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- •Chapter 1
- •Introduction to linear singular optics
- •I.I. Mokhun
- •Chapter 1
- •Introduction to linear singular optics
- •I.I. Mokhun
- •1.1. IntRoduction
- •1.2. Basic notions of scalar singular optics
- •1.2.1. Phase vortices
- •1.2.2. Topological charge and topological index of singular points. Elementary topological reactions
- •1.2.2.1. Topological charge
- •1.2.2.2. Topological index
- •1.2.2.3. Conservation law for topological charge
- •1.2.2.4. Elementary topological reactions
- •1.2.3. Experimental observation and identification of vortices into scalar fields
- •1.2.4. Generation of vortices using computer-generated holograms
- •1.3. Vortices and phase structure of a scalar field
- •1.3.1. Sign principle
- •1.3.2. Phase speckles. “breathing” of phase speckles
- •1.3.3. Birth of vortices
- •1.3.4. Appearance of wave front dislocations as a result of interference of waves with simple phase surfaces
- •1.3.5. Topological indices of the field of intensity. Extrema of phase and intensity. “correlation” of phase and intensity
- •1.3.6. Vortex nets. Phase skeleton of a scalar field
- •1.3.6.1. Reconstruction of the field’s phase on the basis of shifted vortex nets
- •1.3.6.2. Image reconstruction using a regular sampling found from analysis of the parameters of vortices in random field
- •1.3.6.3. Some remarks on the field reconstruction by the use of nets of the intensity sTationary points
- •1.4. Singularities of a vector field
- •1.4.1. Disclinations. Polarization singularities
- •1.4.2. Vortices of phase difference. Sign principle for a vector field
- •1.4.2.1. Field decomposition into orthogonally linearly polarized components
- •1.4.2.2. Principle of the vortex analysis of vector fields
- •1.4.2.3. Vortices of orthogonally polarized field components. Technique for study of polarizatioN singularities
- •1.4.3. “Correlation” of intensity and polariszation of the vector field
- •1.4.4. Interconnection of the component vortices and -points
- •1.4.5. Elementary polarization structures and elementary polarization singularities of vector fields
- •1.4.5.1. Polarization structures resulting from interference of orthogonally linearly polarized beams
- •1.4.5.2. Elementary polarization singularities resulting from interference of circularly polarized beams
- •1.4.5.3. Experimental mOdeling of elementary polarization singularities
- •1.4.6. Fine structure and averaged polarization characteristics of inhomogeneous vector fields
- •1.4.6.1. Avaraged stokes parameters
- •1.4.6.2. Analysis of the averaged parameters for decomposition of the field into linearly polarized components
- •1.4.6.3. Computer simulation of the vector field’s parameters
- •1.4.6.4. Analysis of the averaged parameters for the field decomposition into circular basis
- •1.4.6.5. Comparison of the experimental results and the data of computer simulation
- •1.4.7. “Stokes-formalism” for polarization singularites. “stokes-vortices”
- •1.5. Singularities of the Poynting vector and the structure of optical fields
- •1.5.1. General assumptions. Components of the poynting vector
- •1.5.2. Singularities of the poynting vector in scalar fields
- •1.5.2.1. Instantaneous singularities of a scalar field
- •1.5.2.2. Averaged singularities of the poynting vector of scalar field
- •1.5.3. Singularities of the Poynting vector at vector fields
- •1.5.3.1. Instantaneous singularities of vector field
- •1.5.3.2. Behavior of the Poynting vector in areas of elementary polarization singularities
- •1.5.3.2.1. Symmetric distributions of amplitude and phase of the interfering beams
- •1.5.3.2.2. Non-symmetrical distributions of amplitudes and phases of the interfering beams
- •1.5.3.2.3. Experimental proving of the existence of the orbital momentum in the vicinity of -point
- •1.5.3.3. The averaged Poynting vector of the vector field
- •Instantaneous singularities of the Poynting vector
- •Appendix 1.1. Wave fronts approximation
- •104. I.Mokhun, r.Brandel and Ju.Viktorovskaya, “Angular momentum of electromagnetic field in areas of polarization singularities”, ujpo, Vol. 7, pp. 63-73, (2006).
104. I.Mokhun, r.Brandel and Ju.Viktorovskaya, “Angular momentum of electromagnetic field in areas of polarization singularities”, ujpo, Vol. 7, pp. 63-73, (2006).
105. G. Korn, T. Korn, “Mathematical Handbook for Scientists and Engineers”, 2nd enlargend and revised edition. McGraw-Hill Book Company, New York San Francisco Toronto London Sydney, (1968).
106. “Handbook of Mathematical Functions”, Edited by Abramowitz and Stegun I., National bureau of standards. Applied mathematics series 55. (1964).
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