Editing Huygens–Fresnel principle (section)

==History==
In 1678, Huygens proposed<ref>Chr. Huygens, ''[[Treatise on Light|Traité de la Lumière]]'' '' (drafted 1678; published in Leyden by Van der Aa, 1690), translated by [[Silvanus P. Thompson]] as ''[[iarchive:treatiseonlight031310mbp|Treatise on Light]]'' (London: Macmillan, 1912; [https://www.gutenberg.org/ebooks/14725 Project Gutenberg edition], 2005), p.19.''</ref> that every point reached by a luminous disturbance becomes a source of a spherical wave. The sum of these secondary waves determines the form of the wave at any subsequent time; the overall procedure is referred to as '''Huygens' construction'''.<ref name = "Born and Wolf"/>{{rp|132}} He assumed that the secondary waves travelled only in the "forward" direction, and it is not explained in the theory why this is the case. He was able to provide a qualitative explanation of linear and spherical wave propagation, and to derive the laws of reflection and refraction using this principle, but could not explain the deviations from rectilinear propagation that occur when light encounters edges, apertures and screens, commonly known as [[diffraction]] effects.<ref name = "Insight into Optics">{{Cite book |last=Heavens |first=Oliver S. |title=Insight into optics |last2=Ditchburn |first2=R. W. |date=1993 |publisher=Wiley |isbn=978-0-471-92901-7 |edition=Reprint with corrections August 1993 |location=Chichester}}</ref> 

In 1818, Fresnel<ref>A. Fresnel, "Mémoire sur la diffraction de la lumière" (deposited 1818, "crowned" 1819), in ''Oeuvres complètes'' (Paris: Imprimerie impériale, 1866&ndash;70), vol.1, pp.&nbsp;247&ndash;363; partly translated as "Fresnel's prize memoir on the diffraction of light", in H.&nbsp;Crew (ed.), ''[https://archive.org/details/wavetheoryofligh00crewrich The Wave Theory of Light: Memoirs by Huygens, Young and Fresnel]'', American Book Co., 1900, pp.&nbsp;81&ndash;144. (Not to be confused with the earlier work of the same title in ''Annales de Chimie et de Physique'', 1:238&ndash;81, 1816.)</ref> showed that Huygens's principle, together with his own principle of [[Interference (wave propagation)|interference]], could explain both the rectilinear propagation of light and also diffraction effects. To obtain agreement with experimental results, he had to include additional arbitrary assumptions about the phase and amplitude of the secondary waves, and also an obliquity factor. These assumptions have no obvious physical foundation, but led to predictions that agreed with many experimental observations, including the [[Poisson spot]].

[[Siméon Denis Poisson|Poisson]] was a member of the French Academy, which reviewed Fresnel's work. He used Fresnel's theory to predict that a bright spot ought to appear in the center of the shadow of a small disc, and deduced from this that the theory was incorrect. However, [[Fran%C3%A7ois Arago]], another member of the committee, performed the experiment and showed that [[Arago spot|the prediction was correct]].<ref name = "Born and Wolf">{{cite book |first1=Max |last1=Born |author-link=Max Born |first2=Emil |last2=Wolf |title=[[Principles of Optics]] |year=1999 |publisher=Cambridge University Press |isbn=978-0-521-64222-4 }}</ref> This success was important evidence in favor of the wave theory of light over then predominant [[corpuscular theory]].

In 1882, [[Gustav Kirchhoff]] analyzed Fresnel's theory in a rigorous mathematical formulation, as an approximate form of an integral theorem.<ref name = "Born and Wolf"/>{{rp|375}} Very few rigorous solutions to diffraction problems are known however, and most problems in optics are adequately treated using the Huygens-Fresnel principle.<ref name = "Born and Wolf"/>{{rp|370}}

In 1939 [[Edward Copson]], extended the Huygens' original principle to consider the polarization of light, which requires a vector potential, in contrast to the scalar potential of a simple [[Gravity wave|ocean wave]] or [[Longitudinal wave|sound wave]].<ref name="TheoryOfHuygens">{{cite web | title=TheoryOfHuygens|website=Archive.org|year=1939|url=https://archive.org/details/in.ernet.dli.2015.84565}}</ref><ref>{{cite journal|author=Bleick, Willard Evan|title=Review: ''The Mathematical Theory of Huygens' Principle'' by B. B. Baker and E. T. Copson|journal=Bull. Amer. Math. Soc.|year=1940|volume=46|issue=5|pages=386–388|url=https://www.ams.org/journals/bull/1940-46-05/S0002-9904-1940-07203-9/S0002-9904-1940-07203-9.pdf|doi=10.1090/s0002-9904-1940-07203-9|doi-access=free}}</ref>

In [[antenna (radio)|antenna theory]] and engineering, the reformulation of the Huygens–Fresnel principle for radiating current sources is known as [[surface equivalence principle]].<ref>{{cite book|last=Balanis|first= Constantine A.|author-link=Constantine A. Balanis|title=Advanced Engineering Electromagnetics|date=2012|publisher=John Wiley & Sons|isbn=978-0-470-58948-9|pages=328–331}}</ref><ref>{{cite book |last=Balanis |first=Constantine A.|author-link=Constantine A. Balanis |title=Antenna Theory: Analysis and Design |edition=3rd |publisher=John Wiley and Sons |date=2005|isbn=047166782X|page=333}}</ref>

Issues in Huygens-Fresnel theory continue to be of interest.  In 1991, [[David A. B. Miller]] suggested that treating the source as a dipole (not the monopole assumed by Huygens) will cancel waves propagating in the reverse direction, making Huygens' construction quantitatively correct.<ref>{{cite journal |first=David A. B. |last=Miller |title=Huygens's wave propagation principle corrected |journal=Optics Letters |volume=16 |issue= 18|pages=1370–1372 |date=1991 |doi=10.1364/OL.16.001370 |pmid=19776972 |bibcode=1991OptL...16.1370M |s2cid=16872264 }}</ref> In 2021, Forrest L. Anderson showed that treating the wavelets as [[Dirac delta function]]s, summing and differentiating the summation is sufficient to cancel reverse propagating waves.<ref>{{Cite journal |last=Anderson |first=Forrest L. |date=2021-10-12 |title=Huygens' Principle geometric derivation and elimination of the wake and backward wave |url=https://www.nature.com/articles/s41598-021-99049-7 |journal=Scientific Reports |language=en |volume=11 |issue=1 |doi=10.1038/s41598-021-99049-7 |issn=2045-2322 |pmc=8511121 |pmid=34642401}}</ref>