Mathematical devices for optical sciences /

The Lorentz group which is the underlying scientific language for modern optics has been most notably used for understanding Einstein's special relativity. By using a simplified approach of two-by-two matrices and Wigner functions, this book provides a basic and novel approach to classical and...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autores principales: Başkal, Sibel (Autor), Kim, Y. S. (Autor), Noz, Marilyn E. (Autor)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Bristol [England] (Temple Circus, Temple Way, Bristol BS1 6HG, UK) : IOP Publishing, [2019]
Colección:IOP (Series). Release 6.
IOP expanding physics.
Temas:
Optics > Mathematics.
Quantum optics.
Mathematical physics.
SCIENCE / Physics / Mathematical & Computational.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • 1. Forms of quantum mechanics
  • 1.1. The Schrödinger and Heisenberg pictures
  • 1.2. Interaction picture
  • 1.3. Density-matrix formulation of quantum mechanics
  • 1.4. Further contents of Heisenberg's commutation relations
  • 2. Lorentz group and its representations
  • 2.1. Lie algebra of the Lorentz group
  • 2.2. Two-by-two representation of the Lorentz group
  • 2.3. Four-vectors in the two-by-two representation
  • 2.4. Transformation properties in the two-by-two representation
  • 2.5. Subgroups of the Lorentz group
  • 2.6. Decompositions of the Sp(2) matrices
  • 2.7. Bilinear conformal representation of the Lorentz group
  • 3. Internal space-time symmetries
  • 3.1. Wigner's little groups
  • 3.2. Little groups in the light-cone coordinate system
  • 3.3. Two-by-two representation of the little groups
  • 3.4. One expression with three branches
  • 3.5. Classical damped oscillators
  • 4. Photons and neutrinos in the relativistic world of Maxwell and Wigner
  • 4.1. The Lorentz group and Wigner's little groups
  • 4.2. Massive and massless particles
  • 4.3. Polarization of massless neutrinos
  • 4.4. Scalars, vectors, tensors, and the polarization of photons
  • 5. Wigner functions
  • 5.1. Basic properties of the Wigner phase-space distribution function
  • 5.2. Time dependence of the Wigner function
  • 5.3. Wave packet spread
  • 5.4. Harmonic oscillators
  • 5.5. Minimum uncertainty in phase space
  • 5.6. Density matrix
  • 5.7. Measurable quantities
  • 6. Coherent states of light
  • 6.1. Phase-number uncertainty relation
  • 6.2. Baker-Campbell-Hausdorff relation
  • 6.3. Coherent states
  • 6.4. Symmetry of coherent states
  • 6.5. Coherent states in phase space
  • 6.6. Single-mode squeezed states
  • 7. Squeezed states and their symmetries
  • 7.1. Two-mode states
  • 7.2. Unitary transformations
  • 7.3. Symmetries of two-mode states
  • 7.4. Dirac matrices and O(3,3) symmetry
  • 7.5. Symmetries in phase space
  • 7.6. Two coupled oscillators
  • 8. Entanglement and entropy
  • 8.1. Density matrix and entropy
  • 8.2. Two-by-two density matrices
  • 8.3. Density matrix for two-oscillator states
  • 8.4. Entropy for the two-mode state
  • 8.5. Entangled excited states
  • 8.6. Wigner functions and uncertainty relations
  • 9. Ray optics and optical activities
  • 9.1. Ray optics using the group of ABCD matrices
  • 9.2. Physical examples using ABCD matrices
  • 9.3. Optical activities
  • 10. Polarization optics
  • 10.1. Jones vector, phase shifters, and attenuators
  • 10.2. New filters and possible applications
  • 10.3. Non-orthogonal coordinate systems
  • 11. Stokes parameters and Poincaré sphere
  • 11.1. Polarization optics and decoherence
  • 11.2. Coherency matrix and Stokes parameters
  • 11.3. Poincaré sphere
  • 11.4. The entropy problem
  • 11.5. Further symmetries from the Poincaré sphere
  • Appendix A. Covariant harmonic oscillators and the quark-parton puzzle
  • A.1. The covariant harmonic oscillator
  • A.2. Quark-parton puzzle.

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