Jones matrix of non-uniform birefringent film

For layer j, the angle of the slow axis with respect to the x axis is Pj and the phase retardation is Tj = l7t[ne z=j h)-no z=jish)]ishlX. In the lab frame, the Jones vector of the incident 

The Jones vector, Eo, of the outgoing light is related to the Jones vector, Ei of the incident light by 

Usually the multiplication of the matrices is carried out numerically. Analytical solutions can be obtained in some special cases. 

The Jones matrix method has the limitation that it only works well for normally incident and paraxial rays. It neglects the reflection and refraction from the interface between two optic media whose refractive indices are different. The extended Jones matrix method takes account of the reflection and refraction, but still neglect multiple reflection, and can be used to calculate the optical properties of media for obhquely incident hght [4—7]. 

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