Control of the orbital angular momentum via radial numbers of structured Laguerre–Gaussian beams

Abstract

We found that the internal perturbations of the structured Laguerre–Gaussian beam in the form of two-parametric harmonic excitations of the Hermite–Gaussian (HG) modes in its composition mix up the radial and azimuthal numbers. The harmonic excitation is characterized by two parameters, one of them controls the amplitude of the HG modes, and the second parameter controls the phases of each HG mode. It was revealed that this mixing of the beam quantum numbers leads to the possibility of controlling the orbital angular momentum (OAM) by means of radial numbers. Non-zero radial numbers lead to rapid OAM oscillations as the phase parameter changes, while oscillations disappear if the radial number is zero. We have also shown that the variation of the phase parameter in a wide range of values does not change the modulus of the total topological charge of the structured beam, despite the fast OAM oscillations.

Engineering Orbital Angular Momentum in Structured Beams in General Astigmatic Systems via Symplectic Matrix Approach

“…The associated ellipses in Figure 2, obtained from Equation (20), track the intensity pattern deformations with a variation of the distance Z 1 . In Figure 6, we have depicted the evolution of associated ellipses with variations of the θ-phase parameter for two groups of beams: standard sLG beams with ε = 1 (Figure 6a) and hybrid HLG (Figure 6b) beams [4] rotated by π/4 (i.e., the sLG beams with ε ≫ 1 [13]). Both in free space (Figure 6a,b) and the astigmatic system (Figure 6c,d), the directions of the ellipse axes strictly follow the shape of the intensity pattern only for the HLG beam (i.e., asLG beam with ε ≫ 1), although astigmatism tries to hold the axes of the ellipse and the intensity pattern (Figure 6c) for the standard asLG beam.…”

“…In this stream, the method of obtaining super-high OAM bursts by controlling the mode radial number in the structured beams, when propagating through astigmatic elements, looks quite usual but informative. One such large family of beams with broken symmetry is two-parametric structured Laguerre-Gaussian (sLG) beams [13] with a complex amplitude in the form sLG n,±ℓ (r) = (−1) n 2 2n+3ℓ/2 n! 2n+ℓ ∑ j=0 (±i) j (1 + εe ijθ )P (n+ℓ−j,n−j) j (0)HG 2n+ℓ−j,j (r), (1) where r = (x, y) is a 2D vector, and P (n+ℓ−j,n−j) j (•) is a Jacobi polynomial.…”

“…The control ε and θ parameters of the sLG beam can be treated as additional independent degrees of freedom. Weak changing of the phase parameter θ leads to fast OAM oscillations [13], the frequency of which is controlled by the radial number n, whereas the beam OAM cannot exceed the TC of the beam OAM ≤ ℓ. At the same time, at large amplitude parameters, ε ≫ 1, the astigmatic sLG beam turns into a hybrid Hermite-Laguerre-Gaussian (HLG) beam with symmetry but rotated by −π/4 relative to the standard HLG beam [4,15].…”

Structurally Stable Astigmatic Vortex Beams with Super-High Orbital Angular Momentum (ABCD Matrix Approach)

“…A sketch of the optical system is shown in Figure 1a. We assume that a structured sLG n, beam [33] with radial n, azimuthal numbers, and a complex parameter q(z) = z − iz 0 (where z 0 = kw 0 /2 is a Rayleigh length) falls onto the cylindrical lens with the focal length f x located at z = 0 so that the initial complex parameter is q 0 = −iz and has a Gaussian beam waist radius of w 0 . The spherical lens performs a Fourier transform and allows for not only separation of the vortex and astigmatic OAM constitutes, but also for transforming a structurally unstable beam into a structurally stable one without losing the OAM super-burst due to variations in the optical system parameters.…”

Dynamics of Hermite-Gaussian Beam Propagation in a Five-Level Tripod-Type Atomic Medium with Spatially Dependent Refractive Index

“…LG and HG beams with different modifications have wide practical applications. For example, structurally stable beams, which are coaxial superpositions of a finite number of conventional HG beams with complex coefficients-parameters, are considered in works [3,4]. The authors showed that altering these parameters causes the orbital angular momentum of this kind of superposition to oscillate, and that these oscillations can reach significant positive and negative values.…”