Editing Optics (section)

====Modelling and design of optical systems using physical optics====

Many simplified approximations are available for analysing and designing optical systems. Most of these use a single [[Scalar (physics)|scalar]] quantity to represent the electric field of the light wave, rather than using a [[Euclidean vector|vector]] model with orthogonal electric and magnetic vectors.<ref name = "Born and Wolf">M. Born and E. Wolf (1999). ''Principle of Optics''. Cambridge: Cambridge University Press. {{ISBN|0-521-64222-1}}.</ref>
The [[Huygens–Fresnel principle|Huygens–Fresnel]] equation is one such model. This was derived empirically by Fresnel in 1815, based on Huygens' hypothesis that each point on a wavefront generates a secondary spherical wavefront, which Fresnel combined with the principle of [[Superposition principle|superposition]] of waves. The [[Kirchhoff's diffraction formula|Kirchhoff diffraction equation]], which is derived using Maxwell's equations, puts the Huygens-Fresnel equation on a firmer physical foundation. Examples of the application of Huygens–Fresnel principle can be found in the articles on diffraction and [[Fraunhofer diffraction]].

More rigorous models, involving the modelling of both electric and magnetic fields of the light wave, are required when dealing with materials whose electric and magnetic properties affect the interaction of light with the material. For instance, the behaviour of a light wave interacting with a metal surface is quite different from what happens when it interacts with a dielectric material. A vector model must also be used to model polarised light.

[[Computer simulation|Numerical modeling]] techniques such as the [[finite element method]], the [[boundary element method]] and the [[transmission-line matrix method]] can be used to model the propagation of light in systems which cannot be solved analytically. Such models are computationally demanding and are normally only used to solve small-scale problems that require accuracy beyond that which can be achieved with analytical solutions.<ref>{{cite book|author=J. Goodman|year=2005|title=Introduction to Fourier Optics|edition=3rd|publisher=Roberts & Co Publishers|isbn=978-0-9747077-2-3|url= https://books.google.com/books?id=ow5xs_Rtt9AC}}</ref>

All of the results from geometrical optics can be recovered using the techniques of [[Fourier optics]] which apply many of the same mathematical and analytical techniques used in [[acoustic engineering]] and [[signal processing]].

[[Gaussian beam|Gaussian beam propagation]] is a simple paraxial physical optics model for the propagation of coherent radiation such as laser beams. This technique partially accounts for diffraction, allowing accurate calculations of the rate at which a laser beam expands with distance, and the minimum size to which the beam can be focused. Gaussian beam propagation thus bridges the gap between geometric and physical optics.<ref>{{cite book|author=A.E. Siegman|year=1986|title=Lasers|url=https://archive.org/details/lasers0000sieg|url-access=registration|publisher=University Science Books|isbn=978-0-935702-11-8}} Chapter 16.</ref>