(1)
6.3.2 TE Numerical Simulation Results
215(9)
6.3.3 TM Numerical Simulation Results
224(2)
6.3.4 Discussion of Results from Approximate Analysis
226(1)
6.4 Exact Analysis
227(13)
6.4.1 Finite Difference Kukhtarev Analysis
229(2)
6.4.2 TM Numerical Simulation Results
231(9)
6.5 Reflection Gratings
240(6)
6.5.1 RCWA Optical Field Analysis
240(1)
6.5.2 Material Analysis
241(3)
6.5.3 Numerical Results
244(2)
6.6 Conclusion
246(2)
Problems
248(1)
References
249(4)
Chapter 7 Rigorous Coupled Wave Analysis of Inhomogeneous Cylindrical and Spherical Systems 253(40)
7.1 Introduction
253(1)
7.2 Rigorous Coupled Wave Analysis Circular Cylindrical Systems
254(1)
7.3 Rigorous Coupled Wave Analysis Mathematical Formulation
255(9)
7.3.1 Introduction
255(1)
7.3.2 Basic Equations
256(5)
7.3.3 Numerical Results
261(3)
7.4 Anisotropic Cylindrical Scattering
264(11)
7.4.1 Introduction
264(1)
7.4.2 State Variable Analysis
265(4)
7.4.3 Numerical Results
269(6)
7.5 Spherical Inhomogeneous Analysis
275(14)
7.5.1 Introduction
275(1)
7.5.2 Rigorous Coupled Wave Theory Formulation
275(8)
7.5.3 Numerical Results
283(6)
Problems
289(2)
References
291(2)
Chapter 8 Rigorous Coupled Wave Analysis of Inhomogeneous Bipolar Cylindrical Systems 293(48)
8.1 Introduction
293(3)
8.2 RCWA Bipolar Coordinate Formulation
296(5)
8.2.1 Bipolar and Eccentric Circular Cylindrical, Scattering Region Coordinate Description
296(1)
8.2.2 Bipolar RCWA State Variable Formulation
297(1)
8.2.3 Second-Order Differential Matrix Formulation
298(1)
8.2.4 Thin-Layer, Bipolar Coordinate Eigenfunction Solution
299(2)
8.3 Bessel Function Solutions in Homogeneous Regions of Scattering System
301(1)
8.4 Thin-Layer SV Solution in the Inhomogeneous Region of the Scattering System
301(1)
8.5 Matching of EM Boundary Conditions at Interior-Exterior Interfaces of the Scattering System
302(7)
8.5.1 Bipolar and Circular Cylindrical Coordinate Relations
302(1)
8.5.2 Details of Region 2 (Inhomogenous Region) Region 3 (Homogenous Interior Region) EM Boundary Value Matching
303(3)
8.5.3 Region 0 (Homogenous Exterior Region) Region 2 (Inhomogenous Region) EM Boundary Value Matching
306(1)
8.5.4 Details of Layer-to-Layer EM Boundary Value Matching in the Inhomogeneous Region
306(2)
8.5.5 Inhomogeneous Region Ladder-Matrix
308(1)
8.6 Region 1 Region 3 Bessel-Fourier Coefficient Transfer Matrix
309(3)
8.7 Overall System Matrix
312(1)
8.8 Alternate Forms of the Bessel-Fourier Coefficient Transfer Matrix
313(1)
8.9 Bistatic Scattering Width
314(1)
8.10 Validation of Numerical Results
315(1)
8.11 Numerical Results, Examples of Scattering from Homogeneous and Inhomogeneous Material Objects
315(6)
8.12 Error and Convergence Analysis
321(6)
8.13 Summary, Conclusions, and Future Work
327(1)
Problems
328(5)
Appendix 8.A
333(3)
Appendix 8.B
336(2)
References
338(3)
Chapter 9 Bipolar Coordinate RCWA Computational Examples and Case Studies 341(66)
9.1 Introduction
341(2)
9.2 Case Study I: Fourier Series Expansion, Eigenvalue and Eigenfunction Analysis, and Transfer Matrix Analysis
343(10)
9.3 Case Study II: Comparison of KPE BA, BC Validation Methods, and SV Methods for Relatively Small Diameter Scattering Objects
353(3)
9.4 Case Study III: Comparison of BA, BC, and SV Methods for Gradually, Stepped-Up, Index Profile Scattering Objects
356(12)
9.5 Case Study IV: Comparison of BA, BC, and SV Methods for Mismatched, Index Profile, Scattering Objects
368(9)
9.6 Case Study V: Comparison of BA, BC, and SV Methods for Gradually, Stepped-Up, Index Scattering Objects with High Index Core
377(7)
9.7 Case Study VI: Calculation and Convergence Analysis of EM Fields of an Inhomogeneous Region Material Object Using the SV Method, Δepsilon = 1, α = 5.5, Λ = 0, Example
384(4)
9.8 Case Study VII: Calculation and Convergence Analysis of EM Fields of an Inhomogeneous Region Material Object Using the SV Method, Δepslon = 0.4, α = 5.5, Λ = 0 Example
388(5)
9.9 Case Study VIII: Comparison of Homogeneous and Inhomogeneous Region Bistatic Line Widths
393(3)
9.10 Case Study IX: Conservation of Power Analysis
396(9)
Appendix 9.A: Interpolation Equations
405(2)
References 407(2)
Index 409
John M. Jarem, Partha P. Banerjee
Lisainfo e-raamatute kohta Lisainfo e-raamatute kohta
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