Basis Expansions for Monochromatic Field Propagation in Free Space

98Basis expansions are an extremely useful tool in mathematical physics. By using them, we can express a function representing a physical distribution as a linear combination of simpler distributions with well-known properties. They are particularly useful for modeling propagation or evolution of fields through certain simple systems. Perhaps the best known expansion of this type is the Fourier synthesis of a distribution as a superposition of simple sinusoidal elements, originally proposed by Fourier to study heat transfer.