SPFCU41

UE Advanced theoretical optics

Unité d'enseignement (UE) de 4 crédits

^En UE enseignée en Anglais

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Rays and Waves

An overview is given of the many ways to understand the connection between the ray and wave models, and the corresponding ways to construct models for propagating waves based exclusively on rays. Analogies with other areas of physics are stressed, particularly that with the connection between the classical and quantum models for particles.

1.1 Mathematical elements

Asymptotic methods: stationary phase and saddle points
Fourier uncertainty
Phase-space representations: Wigner, Husimi/Q/Spectrogram, Kirkwood/Rihaczek/Dirac

1.2 Ray-wave connection in the paraxial limit

Review of wave optics in the paraxial regime
Review of ray optics in the paraxial regime: phase space representation
Collins formula and LCT for connecting rays and waves
Complex ray bundles and Gaussian beams

1.3 Ray-wave connection in the short-wave limit

Nonparaxial scalar wave optics in terms of amplitude and phase: super- and sub-oscillations (Gouy phase)
Use of stationary phase and Feynman integral picture.
Flux lines and Bohmian paths
Debye asymptotic series
The many faces of ray optics: Eikonal equation, Fermat’s principle and the Ibn Sahl-Decartes-Snell law
Ray-based wave estimates in the position representation: connection with WKB
Caustics
Angular spectrum/Fourier regime
Ray-based wave estimates in the direction/momentum representation: connection with Debye-Wolf (& Richards-Wolf)
Direction/momentum caustics
Connections through stationary phase
Diffraction: Keller’s diffracted rays
Uniform asymptotics
Gaussian summation methods

1.4 Ray-wave connection in the low coherence limit

Basic elements of spatial coherence: the cross-spectral density and the Wolf equations
Radiative transfer equation: the radiance or specific intensity
Wave-based definitions of the radiance and conservation along rays
Analogies in other areas of optics and physics.

Structured light

This course presents the basic elements of structured light beams, including properties and applications. General aspects of optical fields are also discussed such as polarization, geometric phase, energy flow, and gradient and scattering forces on particles.

2.1 Scalar solutions

Types of self-similarity
Plane-wave superposition
Talbot effect
Closed-form solutions of wave equations through separation of variables
Propagation-invariant beams: Bessel, Mathieu, others
“Accelerating” beams: Airy and its variants
“Self-healing”, “acceleration” and other apparently strange behavior
Structured Gaussian beams: Hermite-Gauss, Laguerre-Gauss, Ince-Gauss, others
Ray pictures
Applications in imaging, machining, manipulation, and information transfer

2.2 Polarization

Review: Jones vectors, Stokes parameters, Poincaré sphere
Polarizers, birefringent elements, and geometric phase
Vector beams and non-uniform polarization
Orbital and Spin angular momentum in the paraxial regimes; interaction with particles.

2.3 Nonparaxial generalizations

Modeling strongly focused light: angular spectrum, Debye-Wolf and Richard-Wolf integrals
Multipolar expansions
Scalar structured nonparaxial fields
Montgomery effect
Orbital and spin angular momenta in the nonparaxial regime, and spin-orbit coupling
Nonparaxial descriptions of polarization
Trapping forces and torques
Principles of Mie theory: forces and torques.

UE Advanced theoretical optics

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