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Frontiers of Optoelectronics

Front. Optoelectron.    2019, Vol. 12 Issue (1) : 69-87
Modulation of orbital angular momentum on the propagation dynamics of light fields
Peng LI(), Sheng LIU, Yi ZHANG, Lei HAN, Dongjing WU, Huachao CHENG, Shuxia QI, Xuyue GUO, Jianlin ZHAO
MOE Key Laboratory of Material Physics and Chemistry under Extraordinary Conditions, and Shaanxi Key Laboratory of Optical Information Technology, School of Science, Northwestern Polytechnical University, Xi’an 710072, China
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Optical vortices carrying orbital angular momentum (OAM) have attracted extensive attention in recent decades because of their interesting applications in optical trapping, optical machining, optical communication, quantum information, and optical microscopy. Intriguing effects induced by OAMs, such as angular momentum conversion, spin Hall effect of light (SHEL), and spin–orbital interaction, have also gained increasing interest. In this article, we provide an overview of the modulations of OAMs on the propagation dynamics of scalar and vector fields in free space. First, we introduce the evolution of canonical and noncanonical optical vortices and analyze the modulations by means of local spatial frequency. Second, we review the Pancharatnam–Berry (PB) phases arising from spin–orbital interaction and reveal the control of beam evolution referring to novel behavior such as spin-dependent splitting and polarization singularity conversion. Finally, we discuss the propagation and focusing properties of azimuthally broken vector vortex beams.

Keywords orbital angular momentum      polarization      spin angular momentum      Pancharatnam–Berry (PB) phase      angular diffraction     
Corresponding Author(s): Peng LI   
Just Accepted Date: 30 October 2017   Online First Date: 29 November 2017    Issue Date: 29 April 2019
 Cite this article:   
Peng LI,Sheng LIU,Yi ZHANG, et al. Modulation of orbital angular momentum on the propagation dynamics of light fields[J]. Front. Optoelectron., 2019, 12(1): 69-87.
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Peng LI
Sheng LIU
Dongjing WU
Huachao CHENG
Shuxia QI
Xuyue GUO
Jianlin ZHAO
Fig.1  (a)−(d) Intensity and phase (insets) distributions of canonical vortices; (e) the divergence of vortex beams keeping the Gaussian waist or rrms constant. Two kinds of vortex beams are generated by using forked diffraction grating or cylindrical lens, respectively [58]
Fig.2  Evolutions of (a) zeroth-order Bessel beam and LG beams with parameters of (b) l = 0, p = 10 and (c) l = 2, p = 10, respectively
Fig.3  (a) Phase structure of a triangle vortex with l = 34; (b) beam shape at the focal plane; (c) experimental results of optical tweezer [78]
Fig.4  (a) Local spatial frequencies mapping to the focal field; (b) focal filed intensity of AAB with a power-exponent-phase vortex [79]
Fig.5  (a) Side view of propagation dynamic (in y-z plane) of AAB with l = 8 and n = 2; (b)−(e) intensity distributions at different propagation distances of z = 19.52, 20.50, 21.48 and 22.45 cm, respectively [79]
Fig.6  Simulation intensity distributions of vector AAB with polarization order m = 2 and different phase parameters n in the focal plane. I0, IL and IR correspond to the total intensity, left- and right-handed spin components, respectively. The insets represent the phase profiles. The dashed curves denote the local spatial frequencies distributions [84]
Fig.7  Schematic illustration of PB phases generation in the process of polarization transformation. Insert: schematic illustration of polarization transformation on the Poincaré sphere [99]
Fig.8  Distributions of intensity (top row), s3 (second row), polarization orientation (third row) and phase (bottom row) of different states. |H〉 denotes the sate composed by two spin components with OAMs defined by subscripts [113]
Fig.9  Intensity and polarization distributions of the focal fields of the azimuthally polarized beams with vortex phases of l = 1, 2 and 3, respectively. The dotted, dashed and solid lines in the top row depict the zero contours of s1, s2 and s3, respectively; the background and short lines in the bottom row denote the ellipticity and the orientation of polarization ellipse, respectively [114]
Fig.10  Autofocusing of radially polarized AABs without (top) and with (bottom) a single charged vortex phase. (a) and (c) depict the beam intensity patterns at input and output, respectively; (b) and (d) side view of the beam propagation from numerical simulation and measured beam polarizations at output [116]
Fig.11  Spin-dependent separation with the bifurcation of orbital angular momentum. (a) Initial beam with polarization direction marked with red arrowheads; (b) horizontally and vertically polarized components; (c) interference pattern of output beam with a plane wave (top), and the corresponding s3 distribution (bottom); (d) side view of the beam propagation
Fig.12  (a) Schematic illustration of the longitudinal three-foci metasurface lens; each focal point is focused from segmented region with distinct PB phase response; (b) the observed light spots correspond to the three focal points. Adapted from Ref. [127]
Fig.13  Schematic representation of z-dependent polarization distribution and transformation; (b)−(f) experimentally measured intensity distributions of first-order Bessel beam propagating through a vertical polarizer at planes with equal space [133]
Fig.14  Measured transverse intensity and local polarization distributions of the reconstructed second-order BG beam with hybrid polarizations at propagation distances of z = 21, 23.8, 26.6, 29.5, 32.2 cm, respectively. The red and green ellipses denote the RH and LH elliptical polarizations, respectively. The linear obstacle with a diameter of about D = 70 mm is placed at plane z = 16.6 cm [133]
Fig.15  (a) Rotation angles |Dq| versus the topological charges; (b)−(e) Intensity distributions of fan-shaped vortex beams at z = 0 and 25 cm planes. (c) l = -4; (d) l = -20; (e) l =±20. |R〉 and |L〉 correspond to two spin states. The red and blue areas correspond to the positive and negative vortex beams, respectively
Fig.16  (a) Rotation angles |Dq| versus propagation distance z. (b)−(d) Focal intensity distributions of l = 1, 4 and 20 fan-shaped vortex beams with b = p/2, respectively. The incident fan-shaped vortex beams have the same profile as shown in Fig. 15(b)
Fig.17  Measured s3 distributions of fan-shaped pure CV beams with b = p/2 in the planes of z = 25 cm (upper row) and z→∞ (the focal plane of a lens, below row). The red and blue areas correspond to the right- and left-handed spin components, the dashed areas schematically show the incident beams. The polarization orders are m = 1, 2 and 4, respectively
Fig.18  Schematic illustration of the focusing dynamics of a fan-shaped azimuthally polarized beam [149]
Fig.19  Distributions of intensity and s3 in the focal field of azimuthally polarized beams with different rotation symmetries. Insets: the intensity distributions of beams in the pupil plane [149]
Fig.20  Distributions of s3 for fan-shaped beams with angular width of p/2, after propagating 25 cm. (a) m = 2, l = 2; (b) m = 2, l = -1; (c) m = 2, l = 3 [145]
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