Diffraction Optics of Complex-Structured Periodic Media

1 Waves in Media with One-Dimensional Periodicity (Exact Solution).- 1.1 Layered Medium.- 1.1.1 Harmonic Modulation of Media.- 1.1.2 Properties of Eigenwaves.- 1.2 Optics of Cholesterics (Exact Solution).- 1.2.1 Dielectric Properties of Cholesterics.- 1.2.2 Eigenwaves.- 1.2.3 Properties of Eigensolutions.- 1.3 Solution of Boundary Problem.- 1.3.1 Planar Cholesteric Texture.- 1.3.2 Reflection from Thick Layers.- 1.3.3 The Case Where Medium and Cholesteric Have Equal Dielectric Constants.- 1.3.4 Dependence of Reflection on Polarization.- 1.3.5 Effect of Dielectric Boundaries.- 1.3.6 Method of Characteristic Matrices.- References.- 2 Approximate Description of Interaction of Radiation with Regular Media.- 2.1 Kinematical Approximation.- 2.1.1 Scattering Cross Section.- 2.1.2 Polarization Characteristics.- 2.1.3 Scattering of Light in Cholesterics.- 2.1.4 Kinematical Approximation Limitations.- 2.2 Dynamical Theory.- 2.2.1 Set of Dynamical Equations.- 2.2.2 Dispersion Surfaces.- 2.2.3 Solution of the Boundary Problem.- References.- 3 Diffraction of Mössbauer Radiation in Magnetically Ordered Crystals.- 3.1 Diffraction of Mössbauer Radiation.- 3.2 Amplitude of Coherent Mössbauer Scattering.- 3.2.1 Amplitude of Elastic Scattering.- 3.2.2 Isotope and Spin Incoherence.- 3.2.3 Coherent Amplitude in Limiting Cases of Completely Split and Unsplit Lines.- 3.3 Kinematical Theory of Mössbauer Diffraction.- 3.3.1 Structure Amplitude.- 3.3.2 Phase Determination.- 3.3.3 Diffraction at Magnetically Ordered Crystals.- 3.3.4 Resolved Zeeman Splitting of a Mössbauer Line.- 3.3.5 Crystals with Mössbauer Nuclei at Sites with Inhomogeneous Electric Field (EFG).- 3.4 Dynamical Theory of Mössbauer Diffraction.- 3.4.1 Unsplit Mössbauer Line.- 3.4.2 Suppression of Inelastic Channels of Nuclear Reactions.- 3.4.3 Bragg Reflection from Crystals.- 3.4.4 Solution of the Dynamical Equations for Hyperfine Splitting of Mössbauer Line.- 3.4.5 Polarization-Independent Amplitude of Scattering at Zero Angle.- 3.4.6 Completely Resolved Zeeman Splitting of Mössbauer Line.- References.- 4 Optics of Chiral Liquid Crystals.- 4.1 Optics of Cholesteric Liquid Crystals (CLC).- 4.1.1 The Fundamental Equations.- 4.1.2 Eigensolutions.- 4.1.3 The Solution of the Boundary Problem.- 4.1.4 High-Order Reflection for Oblique Incidence.- 4.1.5 A Planar Layer.- 4.1.6 Optical Rotation.- 4.2 Absorbing Cholesteric Liquid Crystals.- 4.2.1 The Dielectric Tensor of Absorbing CLCs.- 4.2.2 Suppression of Absorption.- 4.2.3 Optical Rotation.- 4.2.4 Borrmann Effect for Oblique Incidence.- 4.3 Chiral Smectic Liquid Crystals.- 4.3.1 Dielectric Permittivity Tensor of a C*.- 4.3.2 Second-Order Diffraction Reflection.- 4.3.3 First-Order Reflection.- 4.3.4 Boundary Problem.- 4.4 Blue Phase of Liquid Crystals.- 4.4.1 Observed Properties of Blue Phases.- 4.4.2 Symmetry Restrictions for the Dielectric Permittivity Tensor.- 4.4.3 Fourier Harmonics of $$ \hat{\epsilon }\left( r \right) $$.- 4.4.4 The Explicit Form of $$ \hat{\epsilon }\left( r \right) $$
(r).- 4.4.5 Optical Properties.- 4.4.6 Structure Studies of the Blue Phase.- References.- 5 Radiation of Fast Charged Particles in Regular Media.- 5.1 Structure Cherenkov Radiation (Kinematical Approximation).- 5.1.1 Formulation of the Problem.- 5.1.2 Radiation of a Particle in a Crystal.- 5.1.3 Photon Emission Cross Section.- 5.1.4 The Structure Factor.- 5.1.5 Temperature Dependence.- 5.1.6 Dimension of the Emitting Region.- 5.1.7 Estimations of the Structure Radiation Intensity.- 5.1.8 On the Phenomenological Approach.- 5.2 Coherent Coulomb Excitation of a Mössbauer Transition in a Single Crystal.- 5.2.1 Coherent Coulomb Excitation in a “Frozen” Lattice.- 5.2.2 Influence of Thermal Motion of Atoms.- 5.2.3 Radiation Intensity.- 5.3 Structure Cherenkov Radiation in a Cholesteric Liquid Crystal.- 5.3.1 Basic Equations.- 5.3.2 Intensity and Polarization Properties of Radiation.- 5.4 Dynamic Theory of Coherent Radiation of Fast Charged Particles in Regular Media.- 5.4.1 Dynamic Theory of the Structure Cherenkov Radiation.- 5.4.2 Coherent Coulomb Excitation of a Mössbauer Transition.- 5.4.3 Cherenkov Radiation in Chiral Liquid Crystals.- 5.4.4 The Shift of Cherenkov Radiation Threshold.- References.- 6 Nonlinear Optics of Periodic Media.- 6.1 Enhancement of Efficiency of the Nonlinear Transformation of Optical Frequencies in Periodic Medium.- 6.2 Third Harmonic Generation in a Cholesteric Liquid Crystal.- 6.2.1 Conditions for Phase Matching.- 6.2.2 Solution of the Boundary Problem.- 6.2.3 Third Harmonic Generation in the Band of Selective Reflection.- 6.2.4 Extreme Efficiency of Transformation.- 6.2.5 The Conditions for the Enhancement Effect.- 6.3 Phase-Matching Conditions Independent of Frequency Dispersion.- 6.4 Nonlinear Generation of Harmonics in Blue Phase of Liquid Crystals.- 6.4.1 Phase-Matching Condition.- 6.4.2 Symmetry Restrictions for the Tensor of Nonlinear Susceptibility.- 6.4.3 Fourier Components of the $$\hat X\left( r \right)$$
(r) Tensor.- References.- 7 Dynamic Scattering of Thermal Neutrons in Magnetically Ordered Crystals.- 7.1 Scattering Amplitude of Thermal Neutrons.- 7.2 System of Dynamic Equations.- 7.3 Structures with Compensated Magnetic Moment of a Unit Cell.- 7.3.1 Matrix of the Dynamic System.- 7.3.2 Eigenpolarizations.- 7.3.3 Solution to the Boundary Problem.- 7.3.4 Averaged Scattering Parameters.- 7.3.5 Observed Dynamic Effects.- 7.4 Dynamic Scattering in Magnetically Ordered Structures of the General Type.- 7.4.1 Eigensolutions to the Dynamic System.- 7.4.2 Solution to the Boundary Problem.- 7.4.3 The Cases of Analytical Solution of the Dynamic Problem.- 7.4.4 Bragg Reflection from Thick Crystals.- 7.4.5 Reflection in the Case of Strong Birefringence.- 7.4.6 Concluding Remarks.- References.- 8 Polarization Phenomena in X-Ray Optics.- 8.1 Polarization Phenomena in Diffraction.- 8.1.1 Diffraction in Perfect Crystals.- 8.1.2 Polarization Tensor and Integrated Polarization Parameters.- 8.1.3 Diffractive Birefringence and Dichroism.- 8.1.4 Diffraction in Imperfect Crystals.- 8.2 Anisotropy of X-Ray Susceptibility.- 8.2.1 Birefringence and Dichroism near Absorption Edges.- 8.2.2 Symmetry Restriction on the X-Ray Susceptibility Tensor of a Crystal.- 8.2.3 Forbidden Reflections.- 8.3 Polarization Effects in X-Ray Optical Components.- 8.3.1 Polarization of Radiation Produced by X-Ray Sources.- 8.3.2 Production and Analysis of Linear Polarization.- 8.3.3 The X-Ray Quarter-Wave Plate.- 8.304 Pendelosung.- 804 Conclusions.- References.- 9 Magnetic X-Ray Scattering.- 9.1 Magnetic Scattering.- 9.2 Polarization Properties of Magnetic Scattering.- 9.3 X-Ray Resonance Magnetic Scattering.- 904 X-Ray Magnetic Birefringence and Dichroism.- References.- 10 Mössbauer Filtration of Synchrotron Radiation.- 10.1 On Synchrotron Radiation Sources and Mössbauer Filtration.- 10.2 The First Observations of Mössbauer Filtration.- 10.3 Speed-Up of Mössbauer Scattering in Crystals.- 10.4 Temporal Quantum Beats in Mössbauer Filtration of SR.- 10.5 Future Mössbauer Experiments with Synchrotron Radiation.- 10.6 Coherent Inelastic Mössbauer Scattering.- 10.7 Recent Experiments on Mössbauer Filtration.- References.