Abstract
We studied paraxial light beams, obtained by a continuous superposition of off-axis Gaussian beams with their phases chosen so that the whole superposition is invariant to free-space propagation, i.e., does not change its transverse intensity shape. Solving a system of five nonlinear equations for such superpositions, we obtained an analytical expression for a propagation-invariant off-axis elliptic Gaussian beam. For such an elliptic beam, an analytical expression was derived for the orbital angular momentum, which was shown to consist of two terms. The first one is intrinsic and describes the momentum with respect to the beam center and is shown to grow with the beam ellipticity. The second term depends parabolically on the distance between the beam center and the optical axis (similar to the Steiner theorem in mechanics). It is shown that the ellipse orientation in the transverse plane does not affect the normalized orbital angular momentum. Such elliptic beams can be used in wireless optical communications, since their superpositions do not interfere in space, if they do not interfere in the initial plane.
Highlights
Photonics 2021, 8, 190. https://Among the different kinds of light fields, of special interest are form-invariant fields
In [8], a general procedure is described for calculating the paraxial propagation-invariant beams, whose transverse intensity distribution has the shape of an arbitrary curve
The procedure is based on using an elementary spiral beam as a building block
Summary
Among the different kinds of light fields, of special interest are form-invariant (or, propagation-invariant) fields. In this work, based on the theory of paraxial structurally stable light beams developed in [8], we studied paraxial propagation-invariant elliptic Gaussian beams, similar to [21], but with an arbitrary position of the ellipse center in the transverse plane and with an arbitrary ellipse tilt. For this purpose, as in [8,9], we use simple beams as building blocks and construct a continuous superposition of elementary spiral light beams [8] on a plane. It turns out that the ellipse orientation in the transverse plane (tilt angle of the ellipse’s axes to the Cartesian coordinate axes) does not affect the normalized orbital angular momentum
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