Absorption-free beam generated by a phase-engineered optical element

Phase engineering of an axicon's phase transmission function results in an exponential growth of an on-axis intensity of a diffraction-free or Bessel beam. We show that in a lossy medium obeying Beer's absorption law/exponential intensity decrease, a beam focused by such an optical element propagates with nearly constant intensity while preserving the quasi-diffraction-free property. Absorption-free beams may find applications in illumination, atmospheric propagation, biomedicine/light diffusion in live tissues, and other situations where light absorption hinders beam propagation.