High-order Laguerre Gaussian Research Articles

Intrinsic angular momentum, spin and helicity of higher-order Poincaré modes

Abstract The availability of coherent sources of higher order Poincaré optical beams have opened up new opportunities for applications such as in the optical trapping of atoms and small particles, the manipulation of chirally-sensitive systems and in improved encoding schemes for broad-bandwidth communications. Here we determine the intrinsic properties of integer order m ⩾ 0 Poincaré Laguerre–Gaussian (LG) modes which have so far neither been evaluated, nor their significance highlighted. The theoretical framework we adopt here is both novel and essential because it emphasises the crucial role played by the normally ignored axial components of the twisted light fields of these modes. We show that the inclusion of the axial field components enables the intrinsic properties of the Poincaré modes, notably their angular momentum, both spin and orbital as well as their helicity and chirality, to be determined. We predict significant enhancements of the intrinsic properties of these modes when compared with those due to the zero order LG modes. In particular, we show that higher order LG Poincaré modes exhibit super-chirality and, significantly so, even in the case of the first order m = 1.

Research on the intensity profiles of high-order Laguerre-Gaussian mode laser beams

Here we analyzed the intensity profile properties of the Laguerre-Gaussian (LG) mode laser beams, to facilitate the intracavity intensity modulation for high-order LG mode laser output. The commonly used definitions of ring-like beam size are discussed, including the second moment of light intensity, power in the bucket, and the peak intensity radius of the ring-like beam. The differences between these methods underscore the importance of selecting appropriate beam size definitions when estimating the mode order, which is particularly worthy of attention when employing certain mode-selection techniques, such as using a defect spot, an aperture, or inducing spherical aberration (SA), to achieve high-order mode outputs. In the experiment, high-order mode LG0,±m output were obtained by utilizing the SA of a short-focal lens in the cavity of an end-pumped Nd:YVO4 laser at 1064 nm. The highest angular indices m reached 355, which is the highest order of LG mode output obtained directly from a laser cavity. The experimental relationship between the mode-order and cavity parameters matched well with the theoretical results, validating the analysis of the intensity profile properties.

Exploring the origin of stronger survival of polarized vortex beams through scattering media

Laguerre–Gaussian (LG) beams carrying orbital angular momentum (OAM) have shown promise in deep tissue imaging, medical diagnostics, and optical communication due to their robust propagation properties through scattering media. The insight on the mechanism for stronger survival of OAM carrying beam in tissue-like turbid media is expected to contribute towards a better understanding of light transport in the presence of scattering, as well as guide optimization of the intensity, phase, and polarization structure of light for use in biomedical applications like in tissue imaging. We examine the scattering properties by studying the propagation of polarized vortex beams transmitted through tissue-like turbid scattering media. We demonstrate that the intensity profile has a much more profound effect on depolarization than the phase profile for LG beams. Our results indicate that the observed stronger propagation for the higher-order LG beams is due to a higher anisotropy factor g, as seen by the incident beam. We have performed the degree of polarization measurements for the forward scattered light in the case of both LG beams and perfect vortex beams with varying topological charges. A comparison between the observed depolarization trends for the two classes of OAM-carrying beams suggests that the robust scattering properties of the LG beams originate from the intensity profile while the phase profile does not seem to play a major role in the stronger survival of OAM-carrying beam in turbid media.

Generation of cylindrical vector modes via astigmatic mode conversion.

In this work, we propose and demonstrate experimentally a compact technique for generating cylindrical vector beams based on a Michelson interferometer and a π-astigmatic mode converter. The latter is required to invert the topological charge of higher-order Laguerre-Gauss (LG) beams. Our proposed technique generalizes the use of astigmatic mode conversion, commonly associated only with scalar beams, to vector beams with a non-homogeneous polarization distribution. We anticipate that many applications based on Michelson interferometers will benefit from the unique properties of vector beams.

Realization of 4 × 200 Gbps 4-QAM OFDM-OWC System Using Higher Order OAM Modes for HAP-to-Satellites Scenario

Recently, there has been an increase in interest in using optical wireless communication (OWC) links on high-altitude platforms (HAPs) for satellite applications. We implement an orbital angular momentum (OAM) multiplexed orthogonal frequency division multiplexing (OFDM) system using an OWC link. A space-to-air scenario is considered in which transmission pointing errors, geometric loss, turbulence, and additional link losses are taken into account to extend the transmission range, system capacity, and throughput. At 200 Gbps per channel data rate, four different OAM modes are implemented with higher order Laguerre–Gaussian (LG) modes of [0,0], [0,13], [0,40], and [0,80]. An aggregate 800 Gbps data rate can deliver a maximum OWC range of 3300–5000 km for all channels. The maximum received power over the 1000 km range is −19.34 to −32.59 dBm with an additional gain of 0–2.5 dB. It is also possible to obtain a better performance over large distances of 500–3500 km with an error vector magnitude of 2.98–17.5%. Furthermore, a high gain of −40.80 dB, a signal-to-noise ratio (SNR) of 55.21 dB, and an optical SNR of 67.25 dB can be achieved for varied transmitter pointing errors of 0.1 rad. As compared to other literature, this system exhibits a superior performance.

ℓ 00 ℓ entanglement and the twisted quantum eraser

We demonstrate the generation of unbalanced two-photon entanglement in the Laguerre–Gaussian (LG) transverse-spatial degree-of-freedom, where one photon carries a fundamental (Gauss) mode and the other a higher-order LG mode with a non-zero azimuthal (ℓ) or radial (p) component. Taking a cue from the N00N state nomenclature, we call these types of states ℓ00ℓ-entangled. They are generated by shifting one photon in the LG mode space and combining it with a second (initially uncorrelated) photon at a beamsplitter, followed by coincidence detection. In order to verify two-photon coherence, we demonstrate a two-photon “twisted” quantum eraser, where Hong–Ou–Mandel interference is recovered between two distinguishable photons by projecting them into a rotated LG superposition basis. Using an entanglement witness, we find that our generated states have fidelities of 95.31% and 89.80% to their respective ideal maximally entangled states. In addition to being of fundamental interest, this type of entanglement will likely have a significant impact on tickling the average quantum physicist's funny bone.

Analysis of rotational Doppler shift with multi-ring vortex beams.

Vortex beams (VBs) with orbital angular momentum have shown great potential in the detection of transverse rotational motion of spatial targets which is undetectable in the classical radar scheme. However, most of the reported rotational Doppler measurements based on VBs can only be realized under ideal experimental conditions. The long-range detection is still a challenge. The detection distance based on rotational Doppler effect (RDE) is mainly limited by the scattered signal's signal-to-noise ratio (SNR). In this work, we investigated the influence of multi-ring vortex beams (MVBs) on the rotational Doppler frequency spectrum of scattered light from an object based on RDE and proposed a method of SNR enhancement of RDE signal. Firstly, different types of MVBs composed of a set of single-ring VBs with the same topological charge and different radii are designed, including multi-ring Laguerre Gaussian beam (MLGB), multi-ring perfect vortex beams (MPVB), and high-order Laguerre Gaussian beam (HLGB). Then, the influence of the number of rings and radial radius interval on the intensity profiles of MVBs and rotational Doppler frequency spectra under aligned and misaligned conditions is studied in detail. And the reasons why different types of MVBs lead to different SNR enhancement effectiveness with the increase of rings are also analyzed theoretically. Finally, proof-of-concept experiments were conducted to verify the effectiveness of the SNR enhancement method for RDE signals. The results showed that the amplitudes of the Doppler spectra generated by the MLGB and MPVB are improved substantially with the increase of rings, but the enhancement effect caused by the former is superior to the latter. The gain of HLGB on the RDE signal is the lowest. This study provides a useful reference for the optimization of rotational Doppler detection systems and may be of great application value in telemetry, long-range communication and optical imaging.

Controllable experimental modulation of high-order Laguerre-Gaussian laser modes.

High-order helical and sinusoidal Laguerre-Gaussian (LG) laser modes have uneven energy distribution among their multiple concentric vortex core rings and lobes, respectively. Here, we explore an experimental method to reshuffle the optical energy among their multiple concentric vortex core rings and lobes of high-order LG modes in a controllable manner. We numerically designed a diffractive optical element displayed over a spatial light modulator to rearrange optical energy among multiple concentric vortex core rings. This changes outer low-intensity concentric vortex core rings into high-intensity vortex core rings of high-order helical LG modes at the Fourier plane. The precise generation of a high-order modulated helical LG laser mode has a maximum number of highly intense concentric vortex core rings compared to known standard helical LG modes. Further, this method is extended to high-order sinusoidal LG modes consisting of both low- and high-intensity lobes to realize modulated sinusoidal LG modes with a maximum number of highly intense lobes in a controllable manner. We envisage that the modulated helical and sinusoidal high-order LG modes may surpass standard LG modes in many applications where highly intense rings and lobes are crucial, as in particle manipulation of micro- and nanoparticles, and optical lithography.

Optical patterning fullerene nanostructures with high purity and high surface quality

Nanoscale patterning of fullerene materials with peculiar intrinsic electronic and optical properties is of crucial importance for their widespread applications. However, it remains a daunting challenge for current methods that suffer from both complicated lithography procedures and additives of photopolymers or photochemicals detrimental to the pristine properties of fullerene. Here, we developed a contamination-free laser printing approach for in situ patterning of fullerene with nanoscale resolution and high purity. The optical trapping force within the tight focus provides a lithography-free means to form densely packed fullerene nanostructures with two-order-of-magnitude enhanced fluorescence emission and a surface roughness of 6 nm. In addition, versatile fullerene nano-patterns from dots to concentric rings can be realized by flexibly shaping the optical trapping force of higher-order Laguerre–Gaussian beams. These results open a new route to programmable and high-quality patterning of fullerene optoelectronic devices with complex nanostructures.

Generation of higher-order Laguerre–Gaussian modes from a diode-pumped Pr3+:LiYF4 laser with an intra-cavity spherical aberration

We demonstrate, for the first time to the best of our knowledge, the direct generation of higher-order Laguerre–Gaussian (LG) petal modes, formed of the coherent superposition of positive and negative LG modes with the topological charge of ± ℓ as an eigen mode, from a compact diode end-pumped P r 3 + : L i Y F 4 (YLF) laser with an intra-cavity lens configuration. The on-axis displacement of the intra-cavity lens with spherical aberration allows the selective operation of the desired higher-order LG modes with | ℓ | ≤ 31 from the laser cavity at 640 nm and 607 nm. Such visible higher-order LG modes will offer new applications in optical manipulation, quantum/optical underwater telecommunication, and microfabrication.

A Low-Divergence Circularly Polarized Dual-Mode OAM Antenna Based on Higher Order Laguerre–Gaussian Modes

An open resonator antenna for orbital angular momentum (OAM) generation and dual-mode application is proposed. The excitation of OAM mode is deduced by the open resonator theory and the circular array theory. In the cavity, eight aperture coupled patch antenna elements are used to excite two higher-order Laguerre-Gaussian HE <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">21</sub> modes with a 90° phase difference. Verifying by simulation and experiment, the proposed low-profile antenna can radiate left-hand or right-hand circularly polarized waves of OAM modes l=±1, which have a relatively low divergence angle of ±9° and high gain of around 13 dBi.

Laguerre-Gaussian beam generation via enhanced intracavity spherical aberration

We demonstrate an end-pumped Laguerre-Gaussian (LG) mode-selectable Nd:YVO4 laser utilizing enhanced intracavity spherical aberration. The cavity was designed to exploit strong spherical aberration generated by an expanded beam, incident on a short-focal-length lens, which enabled oscillation of cavity modes of different order. This compact-cavity laser could operate efficiently with high-order LG mode, with the order of this mode being selectively changed by simply adjusting the distance between the short-focal-length lens and the output coupler. Scalar LG modes from LG0,±10 to up to LG0,±33 were observed in the experiment. The output power of the LG0, ±33 mode was 1.87 W under an absorbed pump power of 6.6 W.

Longitudinal magnetization superoscillation enabled by high-order azimuthally polarized Laguerre-Gaussian vortex modes.

We present an all-optical scheme for the generation of longitudinal magnetization superoscillation based on the vectorial diffraction theory and the inverse Faraday effect. To achieve this, an azimuthally polarized high-order Laguerre-Gaussian vortex mode is firstly focused by a high numerical aperture (NA) objective and then impinges on an isotropic magneto-optical material. It is found that, by judiciously controlling the intrinsic arguments (radial mode index (p) and truncation parameter (β)) of such a configurable vectorial vortex beam, the longitudinal magnetic domain induced in the focal plane can be switched from a peak sub-wavelength magnetization (> 0.36λ/NA), via the fastest Fourier magnetization component (∼0.36λ/NA), to a super-oscillation magnetization hotspot (< 0.36λ/NA). We further examine the dependence of the transverse size, the side lobe, and the energy conversion efficiency within the focal magnetization domain on both the p and β of the initial vortex modes, confirming that the higher-order structured vortex beams are preferable alternatives to trigger robust longitudinal magnetization superoscillation. In addition, the underlying mechanisms behind the well-defined magnetization phenomena are unveiled. The ultra-small-scale longitudinal magnetization demonstrated here may hold massive potential applications in high-density all-optical magnetic recording/storage, super-resolution magnetic resonance imaging, atom trapping and spintronics.

768-ary Laguerre-Gaussian-mode shift keying free-space optical communication based on convolutional neural networks.

Beyond orbital angular momentum of Laguerre-Gaussian (LG) modes, the radial index can also be exploited as information channel in free-space optical (FSO) communication to extend the communication capacity, resulting in the LG- shift keying (LG-SK) FSO communications. However, the recognition of radial index is critical and tough when the superposed high-order LG modes are disturbed by the atmospheric turbulences (ATs). In this paper, the convolutional neural network (CNN) is utilized to recognize both the azimuthal and radial index of superposed LG modes. We experimentally demonstrate the application of CNN model in a 10-meter 768-ary LG-SK FSO communication system at the AT of Cn2 = 1e-14 m-2/3. Based on the high recognition accuracy of the CNN model (>95%) in the scheme, a colorful image can be transmitted and the peak signal-to-noise ratio of the received image can exceed 35 dB. We anticipate that our results can stimulate further researches on the utilization of the potential applications of LG modes with non-zero radial index based on the artificial-intelligence-enhanced optoelectronic systems.

Higher-order Hermite-Gauss modes as a robust flat beam in interferometric gravitational wave detectors

Higher-order Laguerre-Gauss (LG) modes have previously been investigated as a candidate for reducing test-mass thermal noise in ground-based gravitational-wave detectors like Advanced LIGO. It has been shown however that LG modes' fragility against mirror surface figure imperfections limits their compatibility with the current state-of-the-art test masses. In this paper we explore the alternative of using higher-order Hermite-Gauss (HG) modes for thermal noise reduction, and show that with the deliberate addition of astigmatism they are orders of magnitude more robust against mirror surface distortions than LG modes of equivalent order. We present simulations of Advanced LIGO-like arm cavities with realistic mirror figures which can support HG$_{33}$ modes with average arm losses and contrast defects in a Fabry-Perot Michelson interferometer configuration which are well below the typical measured values in Advanced LIGO. This demonstrates that the mirror surface flatness errors will not be a limiting factor for the use of these modes in future gravitational-wave detectors.

Laguerre–Gaussian induced temperature and refractive index profiles in thermal lens effect

In this work, we present a theoretical model that describes induced temperature and refractive index profiles generated by the Laguerre–Gaussian (LG) excitation beam. A comparison between LG and conventional fundamental mode T E M 00 is drawn. It indicates that there is a decrease or increase around the optical axis ( z , r = 0 ) in the refractive index by L G 1 0 and L G 0 5 , thus enabling an enhancement of the refractive index gradient along the radius r . The temperature and refractive index profiles produced by the higher-order LG modes are compared with those of a conventional fundamental T E M 00 Gaussian beam. The results indicate that there is an increase along the radius in the refractive index gradient generated by L G 1 0 and L G 0 5 , which could enhance the sensitivity in photothermal lens detection.

Generation of super-high-order petal-like laser beam using Theon-sieve resonator

The Laguerre–Gaussian (LG) mode beam has very important applications in many research fields. Here, the Theon sieve is first introduced into the laser resonator to generate petal-like laser beams by coherently superimposing two high-order LG modes. The effectiveness was verified by GLAD software. The petal-like laser beam is derived from the light field redistribution and coherent superposition caused by the diffraction effect of the Theon sieve. The relationship between the order of the petal-like laser and the cavity structures has also been investigated in detail. Light field operation in the laser cavity greatly simplifies the optical structure and is more beneficial to optical diagnostics and imaging.

Standard and elegant higher-order Laguerre–Gaussian correlated Schell-model beams

To date, all of the Laguerre–Gaussian (LG) correlated Schell-model beams proposed and studied are restricted to the standard form with the beam mode indices (0, l), termed as a SLG0lCSM beam. We propose, for the first time, the elegant and standard higher-order LG correlated Schell-model beams as an extension to a SLG0lCSM beam. We develop theoretical formulae to determine the beam mode indices of a vortex beam and describe propagation effects of such beams. We demonstrate that by controlling the beam mode indices, one can produce different intensity distribution patterns during propagation, for example, a dark or solid core surrounded by bright concentric rings. Moreover, using our proposed beams, we illustrate how single-layer and multi-layer adjustable optical cages can be formed near the back of the focal zone of a lens. As anticipated, the proposed beams may find important applications in particle trapping, optical manipulation and optical communications.

LG11-mode vortex Nd:YAG laser by applying second-order circular Dammann grating for annular pumping

The excitation of high-order Laguerre–Gaussian (LG) modes in a neodymium-doped yttrium aluminum garnet (Nd:YAG) laser resonator was presented by applying the diffraction of a second-order circular Dammann grating (CDG) for annular pumping. In the study, the 808 nm pump light was shaped into a double-ring structure by the CDG and matched spatially with that of an ideal LG11 mode. As a result, the laser resonator generated an LG11 vortex mode, and the laser power reached 204 mW with 14.5% slope efficiency. Also, when the cavity mirror was tilted, the laser output could switch to the LG01 vortex mode. The results showed the convenience and versatility of CDG in an annular-pumped vortex laser.

Enhanced Imbert–Fedorov shifts of higher-order Laguerre–Gaussian beams by lossy mode resonance

Abstract The enhanced Imbert–Fedorov (IF) shifts of light beams carrying orbital angular momentum by lossy mode resonance (LMR) are investigated. The LMR can be excited when horizontally (H) or vertically (V) linearly polarized incident beams reflected by a three-layer structure composed of glass, ITO, and surrounding medium. The IF shift is generally a tenth of the incident wavelength. While it can reach 51 μ m for | l | = 1 with λ =980 nm when LMR is excited. And the IF shift could be increased to ∼ 290 μ m for | l | = 15 . These findings provide a powerful method in the control of IF shifts, thus have applications in quantum information, optical sensing, and precision metrology.