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Beam Propagation Method for Design of Optical Waveguide Devices [Kõva köide]

  • Formaat: Hardback, 408 pages, kõrgus x laius x paksus: 252x175x25 mm, kaal: 758 g
  • Ilmumisaeg: 11-Dec-2015
  • Kirjastus: John Wiley & Sons Inc
  • ISBN-10: 1119083370
  • ISBN-13: 9781119083375
Teised raamatud teemal:
Beam Propagation Method for Design of Optical Waveguide DevicesSuurem pilt
  • Formaat: Hardback, 408 pages, kõrgus x laius x paksus: 252x175x25 mm, kaal: 758 g
  • Ilmumisaeg: 11-Dec-2015
  • Kirjastus: John Wiley & Sons Inc
  • ISBN-10: 1119083370
  • ISBN-13: 9781119083375
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9781119083375.html
Märksõnad:

The basic of the BPM technique in the frequency domain relies on treating the slowly varying envelope of the monochromatic electromagnetic field under paraxial propagation, thus allowing efficient numerical computation in terms of speed and allocated memory. In addition, the BPM based on finite differences is an easy way to implement robust and efficient computer codes. This book presents several approaches for treating the light: wide-angle, scalar approach, semivectorial treatment, and full vectorial treatment of the electromagnetic fields. Also, special topics in BPM cover the simulation of light propagation in anisotropic media, non-linear materials, electro-optic materials, and media with gain/losses, and describe how BPM can deal with strong index discontinuities or waveguide gratings, by introducing the bidirectional-BPM. BPM in the time domain is also described, and the book includes the powerful technique of finite difference time domain method, which fills the gap when the standard BPM is no longer applicable.  Once the description of these numerical techniques have been detailed, the last chapter includes examples of passive, active and functional integrated photonic devices, such as waveguide reflectors, demultiplexers, polarization converters, electro-optic modulators, lasers or frequency converters.  The book will help readers to understand several BPM approaches, to build their own codes, or to properly use the existing commercial software based on these numerical techniques. 

Preface xii
List of Acronyms
xiv
List of Symbols
xvi
1 Electromagnetic Theory of Light
1(21)
Introduction
1(1)
1.1 Electromagnetic Waves
2(5)
1.1.1 Maxwell's Equations
2(3)
1.1.2 Wave Equations in Inhomogeneous Media
5(1)
1.1.3 Wave Equations in Homogeneous Media: Refractive Index
6(1)
1.2 Monochromatic Waves
7(9)
1.2.1 Homogeneous Media: Helmholtz's Equation
9(1)
1.2.2 Light Propagation in Absorbing Media
9(2)
1.2.3 Light Propagation in Anisotropic Media
11(2)
1.2.4 Light Propagation in Second-Order Non-Linear Media
13(3)
1.3 Wave Equation Formulation in Terms of the Transverse Field Components
16(6)
1.3.1 Electric Field Formulation
16(2)
1.3.2 Magnetic Field Formulation
18(1)
1.3.3 Wave Equation in Anisotropic Media
19(1)
1.3.4 Second Order Non-Linear Media
20(1)
References
21(1)
2 The Beam-Propagation Method
22(49)
Introduction
22(1)
2.1 Paraxial Propagation: The Slowly Varying Envelope Approximation (SVEA). Full Vectorial BPM Equations
23(6)
2.2 Semi-Vectorial and Scalar Beam Propagation Equations
29(2)
2.2.1 Scalar Beam Propagation Equation
30(1)
2.3 BPM Based on the Finite Difference Approach
31(1)
2.4 FD-Two-Dimensional Scalar BPM
32(5)
2.5 Von Neumann Analysis of FD-BPM
37(7)
2.5.1 Stability
38(1)
2.5.2 Numerical Dissipation
39(1)
2.5.3 Numerical Dispersion
40(4)
2.6 Boundary Conditions
44(12)
2.6.1 Energy Conservation in the Difference Equations
45(2)
2.6.2 Absorbing Boundary Conditions (ABCs)
47(2)
2.6.3 Transparent Boundary Conditions (TBC)
49(2)
2.6.4 Perfectly Matched Layers (PMLs)
51(5)
2.7 Obtaining the Eigenmodes Using BPM
56(15)
2.7.1 The Correlation Function Method
58(6)
2.7.2 The Imaginary Distance Beam Propagation Method
64(4)
References
68(3)
3 Vectorial and Three-Dimensional Beam Propagation Techniques
71(59)
Introduction
71(1)
3.1 Two-Dimensional Vectorial Beam Propagation Method
72(12)
3.1.1 Formulation Based on the Electric Field
72(9)
3.1.2 Formulation Based on the Magnetic Field
81(3)
3.2 Three-Dimensional BPM Based on the Electric Field
84(29)
3.2.1 Semi-Vectorial Formulation
88(8)
3.2.2 Scalar Approach
96(6)
3.2.3 Full Vectorial BPM
102(11)
3.3 Three-Dimensional BPM Based on the Magnetic Field
113(17)
3.3.1 Semi-Vectorial Formulation
116(4)
3.3.2 Full Vectorial BPM
120(9)
References
129(1)
4 Special Topics on BPM
130(92)
Introduction
130(1)
4.1 Wide-Angle Beam Propagation Method
130(10)
4.1.1 Formalism of Wide-Angle-BPM Based on Pade Approximants
131(2)
4.1.2 Multi-step Method Applied to Wide-Angle BPM
133(2)
4.1.3 Numerical Implementation of Wide-Angle BPM
135(5)
4.2 Treatment of Discontinuities in BPM
140(8)
4.2.1 Reflection and Transmission at an Interface
140(4)
4.2.2 Implementation Using First-Order Approximation to the Square Root
144(4)
4.3 Bidirectional BPM
148(9)
4.3.1 Formulation of Iterative Bi-BPM
148(3)
4.3.2 Finite-Difference Approach of the Bi-BPM
151(3)
4.3.3 Example of Bidirectional BPM: Index Modulation Waveguide Grating
154(3)
4.4 Active Waveguides
157(8)
4.4.1 Rate Equations in a Three-Level System
158(2)
4.4.2 Optical Attenuation/Amplification
160(1)
4.4.3 Channel Waveguide Optical Amplifier
161(4)
4.5 Second-Order Non-Linear Beam Propagation Techniques
165(8)
4.5.1 Paraxial Approximation of Second-Order Non-Linear Wave Equations
166(3)
4.5.2 Second-Harmonic Generation in Waveguide Structures
169(4)
4.6 BPM in Anisotropic Waveguides
173(4)
4.6.1 TE ↔ TM Mode Conversion
175(2)
4.7 Time Domain BPM
177(16)
4.7.1 Time-Domain Beam Propagation Method (TD-BPM)
178(1)
4.7.2 Narrow-Band 1D-TD-BPM
179(1)
4.7.3 Wide-Band 1D-TD-BPM
180(7)
4.7.4 Narrow-Band 2D-TD-BPM
187(6)
4.8 Finite-Difference Time-Domain Method (FD-TD)
193(29)
4.8.1 Finite-Difference Expressions for Maxwell's Equations in Three Dimensions
194(4)
4.8.2 Truncation of the Computational Domain
198(1)
4.8.3 Two-Dimensional FDTD: TM Case
199(9)
4.8.4 Setting the Field Source
208(1)
4.8.5 Total-Field/Scattered-Field Formulation
209(3)
4.8.6 Two-Dimensional FDTD: TE Case
212(7)
References
219(3)
5 BPM Analysis of Integrated Photonic Devices
222(78)
Introduction
222(1)
5.1 Curved Waveguides
222(6)
5.2 Tapers: Y-Junctions
228(3)
5.2.1 Taper as Mode-Size Converter
228(2)
5.2.2 Y-Junction as 1 × 2 Power Splitter
230(1)
5.3 Directional Couplers
231(6)
5.3.1 Polarization Beam-Splitter
232(3)
5.3.2 Wavelength Filter
235(2)
5.4 Multimode Interference Devices
237(11)
5.4.1 Multimode Interference Couplers
237(2)
5.4.2 Multimode Interference and Self-Imaging
239(4)
5.4.3 1×N Power Splitter Based on MMI Devices
243(1)
5.4.4 Demultiplexer Based on MMI
244(4)
5.5 Waveguide Gratings
248(9)
5.5.1 Modal Conversion Using Corrugated Waveguide Grating
249(1)
5.5.2 Injecting Light Using Relief Gratings
250(2)
5.5.3 Waveguide Reflector Using Modulation Index Grating
252(5)
5.6 Arrayed Waveguide Grating Demultiplexer
257(13)
5.6.1 Description of the AWG Demultiplexer
257(6)
5.6.2 Simulation of the AWG
263(7)
5.7 Mach-Zehnder Interferometer as Intensity Modulator
270(6)
5.8 TE-TM Converters
276(6)
5.8.1 Electro-Optical TE-TM Converter
277(3)
5.8.2 Rib Loaded Waveguide as Polarization Converter
280(2)
5.9 Waveguide Laser
282(11)
5.9.1 Simulation of Waveguide Lasers by Active-BPM
283(3)
5.9.2 Performance of a Nd3+-Doped LiNbO3 Waveguide Laser
286(7)
5.10 SHG Using QPM in Waveguides
293(7)
References
297(3)
Appendix A Finite Difference Approximations of Derivatives
300(4)
A.1 FD-Approximations of First-Order Derivatives
300(1)
A.2 FD-Approximation of Second-Order Derivatives
301(3)
Appendix B Tridiagonal System: The Thomas Method Algorithm
304(3)
Reference
306(1)
Appendix C Correlation and Relative Power between Optical Fields
307(3)
C.1 Correlation between Two Optical Fields
307(1)
C.2 Power Contribution of a Waveguide Mode
307(3)
References
309(1)
Appendix D Poynting Vector Associated to an Electromagnetic Wave Using the SVE Fields
310(13)
D.1 Poynting Vector in 2D-Structures
310(4)
D.1.1 TE Propagation in Two-Dimensional Structures
310(2)
D.1.2 TM Propagation in Two-Dimensional Structures
312(2)
D.2 Poynting Vector in 3D-Structures
314(9)
D.2.1 Expression as a Function of the Transverse Electric Field
315(4)
D.2.2 Expression as Function of the Transverse Magnetic Field
319(3)
Reference
322(1)
Appendix E Finite Difference FV-BPM Based on the Electric Field Using the Scheme Parameter Control
323(7)
E.1 First Component of the First Step
325(1)
E.2 Second Component of the First Step
326(1)
E.3 Second Component of the Second Step
327(1)
E.4 First Component of the Second Step
328(2)
Appendix F Linear Electro-Optic Effect
330(3)
Reference
332(1)
Appendix G Electro-Optic Effect in GaAs Crystal
333(7)
References
339(1)
Appendix H Electro-Optic Effect in LiNbO3 Crystal
340(6)
References
345(1)
Appendix I Pade Polynomials for Wide-Band TD-BPM
346(3)
Appendix J Obtaining the Dispersion Relation for a Monomode Waveguide Using FDTD
349(2)
Reference
350(1)
Appendix K Electric Field Distribution in Coplanar Electrodes
351(9)
K.1 Symmetric Coplanar Strip Configuration
351(5)
K.2 Symmetric Complementary Coplanar Strip Configuration
356(3)
References
359(1)
Appendix L Three-Dimensional Anisotropic BPM Based on the Electric Field Formulation
360(10)
L.1 Numerical Implementation
365(5)
L.1.1 First Component of the First Step
365(1)
L.1.2 Second Component of the First Step
366(1)
L.1.3 Second Component of the Second Step
367(1)
L.1.4 First Component of the Second Step
368(1)
References
369(1)
Appendix M Rate Equations in a Four-Level Atomic System
370(3)
References
372(1)
Appendix N Overlap Integrals Method
373(4)
References
376(1)
Index 377
Ginés Lifante Pedrola, Professor, Dept. of Materials Science, Universidad Autónoma de Madrid, Spain. Lifante has been working in the area of integrated photonic devices; optical properties of active materials for over 30 years, and has taught Optics (undergraduate level) and Integrated Photonics (graduate level). He has published 177 Articles and is the author of Integrated Photonics: Fundamentals (Wiley, 2003).