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.
1. Chapter 13. Introduction to modulation formats - p. 221 2. Chapter 14. Required bandwidth for heterodyne and homodyne detection - p. 241 3. Chapter 15. Bandpass noise - p. 247 4. Chapter 16. Bit error rate - p. 255 5. Chapter 17. Pulse shaping using optical Fourier transform - p. 263 6. Abstract - p. 263 7. 17.1 Output pulse shaping using Cd configuration - p. page263 8. 17.2 Output spectrum shaping using a dC configuration - p. 267 9. 17.3 OTDM-to-WDM conversion using a dC configuration - p. 268 10. 17.4 OTDM-to-WDM conversion in WDM-PON - p. 272 11. 17.5 WDM-to-OTDM conversion using a dC conversion - p. 274 12. 17.6 WDM-to-OTDM conversion using a complete dCd configuration - p. 277 13. 17.7 WDM-to-OTDM conversion using a Cd configuration - p. 279 14. 17.8 WDM-to-OTDM conversion using a complete CdC configuration - p. 280 15. 17.9 Optical Nyquist transmission using time-domain optical Fourier transformation - p. 282 16. 17.10 Summary - p. 288 17. Bibliography - p. 288 18. Chapter 18. Spectrum magnification - p. 289 19. Chapter 19. Optical Fourier transformation, dispersion compensation, jitter suppression - p. 297 20. Chapter 20. Regeneration of WDM phase-modulated signals - p. 307 21. Abstract - p. 307 22. 20.1 FWM basics - p. page307 23. 20.2 Nonlinear equations for nonstatic fields - p. 315 24. 20.3 Degenerate FWM - p. 317 25. 20.4 Degenerate signal and idler. Phase sensitive amplifier - p. 326 26. 20.5 Time lenses and WDM phase regeneration for BPSK modulation - p. 325 27. 20.6 Summary - p. 333 28. Bibliography - p. 333 29. Chapter 21. Time–space duality, dispersion and diffraction, time lens - p. 335 30. Chapter 22. Couplers and their use for optical DFT - p. 345 31. Chapter 23. Multicarrier modulation, OFDM, DFT, Nyquist modulation - p. 353 32. Chapter 24. Optical orthogonal frequency division modulation - p. 373 33. Appendix A. Acronyms - p. 391 34. Appendix B. Analytic complex functions, Cauchy's integral theorem, and integral formula - p. 395 35. Appendix C. Fourier series expansion of the comb function - p. 409 36. Appendix D. Calculation of the integral of a Gaussian function - p. 410 37. Appendix E. Time–bandwidth product - p. 413 38. Appendix F. Examples of MATLAB® programs - p. 417 39. Appendix G. Proof of autocorrelation going to zero for large values of τ - p. 421 40. Appendix H. Autocorrelation of digital signal - p. 425 41. Appendix I. Ensemble averaging and pdf averaging - p. 429 42. Appendix J. Probability density functions and jointly Gaussian random variables - p. 431 43. Appendix K. Poisson statistics - p. 443 44. Appendix L. RMS widths of convoluted signals - p. 447 45. Appendix M. Example of Fourier–Mellin integral determined by Cauchy integral theorem - p. 449 46. Appendix N. Proof of Thévenin's and Norton's theorems - p. 453 47. Appendix O. Propagation of a Gaussian pulse in a single-mode fiber - p. 457 48. Appendix P. Carrier envelope offset - p. 459 49. Appendix Q. Bandwidth of random ASK and PSK signals - p. 463 50. Appendix R. Solution of coupled wave equations - p. 467 51. Appendix S. Matched filter - p. 471 52. Bibliography - p. 473 53. Index - p. 479
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.
1. Chapter 13. Introduction to modulation formats - p. 221 2. Chapter 14. Required bandwidth for heterodyne and homodyne detection - p. 241 3. Chapter 15. Bandpass noise - p. 247 4. Chapter 16. Bit error rate - p. 255 5. Chapter 17. Pulse shaping using optical Fourier transform - p. 263 6. Abstract - p. 263 7. 17.1 Output pulse shaping using Cd configuration - p. page263 8. 17.2 Output spectrum shaping using a dC configuration - p. 267 9. 17.3 OTDM-to-WDM conversion using a dC configuration - p. 268 10. 17.4 OTDM-to-WDM conversion in WDM-PON - p. 272 11. 17.5 WDM-to-OTDM conversion using a dC conversion - p. 274 12. 17.6 WDM-to-OTDM conversion using a complete dCd configuration - p. 277 13. 17.7 WDM-to-OTDM conversion using a Cd configuration - p. 279 14. 17.8 WDM-to-OTDM conversion using a complete CdC configuration - p. 280 15. 17.9 Optical Nyquist transmission using time-domain optical Fourier transformation - p. 282 16. 17.10 Summary - p. 288 17. Bibliography - p. 288 18. Chapter 18. Spectrum magnification - p. 289 19. Chapter 19. Optical Fourier transformation, dispersion compensation, jitter suppression - p. 297 20. Chapter 20. Regeneration of WDM phase-modulated signals - p. 307 21. Abstract - p. 307 22. 20.1 FWM basics - p. page307 23. 20.2 Nonlinear equations for nonstatic fields - p. 315 24. 20.3 Degenerate FWM - p. 317 25. 20.4 Degenerate signal and idler. Phase sensitive amplifier - p. 326 26. 20.5 Time lenses and WDM phase regeneration for BPSK modulation - p. 325 27. 20.6 Summary - p. 333 28. Bibliography - p. 333 29. Chapter 21. Time–space duality, dispersion and diffraction, time lens - p. 335 30. Chapter 22. Couplers and their use for optical DFT - p. 345 31. Chapter 23. Multicarrier modulation, OFDM, DFT, Nyquist modulation - p. 353 32. Chapter 24. Optical orthogonal frequency division modulation - p. 373 33. Appendix A. Acronyms - p. 391 34. Appendix B. Analytic complex functions, Cauchy's integral theorem, and integral formula - p. 395 35. Appendix C. Fourier series expansion of the comb function - p. 409 36. Appendix D. Calculation of the integral of a Gaussian function - p. 410 37. Appendix E. Time–bandwidth product - p. 413 38. Appendix F. Examples of MATLAB® programs - p. 417 39. Appendix G. Proof of autocorrelation going to zero for large values of τ - p. 421 40. Appendix H. Autocorrelation of digital signal - p. 425 41. Appendix I. Ensemble averaging and pdf averaging - p. 429 42. Appendix J. Probability density functions and jointly Gaussian random variables - p. 431 43. Appendix K. Poisson statistics - p. 443 44. Appendix L. RMS widths of convoluted signals - p. 447 45. Appendix M. Example of Fourier–Mellin integral determined by Cauchy integral theorem - p. 449 46. Appendix N. Proof of Thévenin's and Norton's theorems - p. 453 47. Appendix O. Propagation of a Gaussian pulse in a single-mode fiber - p. 457 48. Appendix P. Carrier envelope offset - p. 459 49. Appendix Q. Bandwidth of random ASK and PSK signals - p. 463 50. Appendix R. Solution of coupled wave equations - p. 467 51. Appendix S. Matched filter - p. 471 52. Bibliography - p. 473 53. Index - p. 479
