Generalized optical angular momentum sorter and its application to high-dimensional quantum cryptography

Arbitrary optical wave evolution with Fourier transforms and phase masks

A large number of applications in classical and quantum photonics require the capability of implementing arbitrary linear unitary transformations on a set of optical modes. In a seminal work by Reck et al. [Phys. Rev. Lett.73, 58 (1994)10.1103/PhysRevLett.73.58], it was shown how to build such multiport universal interferometers with a mesh of beam splitters and phase shifters, and this design became the basis for most experimental implementations in the last decades. However, the design of Reck et al. is difficult to scale up to a large number of modes, which would be required for many applications. Here we present a deterministic algorithm that can find an exact and efficient implementation of any unitary transformation, using only Fourier transforms and phase masks. Since Fourier transforms and phase masks are routinely implemented in several optical setups and they do not suffer from some of the scalability issues associated with building extensive meshes of beam splitters, we believe that our design can be useful for many applications in photonics.

Mitigating the effect of atmospheric turbulence on orbital angular momentum-based quantum key distribution using real-time adaptive optics with phase unwrapping

Quantum key distribution (QKD) employed orbital angular momentum (OAM) for high-dimensional encoding enhances the system security and information capacity between two communication parties. However, such advantagesare significantly degraded because of the fragility of OAM states in atmospheric turbulence. Unlike previous researches, we first investigate the performance degradation of OAM-based QKD by infinitely long phase screen (ILPS), which offers a feasible way to study how adaptive optics (AO) dynamically corrects the turbulence-induced aberrations in real time. Secondly, considering the failure of AO while encountering phase cuts, we evaluate the quality enhancement of OAM-based QKD under a moderate turbulence strength by AO after implementing the wrapped cuts elimination. Finally, we simulate that, with more realistic considerations; real-time AO can still mitigate the impact of atmospheric turbulence on OAM-based QKD even in the large wind velocity regime.

Analysis of misaligned optical rotational Doppler effect by modal decomposition

The optical rotational Doppler effect (RDE) is closely related to the unique orbital angular momentum (OAM) carried by optical vortex, whose topological charge means the mode of OAM. Compared with the coaxial incidence, the rotational Doppler frequency shift spectrum of a misaligned optical vortex (misaligned RDE) widens according to a certain law. In this paper, an OAM modal decomposition method of the misaligned optical RDE is proposed and the relative intensity of different OAM modes, namely the OAM spectrum, is derived based on an inner product computation. Analyses show that lateral displacements and angular deflections change the distribution of OAM modes relative to the rotation axis of the object. A misaligned Laguerre-Gaussian (LG) vortex can be represented as a specific combination of coaxial LG modes, and the difference between the topological charge of two adjacent modes is 1 or 2 with lateral displacements or angular deflections respectively. An experiment of misaligned optical RDE using a superimposed LG vortex is executed, and the obtained frequency shift spectrum with misaligned incidence expands into a set of discrete signals, which agrees well with the theoretical results. Moreover, we can get the rotation frequency of the object from an expanded frequency spectrum more quickly and accurately based on the difference between two adjacent signal peaks. The proposed method contributes to analyze the misaligned optical RDE comprehensively, which is significant in remote sensing and optical metrology.

OAM-inspired new optics: the angular metalens

Analogous to the behavior of a common converging lens for the input of tilted waves, a recent publication suggests a new optical element with an azimuthal-quadratic phase profile for the focusing of orbital angular momentum beams at distinct angular positions. Its realization in a metasurface form enables the combined measurement of orbital and spin angular momentum using a single optical component.

Design of continuously variant metasurfaces for conformal transformation optics

Metasurfaces optics and structured light represent two emerging paradigms which are revolutionizing optics in a wide range of fields, from imaging to telecommunications, both in the classical and single-photon regimes. In this work, we present and describe a method for the design of high-resolution geometric-phase metasurfaces in the form of continuously variant sub-wavelength gratings, and we demonstrate how this technique is suitable for harmonic phase masks implementing conformal optical transformations. In this framework, we revisit the metasurface design of blazed gratings and spiral phase plates, the so-called q-plates, and we extend the method to the metasurface implementation of two conformal mappings, the log-pol and the circular-sector transformation, which have been exploited successfully to perform the generation, sorting and manipulation of structured light beams carrying orbital angular momentum.

Liquid-Crystal-Mediated Geometric Phase: From Transmissive to Broadband Reflective Planar Optics

Planar optical elements that can manipulate the multidimensional physical parameters of light efficiently and compactly are highly sought after in modern optics and nanophotonics. In recent years, the geometric phase, induced by the photonic spin-orbit interaction, has attracted extensive attention for planar optics due to its powerful beam shaping capability. The geometric phase can usually be generated via inhomogeneous anisotropic materials, among which liquid crystals (LCs) have been a focus. Their pronounced optical properties and controllable and stimuli-responsive self-assembly behavior introduce new possibilities for LCs beyond traditional panel displays. Recent advances in LC-mediated geometric phase planar optics are briefly reviewed. First, several recently developed photopatterning techniques are presented, enabling the accurate fabrication of complicated LC microstructures. Subsequently, nematic LC-based transmissive planar optical elements and chiral LC-based broadband reflective elements are reviewed systematically. Versatile functionalities are revealed, from conventional beam steering and focusing, to advanced structuring. Combining the geometric phase with structured LC materials offers a satisfactory platform for planar optics with desired functionalities and drastically extends exceptional applications of ordered soft matter. Some prospects on this rapidly advancing field are also provided.

Sorting full angular momentum states with Pancharatnam-Berry metasurfaces based on spiral transformation

Full angular momentum states constitute a complete and higher state space of a photon, which are significant not only for fundamental study of light but also for practical applications utilizing cylindrical optics such as optical fibers. Here we propose and demonstrate a simple yet effective scheme of combining the spiral transformation with Pancharatnam-Berry (PB) metasurfaces for high-resolution sorting of full angular momentum states. The scheme is verified by successfully sorting full angular momentum states with 7 orbital angular momentum states and 2 spin angular momentum states via numerical simulations and experiments. We expect that our work paves the way for simple high-resolution sorting of full angular momentum states, which could be highly useful in both classical and quantum information systems.

A Minimalist Single-Layer Metasurface for Arbitrary and Full Control of Vector Vortex Beams

Vector vortex beams (VVBs) possess ubiquitous applications from particle trapping to quantum information. Recently, the bulky optical devices for generating VVBs have been miniaturized by using metasurfaces. Nevertheless, it is quite challenging for the metasurface-generated VVBs to possess arbitrary polarization and phase distributions. More critical is that the VVBs' annular intensity profiles demonstrated hitherto are dependent on topological charges and are hence not perfect, posing difficulties in spatially shared co-propagation of multiple vortex beams. Here, a single-layer metasurface to address all those aforementioned challenges in one go is proposed, which consists of two identical crystal-silicon nanoblocks with varying positions and rotation angles (i.e., four geometric parameters throughout). Those four geometric parameters are found to be adequate for independent and arbitrary control of the amplitude, phase, and polarization of light. Perfect VVBs with arbitrary polarization and phase distributions are successfully generated, and the constant intensity profiles independent of their topological charges and polarization orders are demonstrated. The proposed strategy casts a distinct perception that a minimalist design of just one single-layer metasurface can empower such robust and versatile control of VVBs. That provides promising opportunities for generating more complex vortex field for advanced applications in structural light, optical micromanipulation, and data communication.

Sorting-based approach to multiphoton interference

Multiphoton interference is an essential component of quantum technologies such as quantum computation, quantum communication, and quantum metrology. We introduce a sorting-based approach to multiphoton interference and examine its implications for quantum metrology and teleportation. Our examination reveals an extension of the seminal Hong-Ou-Mandel effect whose resultant state is the highly desired multiphoton NOON state. Application of the above perspective to entangled photons reveals a novel approach to quantum qudit teleportation.

Holographic Silicon Metasurfaces for Total Angular Momentum Demultiplexing Applications in Telecom

The simultaneous processing of orbital angular momentum (OAM) and polarization has recently acquired particular importance and interest in a wide range of fields ranging from telecommunications to high-dimensional quantum cryptography. Due to their inherently polarization-sensitive optical behavior, Pancharatnam–Berry optical elements (PBOEs), acting on the geometric phase, have proven to be useful for the manipulation of complex light beams with orthogonal polarization states using a single optical element. In this work, different PBOEs have been computed, realized, and optically analyzed for the sorting of beams with orthogonal OAM and polarization states at the telecom wavelength of 1310 nm. The geometric-phase control is obtained by inducing a spatially-dependent form birefringence on a silicon substrate, patterned with properly-oriented subwavelength gratings. The digital grating structure is generated with high-resolution electron beam lithography on a resist mask and transferred to the silicon substrate using inductively coupled plasma-reactive ion etching. The optical characterization of the fabricated samples confirms the expected capability to detect circularly-polarized optical vortices with different handedness and orbital angular momentum.

Total angular momentum sorting in the telecom infrared with silicon Pancharatnam-Berry transformation optics

Parallel sorting of orbital angular momentum (OAM) and polarization has recently acquired paramount importance and interest in a wide range of fields ranging from telecommunications to high-dimensional quantum cryptography. Due to their inherently polarization-sensitive optical response, optical elements acting on the geometric phase prove to be useful for processing structured light beams with orthogonal polarization states by means of a single optical platform. In this work, we present the design, fabrication and test of a Pancharatnam-Berry optical element in silicon implementing a log-pol optical transformation at 1310 nm for the realization of an OAM sorter based on the conformal mapping between angular and linear momentum states. The metasurface is realized in the form of continuously variant subwavelength gratings, providing high-resolution in the definition of the phase pattern. A hybrid device is fabricated assembling the metasurface for the geometric-phase control with multi-level diffractive optics for the polarization-independent manipulation of the dynamic phase. The optical characterization confirms the capability to sort orbital angular momentum and circular polarization at the same time.

Liquid crystal-based order electrically controlled q-plate system

This paper proposes a liquid crystal-based order adjustable q-plate system. The system, which is solid-state and electrically controlled without any mechanical components, consists of several bit cells and one symbol cell. The bit cells can be electrically selected whether to modulate the beam. The magnitude of the order of the q-plate system can be controlled by activating specific bit cells. And the sign of the order can be changed by controlling the voltages in the symbol cell. The whole system can realize the function of the order adjustable q-plate with the order ranging from -2n + 1 to 2n-1 with n bit cells. In our experiment, the system with 4 bits is verified. Based on the q-plate system, the vector beams and optical vortexes with the orders ranging from -15 to 15 can be generated.

Multi-focus hologram utilizing Pancharatnam-Berry phase elements based metamirror

An ultrathin reflection-type metamirror is proposed for multi-focusing with any desired focusing fashion including focal number and location. The metamirror is composed of reflection-type Pancharatnam-Berry (P-B) phase elements, which are able to provide full reflection phase of 2π, together with near-unity reflection efficiency by judiciously engineering the rotation angle of each latter element. A holographic algorithm is utilized to calculate the phase distribution at the interface of the metamirror to achieve the desired multi-focus spots. Experimental demonstrations performed in microwave region show good imaging quality with high reflection efficiency and imaging efficiency. The proposed metamirror provides a high-performance solution for low-cost and lightweight beam-shaping and beam-focusing devices.

Using all transverse degrees of freedom in quantum communications based on a generic mode sorter

The dimension of the state space for information encoding offered by the transverse structure of light is usually limited by the finite size of apertures. The widely used orbital angular momentum (OAM) number of Laguerre-Gaussian (LG) modes in free-space communications cannot achieve the theoretical maximum transmission capacity unless the radial degree of freedom is multiplexed into the protocol. While the methodology to sort the radial quantum number has been developed, the application of radial modes in quantum communications requires an additional ability to efficiently measure the superposition of LG modes in the mutually unbiased basis. Here we develop and implement a generic mode sorter that is capable of sorting the superposition of LG modes through the use of a mode converter. As a consequence, we demonstrate an 8-dimensional quantum key distribution experiment involving all three transverse degrees of freedom: spin, azimuthal, and radial quantum numbers of photons. Our protocol presents an important step towards the goal of reaching the capacity limit of a free-space link and can be useful to other applications that involve spatial modes of photons.

Efficient High-Dimensional Quantum Key Distribution with Hybrid Encoding

We propose a schematic setup of quantum key distribution (QKD) with an improved secret key rate based on high-dimensional quantum states. Two degrees-of-freedom of a single photon, orbital angular momentum modes, and multi-path modes, are used to encode secret key information. Its practical implementation consists of optical elements that are within the reach of current technologies such as a multiport interferometer. We show that the proposed feasible protocol has improved the secret key rate with much sophistication compared to the previous 2-dimensional protocol known as the detector-device-independent QKD.

Realization of a scalable Laguerre-Gaussian mode sorter based on a robust radial mode sorter

The transverse structure of light is recognized as a resource that can be used to encode information onto photons and has been shown to be useful to enhance communication capacity as well as resolve point sources in superresolution imaging. The Laguerre-Gaussian (LG) modes form a complete and orthonormal basis set and are described by a radial index p and an orbital angular momentum (OAM) index ℓ. Earlier works have shown how to build a sorter for the radial index p or/and the OAM index ℓ of LG modes, but a scalable and dedicated LG mode sorter which simultaneous determinate p and ℓ is immature. Here we propose and experimentally demonstrate a scheme to accomplish complete LG mode sorting, which consists of a novel, robust radial mode sorter that can be used to couple radial modes to polarizations, an ℓ-dependent phase shifter and an OAM mode sorter. Our scheme is in principle efficient, scalable, and crosstalk-free, and therefore has potential for applications in optical communications, quantum information technology, superresolution imaging, and fiber optics.

Quantum cryptography with structured photons through a vortex fiber

Optical fiber links and networks are integral components within and between cities' communication infrastructures. Implementing quantum cryptographic protocols on either existing or new fiber links will provide information-theoretical security to fiber data transmissions. However, there is a need for ways to increase the channel bandwidth. Using the transverse spatial degree of freedom is one way to transmit more information and increase tolerable error thresholds by extending the common qubit protocols to high-dimensional quantum key distribution (QKD) schemes. Here we use one type of vortex fiber where the transverse spatial modes serves as an additional channel to encode quantum information by structuring the spin and orbital angular momentum of light. In this proof-of-principle experiment, we show that two-dimensional structured photons can be used in such vortex fibers in addition to the common two-dimensional polarization encryption, thereby paving the path to QKD multiplexing schemes.

Parallel sorting of orbital and spin angular momenta of light in a record large number of channels

Parallel sorting of orbital and spin angular momentum components of structured optical beams is demonstrated. Both spin channels are multiplexed within the novel orbital angular momentum (OAM) sorter, reducing the size, weight, and number of elements. The sorted states are linearly spaced over 70 topological charge values. We experimentally and theoretically evaluate the operational range and crosstalk between neighboring channels and find that 30 orbital angular momentum states are available per spin channel for quantum communication or cryptography. This is achieved using an angular momentum sorter that we developed based on geometric phase optical elements. We present two devices consisting of liquid crystal polymer films photoaligned with complex two-dimensional patterns.