Analytic description of Airy-type beams when truncated by finite apertures

Abstract

-In this paper, we have developed an analytic method for describing AiryType beams truncated by finite apertures. This new approach is based on suitable superposition of exponentially decaying Airy beams. Regarding both theoretical and numerical aspects, the results here shown are interesting because they have been quickly evaluated through a simple analytic solution, whose characteristics of propagation has agreed with those already published in literature through the use of numerical methods. To demonstrate the method's potentiality, three different truncated beams have been analyzed: ideal Airy, Airy-Gauss and Airy-Exponential.

Diffraction-resistant scalar beams generated by a parabolic reflector and a source of spherical waves

“…Here we define "diffraction resistant beams" as finite power beams that can maintain their spot size for long distances when compared to usual beams. The truncated Bessel beam is an example, but there are many other beams with this characteristic [12][13][14][15][16].…”

“…With these parameters, our approximative equations (6,7,8,12,13,14,15) Figure 6a shows the beam intensity and Fig.6b its orthogonal projection. We can see that the extended focus occurs as predicted, but due to the intensity variation along the distance, the details about the spot size behavior are not very clear, although it is clear its resistance to the diffraction effects along the extended focus range.…”

Propagation of time-truncated Airy-type pulses in media with quadratic and cubic dispersion

“…This approach is a variant/extension of the one developed to deal with spatially truncated Airy beams [14], where the equivalent to the third-order term in Eq. (1) was not considered.…”

“…The mathematical method used here is an extension of the one used for describing spatially truncated Airy beams [14].…”

Incomplete Airy beams: finite energy from a sharp spectral cutoff

“…Alternatively, finite-energy can be enforced by modulating the Airy function with a wide Gaussian profile [6], or even by a sharp truncation [7][8][9]. These beams display good approximations of the transverse acceleration of infinite-energy Airy beams over an appreciable propagation distance.…”