Transverse rotation of the instantaneous field distribution and the orbital angular momentum of a light beam

Abstract

The transverse beam pattern, usually observed in experiment, is a result of averaging the optical-frequency oscillations of the electromagnetic field distributed over the beam cross section. An analytical criterion is derived that these oscillations are coupled with a sort of rotation around the beam axis. This criterion appears to be in direct relation with the usual definition of the beam orbital angular momentum.OCIS codes: 070.2580, 080.4865, 140.3295, 260.6042 Light beams carrying the mechanical orbital angular momentum (OAM) with respect to the propagation axis attract great attention due to their unique physical properties and promising applications [1][2][3][4]. The question of physical origin of the vortex properties of such beams is interesting and insistent [3][4][5][6][7][8][9][10][11][12]. In attempts to answer it, researchers have employed the momentary patterns of the light field behaviour during a cycle of oscillation [3,4]. It was found that, in contrast to usual (non-vortex) beams where the evolution of the momentary transverse field distribution consists in periodical change of the field strength synchronously over the whole beam cross section, in the "classical" vortex beams (circular Laguerre-Gaussian modes) the momentary distribution of the electric field rotates with the field oscillation frequency (see Fig. 1a which illustrates the same behaviour as Fig. 10 of [3]).

Internal energy flows and instantaneous field of a monochromatic paraxial light beam

“…On this note we intend to generalize the statements of previous works [11,12] and to show that (i) any identifiable directed motion of the instantaneous two-dimensional (2D) pattern of the field oscillation ("running" behavior of the instant oscillation pattern) corresponds to the transverse energy flow (or, which is almost the same [8,13,14], to the transverse momentum) of the time-averaged field, and (ii) the transverse energy flow density provides a natural geometric and kinematic characterization of this running behavior. The idea seems rather simple and transparent; however, to the best of our knowledge, it was never formulated in a clear and explicit form.…”

“…Likewise, the orbital flow is expected to be in a similar relationship with instantaneous motion of the light energy in the real space. This suggestion is supported by the known fact that the orbital angular momentum of a paraxial beam is associated with the rotational performance of the instantaneous field pattern and, moreover, appears to be a direct geometric and kinematic measure of this rotational motion [11,12].…”

“…The instantaneous beam pattern [Eq. (4)] has been discussed elsewhere [11,12] and is the central issue of this paper. The constant-level points r c of the cosine argument in Eq.…”

Rotation dynamics of particles trapped in a rotating beam

“…Thus, as a result of this method, many improved ways for generating a rotating beam have been proposed [21][22][23][24]. In the theoretical aspect, some works concerning the angular momentum of the rotating beam have been developed [25][26][27][28][29], but research on the mechanical effect of the rotating beam on the microtrapped particle, to the best of our knowledge, has never before been reported. To gain a better understanding of such effect, in the present paper, we will make a theoretical investigation on the rotation dynamics of the particle trapped in a rotating beam.…”

Singular Optics: more ado about nothing

“…• Optical vortices and circulations: connections of optical singularities with currents [10,11], with optical angular momentum [12][13][14], and the creation of vortices from rotating beams [15,16].…”