There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Nonlinear fiber optics concerns with the nonlinear optical phenomena occurring inside optical fibers. Although the field ofnonlinear optics traces its beginning to 1961, when a ruby laser was first used to generate the second-harmonic radiation inside a crystal [1], the use ofoptical fibers as a nonlinear medium became feasible only after 1970 when fiber losses were reduced to below 20 dB/km [2]. Stimulated Raman and Brillouin scatterings in single-mode fibers were studied as early as 1972 [3] and were soon followed by the study of other nonlinear effects such as self- and crossphase modulation and four-wave mixing [4]. By 1989, the field ofnonlinear fiber optics has advanced enough that a whole book was devoted to it [5]. This book or its second edition has been translated into Chinese, Japanese, and Russian languages, attesting to the worldwide activity in the field of nonlinear fiber optics.

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Nonlinear Fiber Optics

A topical review of numerical and experimental studies of supercontinuum generation in photonic crystal fiber is presented over the full range of experimentally reported parameters, from the femtosecond to the continuous-wave regime. Results from numerical simulations are used to discuss the temporal and spectral characteristics of the supercontinuum, and to interpret the physics of the underlying spectral broadening processes. Particular attention is given to the case of supercontinuum generation seeded by femtosecond pulses in the anomalous group velocity dispersion regime of photonic crystal fiber, where the processes of soliton fission, stimulated Raman scattering, and dispersive wave generation are reviewed in detail. The corresponding intensity and phase stability properties of the supercontinuum spectra generated under different conditions are also discussed.

Supercontinuum generation in photonic crystal fiber

Topological photonics is a rapidly emerging field of research in which geometrical and topological ideas are exploited to design and control the behavior of light. Drawing inspiration from the discovery of the quantum Hall effects and topological insulators in condensed matter, recent advances have shown how to engineer analogous effects also for photons, leading to remarkable phenomena such as the robust unidirectional propagation of light, which hold great promise for applications. Thanks to the flexibility and diversity of photonics systems, this field is also opening up new opportunities to realize exotic topological models and to probe and exploit topological effects in new ways. This article reviews experimental and theoretical developments in topological photonics across a wide range of experimental platforms, including photonic crystals, waveguides, metamaterials, cavities, optomechanics, silicon photonics, and circuit QED. A discussion of how changing the dimensionality and symmetries of photonics systems has allowed for the realization of different topological phases is offered, and progress in understanding the interplay of topology with non-Hermitian effects, such as dissipation, is reviewed. As an exciting perspective, topological photonics can be combined with optical nonlinearities, leading toward new collective phenomena and novel strongly correlated states of light, such as an analog of the fractional quantum Hall effect.

Topological Photonics

Preface. About the Editors. Part I: Quantum Computing. 1. Quantum computing with qubits S.L. Braunstein, A.K. Pati. 2. Quantum computation over continuous variables S. Lloyd, S.L. Braunstein. 3. Error correction for continuous quantum variables S.L. Braunstein. 4. Deutsch-Jozsa algorithm for continuous variables A.K. Pati, S.L. Braunstein. 5. Hybrid quantum computing S. Lloyd. 6. Efficient classical simulation of continuous variable quantum information processes S.D. Bartlett, B.C. Sanders, S.L. Braunstein, K. Nemoto. Part II: Quantum Entanglement. 7. Introduction to entanglement-based protocols S.L. Braunstein, A.K. Pati. 8. Teleportation of continuous uantum variables S.L. Braunstein, H.J. Kimble. 9. Experimental realization of continuous variable teleportation A. Furusawa, H.J. Kimble. 10. Dense coding for continuous variables S.L. Braunstein, H.J. Kimble. 11. Multipartite Greenberger-Horne-Zeilinger paradoxes for continuous variables S. Massar, S. Pironio. 12. Multipartite entanglement for continuous variables P. van Loock, S.L. Braunstein. 13. Inseparability criterion for continuous variable systems Lu-Ming Duan, G. Giedke, J.I. Cirac, P. Zoller. 14. Separability criterion for Gaussian states R. Simon. 15. Distillability and entanglement purification for Gaussian states G. Giedke, Lu-Ming Duan, J.I. Cirac, P. Zoller. 16. Entanglement purification via entanglement swapping S. Parke, S. Bose, M.B. Plenio. 17. Bound entanglement for continuous variables is a rare phenomenon P. Horodecki, J.I. Cirac, M. Lewenstein. Part III: Continuous Variable Optical-Atomic Interfacing. 18. Atomic continuous variable processing and light-atoms quantum interface A. Kuzmich, E.S. Polzik. Part IV: Limits on Quantum Information and Cryptography. 19. Limitations on discrete quantum information and cryptography S.L. Braunstein, A.K. Pati. 20. Quantum cloning with continuous variables N.J. Cerf. 21. Quantum key distribution with continuous variables in optics T.C. Ralph. 22. Secure quantum key distribution using squeezed states D. Gottesman, J. Preskill. 23. Experimental demonstration of dense coding and quantum cryptography with continuous variables Kunchi Peng, Qing Pan, Jing Zhang, Changde Xie. 24. Quantum solitons in optical fibres: basic requisites for experimental quantum communication G. Leuchs, Ch. Silberhorn, E. Konig, P.K. Lam, A. Sizmann, N. Korolkova. Index.

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Quantum Information with Continuous Variables

Preface. 1 Introduction. 1.1 Historical Perspective. 1.2 Basic Concepts. 1.3 Optical Communication Systems. 1.4 Lightwave System Components. Problems. References. 2 Optical Fibers. 2.1 Geometrical-Optics Description. 2.2 Wave Propagation. 2.3 Dispersion in Single-Mode Fibers. 2.4 Dispersion-Induced Limitations. 2.5 Fiber Losses. 2.6 Nonlinear Optical Effects. 2.7 Fiber Design and Fabrication. Problems. References. 3 Optical Transmitters. 3.1 Semiconductor Laser Physics. 3.2 Single-Mode Semiconductor Lasers. 3.3 Laser Characteristics. 3.4 Optical Signal Generation. 3.5 Light-Emitting Diodes. 3.6 Transmitter Design. Problems. References. 4 Optical Receivers. 4.1 Basic Concepts. 4.2 Common Photodetectors. 4.3 Receiver Design. 4.4 Receiver Noise. 4.5 Coherent Detection. 4.6 Receiver Sensitivity. 4.7 Sensitivity Degradation. 4.8 Receiver Performance. Problems. References. 5 Lightwave Systems. 5.1 System Architectures. 5.2 Design Guidelines. 5.3 Long-Haul Systems. 5.4 Sources of Power Penalty. 5.5 Forward Error Correction. 5.6 Computer-Aided Design. Problems. References. 6 Multichannel Systems. 6.1 WDM Lightwave Systems. 6.2 WDM Components. 6.3 System Performance Issues. 6.4 Time-Division Multiplexing. 6.5 Subcarrier Multiplexing. 6.6 Code-Division Multiplexing. Problems. References. 7 Loss Management. 7.1 Compensation of Fiber Losses. 7.2 Erbium-Doped Fiber Amplifiers. 7.3 Raman Amplifiers. 7.4 Optical Signal-To-Noise Ratio. 7.5 Electrical Signal-To-Noise Ratio. 7.6 Receiver Sensitivity and Q Factor. 7.7 Role of Dispersive and Nonlinear Effects. 7.8 Periodically Amplified Lightwave Systems. Problems. References. 8 Dispersion Management. 8.1 Dispersion Problem and Its Solution. 8.2 Dispersion-Compensating Fibers. 8.3 Fiber Bragg Gratings. 8.4 Dispersion-Equalizing Filters. 8.5 Optical Phase Conjugation. 8.6 Channels at High Bit Rates. 8.7 Electronic Dispersion Compensation. Problems. References. 9 Control of Nonlinear Effects. 9.1 Impact of Fiber Nonlinearity. 9.2 Solitons in Optical Fibers. 9.3 Dispersion-Managed Solitons. 9.4 Pseudo-linear Lightwave Systems. 9.5 Control of Intrachannel Nonlinear Effects. Problems. References. 10 Advanced Lightwave Systems. 10.1 Advanced Modulation Formats. 10.2 Demodulation Schemes. 10.3 Shot Noise and Bit-Error Rate. 10.4 Sensitivity Degradation Mechanisms. 10.5 Impact of Nonlinear Effects. 10.6 Recent Progress. 10.7 Ultimate Channel Capacity. Problems. References. 11 Optical Signal Processing. 11.1 Nonlinear Techniques and Devices. 11.2 All-Optical Flip-Flops. 11.3 Wavelength Converters. 11.4 Ultrafast Optical Switching. 11.5 Optical Regenerators. Problems. References. A System of Units. B Acronyms. C General Formula for Pulse Broadening. D Software Package.

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Fiber-Optic Communication Systems

Preface 1. Introduction 2. Spatial Solitons 3. Temporal Solitons 4. Dark Solitons 5. Bragg Solitons 6. Two-Dimensional Solitons 7. Spatiotemporal Solitons 8. Vortex Solitons 9. Vector Solitons 10. Parametric Solitons 11. Discrete Solitons 12. Solitons in Photonic Crystals 13. Incoherent Solitons 14. Related Concepts References Index

Optical solitons : from fibers to photonic crystals

Nonlinear fiber optics concerns with the nonlinear optical phenomena occurring inside optical fibers Although the field ofnonlinear optics traces its beginning to 1961, when a ruby laser was first used to generate the second-harmonic radiation inside a crystal [1], the use ofoptical fibers as a nonlinear medium became feasible only after 1970 when fiber losses were reduced to below 20 dB/km [2] Stimulated Raman and Brillouin scatterings in single-mode fibers were studied as early as 1972 [3] and were soon followed by the study of other nonlinear effects such as self- and crossphase modulation and four-wave mixing [4] By 1989, the field ofnonlinear fiber optics has advanced enough that a whole book was devoted to it [5] This book or its second edition has been translated into Chinese, Japanese, and Russian languages, attesting to the worldwide activity in the field of nonlinear fiber optics

Govind P. Agrawal

Papers

Nonlinear Fiber Optics

Fiber-Optic Communication Systems

Optical solitons : from fibers to photonic crystals

Nonlinear Fiber Optics

Nonlinear Fiber Optics