A spectral method for modeling high-frequency electromagnetic waves in axisymmetric geometry is proposed. The method is based on the expansion of the solutions of Maxwell’s equations in Laguerre functions in the time region.

The spectral method is used to solve Maxwell’s equations for both 2D media and stratified media. In the case of stratified media, a Fourier–Bessel expansion in the radial variable is used. The effectiveness of the spectral and finite-difference methods is compared. Harmonic solutions and solitary solutions by the Laguerre method are considered, and the dynamics of monochromatic and broadband electromagnetic pulses are examined.

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