Solution of electromagnetic wave in time-varying media in two-dimensional space

The analytical solution of gradual change media in two-dimensional free space is studied. Using separation of variables, the solution of electromagnetic wave in time-varying media, which is an exponential function of time, is derived in two-dimensional space. The rationality of the solution is verified indirectly. According to the solution, the figures of the wave are depicted. Based on these figures, the character of the wave in time-varying media is obtained, which shows frequency shift and changes of phase velocity and amplitude.