Vortex beam: generation and detection of orbital angular momentum [Invited]

Light beams, as electromagnetic waves, can carry both energy and momentum. We know that momentum can be classified into linear and angular momentum, and there are two particular kinds of angular momenta: spin angular momentum (SAM) and orbital angular momentum (OAM). SAM is related to the photon spin, namely, the circularly polarized light carries a SAM of per photon. vortex beams with an azimuthal phase factor can carry OAM of per photon, where l can be any integer number, named topological charge[1]. The discovery of OAM of light has changed the way we understand and employ light. Different from traditional Gaussian beams, vortex beams exhibit a phase singularity in the center, which leads a doughnut shaped intensity profile. There are many types of vortex beams such as Laguerre-Gaussian beams, non-zeroth order Bessel beams and Mathieu beams.

 

Recent advances in the research of vortex beams, structured beams carrying orbital angular momentum (OAM), have revolutionized the applications of light beams, such as advanced optical manipulations, high-capacity optical communications, and super-resolution imaging. Undoubtedly, the methods for generation of vortex beam and detection of its OAM are of vital importance for the applications of vortex beams. In this review, we first introduce the fundamental concepts of vortex beams briefly and then summarize approaches to generating and detecting the vortex beams separately, from bulky diffractive elements to planar elements. Finally, we make a concise conclusion and outline what is yet to be explored.

 

Generation of Vortex Beams

 

Hitherto, to enable emerging applications, varieties of techniques have been proposed for the generation of vortex beams over the past few decades. Here, we first summarize the approaches and recent advances in the field of vortex beams generation including classical optical elements[2] [such as mode conversion, spiral phase plate (SPP), and computer-generated holograms], digital devices[3] [such as spatial light modulator (SLM) and digital micro-mirror device (DMD)], photon sieve[4], more recently metasurfaces[5], and other methods (such as q-plate and active vortex laser generators).

 

Classical optical elements such as spiral phase plate can generate vortex beams with extremely high conversion efficiency, whereas the requirement for manufacturing techniques is rather high. With the development of liquid crystal technology, digital devices are commonly used to produce vortex beams for their versatility. Moreover, binary amplitude masks such as photon and electron sieves can also be adopted for the generation of vortex beams. Nanofabrication technology makes it possible to generate such beams via ultrathin optical devices such as metasurfaces.

 

Beijersbergen et al. first experimentally generated vortex beams by using two cylindrical lenses, which can directly convert Laguerre-Gaussian (LG) modes of arbitrary order from Hermitian-Gaussian modes to LG modes and vice versa. The most direct and efficient device for generating vortex beams is the spiral phase plate (SPP), which is a transparent plate with a helical thickness profile whose optical height is proportional to the azimuth angle. In the case of helical phase retardation, beams with helical wavefronts can be directly transformed by SPP. In addition, when the Gaussian beams passes through the fork-shaped grating, a vortex beams will appear in the far field, and the fork-shaped grating is usually fabricated by the method of computer-generated hologram. Vortex beams can also be generated using digital devices, such as a spatial light modulator (SLM), an electro-optical device that allows us to manipulate the amplitude and phase of a light field; DMD, as another candidate to generate vortex beams, is able to control incident light with high frame rate and a great number of spatial degrees of freedom. Apart from the aforementioned methods, a binary amplitude mask is usually used to shape both the phase and amplitude of lights; one example is the photon sieve composed of a large number of pinholes that can tightly focus the incident light. Recently, the development of metasurface has provided a new solution for the generation of vortex beams, which is an equivalent two-dimensional device, is constructed by artificial arrays of meta-atoms etched on the ultrathin plate that can control the phase, amplitude, and polarization state arbitrarily.

 

Figure.1 Generation of optical vortices based on (a) classical optical elements (fork-grating); (b) digital devices (spatial light modulator, SLM) [3]; (c) photon sieve[4] and (d) metasurface[5].

 

Detection of OAM

 

As a new degree of freedom, OAM of vortex beam has been widely used in various applications such as of optical communication. Therefore, it is imperative to measure the topological charges of vortex beams. In this section, various methods for the detection of OAM are reviewed based on interference[6] and diffraction method[7], geometric coordinate transformation[8], deep learning[9], and surface plasmon polaritons[10].

 

Figure.2 Methods for detecting OAM modes based on interference[6](a) and diffraction method[7] (b), deep learning[9] (c), and surface plasmon polaritons[10 ](d).

 

The most basic method to detect OAM is to use inclined plane waves to interfere, so as to obtain the forked interference pattern. Diffraction method can also be used. When the vortex beams irradiates the diffraction grating, a special shape related to the angular quantum number will appear in the far field, and the OAM can be detected by the diffraction pattern. Separation of OAM modes by the use of geometric coordinate transformation is also an effective method for vortex beams detection, the basis of which is the conversion from OAM into linear momentum. With the wide application of deep learning in the field of image recognition, the vortex beams intensity images of different modes are collected and sent to the convolutional neural network for training. Finally, the trained network is used to detect OAM, which has the advantages of high efficiency, high precision and no need for redundant optical equipment. In addition to the aforementioned methods, owing to the excellent ability of manipulating the nanoscale field, surface plasmon polaritons have aroused interest to detect the OAM of vortex beams, such as on-chip plasmonic nanogratings.

 

Vortex beams carrying OAM have broadened the perspectives in the optical realm owing to unique properties. We review the methods for generating and detecting the OAM in a concise way to facilitate further research on the vortex beams. Notwithstanding the aforementioned approaches, there still exist challenges for both generation and detection of OAM. Hopefully, vortex beams in light, as well as other forms of waves, will continue to thrive and enable new applications in many other fields.