Variable States of Polarization Incident on a Wave Plate

This Demonstration uses a series of Jones matrices and vectors to predict a transmitted wave through a series of optical elements. A Jones vector describes the electric field vector as two scalar components. The phase information is preserved as a complex exponent. When a polarized beam, expressed as a Jones vector, passes through an optical element, it undergoes a transformation that can be expressed as a 2×2 matrix. Each linear optical element has a Jones matrix that describes its transformation of the transmitted wave.

The following equation shows the multiplication of the Jones vector by the polarizer and wave plate Jones matrices; and are the incident electric field components.

, where is the Jones matrix for the polarizer and is the Jones matrix for the wave plate.

The transmitted beam is a vector with components and . The irradiance is found by summing the squares of the complex conjugates of each component.