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High-purity orbital angular momentum states from a visible metasurface laser

DOI:10.1038/s41566-020-0623-z
Authors:
Hend Sroor at University of the Witwatersrand
Hend Sroor
Yao-Wei Huang at Harvard University
Yao-Wei Huang
Bereneice Sephton at University of Naples Federico II
Bereneice Sephton
Darryl Naidoo at Council for Scientific and Industrial Research, South Africa
Darryl Naidoo
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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 design and characterization a, Schematic of the central part of our metasurface, which imprints two kinds of helical phase profiles for x- and y-incident polarization, resulting in output beams with OAM of ℓ1ℏ and ℓ2ℏ. The metasurface elements are rectangular nanopillars made of amorphous TiO2 with fixed height, h = 600 nm. By changing the width along the x and y directions, the nanoposts impart azimuthal phase delays given by δx and δy. b, Required phase delays for output beam OAM values of ℓ1 = 1 and ℓ2 = 5 (JP2). c, Optical micrograph of JP3 with OAM values of ℓ1 = 10 and ℓ2 = 100. d–f, Scanning electron micrographs of the central parts of JP1 (d), JP2 (e) and JP3 (f). g, Tilted scanning electron micrograph showing the nanoposts of JP2. All our J-plates were fabricated using the process detailed in ref. ⁴⁵.
Metasurface design and characterization a, Schematic of the central part of our metasurface, which imprints two kinds of helical phase profiles for x- and y-incident polarization, resulting in output beams with OAM of ℓ1ℏ and ℓ2ℏ. The metasurface elements are rectangular nanopillars made of amorphous TiO2 with fixed height, h = 600 nm. By changing the width along the x and y directions, the nanoposts impart azimuthal phase delays given by δx and δy. b, Required phase delays for output beam OAM values of ℓ1 = 1 and ℓ2 = 5 (JP2). c, Optical micrograph of JP3 with OAM values of ℓ1 = 10 and ℓ2 = 100. d–f, Scanning electron micrographs of the central parts of JP1 (d), JP2 (e) and JP3 (f). g, Tilted scanning electron micrograph showing the nanoposts of JP2. All our J-plates were fabricated using the process detailed in ref. ⁴⁵.
… 
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.
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.
… 
Extreme SO lasing Various measured states from the laser, displayed on a generalized OAM sphere. Here, the poles are asymmetric with OAM order ℓ1 = 10 (north pole) and ℓ2 = 100 (south pole). The transition from one to the other allows visualization of lasing across vastly differing OAM values as superpositions with two concentric rings. The operating pump energy was 315 mJ. The colour bar shows normalized intensity plotted with a false colour scale of 0 to 1.
Extreme SO lasing Various measured states from the laser, displayed on a generalized OAM sphere. Here, the poles are asymmetric with OAM order ℓ1 = 10 (north pole) and ℓ2 = 100 (south pole). The transition from one to the other allows visualization of lasing across vastly differing OAM values as superpositions with two concentric rings. The operating pump energy was 315 mJ. The colour bar shows normalized intensity plotted with a false colour scale of 0 to 1.
… 
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.
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 communication2–5, 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
i‘ϕ
Þ
I
about the azimuth (ϕ) with helicity ℓ.
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 OAM15–21, 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 (±ℓ).
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 light25–27.
An ongoing challenge is to control light’s chirality, spin and
orbital at source28–31. 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 devices34–40, 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 ±ℓ and ±σ, which add to a total
angular momentum of zero, and with modest OAM values of up
to ∣ℓ∣ = ±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 ℓ = 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 Δℓ = 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
ℓ = 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 (±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 indepen-
dent 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.
NATURE PHOTONICS | VOL 14 | AUGUST 2020 | 498–503 | www.nature.com/naturephotonics
498
Content courtesy of Springer Nature, terms of use apply. Rights reserved
... [15] Therefore, non-separable classical states, as a useful simulation toolkit, provide an effective platform to perform entanglement-analogy information processing, [16][17][18][19][20][21][22][23][24] such as measurements of optical coherence, [19] exploration quantum-classical boundary, [20] as well as in characterizing quantum channels in free-space communication. [21] To date, most of non-separable states have been generally constructed in two coupled intrinsic DoFs of laser beam, for instance, space-polarization, [25][26][27][28] or space-time. [29][30][31] In particular, the most popular non-separable state is the spin-orbit state, as a combination of spin angular momentum (SAM) and orbital angular momentum (OAM). ...
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Article
  • Oct 2019
Structured light is derived from the ability to tailor light, usually referring to the spatial control of its amplitude, phase, and polarization. Although a venerable topic that dates back to the very first laser designs, structuring light at the source has seen an explosion in activity over the past decade, fuelled by a modern toolkit that exploits the versatility of diffractive structures, liquid crystals, metasurfaces/metamaterials, and exotic laser geometries, as well as a myriad of applications that range from imaging, microscopy, and laser material processing to optical communication. Here, the recent progress in creating and controlling structured light is reviewed, with particular emphasis on structuring light at the source: structured light lasers. The various design approaches, including pump shaping, cavity geometries, and the use of custom intracavity optical elements, implemented in a variety of lasers from microchip solutions to high‐power fibers are covered in a tutorial style. The history and latest developments in the field are reviewed, elucidating the various structured light patterns that have been created from lasers, including orbital angular momentum and vector states of light. Finally, the present challenges and limitations are highlighted, along with comments on likely future trends. Structured light refers to the ability to tailor light in amplitude, phase, and polarization. Although traditionally performed external to lasers, there is going demand for structured light at the source. The topic of structured light from lasers is reviewed in a tutorial style, highlighting the exciting recent developments in the field.
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Direct Generation of Tunable Orbital Angular Momentum Beams in Microring Lasers with Broadband Exceptional Points
Article
  • Aug 2019
Non-Hermitian exceptional points (EPs) represent a special type of degeneracy where not only the eigenvalues coalesce, but also the eigenstates tend to collapse on each other. Recent studies have shown that in the presence of an EP, light-matter interactions are profoundly modified, leading to a host of unexpected optical phenomena ranging from enhanced sensitivity to chiral light transport. Here we introduce a family of unidirectional resonators based on a novel type of broadband exceptional points. In active settings, the resulting unidirectionality exhibits resilience to perturbations, thus providing a robust and tunable approach for directly generating beams with distinct orbital angular momenta (OAM). This work could open up new possibilities for manipulating OAM degrees of freedom in applications pertaining to telecommunications and quantum information sciences, while at the same time may expand the notions of non-Hermiticity in the orbital angular momentum space.
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Q-plate technology: A progress review [Invited]
Article
  • May 2019
Since their first introduction in 2006, q-plates have found a constantly increasing number of uses in diverse contexts, ranging from fundamental research on complex structured light fields to more applicative innovations of established experimental techniques, passing through a variety of other emerging topics, such as, for instance, quantum information protocols based on the angular momentum of light. In this paper, we present a bird’s-eye view of the progress of this technology in recent years and offer some educated guesses on the most likely future developments.
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Multispectral Management of the Photon Orbital Angular Momentum
Article
  • Nov 2018
We report on a programmable liquid crystal spatial light modulator enabling independent orbital angular momentum state control on multiple spectral channels. This is done by using electrically controllable “topological pixels" that independently behave as geometric phase micro-optical elements relying on self-engineered liquid crystal defects. These results open interesting opportunities in optical manipulation, sensing, imaging, and communications, as well as information processing. In particular, spectral vortex modulation allows considering singular spatiotemporal shaping of ultrashort pulses which may find applications in many areas such as material processing, spectroscopy, or elementary particles acceleration.
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A review of complex vector light fields and their applications
Article
  • Dec 2018
Vector beams, and in particular vector vortex beams, have found many applications in recent times, both as classical fields and as quantum states. While much attention has focused on the creation and detection of scalar optical fields, it is only recently that vector beams have found their place in the modern laboratory. In this review, we outline the fundamental concepts of vector beams, summarise the various approaches to control them in the laboratory, and give a concise overview of the many applications they have spurned.
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Tunable High-Resolution Macroscopic Self-Engineered Geometric Phase Optical Elements
Article
  • Jul 2018
Artificially engineered geometric phase optical elements may have tunable photonic functionalities owing to their sensitivity to external fields, as is the case for liquid crystal based devices. However, liquid crystal technology combining high-resolution topological ordering with tunable spectral behavior remains elusive. Here, by using a magnetoelectric external stimulus, we create robust and efficient self-engineered liquid crystal geometric phase vortex masks with a broadly tunable operating wavelength, centimeter-size clear aperture, and high-quality topological ordering.
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Polarization Singularity Explosions in Tailored Light Fields
Article
  • May 2018
Complex propagation dynamics of higher‐order polarization singularities are investigated within tailored Poincaré beams. Spatial polarization modulation and additional phase vortices of higher strength are combined, evoking polarization singularity splitting, type conversion, creation and annihilation. These phenomena form singularity “explosions” along their longitudinal evolution. These dynamics of propagating customized light fields and embedded singularities are analyzed experimentally and numerically. Furthermore, similarities of polarization singularity explosion and phase vortex unfolding are discussed, exploring fundamental propagation and spatio‐temporal interaction properties of optical singularities.
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