Under certain simplifying assumptions, Maxwell’s equations reduce to the scalar wave equation. Many optical phenomena, such as diffraction of unpolarized light, can be derived from the wave equation, which is simpler than Maxwell’s equations.
We thus first introduce the wave model from which the wave equation is derived, and then discuss the physical and mathematical properties of waves. Except for the effects of polarization, the properties of scalar waves are the same as those of light waves. As is the case with the electromagnetic waves described by Maxwell’s equations, scalar waves also obey various conditions on the boundaries between different media.
Both the wave equation and Maxwell’s equations contain time. Light waves are characterized by their oscillation frequency. Given the oscillation frequency, wave equation and Maxwell’s equations can be expressed in the frequency domain by the Helmholtz equation.
Key concepts covered include:
- General waves and their properties
- Wave model
- The wave equation to describe light propagation in time domain
- Derivation of Helmholtz Equation in frequency domain
- Boundary value problems in optics
- Hands-on training on writing codes in Python/Matlab to solve real-life problems