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Transfer-matrix method (optics)
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<p>The transfer-matrix method is a method used in <a href="/facts/Optics/p0vq4S1T">optics</a> and <a href="/facts/Acoustics/2GpQUymy">acoustics</a> to analyze the propagation of <a href="/facts/Electromagnetic_wave/Ynx7ujCW">electromagnetic</a> or <a href="/facts/Acoustic_wave/Mf8m46AI">acoustic waves</a> through a <a href="/facts/Stratified_medium/CNTGkczX">stratified medium</a>; a stack of <a href="/facts/Thin_film/nSeoUT4Q">thin films</a>. This is, for example, relevant for the design of <a href="/facts/Anti-reflective_coating/BN2xVy4k">anti-reflective coatings</a> and <a href="/facts/Dielectric_mirror/c9wsmYGp">dielectric mirrors</a>. </p><p>The <a href="/facts/Reflection_(physics)/BhcjDs79">reflection</a> of <a href="/facts/Light/jeofpMn4">light</a> from a single interface between two <a href="/facts/Medium_(optics)/gm6LqshC">media</a> is described by the <a href="/facts/Fresnel_equations/6SEao7ua">Fresnel equations</a>. However, when there are multiple interfaces, such as in the figure, the reflections themselves are also partially transmitted and then partially reflected. Depending on the exact path length, these reflections can <a href="/facts/Interference_(wave_propagation)/lI5f78I4">interfere</a> destructively or constructively. The overall reflection of a layer structure is the sum of an infinite number of reflections. </p><p>The transfer-matrix method is based on the fact that, according to <a href="/facts/Maxwell%2527s_equations/LfJ1drHS">Maxwell's equations</a>, there are simple continuity conditions for the <a href="/facts/Electric_field/tt4MooBs">electric field</a> across boundaries from one medium to the next. If the field is known at the beginning of a layer, the field at the end of the layer can be derived from a simple <a href="/facts/Matrix_(mathematics)/qa8FI4ko">matrix</a> operation. A stack of layers can then be represented as a system matrix, which is the product of the individual layer matrices. The final step of the method involves converting the system matrix back into reflection and <a href="/facts/Transmission_coefficient/893q1h2K">transmission coefficients</a>. </p>