The global quantum network requires the distribution of entangled states over long distances, with substantial advances already demonstrated using polarization. While Hilbert spaces with higher dimensionality, e.g., spatial modes of light, allow higher information capacity per photon, such spatial mode entanglement transport requires custom multimode fiber and is limited by decoherence-induced mode coupling. Here, we circumvent this by transporting multidimensional entangled states down conventional single-mode fiber (SMF). By entangling the spin-orbit degrees of freedom of a biphoton pair, passing the polarization (spin) photon down the SMF while accessing multiple orbital angular momentum (orbital) subspaces with the other, we realize multidimensional entanglement transport. We show high-fidelity hybrid entanglement preservation down 250 m SMF across multiple 2 × 2 dimensions, confirmed by quantum state tomography, Bell violation measures, and a quantum eraser scheme. This work offers an alternative approach to spatial mode entanglement transport that facilitates deployment in legacy networks across conventional fiber.

https://advances.sciencemag.org/content/advances/6/4/eaay0837.full.pdf

Multidimensional entanglement transport through single-mode fiber

Optical communication is an integral part of the modern economy, having all but replaced electronic communication systems. Future growth in bandwidth appears to be on the horizon using structured light, encoding information into the spatial modes of light, and transmitting them down fibre and free-space, the latter crucial for addressing last mile and digitally disconnected communities. Unfortunately, patterns of light are easily distorted, and in the case of free-space optical communication, turbulence is a significant barrier. Here we review recent progress in structured light in turbulence, first with a tutorial style summary of the core concepts, before highlighting the present state-of-the-art in the field. We support our review with new experimental studies that reveal which types of structured light are best in turbulence, the behaviour of vector versus scalar light in turbulence, the trade-off of diversity and multiplexing, and how turbulence models can be exploited for enhanced optical signal processing protocols. This comprehensive treatise will be invaluable to the large communities interested in free-space optical communication with spatial modes of light.

Structured Light in Turbulence

A quantitative analysis of optical fields is essential, particularly when the light is structured in some desired manner, or when there is perhaps an undesired structure that must be corrected for. A ubiquitous procedure in the optical community is that of optical mode projections—a modal analysis of light—for the unveiling of amplitude and phase information of a light field. When correctly performed, all the salient features of the field can be deduced with high fidelity, including its orbital angular momentum, vectorial properties, wavefront, and Poynting vector. Here, we present a practical tutorial on how to perform an efficient and effective optical modal decomposition, with emphasis on holographic approaches using spatial light modulators, highlighting the care required at each step of the process.

Modal analysis of structured light with spatial light modulators: a practical tutorial.

We present a method to efficiently multiply or divide the orbital angular momentum (OAM) of light beams using a sequence of two optical elements. The key element is represented by an optical transformation mapping the azimuthal phase gradient of the input OAM beam onto a circular sector. By combining multiple circular-sector transformations into a single optical element, it is possible to multiply the value of the input OAM state by splitting and mapping the phase onto complementary circular sectors. Conversely, by combining multiple inverse transformations, the division of the initial OAM value is achievable by mapping distinct complementary circular sectors of the input beam into an equal number of circular phase gradients. Optical elements have been fabricated in the form of phase-only diffractive optics with high-resolution electron-beam lithography. Optical tests confirm the capability of the multiplier optics to perform integer multiplication of the input OAM, whereas the designed dividers are demonstrated to correctly split up the input beam into a complementary set of OAM beams. These elements can find applications for the multiplicative generation of higher-order OAM modes, optical information processing based on OAM beam transmission, and optical routing/switching in telecom.

/pdf/multiplication-and-division-of-the-orbital-angular-momentum-329m3ix32m.pdf

Multiplication and division of the orbital angular momentum of light with diffractive transformation optics

Orbital angular momentum (OAM), one of the most recently discovered degrees of freedom of light beam field has fundamentally revolutionized optical physics and its technological capabilities. Optical beams with OAM have enabled a large variety of applications, including super-resolution imaging, optical trapping, classical and quantum optical communication, and quantum computing, to mention a few. To enable these and several other emerging applications, optical beams with OAM have been generated using a variety of methods and technologies, such as a simple astigmatic lens pair, one-/two-dimensional holographic optical elements, three-dimensional spiral phase plates, optical fibers, and recent entrants such as metasurfaces. All these techniques achieve spatial light modulation and can be implemented with either passive elements or active devices, such as liquid crystal on silicon and digital micromirror devices. Many of these devices and technologies are not only used for the generation of amplitude phase-polarization structured light beams but are also capable of analyzing them. We have attempted to encompass a wide variety of such technologies as well as a few emerging methodologies, broadly categorized into generation and detection protocols. We address the needs of scientists and engineers who desire to generate/detect OAM modes and are looking for the technique (active or passive) best suited for their application.

/pdf/generation-and-decomposition-of-scalar-and-vector-modes-4gpcle709y.pdf

Generation and decomposition of scalar and vector modes carrying orbital angular momentum: a review

The design and fabrication of a compact diffractive optical element is presented for the sorting of beams carrying orbital angular momentum (OAM) of light. The sorter combines a conformal mapping transformation with an optical fan-out, performing demultiplexing with unprecedented levels of miniaturization and OAM resolution. Moreover, an innovative configuration is proposed which simplifies alignment procedures and further improves the compactness of the optical device. Samples have been fabricated in the form of phase-only diffractive optics with high-resolution electron-beam lithography (EBL) over a glass substrate. A soft-lithography process has been optimized for fast and cheap replica production of the EBL masters. Optical tests with OAM beams confirm the designed performance, showing excellent efficiency and low cross-talk, with high fidelity even with multiplexed input beams. This work paves the way for practical OAM multiplexing and demultiplexing devices for use in classical and quantum communication.

/pdf/a-compact-diffractive-sorter-for-high-resolution-3jrexu8crr.pdf

A compact diffractive sorter for high-resolution demultiplexing of orbital angular momentum beams.

A novel optical architecture is designed and fabricated in order to overcome the limits of the traditional sorter based on log-pol optical transformation for the demultiplexing of optical beams carrying orbital angular momentum (OAM) of light The proposed configuration simplifies the alignment procedure and significantly improves the compactness of the optical device In addition, the integration of an optical fan-out provides higher resolution on OAM modes separation Since the miniaturization level and the optical configuration require to operate beyond the paraxial approximation, a rigorous formulation of transformation optics in the non-paraxial regime is developed and applied for the first time Samples have been fabricated as 256-level phase-only diffractive optics with high-resolution electron-beam lithography and tested for the demultiplexing of optical vortex superposition in a 8-bit free-space optical link The results confirm the expected high efficiency and resolution in OAM sorting

Compact diffractive optics for high-resolution sorting of orbital angular momentum beams

Multiple applications of relevance in photonics, such as spectrally efficient coherent communications, microwave synthesis or the calibration of astronomical spectrographs, would benefit from soliton microcombs operating at repetition rates <50GHz. However, attaining soliton microcombs with low repetition rates using photonic integration technologies represents a formidable challenge. Expanding the cavity volume results in a drop of intracavity intensity that can only be offset by an encompassing rise in quality factor. In addition, reducing the footprint of the microresonator on a planar integrated circuit requires race-track designs that typically result into extra modal coupling losses and disruptions into the dispersion, preventing the generation of the dissipative single soliton state. Here, we report the generation of sub-50GHz soliton microcombs in dispersion-engineered silicon nitride microresonators. In contrast to other approaches, our devices feature an optimized racetrack design that minimizes the coupling to higher-order modes and reduces the footprint size by an order of magnitude to ~1mm2. The statistical intrinsic Q reaches 19 million, and soliton microcombs at 20.5GHz and 14.0GHz repetition rates are successfully generated. Importantly, the fabrication process is entirely subtractive, meaning that the devices can be directly patterned on the Si3N4 film. This standard approach facilitates integration with further components and devices.

Integrated, ultra-compact high-Q silicon nitride microresonators for low-repetition-rate soliton microcombs

A novel diffractive optical element is designed, fabricated and tested exhibiting unprecedented levels of miniaturization, integration and resolution in orbital angular momentum mode demultiplexing. The device has been fabricated with high-resolution electron-beam lithography and characterized for OAM-beams both in free-space and optical fibers.

Marcello Girardi

Papers

A compact diffractive sorter for high-resolution demultiplexing of orbital angular momentum beams.

Compact diffractive optics for high-resolution sorting of orbital angular momentum beams

Integrated, ultra-compact high-Q silicon nitride microresonators for low-repetition-rate soliton microcombs

Demultiplexing of Orbital Angular Momentum Beams by Diffractive Optics