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Abstract and Figures

Orbital angular momentum (OAM) from lasers holds promise for compact, at-source solutions for applications ranging from imaging to communications. However, conjugate symmetry between circular spin and opposite helicity OAM states (±ℓ) from conventional spin–orbit approaches has meant that complete control of light’s angular momentum from lasers has remained elusive. Here, we report a metasurface-enhanced laser that overcomes this limitation. We demonstrate new high-purity OAM states with quantum numbers reaching ℓ = 100 and non-symmetric vector vortex beams that lase simultaneously on independent OAM states as much as Δℓ = 90 apart, an extreme violation of previous symmetric spin–orbit lasing devices. Our laser conveniently outputs in the visible, producing new OAM states of light as well as all previously reported OAM modes from lasers, offering a compact and power-scalable source that harnesses intracavity structured matter for the creation of arbitrary chiral states of structured light. A metasurface laser generates orbital angular momentum states with quantum numbers reaching ℓ = 100. Simultaneous output vortex beams, with Δℓ as great as 90, are demonstrated in the visible regime.
Metasurface laser and modes a, Illustration of laser cavity with an intracavity nonlinear crystal (KTP), polarizer (Pol) and metasurface (J-plate), excited by an infrared pump (between mirror M1 and the back KTP crystal face), with the green light emerging from the output coupler (OC) mirror. b, Replication of previous SO laser results showing symmetric states of ∣ℓ∣ = ±1 for three orientations of the fast axis of JP1 (red arrows). c, Creation of a new angular momentum state with ℓ1 = 1 and ℓ2 = 5. As θ (J-plate orientation) is varied, the modal spectrum shifts from H,1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left|H,1\right\rangle$$\end{document} (red squares) to V,5\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left|V,5\right\rangle$$\end{document} (blue circles), in agreement with theory (curves). Insets: the OAM spectrum at different θ. Error bars show standard deviations. d, Creation of an arbitrary vector superposition state of coherently mixed vortices showing five distinct phase singularities (indicated by white circles), in agreement with theory (shown in the inset). All results were taken at an average pump energy of 230 mJ. For b and d, the colour bar shows normalized intensity plotted with a false colour scale of 0 to 1.
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Ultrapure OAM lasing modes a, Measured modal spectrum for ℓ = 10, both internal (blue) and external (red) to the laser. ∣cp,ℓ∣2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$|c_{p,{{\ell}}}|^2$$\end{document} is the modal power in the pth radial mode and ℓth\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\ell{\rm{th}}$$\end{document} OAM mode. b,c, The corresponding beam intensities are shown for the internal modes (b) and external modes (c). The bottom inset in a shows an enlarged version with experimental data (lollipop bars) and theoretical predictions (solid line). d,e, The same analysis, performed on the ℓ = 100 modes, showing intensity profiles created external (d) and internal (e) to the laser. The colour bar shows normalized intensity plotted with a false colour scale of 0 to 1. f, OAM distribution of external (red lollipops) and laser (blue bars) modes, where ∣cℓ∣² represents the total OAM modal power (summed over all p modes). g, Comparison of the p = 0 mode weightings for the externally generated beams (red lollipops) versus cavity modes (blue bars). The operating pump energy was 315 mJ for all measurements.
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Articles
https://doi.org/10.1038/s41566-020-0623-z
1School of Physics, University of the Witwatersrand, Wits, South Africa. 2Harvard John A. Paulson School of Engineering and Applied Sciences, Harvard
University, Cambridge, MA, USA. 3Department of Electrical and Computer Engineering, National University of Singapore, Singapore, Singapore. 4CSIR
National Laser Centre, Pretoria, South Africa. 5Applied Physics, Vrije Universiteit Brussel, Brussels, Belgium. 6Center for Nanoscale Systems, Harvard
University, Cambridge, MA, USA. 7CNST – Fondazione Istituto Italiano di Tecnologia Via Giovanni Pascoli, Milan, Italy. 8Present address: Molecular
Chirality Research Center, Chiba University, Inage-ku, Chiba, Japan. e-mail: andrew.forbes@wits.ac.za
In recent years it has become possible to tailor light in what is com-
monly referred to as structured light1, suppporting applications
including high-bandwidth optical communication25, access to
high-dimensional quantum states6,7, enhanced resolution in imag-
ing8 and microscopy9 and control of matter by optical trapping and
tweezing10,11. Foremost among the family of structured light fields are
those related to chiral light, which carries spin angular momentum
and orbital angular momentum (OAM)12, the latter characterized
by a helical phase
expð
iϕ
Þ
I
about the azimuth (ϕ) with helicity .
Driven by the many applications these beams have spurred13, much
attention has been focused on their efficient creation.
Scalar OAM modes are easily created by dynamic phase
approaches14, while geometric phase is a convenient mechanism for
creating vector combinations of spin and OAM1521, forming cylin-
drical vector vortex beams that are rotationally symmetric complex
states of light with an internal intensity null due to a polarization
singularity22. They are conveniently expressed on the higher-order
Poincaré sphere (HOPS)23,24, where the poles are combinations of
left- and right-circular spin angular momentum states (±σ) com-
bined with symmetrical left- and right-helicity OAM states (±).
This vector addition has opened many exciting possibilities for new
applications that exploit chiral control of both spin angular momen-
tum and OAM degrees of freedom of light2527.
An ongoing challenge is to control light’s chirality, spin and
orbital at source2831. So far, advances have been limited, in part due
to fundamental symmetry restrictions when using geometric phase
and topological photonics and in part due to implementation restric-
tions, for example, in regard to the physical size and spatial resolu-
tion of the optical elements. Such advances include the generation
of symmetric OAM states via the geometric phase32,33, as integrated
on-chip devices3440, in organic lasers41 and as fibre lasers42. Despite
these impressive advances, breaking the symmetry of the spin and
orbital states for arbitrary angular momentum control of light
at source has remained elusive. Arbitrary angular momentum con-
trol requires the ability to produce any desired spin–orbital chiral
state of light, including arbitrary, differing and non-symmetric
OAM values coupled to user-defined polarizations, an infinitely
larger set than the special case of symmetric OAM states, allow-
ing access to super-chiral light with high angular momentum. In
contrast, OAM lasers so far have been demonstrated with only
symmetric superpositions of ± and ±σ, which add to a total
angular momentum of zero, and with modest OAM values of up
to = ±10 (ref. 32). However, super-chiral light with high angu-
lar momentum is known to be important in many fundamental
and applied studies, for example, in quantum studies with Bose–
Einstein condensates, remote sensing with structured light, accurate
rotation measurements, metrology of chiral media and for larger
photon information capacity43.
Here, we report a laser with an intracavity metasurface for
control of light’s angular momentum at source. We design custom
metasurfaces for arbitrary OAM coupling to linear polarization
states, including a metasurface with an extreme imbued helicity of
up to = 100. By doing so, we are able to produce new chiral states
of light from a laser, including simultaneous lasing across vastly dif-
fering and non-symmetric OAM values that are up to Δ = 90 apart,
an extreme violation of previous symmetric spin–orbit (SO) lasing
devices, and demonstrate some intriguing lasing phenomena, for
example, vortex splitting inside a laser medium and coherent lasing
across modes with no spatial overlap. By designing a cavity for mode
metamorphosis, our laser is able to generate ultrahigh-purity OAM
modes with orders of magnitude enhanced purity over their exter-
nally created counterparts, which we show with OAM modes up to
= 100. Importantly, the coupling to linear polarization states facili-
tates a compact design with a reduction in complexity and number
of optical elements over previous geometric phase lasers, the latter
of course restricted to only symmetric states. In addition to these
High-purity orbital angular momentum states
from a visible metasurface laser
Hend Sroor1, Yao-Wei Huang 2,3, Bereneice Sephton1, Darryl Naidoo1,4, Adam Vallés 1,8, Vincent Ginis2,5,
Cheng-Wei Qiu 3, Antonio Ambrosio 6,7, Federico Capasso 2 and Andrew Forbes 1 ✉
Orbital angular momentum (OAM) from lasers holds promise for compact, at-source solutions for applications ranging from
imaging to communications. However, conjugate symmetry between circular spin and opposite helicity OAM states (±) from
conventional spin–orbit approaches has meant that complete control of light’s angular momentum from lasers has remained
elusive. Here, we report a metasurface-enhanced laser that overcomes this limitation. We demonstrate new high-purity OAM
states with quantum numbers reaching = 100 and non-symmetric vector vortex beams that lase simultaneously on indepen-
dent OAM states as much as Δ= 90 apart, an extreme violation of previous symmetric spin–orbit lasing devices. Our laser
conveniently outputs in the visible, producing new OAM states of light as well as all previously reported OAM modes from
lasers, offering a compact and power-scalable source that harnesses intracavity structured matter for the creation of arbitrary
chiral states of structured light.
NATURE PHOTONICS | VOL 14 | AUGUST 2020 | 498–503 | www.nature.com/naturephotonics
498
Content courtesy of Springer Nature, terms of use apply. Rights reserved
... The phase and amplitude of the holographic mirror can be controlled simply by writing a computer-generated hologram. for generating an arbitrary OAM state [93]. ...
... polarization states) on the FOPS equator produced, we discuss in the following sections the method to reach an arbitrary point on the FOPS. For any HOP sphere, the most common method of using two coherent beams to conduct such scans is to use circularly polarized light beams with opposite helicity (i.e. the two poles of the sphere) [93,130,139,143,146,154,205,206]. As far as we know, this is the only method that has been used in FOPS analysis. ...
... The J plate can convert any two orthogonal polarization states of the incident light into helical modes with any arbitrary values of OAM. The laser was demonstrated to produce simultaneously two vortex beams with TCs being =100 and 10, respectively[93]. ...
Thesis
A vortex beam possesses a helical phase front and carries a phase singularity along the propagation axis. The salient properties of vortex beams, including the theoretically unbounded orbital angular momentum (OAM) and spatially variant states of polarization (SOPs), have been utilized for a range of applications, including optical sensing, communications, manipulation and imaging. This thesis reports integrated vortex beam emitters and all-optical wavelength tuning based on microring resonators. The work may be further explored for potential applications such as light detection and ranging (LiDAR) and communication systems. An integrated Terahertz (THz) vortex beam emitter is presented for the first time based on simulation to generate tunable OAM states. The design can convert infrared waveguide modes into a freely propagating THz beam via difference-frequency generation. The output OAM state carries a topological charge that is tunable with input wavelengths. Three devices are evaluated in a test frequency range from 9 THz to 13.5 THz, and the topological charge can change from -2 to 4. A frequency shift accompanies the change in the topological charge, and its magnitude depends on the planar dimensions of the emitter. An on-chip vector vortex beam emitter is demonstrated for the first time via numerical simulation to generate all points on a first-order Poincaré sphere (FOPS). It consists of a wave guide coupled, nanostructured Si microring resonator. The fundamental transverse electric and transverse magnetic input modes produce radial and azimuthal polarization, respectively. These two linear polarization states can form a pair of eigenstates for the FOPS. Consequently, tuning the phase contrast and the intensity ratio of these two coherent inputs can control the SOPs of generated vortex beams. Flexible wavelength modulation of the generated vortex beams is desired to enhance sensing and communication performance. An all-optical wavelength tuning device is experimentally demonstrated based on two coupled microrings, which may combine with the proposed emitters. Pumping the symmetric and antisymmetric resonances of the device can induce attractive and repulsive optical gradient forces, respectively. The optical gradient forces can reconfigure the device and tune its resonant wavelengths. Besides, the wavelength difference between the symmetric and antisymmetric resonances can be significantly increased and decreased by the device's positive and negative pull-back instabilities, respectively.
... On the other hand, the RDE frequency is also proportional to the topological charge of the illuminating beam; therefore, the detection sensitivity can be increased by using higher-order OAM beams. Up to now, a myriad of approaches have been developed for the generation of higher-order OAM beams, demonstrating up to ℓ 100 by using a metasurface OAM laser [43], up to ℓ 600 by using a spatial light modulator [44], and as high as ℓ ≈ 10000 with a spiral phase mirror [45]. ...
Article
Full-text available
Structured light beams such as optical vortices can carry the orbital angular momentum (OAM) with an unbounded quantum number. Recent years have witnessed a growing interest in the rotational Doppler effect with vortex light. Here we present an overview on the technical progress in measuring the rotational Doppler effect associated with OAM. This includes how a high-order OAM light beam is crucial for realizing high-sensitivity remote sensing of rotating objects. The basic physical mechanism of rotational Doppler effect is manifested from both perspectives of the wave property and the conservation law of energy. Besides, we summarize the extension of the rotational Doppler effect from linear optics to nonlinear optics, and to quantum realms. Also, we discuss the main challenges and opportunities of angular remote sensing in a realistic scenario for future applications.
... 22,23 In order to have control over the azimuthal and radial indices, we need to be able to modulate not only the phase of the incident beam, but also its amplitude. One approach is to use an active resonator to facilitate the mode conversion necessary for generating pure OAM modes, 24,25 but this requires elaborate cavity configurations. Alternative free-space methods have also been demonstrated, which employ complex amplitude modulation using phase-only devices. ...
Preprint
To exploit the full potential of the transverse spatial structure of light using the Laguerre-Gaussian basis, it is necessary to control the azimuthal and radial components of the photons. Vortex phase elements are commonly used to generate these modes of light, offering precise control over the azimuthal index but neglect the radially dependent amplitude term which defines their associated corresponding transverse profile. Here we experimentally demonstrate the generation of high purity Laguerre-Gaussian beams with a single step on-axis transformation implemented with a dielectric phase-amplitude metasurface. By vectorially structuring the input beam and projecting it onto an orthogonal polarisation basis, we can sculpt any vortex beam in phase and amplitude. We characterize the azimuthal and radial purity of the generated vortex beams, reaching a purity of 98% for a vortex beam with $\ell=50$ and $p=0$. Furthermore, we comparatively show that the purity of the generated vortex beams outperform those generated with other well-established phase-only metasurface approaches. In addition, we highlight the formation of 'ghost' orbital angular momentum orders from azimuthal gratings (analogous to ghost orders in ruled gratings), which have not been widely studied to date. Our work brings higher-order vortex beams and their unlimited potential within reach of wide adoption.
... In recent decades, many authors (Wang et al. 2018;Zhang et al. 2020;Porfirev et al. 2021;Fatkhiev 2021) have reported a significant progress on the generation of optical vortices. Their applications in active resonators have been demonstrated in Maguid (2018), Uren et al. (2019) and Sroor et al. (2020). The dynamics of the vortices during their propagation in optical fibers has been practically investigated by the authors in Kotlyar et al. (1998), Bolshtyansky et al. (1999), Karpeev and Khonina (2007) and Khonina et al. (2010). ...
Article
Full-text available
In the present work, the formation of optical vortex in waveguides, with spatial dependence of the nonlinear refractive index, is studied. The propagation of such type of laser pulses is governed by a system of amplitude equations for x and y components of the electrical field in which the effects of second-order dispersion and self-phase modulation are taken into account. The corresponding system of equations is solved analytically. New class of exact solutions, describing the generation of vortex structures in the optical fibers with spatial dependence of the nonlinear refractive index and anomalous dispersion, are found. These optical vortices admit only amplitude type singularities. Their stability is a result of the delicate balance between diffraction and nonlinearity, as well as nonlinearity and angular distribution. This kind of singularities can be observed as a depolarization of the vector field in the laser spot.
... [72] In order to increase the compactness of the generating device as well as the purity of the generated modes, novel approaches have proposed the insertion of a metamaterial into the laser cavity, [73] (Figure 4g) to directly generate high-purity nonseparable state with control over SOC even at extremely large topological charges. [74,75] Although compact, the metasurface as solid-state component is hard to reconfigure and does not allow modulation of light. As a recently emerged method, digital holography provides flexible, reconfigurable, and programmable ways not only to generate . ...
Article
Full-text available
Controlling the various degrees‐of‐freedom (DoFs) of structured light at both quantum and classical levels is of paramount importance in optics. It is a conventional paradigm to treat diverse DoFs separately in light shaping. While, the more general case of nonseparable states of light, in which two or more DoFs are coupled in a nonseparable way, has become topical recently. Importantly, classical nonseparable states of light are mathematically analogue to quantum entangled states. Such similarity has hatched attractive studies in structured light, for example, the spin‐orbit coupling in vector beams. However, nonseparable classical states of light are still treated in a fragmented fashion, while its forms are not limited by vector beams and its potential is certainly not fully exploited. For instance, exotic space‐time coupled pulses open nontrivial light shaping toward ultrafast time scales, and ray‐wave geometric beams provide new dimensions in optical manipulations. Here, a bird's eye view on the rapidly growing but incoherent body of work on general nonseparable states involving various DoFs of light is provided and a unified framework for their classification and tailoring, providing a perspective on new opportunities for both fundamental science and applications, is introduced. A toroidal light pulse, as a complex nonseparable state of space, time (frequency), and polarization, is generated from a metamaterial.
Article
Semiconductor nanowires have demonstrated great potential in all-photonic integrated circuit applications. However, the development of a controllable multidimensional nanowire assembly technique is still arguably in its infancy. Here, we numerically demonstrate the optical trapping and manipulation of cylindrical zinc oxide nanowires using an all-dielectric silicon nanononamer for designing programmable nanolasers. The nanononamer is composed of nine identical silicon nanocylinders arranged in a square grid on top of a glass substrate. This is a suitable choice, as optical trapping with the proposed silicon nanononamer is envisioned as an effective technique for the contactless manipulation of suspended nanowires with multiple hotspots and with negligible heating generation. We determine optical forces and torques applied to nanowires using the Maxwell stress tensor method. We investigate the influence of light polarization on the field confining and laser tweezing properties. For this work, the simple nanowire-based silicon photonic platform is compatible with the complementary metal–oxide–semiconductor technology, which allows low-cost fabrication of such structures and the integration with other on-chip optical components.
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Vector optical field (VOF) manipulation greatly extended the boundaries of traditional scalar optics over the past decades. Meanwhile, the newly emerging techniques enabled by structural functional optical materials have driven the research domain into the subwavelength regime, where abundant new physical phenomena and technologies have been discovered and exploited for practical applications. In this Tutorial, we outline the basic principles, methodologies, and applications of VOF via structural functional materials. Among various technical routes, we focus on the metasurface-based approaches, which show obvious advantages regarding the design flexibility, the compactness of systems, and the overall performances. Both forward and inverse design methods based on the rigorous solution of Maxwell's equations are presented, which provide a valuable basis for future researchers. Finally, we discuss the generalized optical laws and conventions based on VOF manipulation. The applications in optical imaging, communications, precision measurement, laser fabrication, etc. are highlighted.
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On-chip integrated orbital angular momentum (OAM) sorting is of great importance in tackling the severe challenge of exponential growth in data traffic. Despite the continuous success, current demultiplexing techniques either scarify efficiency dramatically or lose the compactness of a system. Here we experimentally demonstrate an ultracompact OAM sorter using TiO2 metasurfaces integrated onto a complementary metal-oxide-semiconductor (CMOS) camera. By utilizing the propagation phases, we transfer the unitary transformation theory in bulky systems into two TiO2 metasurfaces, responsible for the functions of log-polar transformation and fan-out beam copying and focusing as well as the functions of phase correction and Fourier transform. The flatform metasurface doublet enables one to integrate the OAM sorter onto a camera chip. Consequently, OAM beams with topological charges of m = -3 to 3 were separated by a CMOS camera with an average crosstalk of -6.43 dB. This approach shall shed light on next-generation OAM modes processing.
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