TE and TM waves spectrum instabilities in periodic media

The electromagnetic waves in periodic stratified media carried out by means of the analysis of the solutions of the differential equation of the second order is researched. The investigation on Maxwell's equation is insufficient. This paper presents the basic distinction of stability spectrum in solutions of the equations applied to electromagnetic waves of various polarization. Mathieu's equation for electric field which is convenient for analytical research of the equation concerns the magnetic field. The dual nature of the structure of instabilities which has been considered in the present article, improves essentially the theory of electromagnetic waves spectrum in periodic stratified media and other periodical structures.