Optical Communications from a Fourier Perspective

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

Palle Jeppesen is professor emeritus at the Technical University of Denmark (DTU) and a researcher with many years' experiences in optical fiber communications, lasers, fibers, systems, and ultra-high-speed optical communications. He has been a member of the Danish Technical Research Council, the Scientific Council for the Danish National Encyclopedia, and on the boards of a number of large corporate entities. His current research interests are optical signal processing, optical multi-level modulation formats, and terabit optical communication.Bjarne Tromborg was formerly a research and teaching professor at the Technical University of Denmark (DTU) best known for his work in particle physics and photonics. He has been a member of the Danish Natural Science Research Council and many technical program committees. He has published widely on the topics of optoelectronics, semiconductor lasers, and optical communications

1. The Dirac delta function and Heaviside step function2. Fourier series, Parseval's theorem, FFT and Cooley-Tukey algorithm3. Fourier integrals and Fourier series4. Properties of the Fourier transform and Heaviside's step function5. Complex signal, complex envelope and Hilbert transform6. Correlation functions, spectral density, Wiener-Khinchine theorem7. Linear, time-invariant systems8. Transfer matrices and frequency filters9. Laplace transforms, transfer functions, Nyquist criterion10. Maxwell's equations, optical waveguides and Poynting's vector11. Pulse propagation in optical fibers12. Split step Fourier method and nonlinear Schrodinger equation13. Introduction to modulation formats14. Required bandwidth for heterodyne and homodyne detection15. Bandpass noise16. Bit error rate17. Pulse shaping using optical Fourier transform18. Spectrum magnification19. Optical Fourier transformation, dispersion compensation, jitter suppression20. Regeneration of WDM phase-modulated signals21. Time-space duality, dispersion and diffraction, time lens22. Couplers and their use for optical DFT23. Multicarrier modulation, OFDM, DFT, Nyquist modulation24. Optical orthogonal frequency division modulation