Determination of the amplitude and the phase of the elements of electric cross-spectral density matrix by spectral measurements

The amplitudes and the phases of the elements of electric cross-spectral density matrix are determined experimentally for a pair of points in the cross-section of an expanded laser beam. A modified version of the Young’s interferometer is used as an experimental tool, which separates the beams emerging from the double-slit widely and provides ease in insertion of polarizers and half wave rotators in individual beams. To determine these complex elements of the cross-spectral density matrix, the experimentally obtained values of the spectral densities at an off-axis point are put in the mathematical expressions derived by us using the spectral interference law. The four complex generalized Stokes parameters are also determined using the linear combinations of the matrix elements. This unique but simple experimental approach for determining both the two-point parameters might provide a means to investigate the polarization and the coherence properties of the random electromagnetic beams on propagation.