HuygensFresnelprincipe

Huygens–Fresnel principle is a foundational concept in wave optics that describes how light propagates and diffracts. It states that every point on a propagating wavefront acts as a source of secondary spherical wavelets, and the new wavefront is the envelope of these wavelets. The resulting superposition determines the amplitude and phase of the field at subsequent points.

Historical development: The idea originates with Christiaan Huygens, who treated wavefronts as surfaces that advance by sending out wavelets. Augustin-Jean Fresnel added its quantitative aspects, emphasizing interference among the secondary wavelets and introducing a directional weighting (the obliquity factor) to account for angular variation in contributions.

Mathematical formulation: In scalar diffraction theory, the complex amplitude at an observation point is given by an integral over the wavefront of the field on the surface multiplied by a Green's function, roughly proportional to exp(i k R)/R, times an obliquity factor. This leads to the Fresnel diffraction integrals and, in the far field, to Fraunhofer diffraction patterns. The approach can be related to Kirchhoff's diffraction formula in optics.

Modern perspective and scope: The Huygens–Fresnel principle provides an intuitive and widely used framework for understanding diffraction and interference. It is a valid approximation in many optical contexts but is subsumed within the full Maxwellian description of electromagnetic waves; rigorous diffraction theory derives from boundary-value solutions of Maxwell's equations.