Optical Communications from a Fourier Perspective

Fourier Theory and Optical Fiber Devices and Systems

Palle Jeppesen, Bjarne Tromborg

• Publisher: Elsevier
• Year: 2023
• Print ISBN:
  9780443238000
• eBook ISBN:
  9780443238017
• Topic: Mathematics
• Subtopic: Mathematical Analysis
• Index: Mathematics

Optical Communications from a Fourier Perspective: Fourier Theory and Optical Fiber Devices and Systems covers a broad range of subjects spanning Fourier theory and signal analysis over photonic components, including time lenses in optical communication. Some of the theory is more generally applicable beyond optical communication and is of relevance also for communications engineering. The Fourier theory dimension of the book presents the relationship between Fourier series and Fourier integrals and also the related Laplace transform. The book covers wave propagation in optical waveguides based on Maxwell equations and the nonlinear Schrödinger equation. Various modulation formats are addressed along with coherent detection and required bandwidth. Optical Fourier transform in the form of time lens is covered, for example in modulation format conversion and spectrum magnification, and couplers and their use for optical discrete Fourier transformation are also discussed. Other important subjects such as noise, linewidth, and coherence are discussed in relation to semiconductor lasers. Detailed derivations and a deeper background for the chapters are provided in appendices where appropriate. - Introduces Fourier theory and signal analysis tailored to applications in optical communications devices and systems - Provides a strong theoretical background and a ready resource for researchers and advanced students in optical communication and optical signal processing - Starts from basic theory and then develops descriptions of useful applications

Table of contents

• Title of Book
• Cover image
• Title page
• Table of Contents
• Copyright
• Preface
• Chapter 1 The Dirac delta function and Heaviside step function
• Chapter 2 Fourier series, Parseval's theorem, FFT and Cooley–Tukey algorithm
• Chapter 3 Fourier integrals and series
• Chapter 4 Properties of the Fourier transform and Heaviside's step function
• Chapter 5 Complex signal, complex envelope, and Hilbert transform
• Chapter 6 Correlation functions, spectral density, Wiener–Khinchine theorem
• Chapter 7 Linear, time-invariant systems
• Chapter 8 Transfer matrices and frequency filters
• Chapter 9 Laplace transforms, transfer functions, Nyquist criterion
• Chapter 10 Maxwell's equations, optical waveguides, and Poynting vector
• Chapter 11 Pulse propagation in optical fibers
• Chapter 12 Split-step Fourier method and nonlinear Schrödinger equation
• Chapter 13 Introduction to modulation formats
• Chapter 14 Required bandwidth for heterodyne and homodyne detection
• Chapter 15 Bandpass noise
• Chapter 16 Bit error rate
• Chapter 17 Pulse shaping using optical Fourier transform
• Chapter 18 Spectrum magnification
• Chapter 19 Optical Fourier transformation, dispersion compensation, jitter suppression
• Chapter 20 Regeneration of WDM phase-modulated signals
• Chapter 21 Time–space duality, dispersion and diffraction, time lens
• Chapter 22 Couplers and their use for optical DFT
• Chapter 23 Multicarrier modulation, OFDM, DFT, Nyquist modulation
• Chapter 24 Optical orthogonal frequency division modulation
• Appendix A. Acronyms
• Appendix B. Analytic complex functions, Cauchy's integral theorem, and integral formula
• Appendix C. Fourier series expansion of the comb function
• Appendix D. Calculation of the integral of a Gaussian function
• Appendix E. Time–bandwidth product
• Appendix F. Examples of MATLAB® programs
• Appendix G. Proof of autocorrelation going to zero for large values of τ
• Appendix H. Autocorrelation of digital signal
• Appendix I. Ensemble averaging and pdf averaging
• Appendix J. Probability density functions and jointly Gaussian random variables
• Appendix K. Poisson statistics
• Appendix L. RMS widths of convoluted signals
• Appendix M. Example of Fourier–Mellin integral determined by Cauchy integral theorem
• Appendix N. Proof of Thévenin's and Norton's theorems
• Appendix O. Propagation of a Gaussian pulse in a single-mode fiber
• Appendix P. Carrier envelope offset
• Appendix Q. Bandwidth of random ASK and PSK signals
• Appendix R. Solution of coupled wave equations
• Appendix S. Matched filter
• Bibliography
• Index