Probing the fractional topological charge of a vortex light
beam by using dynamic angular double slits
Jing Zhu,
1
Pei Zhang,
1,2,
* Dongzhi Fu,
1
Dongxu Chen,
1
Ruifeng Liu,
1
Yingnan Zhou,
1
Hong Gao,
1
and Fuli Li
1
1
Laboratory of Quantum Information and Quantum Optoelectronic Devices, Shaanxi Province,
Xian Jiaotong University, Xian 710049, China
2
Key Laboratory of Quantum Information, University of Science and Technology of China,
Chinese Academy of Science, Hefei 230026,China
*Corresponding author: zhangpei@mail.ustc.edu.cn
Received June 28, 2016; revised August 6, 2016; accepted August 6, 2016;
posted August 9, 2016 (Doc. ID 269178); published September 8, 2016
Vortex beams with fractional topological charge (FTC) have many special characteristics and novel applications.
However, one of the obstacles for their application is the difficulty of precisely determining the FTC of fractional
vortex beams. We find that when a vortex beam with an FTC illuminates a dynamic angular double slit (ADS), the
far-field interference patterns that include the information of the FTC of the beam at the angular bisector direction
of the ADS vary periodically. Based on this property, a simple dynamic ADS device and data fitting method can be
used to precisely measure the FTC of a vortex light beam with an error of less than 5%. © 2016 Chinese Laser
Press
OCIS codes: (050.4865) Optical vortices; (120.3180) Interferometry; (140.3295) Laser beam characterization.
http://dx.doi.org/10.1364/PRJ.4.000187
Since Allen et al. recognized in 1992 that vortex optical fields
with a phase distribution of the form expimϕ [ϕ is the azimu-
thal angle and m is the azimuthal index referring to the topo-
logical charge (TC) of the optical vortex] may carry orbital
angular momentum (OAM) [1], vortex light beams have been
extensively studied both theoretically and experimentally.
Traditionally, m is an integer, such as Laguerre–Gaussian laser
modes. Then the optical field is called an integral vortex optical
field, which is an eigenstate of the OAM operator with eigen-
value of mℏ, and has an annular intensity distribution with a
dark central node produced by the central phase singularity
[1,2]. Integral vortex light beams have offered a good source
both in classical and quantum optics with many different
applications [3], such as optical tweezers and micromanipula-
tion [4–8], optical communications [9–11], quantum informa-
tion science [12–15], spiral phase contrast imaging [16], and
holographic ghost imaging [17].
On the other hand, the situation becomes more complex
and interesting when the TC is an arbitrary fractional number.
Since Berry introduced the characteristics and the evolving of
fractional vortex beams mathematically in 2004 [18], frac-
tional vortex beams have attracted increasing attention. A
fractional vortex beam has a phase distribution of the form
expiMϕ β somewhere during its propagation, where M
is an arbitrary fractional number and β is the angular position
of the helical wavefront cut (angular phase discontinuity).
Due to the radial phase discontinuity in fractional vortex
optical fields, the axis symmetry of intensity found in inte-
ger-order optical vortices is broken and a low-intensity radial
strip has been observed [18,19]. Meanwhile, the state, instead
of the eigenstate of OAM in integer vortex optical fields, is a
superposition state of the basis of integer OAM states that
depend on both the TC M and angular position β [20–22].
The characteristics of the fractional vortex optical fields en-
dow them with unique advantages compared to the integer
vortex optical fields. For example, as a fractional vortex beam
has a radial opening, this could be used to guide and transport
particles [23] and improve the ability of optical sorting [24].
The asymmetric intensity distribution also could be utilized
to achieve anisotropic edge enhancement [25,26]. In quantum
information processing, it could be used to investigate high-
dimensional entanglement states by utilizing non-integer
OAMs [20,27,28]. One of the key issues for the above applica-
tions is the effective determination of the fractional TC (FTC).
Many methods that have been used for integral TC determi-
nation by calculating the number of interference patterns,
such as dual-triangular aperture diffraction [29], triangular
aperture diffraction [30], mode conversion [31], and interfer-
ence with its mirror image [32], could be used to observe only
the half-integer value of a fractional vortex beam but not for
probing the exact value of an FTC. Nevertheless, there are still
several methods to measure the FTC. Liu put forward a poten-
tial way based on a weak random scattering screen by count-
ing the size of the area of divided bright spots for the fractional
parts of the TC and the number of the complete spots for the
integral parts [33]. Zhang probed the FTC using a vortex
grating spectrum analyzer within a 10% error [34]. During
their experiments the intensity value of the center portion
of the target diffraction order was extracted to calculate
the FTCs, and the target diffraction order was N or N 1,
where N ≤ −M ≤ N 1. This means the range of the FTC
must be known beforehand. Huang et al. designed a method
of cascaded Mach–Zehnder interferometers (MZIs) to mea-
sure the FTC of a light beam [35]. This method needs more
Zhu et al. Vol. 4, No. 5 / October 2016 / Photon. Res. 187
2327-9125/16/050187-04 © 2016 Chinese Laser Press