Localization and paraxiality of pseudo-nondiffracting fields

Degree of paraxiality of cylindrical vector partially coherent Laguerre–Gaussian beams

“…When p ¼0 (Solid line), the degree of paraxiality increases monotonously as the beam waist size increases ð0 o w 0 o 4λÞ, and tends to 1 when w 0 4 4λ, indicating that the light beams become complete paraxial. For another limiting case ðw 0 -0Þ, the light beam reduces to a point source, while the value of degree of paraxiality tends to 0.535, which represents the residual paraxiality the CV partially coherent LG beams remained as described in [34]. For p 40, the value of the degree of paraxiality is almost same to those of p¼ 0 for the two cases: w 0 -0 and w 0 44λ, respectively, but the degree of paraxiality increases in the way of oscillating as the beam waist increases ð0 ow 0 o λÞ, which is much different from the case of p ¼0.…”

“…In 2008, Gawhary et al introduced a parameter named degree of paraxiality to measure the paraxiality of monochromatic light beams [33]. Later, they revised the Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/optcom definition of degree of paraxiality to a more correct form [34], and studied the influence of field correlations and field properties on the degree of paraxiality of monochromatic light beams [34,35]. The behaviors of degree of paraxiality of a Gaussian beam diffracted by a circular aperture were reported in [36].…”

Scaling symmetry and conserved charge for shape-invariant optical fields

“…This is true in optics a well, where, in the last years, there was a notable growth in publication of works that studied and explained some of the features of optical fields by using symmetry arguments [3][4][5][6][7][8]. As an example, we can recall here the beautiful derivation, due to Wünche [5], of Hermite-Gauss and Laguerre-Gauss beams by application of certain differential operators to the fundamental Gaussian beam, introduced in the context of Lie's algebra for the paraxial regime.…”

A bound for the range of a narrow light beam in the near field

“…A major question is how the light beam propagates from the near field to the far field. We do not consider the change of the beam width from midfield to far field, where the influence of the evanescent waves may be neglected [5][6][7][8][9][10][11][12][13][14]. While many studies concentrate on the amplitude enhancement in the far field, the issue of the change of the width and the related acuity of the beam during propagation in the near field is even more important.…”

“…Subsequently we consider the twice-differentiated bandlimited distribution of Eq. (14). The widths wð0Þ and W ð0Þ are calculated analytically, leading to…”