Wolf Progress in Optics

1. Auflage 2005
ISBN: 978-0-08-045944-8
Verlag: Elsevier Science & Techn.
Format: EPUB
Kopierschutz: 6 - ePub Watermark

E-Book, Englisch, Band Volume 47, 492 Seiten

Reihe: Progress in Optics

In this volume, six review articles which cover a broad range of topics of current interest in modern optics are included. The first article by S. Saltiel, A.A. Sukhorukov and Y.S. Kivshar presents an overview of various types of parametric interactions in nonlinear optics which are associated with simultaneous phase-matching of several optical processes in quadratic non-linear media, the so-called multi-step parametric interactions. The second article by H.E. Tureci, H.G.L. Schwefel, Ph. Jacquod and A.D. Stone reviews the progress that has been made in recent years in the understanding of modes in wave-chaotic systems. The next article by C.P. Search and P. Meystre reviews some important recent developments in non-linear optics and in quantum optics. The fourth article by E. Hasman, G. Biener, A. Niv and V. Kleiner discusses space-variant polarization manipulation. The article reviews both theoretical analysis and experimental techniques. The article which follows, by A.S. Desyatnikov, L. Torner and Y.S. Kivshar presents an overview of recent researches on optical vortices and phase singularities of electromagnetic waves in different types of non-linear media, with emphasis on the properties of vortex solitons. The concluding article by K. Iwata presents a review of imaging techniques with X-rays and visible light in which phase of the radiation that penetrates through a transparent object plays an important part.

Autoren/Hrsg.

Wolf, Emil

Inhaltsverzeichnis

1;Front Cover;1
2;Progress in Optics, Volume 47;4
3;Copyright Page;5
4;Contents;8
5;Preface;6
6;Chapter 1. Multistep parametric processes in nonlinear optics;12
6.1;1. Introduction;14
6.2;2. Single-phase-matched processes;16
6.3;3. Multistep phase-matched interactions;19
6.4;4. Phase matching for multistep cascading;50
6.5;5. Multi-color parametric solitons;64
6.6;6. Conclusions;72
6.7;Acknowledgements;72
6.8;References;73
7;Chapter 2. Modes of wave-chaotic dielectric resonators;86
7.1;1. Introduction;88
7.2;2. Failure of eikonal methods for generic dielectric resonators;91
7.3;3. Ray dynamics for generic dielectric resonators;98
7.4;4. Formulation of the resonance problem;101
7.5;5. Reduction of the Maxwell equations;105
7.6;6. Scattering quantization – philosophy and methodology;108
7.7;7. Root-search strategy;114
7.8;8. The Husimi–Poincare' projection technique for optical dielectric resonators;124
7.9;9. Far-field distributions;128
7.10;10. Mode classification: theory and experiment;130
7.11;11. Conclusion;140
7.12;Acknowledgements;141
7.13;Appendix A: Numerical implementation issues;142
7.14;Appendix B: Lens transform;143
7.15;References;146
8;Chapter 3. Nonlinear and quantum optics of atomic and molecular fields;150
8.1;1. Introduction;152
8.2;2. Field quantization;154
8.3;3. Quantum-degenerate atomic systems;160
8.4;4. Collisions;164
8.5;5. Mean-field theory of Bose–Einstein condensation;175
8.6;6. Degenerate Fermi gases;183
8.7;7. Atomic solitons;190
8.8;8. Four-wave mixing;193
8.9;9. Three-wave mixing;205
8.10;10. Outlook;216
8.11;Acknowledgements;218
8.12;Appendix A: Feshbach resonances;218
8.13;References;221
9;Chapter 4. Space-variant polarization manipulation;226
9.1;1. Introduction;228
9.2;2. Formation of space-variant polarization-state manipulations;233
9.3;3. Geometrical phase in space-variant polarization-state manipulation;250
9.4;4. Applications of space-variant polarization manipulation;271
9.5;5. Concluding remarks;295
9.6;References;296
10;Chapter 5. Optical vortices and vortex solitons;302
10.1;1. Introduction;304
10.2;2. Self-trapped vortices in Kerr-type media;321
10.3;3. Composite spatial solitons with phase dislocations;321
10.4;4. Multi-color vortex solitons;335
10.5;5. Stabilization of vortex solitons;347
10.6;6. Other optical beams carrying angular momentum;355
10.7;7. Discrete vortices in two-dimensional lattices;365
10.8;8. Links to vortices in other fields;370
10.9;9. Concluding remarks;382
10.10;Acknowledgements;383
10.11;References;383
11;Chapter 6. Phase imaging and refractive index tomography for X-rays and visible rays,;404
11.1;1. Introduction;406
11.2;2. Properties of X-ray and visible ray;407
11.3;3. Formation of intensity and phase images;411
11.4;4. Phase imaging methods;413
11.5;5. Reference type interferometers;417
11.6;6. Shearing type interferometers;422
11.7;7. Refractive index tomography;430
11.8;8. Discussion on interferometers and refractive index tomography;435
11.9;9. Conclusion;441
11.10;Acknowledgement;441
11.11;References;441
12;Author index for Volume 47;444
13;Subject index for Volume 47;466
14;Contents of previous volumes;470
15;Cumulative index Volumes 1– 47;480

Leseproben

Chapter 1 Multistep parametric processes in nonlinear optics
Solomon M. [e-mail]    Nonlinear Physics Group and Center for Ultra-high bandwidth Devices for Optical Systems (CUDOS), Research School of Physical Sciences and Engineering, Australian National University, Canberra ACT 0200, Australia
Faculty of Physics, University of Sofia, 5 J. Bourchier Bld, Sofia BG-1164, Bulgaria Andrey A. [e-mail]; Yuri S. [e-mail]    Nonlinear Physics Group and Center for Ultra-high bandwidth Devices for Optical Systems (CUDOS), Research School of Physical Sciences and Engineering, Australian National University, Canberra ACT 0200, Australia 1 Introduction
Energy transfer between different modes and phase-matching relations are fundamental concepts in nonlinear optics. Unlike nonparametric nonlinear processes such as self-action and self-focusing of light in a nonlinear Kerr-like medium, parametric processes involve several waves at different frequencies and they require special relations between the wave numbers and wave group velocities to be satisfied, the so-called phase-matching conditions. Parametric coupling between waves occurs naturally in nonlinear materials without inversion symmetry, when the lowest-order nonlinear effects are presented by quadratic nonlinearities, often called (2) nonlinearities because they are associated with the second-order contribution (?(2)E2) to the nonlinear polarization of a medium. Conventionally, the phase-matching conditions for most parametric processes in optics are implemented either by using anisotropic crystals (the so-called perfect phase matching), or in fabricated structures with a periodically reversed sign of the quadratic susceptibility (the so-called quasi-phase matching or QPM). The QPM technique is one of the leading technologies today, and it employs spatial scales (~1–30 µm) which are compatible with the operational wavelengths of optical communication systems. Nonlinear effects produced by the quadratic intensity-dependent response of a transparent dielectric medium are usually associated with parametric frequency conversion, such as second harmonic generation (SHG). The SHG process is among the most intensively studied parametric interactions which may occur in a quadratic nonlinear medium. Moreover, recent theoretical and experimental results demonstrate that quadratic nonlinearities can also produce many of the effects attributed to nonresonant Kerr nonlinearities via cascading of several second-order parametric processes. Such second-order cascading effects can simulate third-order processes, in particular those associated with the intensity-dependent change of the medium refractive index (Stegeman, Hagan and Torner [1996]). Importantly, the effective (or induced) cubic nonlinearity resulting from a cascaded SHG process in a quadratic medium can be several orders of magnitude higher than that usually measured in centrosymmetric Kerr-like nonlinear media, and it is practically instantaneous. The simplest type of phase-matched parametric interaction is based on the simultaneous action of two second-order parametric sub-processes that belong to a single second-order interaction. For example, the so-called two-step cascading associated with type I SHG includes the generation of the second harmonic (SH), +?=2?, followed by the reconstruction of the fundamental wave through the down-conversion frequency-mixing process, ?-?=?. These two sub-processes depend on only a single phase-matching parameter ?k. In particular, for nonlinear (2) media with a periodic modulation of the quadratic nonlinearity, for QPM periodic structures, we have k=k2-2k1+Gm, where 1=k(?), 2=k(2?) and m is the reciprocal vector of the periodic structure, m=2pm/?, where ? is the lattice spacing and m is an integer. For a homogeneous bulk (2) medium, we have m=0. Multistep parametric interactions and multistep cascading represent a special type of second-order parametric processes that involve several different second-order nonlinear interactions; they are characterized by at least two different phase-matching parameters. For example, two parent processes of the so-called third-harmonic cascading are: (i) second-harmonic generation, +?=2?, and (ii) sum-frequency mixing, +2?=3?. Here, we may distinguish five harmonic sub-processes, and the multistep interaction results in their simultaneous action. Different types of multistep parametric processes include third-harmonic cascaded generation, two-color parametric interaction, fourth-harmonic cascading, difference-frequency generation, etc. Various applications of multistep parametric processes have been mentioned in the literature. In particular, multistep parametric interaction can support multi-color solitary waves, it usually leads to larger accumulated nonlinear phase shifts in comparison with simple cascading, it can be employed effectively for the simultaneous generation of higher-order harmonics in a single quadratic crystal, and it can be employed for the generation of a cross-polarized wave and frequency shifting in fiber-optics gratings. In general, simultaneous phase matching of several parametric processes cannot be achieved by traditional methods such as those based on the optical birefringence effect. However, the situation becomes different for media with a periodic sign change of the quadratic nonlinearity, as occurs in QPM structures or two-dimensional nonlinear photonic crystals. In this review, we describe the basic principles of simultaneous phase matching of two (or more) parametric processes in different types of one- and two-dimensional nonlinear quadratic optical lattices. We divide the different types of phase-matched parametric processes studied in nonlinear optics into two major classes, as shown in fig. 1, and discuss different types of parametric interactions associated with simultaneous phase matching of several optical processes in quadratic (or (2)) nonlinear media, the so-called multistep parametric interactions. In particular, we provide an overview of the basic principles of double and multiple phase matching in engineered structures with sign-varying second-order nonlinear susceptibility, including different types of QPM optical superlattices, noncollinear geometry, and two-dimensional nonlinear quadratic photonic crystals (which can be considered two-dimensional QPM lattices). We also summarize the most important experimental results on the multi-frequency generation due to multistep parametric processes, and survey the physics and basic properties of multi-color optical solitons generated by these parametric interactions. Fig. 1 Different types of parametric processes in nonlinear optics, and the specific topics covered by this review. SHG: second-harmonic generation; SFG and DFG: sum- and difference-frequency generation, THG: third-harmonic generation; FWM: four-wave mixing; DFWM: degenerate FWM; OPO: optical parametric oscillator. 2 Single-phase-matched processes
One of the simplest and first-studied parametric processes in nonlinear optics is second-harmonic generation (SHG). The SHG process is a special case of a more general three-wave mixing process which occurs in a dielectric medium with a quadratic intensity-dependent response. The three-wave-mixing and SHG processes require only one phase-matching condition to be satisfied and, therefore, can both be classified as single-phase-matched processes. In this section, we briefly discuss these single-phase-matched processes, and consider parametric interaction between three continuous-wave (CW) waves with electric fields j=12[Ajexp(-ikj·r+i?jt)+c.c.], where =1,2,3, with the three frequencies satisfying the energy-conservation condition, 1+?2=?3. We assume that the phase-matching condition is nearly satisfied, with a small mismatch ?k between the three wave vectors; i.e., k=k3(?3)-k1(?1)-k2(?2). In general, the three waves do not propagate in the same direction, and the beams may walk off from each other as they propagate inside the crystal. If all three wave vectors point in the same direction (e.g., in the case of QPM materials), the waves have the same phase velocity and exhibit no walk-off. The theory of (2)-mediated three-wave mixing is available in several books devoted to nonlinear optics (Shen [1984], Butcher and Cotter [1992], Boyd [1992]). The starting point is the Maxwell wave equation written as ×?×E+1c2?2E?t2=-1?0c2?2P?t2,   (2.1) where 0 is the vacuum permittivity and c is the...