Optimized weak measurement of orbital
angular momentum-induced beam shifts
in optical reflection
WENJIN LONG,
1
JINTAO PAN,
1
XINYI GUO,
2
XIAOHE LIU,
2
HAOLIN LIN,
2
HUADAN ZHENG,
1
JIANHUI YU,
1,4
HEYUAN GUAN,
1
HUIHUI LU,
1
YONGCHUN ZHONG,
2
SHENHE FU,
2
LI ZHANG,
3
WENGUO ZHU,
1,2,
*
AND ZHE CHEN
1
1
Guangdong Provincial Key Laboratory of Optical Fiber Sensing and Communications, Jinan University, Guangzhou 510632, China
2
Department of Optoelectronic Engineering, Jinan University, Guangzhou 510632, China
3
School of Physics and Optoelectronic Engineering, Foshan University, Foshan 528000, China
4
e-mail: kensomyu@gmail.com
*Corresponding author: zhuwg88@163.com
Received 10 May 2019; revised 3 July 2019; accepted 11 September 2019; posted 13 September 2019 (Doc. ID 367234);
published 30 October 2019
Tiny but universal beam shifts occur when a polarized light beam is reflected upon a planar interface.
Although the beam shifts of Gaussian beams have been measured by the weak measurement technique, the weak
measurement for orbital angular momentum (OAM)-induced spatial shifts of vortex beams is still missing.
Here, by elaborately choosing the preselection and postselection states, the tiny OAM-induced Goos–Hänchen
and Imbert–Fedorov shifts are amplified at an air–prism interface. The maximum shifts along directions both
parallel and perpendicular to the incident plane are theoretically predicted and experimentally verified with
optimal preselection and postselection states. These maximum shifts can be used to determine the OAM of
vortex beams.
© 2019 Chinese Laser Press
https://doi.org/10.1364/PRJ.7.001273
1. INTRODUCTION
Reflection and refraction at an interface between two different
media are described by Snell’s law and the Fresnel formula [1–5].
For a bounded beam, however, Goos–Hänchen (GH) and
Imbert–Fedorov (IF) shifts occur [6]. If the incident beam car-
ries orbital angular momentum (OAM), the OAM affects the
GH and IF shifts [6]. Additional OAM-dependent terms ap-
pear in both the GH and IF shifts [6–8]. The OAM-dependent
beam shifts have attracted significant attention owing to the
physical interest and their applications in the determination
of OAM and manipulation of optical spin [6–10]. The giant
optical spin splitting induced by OAM has been predicted
recently when a higher-order Laguerre–Gaussian (LG) beam
transmitted through an epsilon-near-zero metamaterial slab
[10]. As was demonstrated recently, the GH and IF shifts of LG
beams can be optimized by carefully designing the Fresnel
reflection/refraction coefficients [11]. By modulating the
Fresnel coefficients via graphene, the OAM-dependent GH
and IF shifts can be well tuned [12,13 ].
Although methods have been proposed to enhance the GH
and IF shifts, they are generally small, typically a few tenths of
a wavelength [6]. A combination of a position-sensitive detec-
tor and a lock-in amplifier has to be employed to extract these
tiny shifts [14]. In 2008, Hosten and Kwiat observed the spin
Hall effect of light via weak measurement [15]. The spin-
dependent shifts of the refracted beam from an air–prism
interface were amplified and directly observed by a CCD
camera [15]. The measurements of GH and IF shifts via
this simple method were demonstrated by different groups
through appropriately choosing the preselection and postselec-
tion states [16–20]. With the assistance of the weak measure-
ment technique, the beam shifts have been widely used in
precision metrology such as identifying the layer number
of graphene and measuring thickness of Au film [21–23].
However, the weak-value amplifications for GH and IF shifts
are limited within Gaussian beams. The weak measurement
for OAM-induced GH and IF shifts of a vortex beam is still
missing.
Here, weak-value amplification of the tiny OAM-induced
shifts at an air–prism interface is demonstrated by carefully
choosing the preselection and postselection states. The ampli-
fied beam shifts vary linearly with the incident OAM.
Research Article
Vol. 7, No. 11 / November 2019 / Photonics Research 1273
2327-9125/19/111273-06 Journal © 2019 Chinese Laser Press