PROGRESS IN OPTICS VOLUME 4 9. E. Wolf

Transcription

1 PROGRESS IN OPTICS VOLUME 4 9 E. Wolf

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3 Preface v Chapter 1. Gaussian apodization and beam propagation, Virendra N. Mahajan (El Segundo, CA and Tucson, AZ, USA) 1 1. Introduction 3 2. Theory Pupil function Point-spread function Optical transfer function 5 3. Aberration-free Gaussian pupil Pupil function Point-spread function Optical transfer function Defocused Gaussian pupil Pupil function Point-spread function Axial irradiance Optical transfer function Strehl ratio, aberration tolerance, and Zernike-Gauss polynomials Strehl ratio Depth of focus Balanced aberrations Zernike-Gauss polynomials Strehl ratio for primary aberrations Balancing of defocus aberration with spherical aberration or astigmatism Focused beam Collimated beam Aberrated Gaussian pupil Spherical aberration Symmetry properties Line of sight Weakly-truncated Gaussian pupils and beams Pupil function Point-spread function Radius of curvature of the propagating wavefront Collimated beam Beam focusing and waist imaging by a lens Optical transfer function Strehl ratio, aberration balancing, and orthogonal polynomials 85

4 8.8. Beam characterization and measurement Nonparaxial Gaussian beams Conclusions 9 1 Acknowledgements 9 2 Appendix 9 2 References 9 3 Chapter 2. Controlling nonlinear optical processes in multi-leve l atomic systems, Amitabh Joshi and Min Xiao (Fayetteville, AR, USA) Introduction Modified linear and nonlinear optical properties in multi-level atomic systems Absorption reduction and dispersion enhancement Enhanced nonlinearity in EIT systems Enhanced four-wave mixing processes with induced atomic coherence Three-level atomic systems Four-level atomic systems Controlled optical bistability and optical multistability with three-level atoms inside a n optical cavity Theoretical calculation Controllable optical bistability Controllable optical multistability Controllable direction of hysteresis cycle in optical bistability/optical multistability Dynamic hysteresis in optical bistability Controlled optical switching in three-level atomic systems Controlled switching between bistable states All-optical switching controlled by coupling laser beam Controlled optical switching in four-level N-type atomic system Controlled optical instability with three-level atoms inside an optical cavity Theoretical calculation Experimental measurements Summary and outlook 170 Acknowledgement 172 References 172 Chapter 3. Photonic crystals, Henri Benisly (Orsay, France) and Claud e Weisbuch (Palaiseau, France and Santa Barbara, CA, USA) 177 Nomenclature 179 Main variables and notations Introduction Basics of periodic dielectric media and theoretical tools D Bragg structure Density of states, local DOS Generalizing to 2D and 3D periodic crystals Basics of band calculation The discovery of PBG Bloch waves Theoretical tools : a brief overview 209

5 3. Three-dimensional photonic crystals Introduction Fabrication of 3D photonic crystals Measurements Metallodielectric systems and microwave regime Two-dimensional photonic crystals Theoretical aspects D photonic crystal with vertical guidance D realizations Applications and characterization methods Photonic crystal fibers 27 1 Issues of fibre world 27 1 The playing field of photonic crystal fibers 27 1 Single-mode fiber 27 5 True PC guidance 276 High -Delta fiber 278 Special dispersion 27 8 Special applications: nonlinear optics, supercontinuum generation, etc 28 0 Brief overview of PCF modeling tools Conclusion and perspectives 28 3 Acknowledgements 28 8 References and special issues 28 8 Special issues of regular joumals on photonic crystals, in chronological order 28 8 References 28 9 Chapter 4. Symmetry properties and polarization descriptors for an arbitrary electromagnetic wavefield, Christian Brosseau (Brest, France ) and Aristide Dogariu (Orlando, FL, USA) Introduction A brief survey of the interplay between polarization concepts and geometry From Bartholinus (1669) to Stokes (1852) : polarization is a geometric property of light From Stokes (1852) to Poincar6 (1892) : polarization is an electromagnetic propert y of light From Poincare (1892) to Wolf (1954): polarization is a statistical property of light And now: geometric algebra is back Density matrix and the convexity property of the states of polarization Polarization and the density matrix Scalar invariants The convex set of polarization states Summary of geometric algebra Polarization of a plane wave Density matrix and degree of polarization Some important consequences and concrete applications Polarization of an arbitrary wave Density matrix and polarization descriptors Some applications Postscript 363

6 7. Summary and prospects 36 4 Acknowledgements 36 7 Appendix A : Lie groups in polarization optics 36 8 Al.SU(2) A.2. SU(3) 37 0 Appendix B : Madison convention for the density matrix of massive spin-1 particles 37 1 Appendix C : Degree of polarization of a field consisting of a superposition of an ensembl e of evanescent waves of random amplitude and of black-body radiation 374 References 376 Chapter 5. Quantum cryptography, Miloslav Dusek (Olomouc, Czech Republic), Norbert Lütkenhaus (Erlangen, Germany) and Martin Hendryc h (Castelldefels, Barcelona, Spain) Ciphering Introduction, cryptographic tasks Asymmetrical ciphers (public-key cryptography) Symmetrical ciphers (secret-key cryptography) Vemam cipher, key distribution problem Quantum key distribution The principle, eavesdropping can be detected Quantum measurement Quantum states cannot be cloned Protocol BB Eavesdropping, intercept-resend attack Some other discrete protocols for QKD Two-state protocol, B B92 protocol with a strong reference pulse Six-state protocol SARG protocol Decoy-state protocols Entanglement-based protocols Experiments QKD with weak laser pulses Entanglement-based protocols Technology Light sources Detectors Quantum channels Limitations Transmission rate Limit on the distance Quantum repeaters Supporting procedures Estimation of leaked information Error correction for classical bit strings Privacy amplification for classical bit strings Advantage distillation for classical bit strings Authentication of public discussion 428

7 8. Security Attacks on ideal protocols Secure key rates from classical three-party correlations Bounds on quantum key distribution Security proofs Specific attacks Results Side channels and other imperfections Prospects 446 Acknowledgements 446 References 446 Chapter 6. Optical quantum cloning, Nicolas J. Cerf (Bruxelles, Belgium) and Jaromfr Fiuräsek (Olomouc, Czech Republic) Introduction and history The no-cloning theorem Beyond the no-cloning theorem Quantum cloning without signaling Content of this review Overview of quantum cloning machines Universal cloning machines Pauli and Heisenberg cloning machines Phase- and Fourier-covariant cloning machines Group-covariant cloning machines High-d state-dependent cloning machines Cloning a pair of orthogonal qubits Entanglement cloning machines Real cloning machines Highly-asymmetric cloning machines Continuous-variable cloning machines Probabilistic cloning machines Economical cloning machines One-to-two quantum cloning as a CP map Isomorphism between CP maps and operators Covariance condition Cloning as a semidefinite programming problem Double-Bell ansatz Heisenberg cloning machines Three special cases of Heisenberg cloners N-to-M universal quantum cloning Optimal cloning transformation Optimality proof for 1 -a M cloning of qubits Universal asymmetric quantum cloning Universal-NOT gate Universal cloning of photons Amplification of light Symmetrization Universal asymmetric cloning of photons Cloning of orthogonally polarized photons 522

8 6. Phase-covariant cloning of photons Phase-covariant cloning of qubits Phase-covariant cloning of qudits Optical phase-covariant cloning Experimental phase-covariant cloning Cloning of optical continuous variables Cloning of coherent states Cloning by phase-insensitive amplification Experimental cloning of coherent states Gaussian distribution with finite width Cloning of conjugate coherent states Conclusions 54 1 Acknowledgements 54 2 References 54 2 Author index for Volume Subject index for Volume Contents of previous volumes 57 5 Cumulative index - Volumes