Generalized theory of interference, and its applications. Part I. Coherent pencils

Abstract

The superposition of two coherent beams in different states of elliptic polarisation is discussed in a general manner. If A and B represent the states of polarisation of the given beams on the Poincare sphere, and C that of the resultant beam, the result is simply expressed in terms of the sides,a, b, c of the spherical triangle ABC. The intensity I of the resultant beam is given by: I=I₁ + I₂ +2√I₁+I₂cos½Ccosδ; the extent of mutual interference thus varies from a maximum for identically polarised beams (c = 0), to zero for oppositely polarised beams (c = π ). The state of polarisation C of the resultant beam is located by sin² ½a = (I₁/I) sin² ½c and sin² ½b = (I₂/I) sin² ½c. The 'phase difference' δ is equal to the supplement of half the area of the triangle C'BA (where C' is the point diametrically opposite to C). These results also apply to the converse problem of the decomposition of a polarised beam into two others. The interference of two coherent beams after resolution into the same state of elliptic polarisation by an elliptic analyser or compensator is discussed; as also the interference (direct,and after resolution by an analyser) of n coherent pencils in different states of polarisation.