Metamaterials are artificially fabricated materials that allow for the control of light and acoustic waves in a manner that is not possible in nature. This Review covers the recent developments in the study of so-called metasurfaces, which offer the possibility of controlling light with ultrathin, planar optical components. Conventional optical components such as lenses, waveplates and holograms rely on light propagation over distances much larger than the wavelength to shape wavefronts. In this way substantial changes of the amplitude, phase or polarization of light waves are gradually accumulated along the optical path. This Review focuses on recent developments on flat, ultrathin optical components dubbed 'metasurfaces' that produce abrupt changes over the scale of the free-space wavelength in the phase, amplitude and/or polarization of a light beam. Metasurfaces are generally created by assembling arrays of miniature, anisotropic light scatterers (that is, resonators such as optical antennas). The spacing between antennas and their dimensions are much smaller than the wavelength. As a result the metasurfaces, on account of Huygens principle, are able to mould optical wavefronts into arbitrary shapes with subwavelength resolution by introducing spatial variations in the optical response of the light scatterers. Such gradient metasurfaces go beyond the well-established technology of frequency selective surfaces made of periodic structures and are extending to new spectral regions the functionalities of conventional microwave and millimetre-wave transmit-arrays and reflect-arrays. Metasurfaces can also be created by using ultrathin films of materials with large optical losses. By using the controllable abrupt phase shifts associated with reflection or transmission of light waves at the interface between lossy materials, such metasurfaces operate like optically thin cavities that strongly modify the light spectrum. Technology opportunities in various spectral regions and their potential advantages in replacing existing optical components are discussed.

Flat Optics With Designer Metasurfaces

With prevalent attacks in communication, sharing a secret between communicating parties is an ongoing challenge. Moreover, it is important to integrate quantum solutions with classical secret sharing schemes with low computational cost for the real world use. This paper proposes a novel hybrid threshold adaptable quantum secret sharing scheme, using an m-bonacci orbital angular momentum (OAM) pump, Lagrange interpolation polynomials, and reverse Huffman-Fibonacci-tree coding. To be exact, we employ entangled states prepared by m-bonacci sequences to detect eavesdropping. Meanwhile, we encode m-bonacci sequences in Lagrange interpolation polynomials to generate the shares of a secret with reverse Huffman-Fibonacci-tree coding. The advantages of the proposed scheme is that it can detect eavesdropping without joint quantum operations, and permits secret sharing for an arbitrary but no less than threshold-value number of classical participants with much lower bandwidth. Also, in comparison with existing quantum secret sharing schemes, it still works when there are dynamic changes, such as the unavailability of some quantum channel, the arrival of new participants and the departure of participants. Finally, we provide security analysis of the new hybrid quantum secret sharing scheme and discuss its useful features for modern applications.

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Hybrid threshold adaptable quantum secret sharing scheme with reverse Huffman-Fibonacci-tree coding

Silicon has long been established as the material of choice for the microelectronics industry. This is not yet true in photonics, where the limited degrees of freedom in material design combined with the indirect bandgap are a major constraint. Recent developments, especially those enabled by nanoscale engineering of the electronic and photonic properties, are starting to change the picture, and some silicon nanostructures now approach or even exceed the performance of equivalent direct-bandgap materials. Focusing on two application areas, namely communications and photovoltaics, we review recent progress in silicon nanocrystals, nanowires and photonic crystals as key examples of functional nanostructures. We assess the state of the art in each field and highlight the challenges that need to be overcome to make silicon a truly high-performing photonic material.

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Silicon nanostructures for photonics and photovoltaics

Visible, circularly polarised light can be transformed into light-carrying orbital angular momentum by a plasmonic metasurface. That is the finding of Ebrahim Karimi and co-workers at the University of Ottawa in Canada and the University of Rochester in the United States. Light with orbital angular momentum (owing to a twisted phase front) is traditionally generated using specially designed optical elements such as spatial light modulator, cylindrical lens mode converters and q-plate. The researchers have now shown that a plasmonic metasurface comprising an array of nano-antennas can couple spin-to-orbital angular momentum at thickness much smaller than the wavelength of the light with an efficiency of around 3%. The conversion takes place due to the birefringence present in the nanostructure array. This approach could yield ultrathin generators of visible light with orbital angular momentum, for potential applications in spectroscopy, imaging, sensing and quantum information.

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Generating optical orbital angular momentum at visible wavelengths using a plasmonic metasurface

With prevalent attacks in communication, sharing a secret between communicating parties is an ongoing challenge. Moreover, it is important to integrate quantum solutions with classical secret sharing schemes with low computational cost for the real world use. This paper proposes a novel hybrid threshold adaptable quantum secret sharing scheme, using an m-bonacci orbital angular momentum (OAM) pump, Lagrange interpolation polynomials, and reverse Huffman-Fibonacci-tree coding. To be exact, we employ entangled states prepared by m -bonacci sequences to detect eavesdropping. Meanwhile, we encode m -bonacci sequences in Lagrange interpolation polynomials to generate the shares of a secret with reverse Huffman-Fibonacci-tree coding. The advantages of the proposed scheme is that it can detect eavesdropping without joint quantum operations, and permits secret sharing for an arbitrary but no less than threshold-value number of classical participants with much lower bandwidth. Also, in comparison with existing quantum secret sharing schemes, it still works when there are dynamic changes, such as the unavailability of some quantum channel, the arrival of new participants and the departure of participants. Finally, we provide security analysis of the new hybrid quantum secret sharing scheme and discuss its useful features for modern applications.

We engineer aperiodic nanostructures for enhanced omnidirectional light extraction and coupling of 1.55 μm radiation to distinctive optical resonances carrying of orbital angular momentum (OAM) using light emitting Si-based materials. By systematically studying nanopillar arrays with varying pillar separations and increasing degree of rotational symmetry in Fourier space, we show that omnidirectional extraction is achieved with circularly symmetric Fourier space, leading to best light emission enhancement from planar devices such as LEDs or lasers. To demonstrate the potential of active aperiodic structures with azimuthally isotropic k-space, we fabricate nanopillar arrays of erbium doped silicon-rich nitride using electron beam lithography and reactive ion etching. Experimental results obtained using leaky-mode photoluminescence spectroscopy prove over 10 times extraction enhancement at 1.55 μm from aperiodic golden angle spirals (GA spirals), in good agreement with design based on analytical Bragg scatt...

Aperiodic arrays of active nanopillars for radiation engineering

In this paper, we present a general analytical model for light scattering by arbitrary Vogel spiral arrays of circular apertures illuminated at normal incidence. This model suffices to unveil the fundamental mathematical structure of their complex Fraunhofer diffraction patterns and enables the engineering of optical beams carrying multiple values of orbital angular momentum (OAM). By performing analytical Fourier-Hankel decomposition of spiral arrays and far field patterns, we rigorously demonstrate the ability to encode specific numerical sequences onto the OAM values of diffracted optical beams. In particular, we show that these OAM values are determined by the rational approximations (i.e., the convergents) of the continued fraction expansions of the irrational angles utilized to generate Vogel spirals. These findings open novel and exciting opportunities for the manipulation of complex OAM spectra using dielectric and plasmonic aperiodic spiral arrays for a number of emerging engineering applications in singular optics, secure communication, optical cryptography, and optical sensing.

Analytical light scattering and orbital angular momentum spectra of arbitrary Vogel spirals.

Quantum cryptography and quantum key distribution (QKD) have been the most successful applications of quantum information processing, highlighting the unique capability of quantum mechanics, through the no-cloning theorem, to securely share encryption keys between two parties. Here, we present an approach to high-capacity, high-efficiency QKD by exploiting cross-disciplinary ideas from quantum information theory and the theory of light scattering of aperiodic photonic media. We propose a unique type of entangled-photon source, as well as a physical mechanism for efficiently sharing keys. The key-sharing protocol combines entanglement with the mathematical properties of a recursive sequence to allow a realization of the physical conditions necessary for implementation of the no-cloning principle for QKD, while the source produces entangled photons whose orbital angular momenta (OAM) are in a superposition of Fibonacci numbers. The source is used to implement a particular physical realization of the protocol by randomly encoding the Fibonacci sequence onto entangled OAM states, allowing secure generation of long keys from few photons. Unlike in polarization-based protocols, reference frame alignment is unnecessary, while the required experimental setup is simpler than other OAM-based protocols capable of achieving the same capacity and its complexity grows less rapidly with increasing range of OAM used.

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High-capacity quantum Fibonacci coding for key distribution

In this Letter, we experimentally demonstrate structured light carrying multiple values of orbital angular momentum (OAM) in the farfield scattering region of Vogel spiral arrays of metallic nanoparticles. Using Fourier-Hankel mode decomposition analysis and interferometric reconstruction of the complex amplitude of scattered waves, we show the ability to encode well-defined numerical sequences, determined by the aperiodic spiral geometry, into azimuthal OAM values, in excellent agreement with analytical scattering theory. The generation of azimuthal sequences of OAM values by light scattering from engineered aperiodic surfaces is relevant to a number of device applications for secure optical communication, classical cryptography, and quantum cryptography.

Control of optical orbital angular momentum by Vogel spiral arrays of metallic nanoparticles.

Silicon Nanowires prepared by Metal-Assisted Chemical Etching have been nanopatterned into periodic and aperiodic array geometries displaying functionality at visible wavelengths using top-down planar processing techniques. Broadband photoluminescense enhancement up to approximately one order of magnitude is measured from golden-angle spiral arrays over a wide parameter space.

Nate Lawrence

Papers

Aperiodic arrays of active nanopillars for radiation engineering

Analytical light scattering and orbital angular momentum spectra of arbitrary Vogel spirals.

High-capacity quantum Fibonacci coding for key distribution

Control of optical orbital angular momentum by Vogel spiral arrays of metallic nanoparticles.

Nanopatterning of silicon nanowires for enhancing visible photoluminescence.