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Recently, a method for obtaining diffraction-attenuation resistant beams inabsorbing media was developed through suitable superposition of idealzero-order Bessel beams. In this work, we will show that such beams maintaintheir resistance to diffraction and absorption even when generated by finiteapertures. Also, we shall extend the original method to allow a higher controlover the transverse intensity profile of the beams. Although the method hasbeen developed for scalar fields, it can be applied to paraxial vector wavefields as well. These new beams can possess potential applications, such asfree space optics, medical apparatuses, remote sensing, optical tweezers, etc..

Diffraction-Attenuation Resistant Beams: their Higher Order Versions and Finite-Aperture Generations