Interference of plane light waves with different polarizations and the Jones matrix formalism

A new method is developed to solve the interference problem that involves two plane monochromatic waves of equal frequency provided these waves, in general, have different polarizations and their wave vectors are arbitrarily oriented. Using a three-dimensional generalized Jones vector, we find analytical solutions for the spatial-intensity distribution of the total wave and (at certain orientations of the wave vectors) for the parameters characterizing its polarization state. The results of the work are applied to wide variety of interference problems.