  Recognized for their non-diffracting properties, Bessel beams can be
conveniently combined to generate the so-called Frozen Waves, which are
monochromatic beams endowed with topological charge and whose longitudinal
intensity pattern can be shaped according to a previously chosen function.
Continuous superposition of Bessel beams is specially suitable for
micrometer-scale domains, being highly relevant for applications in optical
tweezers, particle trapping and atom guidance. Previous studies have
successfully constructed micrometer Frozen Wave solutions with null topological
charge; nevertheless, some challenges persist in obtaining exact solutions when
dealing with higher topological charge values (i.e., higher-order micrometer
Frozen Waves). Typically, a topological charge raising operator is used to
elevate the order; however, such solutions face significant issues when the
orders become excessively high. In this paper, based in continuous
superposition of higher order Bessel beams, we develop a novel analytic and
exact solution for higher-order micrometer Frozen Waves, so obtaining a method
for modeling the intensity of beams with arbitrary topological charge within
micrometer spatial domains. We also investigate the behavior of the electric
field's longitudinal component in such highly non-paraxial regimes through a
vectorial treatment.
