Ultra-compact broadband polarization diversity orbital angular momentum generator with 3.6 × 3.6 μm2 footprint

Optical mode manipulation using deep spatial diffractive neural networks

In this paper, we investigate the theoretical models and potential applications of spatial diffractive neural network (SDNN) structures, with a particular focus on mode manipulation. Our research introduces a novel diffractive transmission simulation method that employs matrix multiplication, alongside a parameter optimization algorithm based on neural network gradient descent. This approach facilitates a comprehensive understanding of the light field manipulation capabilities inherent to SDNNs. We extend our investigation to parameter optimization for SDNNs of various scales. We achieve the demultiplexing of 5, 11 and 100 orthogonal orbital angular momentum (OAM) modes using neural networks with 4, 10 and 50 layers, respectively. Notably, the optimized 100 OAM mode demultiplexer shows an average loss of 0.52 dB, a maximum loss of 0.62 dB, and a maximum crosstalk of -28.24 dB. Further exploring the potential of SDNNs, we optimize a 10-layer structure for mode conversion applications. This optimization enables conversions from Hermite-Gaussian (HG) to Laguerre-Gaussian (LG) modes, as well as from HG to OAM modes, showing the versatility of SDNNs in mode manipulation. We propose an innovative assembly of SDNNs on a glass substrate integrated with photonic devices. A 10-layer diffractive neural network, with a size of 49 mm × 7 mm × 7 mm, effectively demultiplexes 11 orthogonal OAM modes with minimal loss and crosstalk. Similarly, a 20-layer diffractive neural network, with a size of 67 mm × 7 mm × 7 mm, serves as a highly efficient 25-channel OAM to HG mode converter, showing the potential of SDNNs in advanced optical communications.

Orbital angular momentum-mediated machine learning for high-accuracy mode-feature encoding

Machine learning with optical neural networks has featured unique advantages of the information processing including high speed, ultrawide bandwidths and low energy consumption because the optical dimensions (time, space, wavelength, and polarization) could be utilized to increase the degree of freedom. However, due to the lack of the capability to extract the information features in the orbital angular momentum (OAM) domain, the theoretically unlimited OAM states have never been exploited to represent the signal of the input/output nodes in the neural network model. Here, we demonstrate OAM-mediated machine learning with an all-optical convolutional neural network (CNN) based on Laguerre-Gaussian (LG) beam modes with diverse diffraction losses. The proposed CNN architecture is composed of a trainable OAM mode-dispersion impulse as a convolutional kernel for feature extraction, and deep-learning diffractive layers as a classifier. The resultant OAM mode-dispersion selectivity can be applied in information mode-feature encoding, leading to an accuracy as high as 97.2% for MNIST database through detecting the energy weighting coefficients of the encoded OAM modes, as well as a resistance to eavesdropping in point-to-point free-space transmission. Moreover, through extending the target encoded modes into multiplexed OAM states, we realize all-optical dimension reduction for anomaly detection with an accuracy of 85%. Our work provides a deep insight to the mechanism of machine learning with spatial modes basis, which can be further utilized to improve the performances of various machine-vision tasks by constructing the unsupervised learning-based auto-encoder.

On-Chip Meta-Optics for Engineering Arbitrary Trajectories with Longitudinal Polarization Variation

On-chip integrated meta-optics promise to achieve high-performance and compact integrated photonic devices. To arbitrarily engineer the optical trajectory along the propagation path in an on-chip integrated scheme is of significance in fundamental physics and various emerging applications. Here, we experimentally demonstrate an on-chip metasurface integrated on a waveguide to enable predefined arbitrary optical trajectories in the visible regime. By transformation of the transverse phase to generate longitudinal mapping, the guided waves are extracted and molded into any different optical trajectories (parabola, hyperbola, and cosine). More intriguingly, predefined polarization states with longitudinal variation are also successfully imparted along the trajectory. Owing to the on-chip propagation scheme, the trajectories are uniquely free from zero-order diffraction interference, naturally having a higher signal-to-noise ratio beyond conventional free-space forms. Overall, such on-chip optical trajectory engineering allows for miniaturized integration and can find paths in potential applications of complex optical manipulation, advanced laser fabrication, and microscopic imaging.

Polarization-insensitive vortex beam generator by the holographic grating on an integrated multi-layer waveguide

An integrated polarization-insensitive vortex beam generator is proposed in this study. It is composed of a holographic grating on a multi-layer waveguide, which enables conversion of Transverse Electric (TE) and Transverse Magnetic (TM) waveguide modes to y-polarized and x-polarized optical vortex beams, respectively. The conversion efficiency and the phase fidelity are numerically analyzed, and the working bandwidth is about 100 nm from 1500 nm to 1600 nm with a phase fidelity above 0.7. Moreover, the vortex beam with the superposition of the y-polarization and x-polarization states can be obtained with the incident of the superposition of TE and TM waveguide modes.

Ultra-compact on-chip meta-waveguide phase modulator based on split ring magnetic resonance

With the development of photonic integration technology, meta-waveguides have become a new research hotspot. They have broken through the theoretical diffraction limit by virtue of the strong electromagnetic manipulation ability of the metasurface and the strong electromagnetic field limitation and guidance ability of the waveguide. However, the reported meta-waveguides lack research on dynamic modulation. Therefore, we analyze the modulation effect of the metasurface on the optical field in the waveguide and design an ultra-compact on-chip meta-waveguide phase modulator using split ring magnetic resonance. It has a very short modulation length of only 3.65 µm, wide modulation bandwidth of 116.8 GHz, and low energy consumption of 263.49 fJ/bit. By optimizing the structure, the energy consumption can be further reduced to 90.69 fJ/bit. Meta-waveguides provide a promising method for the design of integrated photonic devices.

On-chip generation of Bessel-Gaussian beam via concentrically distributed grating arrays for long-range sensing

Bessel beam featured with self-healing is essential to the optical sensing applications in the obstacle scattering environment. Integrated on-chip generation of the Bessel beam outperforms the conventional structure by small size, robustness, and alignment-free scheme. However, the maximum propagation distance (Z_max) provided by the existing approaches cannot support long-range sensing, and thus, it restricts its potential applications. In this work, we propose an integrated silicon photonic chip with unique structures featured with concentrically distributed grating arrays to generate the Bessel-Gaussian beam with a long propagation distance. The spot with the Bessel function profile is measured at 10.24 m without optical lenses, and the photonic chip's operation wavelength can be continuously performed from 1500 to 1630 nm. To demonstrate the functionality of the generated Bessel-Gaussian beam, we also experimentally measure the rotation speeds of a spinning object via the rotational Doppler Effect and the distance through the phase laser ranging principle. The maximum error of the rotation speed in this experiment is measured to be 0.05%, indicating the minimum error in the current reports. By the compact size, low cost, and mass production potential of the integrated process, our approach is promising to readily enable the Bessel-Gaussian beam in widespread optical communication and micro-manipulation applications.

Metasurface-Enabled On-Chip Manipulation of Higher-Order Poincaré Sphere Beams

An integrated way to generate and manipulate higher-order Poincaré sphere beams (HOPBs) is a sought-after goal in photonic integrated circuits for high-capacity communication systems. Here, we demonstrate a novel method for on-chip generation and manipulation of HOPBs through combining metasurface with optical waveguides on lithium niobate on insulator platform. With phase modulation by a diatomic geometric metasurface, guided waves are extracted into free space with a high signal-to-noise ratio in the form of two orthogonal circularly polarized optical vortices which are linearly superposed into HOPBs. Meanwhile, a dual-port waveguide crossing is established to reconfigure the output states into an arbitrary point on a higher-order Poincaré sphere based on in-plane interference of two guided waves. Our approach provides a promising solution to generate and manipulate the HOPBs in a compact manner, which would be further enhanced by employing the electro-optical modulation on a lithium niobate waveguide to access a fully tunable scheme.

On-chip ultracompact multimode vortex beam emitter based on vertical modes

Free-space orbital angular momentum (OAM) communication is considered as one of the potential alternative on-chip optical interconnect solutions. The number of OAM modes determines the capacity of high-speed communication. However, existing integrated vortex beam emitters have a constraint relationship between the number of OAM modes and the emitter size, rendering it difficult to emit more OAM modes with a small-sized emitter. In view of the above, this study proposes an on-chip ultracompact multimode vortex beam emitter based on vertical modes, which permits more OAM modes without requiring an increase in the size of the emitter. Vertical modes in large-aspect-ratio waveguides are pointed out to enable multimode microrings with small radii because high-order vertical modes can maintain almost the same horizontal wave vector as that of the fundamental mode. Four-mode and five-mode vortex beam emitters with the same radius of 1.5 µm are designed and the effectiveness of these emitters is verified through simulation. Furthermore, a high-efficiency and low-crosstalk approach for high-order vertical mode coupling by varying the waveguide height is presented. This research not only promotes further integration of on-chip optical interconnection, but also provides a new strategy for optical waveguide mode selection in photonic integrated circuits design.

Data transmission with up to 100 orbital angular momentum modes via commercial multi-mode fiber and parallel neural networks

This work presents an artificial intelligence enhanced orbital angular momentum (OAM) data transmission system. This system enables encoded data retrieval from speckle patterns generated by an incident beam carrying different topological charges (TCs) at the distal end of a multi-mode fiber. An appropriately trained network is shown to support up to 100 different fractional TCs in parallel with TC intervals as small as 0.01, thus overcoming the problems with previous methods that only supported a few modes and could not use small TC intervals. Additionally, an approach using multiple parallel neural networks is proposed that can increase the system's channel capacity without increasing individual network complexity. When compared with a single network, multiple parallel networks can achieve the better performance with reduced training data requirements, which is beneficial in saving computational capacity while also expanding the network bandwidth. Finally, we demonstrate high-fidelity image transmission using a 16-bit system and four parallel 14-bit systems via OAM mode multiplexing through a 1-km-long commercial multi-mode fiber (MMF).

Spin-Orbit Mapping of Light

Spin-orbit photonics, involving the interaction between the spin angular momentum (SAM) and orbital angular momentum (OAM) of light, plays an important role in modern optics. Here, we present the spin-orbit mapping of light in a few-mode fiber that originates from the mode degeneracy lifting (TM_{01} and TE_{01}) property. We demonstrate two kinds of spin-orbit mapping phenomena, i.e., mapping from intrinsic SAM to OAM and mapping from polarization direction rotation to field pattern rotation. The demonstrated spin-orbit mapping shows high efficiency, large bandwidth, availability for short pulses, and scalability to high-order OAM states.

Optical meta-waveguides for integrated photonics and beyond

The growing maturity of nanofabrication has ushered massive sophisticated optical structures available on a photonic chip. The integration of subwavelength-structured metasurfaces and metamaterials on the canonical building block of optical waveguides is gradually reshaping the landscape of photonic integrated circuits, giving rise to numerous meta-waveguides with unprecedented strength in controlling guided electromagnetic waves. Here, we review recent advances in meta-structured waveguides that synergize various functional subwavelength photonic architectures with diverse waveguide platforms, such as dielectric or plasmonic waveguides and optical fibers. Foundational results and representative applications are comprehensively summarized. Brief physical models with explicit design tutorials, either physical intuition-based design methods or computer algorithms-based inverse designs, are cataloged as well. We highlight how meta-optics can infuse new degrees of freedom to waveguide-based devices and systems, by enhancing light-matter interaction strength to drastically boost device performance, or offering a versatile designer media for manipulating light in nanoscale to enable novel functionalities. We further discuss current challenges and outline emerging opportunities of this vibrant field for various applications in photonic integrated circuits, biomedical sensing, artificial intelligence and beyond.

Guided mode meta-optics: metasurface-dressed waveguides for arbitrary mode couplers and on-chip OAM emitters with a configurable topological charge

Metasurface has achieved fruitful results in tailoring optical fields in free space. However, a systematic investigation on applying meta-optics to completely control waveguide modes is still elusive. Here we present a comprehensive catalog to selectively and exclusively couple free space light into arbitrary high-order waveguide modes of interest, leveraging silicon metasurface-patterned silicon nitride waveguides. By simultaneously engineering the matched phase gradient of the nanoantennas and the vectorial spatial modal overlap between the antenna near-field and target waveguide mode profile, either single or multiple high-order modes are successfully launched with high purity reaching 98%. Moreover, on-chip twisted light generators are theoretically proposed with configurable OAM topological charge ℓ from -3 to +2. This work may serve as a comprehensive framework for guided mode meta-optics and motivates further applications such as versatile integrated couplers, multiplexers, and mode-division multiplexing-based communication systems.

Demonstration of generating a 100 Gbit/s orbital-angular-momentum beam with a tunable mode order over a range of wavelengths using an integrated broadband pixel-array structure

We experimentally generate an orbital-angular-momentum (OAM) beam with a tunable mode order over a range of wavelengths utilizing an integrated broadband pixel-array OAM emitter. The emitter is composed of a 3-to-4 coupler, four phase controllers, and a mode convertor. An optical input is split into four waveguides by the coupler. Subsequently, the four waveguide fields are coherently combined and transformed into a free-space OAM beam by the mode convertor. By tuning the phase delay Δφ between the four waveguides using the integrated phase controllers, the OAM order of the generated beam could be changed. Our results show that (a) a single OAM beam with a tunable OAM order (ℓ=-1 or ℓ=+1) is generated with the intermodal power coupling of <-11dB, and (b) in a wavelength range of 6.4 nm, a free-space link of a single 50 Gbaud quadrature-phase-shift-keying (QPSK) channel carried by the tunable OAM beam is achieved with a bit error rate below the forward-error-correction threshold. As proof of concept, a 400 Gbit/s OAM-multiplexed and WDM QPSK link is demonstrated with a ∼1-dB OSNR penalty compared with a single-beam link.

Compact broadband silicon-integrated Airy beam emitter

Optical Airy beams have wide-ranging applications in photonics, but conventional approaches for generating Airy beams require bulky and strictly aligned optical systems. Here, we propose on-chip compact Airy beam emitters by using a shallow-etched holography grating on a silicon platform. The holography grating, formed by the binary interferogram of the guided wave and the spatial Airy beam, can scatter the guided waves into spatial waves with the phase distributions being consistent with those of Airy beam. The simulation demonstrates that a 20µm×20µm holography grating on a strip waveguide enables the realization of 2D Airy beam within the wavelength range from 1490 to 1570 nm. Our results suggest a promising avenue towards potential applications in on-chip imaging, optical forces, optical interconnection, etc.

Compact and broad wavelength range tunable orbital angular momentum mode generator based on cascaded helical photonic crystal fibers

A compact and broad wavelength range tunable orbital angular momentum (OAM) generator was experimentally demonstrated by cascading two helical photonic crystal fibers (HPCFs) with opposite helicity, i.e., clockwise-twisted + anticlockwise-twisted HPCF. Such an OAM generator exhibited a length of approximately 9 mm and generated a high-quality OAM mode with a wavelength range of 35 nm. Moreover, the wavelength range is expected to be tuned from 17.9-51.3 nm by applying mechanical torsion.

Utilizing phase delays of an integrated pixel-array structure to generate orbital-angular-momentum beams with tunable orders and a broad bandwidth

We study the relationship between the input phase delays and the output mode orders when using a pixel-array structure fed by multiple single-mode waveguides for tunable orbital-angular-momentum (OAM) beam generation. As an emitter of a free-space OAM beam, the designed structure introduces a transformation function that shapes and coherently combines multiple (e.g., four) equal-amplitude inputs, with the kth input carrying a phase delay of (k-1)Δφ. The simulation results show that (1) the generated OAM order ℓ is dependent on the relative phase delay Δφ; (2) the transformation function can be tailored by engineering the structure to support different tunable ranges (e.g., l={-1},{-1,+1},{-1,0,+1}, or {-2,-1,+1,+2}); and (3) multiple independent coaxial OAM beams can be generated by simultaneously feeding the structure with multiple independent beams, such that each beam has its own Δφ value for the four inputs. Moreover, there is a trade-off between the tunable range and the mode purity, bandwidth, and crosstalk, such that the increase of the tunable range leads to (a) decreased mode purity (from 91% to 75% for l=-1), (b) decreased 3 dB bandwidth of emission efficiency (from 285 nm for l={-1} to 122 nm for l={-2,-1,+1,+2}), and (c) increased crosstalk within the C-band (from -23.7 to -13.2dB when the tunable range increases from 2 to 4).

On-chip generation of the reconfigurable orbital angular momentum with high order

In this manuscript, the generation of an optical vortex beam with high order and reconfigurable orbital angular momentum (OAM) is studied. Multi-waveguide holographic gratings (MWHG) are deployed to generate OAM beams with high order. The generation of the OAM beam with an order l from +4 to +8 is demonstrated by numerical simulations, and the generated OAM order is manipulable and configurable by incident phase. The working bandwidths of the MWHG for different OAM orders are at the level of 40 nm. This work could provide valuable references for practical implementation of OAM in integrated optics.

Compact high-efficiency four-mode vortex beam generator within the telecom C-band

Vortex beams carrying orbital angular momentum have attracted a great deal of attention over the past few years. An integrated vortex beam generator with high efficiency is desirable for wide-ranging applications. Here we demonstrate a highly efficient silicon photonic integrated vortex beam generator based on superposed holographic fork gratings. A metal mirror is used to enhance emission efficiency by reflecting the power leaking down to the substrate back to air. Experimental characterization confirms that the emission efficiency of the generator increases by ${\sim} 5\,{\rm dB}$∼5dB. Moreover, the present device shows preferable features of broadband, polarization diversity, and compact footprint.

Minimized two- and four-step varifocal lens based on silicon photonic integrated nanoapertures

Integration of optical waveguide and subwavelength structure may help address the problems of large footprint, low robustness, and small operation bandwidth, those of that are typically inborn in traditional integrated optical devices. Here, a design method of an ultra-compact small footprint lens is proposed. Combing particle swarm optimization (PSO) algorithm with spatial multiplexing technology, we successfully integrated two- and four-step varifocal lenses on SOIs chips with small footprint of 35×35 µm², non-mechanically leading to 2.5× and 3.4× zoom capacity, respectively. The proposed designed method may shed a new light on compact on-chip display devices and offer an alternative approach to design integrated optical communication with high information storage capacity.