Study of Frozen Waves’ theory through a continuous superposition of Bessel beams

This paper presents a study of a recent solution to Maxwell's equation, the so-called “Frozen Waves”, whose main characteristics are to remain static in space, and to keep an arbitrary longitudinal field pattern previously chosen. These waves could be obtained by an adequate, but discrete, superposition of monochromatic Bessel beams. Contrary to that, we have here proposed a new way to get these waves through a continuous superposition of Bessel beams, and discussed some physical aspects and then exemplified for both loss and lossless media.