A general theory for the Frozen Waves and their realization through finite apertures

In this paper, we present a generalization of the so-called Frozen Waves, which are new solutions to Maxwell’s equations having the important characteristic of remaining static in space and keeping any previously chosen arbitrary longitudinal field pattern. In the pioneering work, these waves were introduced as a discrete superposition of zero-order Bessel beams. As a fact, here we will represent these waves as a continuous superposition of Bessel beams leading to a simpler and more compact mathematical formalism, which allows us to derive certain inequalities that restrict the physical properties of the Frozen Waves, such as their attainable longitudinal resolution. Besides this, we will discuss losses compensation in a lossy medium and, finally, their practical realization through finite apertures.