This volume aims to familiarize the reader with basic concepts of light propagation in the simplest class of media: linear, homogenous, dispersionless, and isotropic. After a review of Maxwell's equations in both integral and differential forms, the book describes the field propagation from elementary sources (dipoles) and in free space, in 1D, 2D, and 3D. Next, the material covers diffraction of light by a 2D screen, with various levels of approximations, emphasizing the wavevector space calculations. The ABCD matrix propagation is introduced as an efficient tool for both ray optics and Gaussian beam propagation. The volume ends with a chapter on propagation of field correlations, generalizing the coherence concepts introduced in Volume 1.
Key Features:
- A homogeneous, self-consistent reference that covers this interdisciplinary field.
- Books are intended to be used as reference for a two-semester course on Principles of Biophotonics.
- Aim is not only to provide a "how to" user guide for these techniques, but to clearly present the optics foundation that allows them to function.
Author(s): Gabriel Popescu
Series: IPEM–IOP Series in Physics and Engineering in Medicine and Biology
Publisher: IOP Publishing
Year: 2023
Language: English
Pages: 189
City: Bristol
PRELIMS.pdf
Acknowledgement
Author biography
Gabriel Popescu
CH001.pdf
Chapter 1 Maxwell’s equation in integral form
1.1 Faraday’s law
1.2 Ampère’s law
1.3 Gauss’s law for electric fields
1.4 Gauss’s law for magnetic fields
1.5 Problems
References and Further reading
CH002.pdf
Chapter 2 Maxwell’s equations in differential form
2.1 The four main equations
2.2 Constitutive relations
2.3 Maxwell’s equations in other representations
2.3.1 Space–frequency representation (r, ω)
2.3.2 Wavevector–time representation (k, t)
2.3.3 Wavevector–frequency representation (k, ω)
2.4 Classification of optical materials
2.4.1 Anisotropic
2.4.2 Dispersive
2.4.3 Inhomogeneous
2.4.4 Nonlinear
2.5 Boundary conditions
2.6 Reflection and refraction at boundaries
2.6.1 Fresnel equations
2.6.2 Total internal reflection: critical angle
2.6.3 Total transmission: Brewster angle
2.7 Characteristic impedance
2.8 Poynting theorem and energy conservation
2.9 Phase, group, and energy velocity
2.10 The wave equation
2.10.1 Vector wave equation
2.10.2 Scalar wave equation
2.11 Wave equation in other representations
2.11.1 Space–frequency representation (r, ω)
2.11.2 Wavevector–time representation (k, t)
2.11.3 Wavevector–frequency representation (k, ω)
2.12 Problems
References and further reading
CH003.pdf
Chapter 3 Propagation of electromagnetic fields
3.1 Dyadic Green’s function
3.2 Electric dipole radiation
3.3 Magnetic dipole radiation
3.4 Problems
References and further reading
CH004.pdf
Chapter 4 Propagation of scalar fields in free space
4.1 Primary and secondary sources
4.2 1D Green’s function: plane wave
4.3 2D Green’s function: cylindrical wave
4.4 3D Green’s function: spherical wave
4.5 Problems
References and further reading
CH005.pdf
Chapter 5 Diffraction of scalar fields
5.1 Diffraction by a 2D object
5.2 Plane wave decomposition of spherical waves: Weyl’s formula
5.3 Angular spectrum propagation approximation
5.4 Fresnel approximation
5.5 Fraunhofer approximation
5.6 Fourier properties of lenses
5.6.1 Lens as a phase transformer
5.6.2 Lens as a Fourier transformer
5.7 Problems
References
CH006.pdf
Chapter 6 Geometrical optics
6.1 Applicability of geometrical optics
6.2 WKB approximation: eikonal equation and geometrical optics
6.3 Fermat’s principle
6.4 Refraction through curved surfaces
6.5 Reflection by curved mirrors
6.5.1 Spherical mirrors
6.5.2 Parabolic mirrors
6.5.3 Elliptical mirrors
6.6 Ray propagation (ABCD) matrices
6.6.1 Free space translation
6.6.2 Refraction through a planar interface
6.6.3 Refraction through a spherical interface
6.6.4 Transmission through a thick lens
6.6.5 Transmission through a thin lens
6.6.6 Reflection by a spherical mirror
6.6.7 Cascading optical systems
6.6.8 Eigen vectors
6.7 Problems
References and further reading
CH007.pdf
Chapter 7 Gaussian beam propagation
7.1 Definition of a light beam
7.2 Fresnel propagation of Gaussian beams
7.3 Gaussian beam characteristics
7.4 Gaussian beam propagation using ABCD matrices
7.4.1 Free space propagation
7.4.2 Refraction through a planar interface
7.4.3 Refraction through a spherical interface
7.4.4 Transmission through a thin lens
7.4.5 Reflection by a spherical mirror
7.4.6 Cascading optical systems
7.5 Problems
References and further reading
CH008.pdf
Chapter 8 Propagation of field correlations
8.1 Heisenberg uncertainty relation and the coherence of light
8.1.1 Uncertainty relations in space and time
8.1.2 Uncertainty relation and the Wiener–Khintchine theorem
8.1.3 Uncertainty relations and diffraction of light
8.2 Spatiotemporal field correlations
8.2.1 Spatiotemporal statistics
8.2.2 Spatial correlations of monochromatic fields
8.2.3 Temporal correlations of plane waves
8.3 Coherence mode decomposition of random fields
8.4 Deterministic signal associated with a random stationary field
8.5 Propagation of field correlations: intuitive picture
8.6 Stochastic wave equation
8.7 Wave equation for the deterministic signal associated with a random field
8.8 Propagation of spatial coherence: van Cittert–Zernike theorem
8.9 Problems
References
