Spin-orbit microlaser emitting in a four-dimensional Hilbert space.

A step towards the next generation of high-capacity, noise-resilient communication and computing technologies is a substantial increase in the dimensionality of information space and the synthesis of superposition states on an N-dimensional (N > 2) Hilbert space featuring exotic group symmetries. Despite the rapid development of photonic devices and systems, on-chip information technologies are mostly limited to two-level systems owing to the lack of sufficient reconfigurability to satisfy the stringent requirement for 2(N - 1) degrees of freedom, intrinsically associated with the increase of synthetic dimensionalities. Even with extensive efforts dedicated to recently emerged vector lasers and microcavities for the expansion of dimensionalities1-10, it still remains a challenge to actively tune the diversified, high-dimensional superposition states of light on demand. Here we demonstrate a hyperdimensional, spin-orbit microlaser for chip-scale flexible generation and manipulation of arbitrary four-level states. Two microcavities coupled through a non-Hermitian synthetic gauge field are designed to emit spin-orbit-coupled states of light with six degrees of freedom. The vectorial state of the emitted laser beam in free space can be mapped on a Bloch hypersphere defining an SU(4) symmetry, demonstrating dynamical generation and reconfiguration of high-dimensional superposition states with high fidelity.

Design approach for photonic quasicrystals to enable multiple nonlinear interactions.

Photonic quasicrystals are poised to transform the field of nonlinear light-matter interactions due to their ability to support an unlimited number of combinations of wavevectors in their reciprocal lattices. Such greatly enhanced flexibility enabled by k-space engineering makes photonic quasicrystals a promising platform for novel approaches to multi-wavelength conversion, supercontinuum generation, and development of classical and quantum optical sources. Here, we develop a new design method for nonlinear photonic quasicrystals, consisting of a combination of one nonlinear material and one linear material that can simultaneously fulfill phase-matching conditions for a desired number of nonlinear optical interactions as long as the frequencies of the interacting waves are outside of the bandgaps of the quasicrystal structure. Our approach provides enhanced design flexibility, enabling new pathways to designing compact, integrated nonlinear photonic devices and systems on a chip.

Spatio-temporal controlled filamentation using higher order Bessel-Gaussian beams integrated in time.

We demonstrate a new method for a systematic, dynamic, high-speed, spatio-temporal control of femtosecond light filamentation in BK7 as a particular example of nonlinear medium. This method is based on using coherent conjugate asymmetric Bessel-Gaussian beams to control the far-field intensity distribution and in turn control the filamentation location. Such spatio-temporal control allows every femtosecond pulse to have a unique intensity distribution that results in the generation of structured filamentation patterns on demand. The switching speed of this technique is dependent on the rise time of the acousto-optic deflector, which can operate in the MHz range while having the ability to handle high peak power pulses that are needed for nonlinear interactions. The proposed and demonstrated spatio-temporal control of structured filaments can enable generation of large filament arrays, opto-mechanical manipulations of water droplets for fog clearing, as well as engineered radiofrequency plasma antennas.

Mode-sorter design using continuous supersymmetric transformation.

We propose to use a continuous supersymmetric (SUSY) transformation of a dielectric permittivity profile in order to design a photonic mode sorter. The iso-spectrality of the SUSY transformation ensures that modes of the waveguide preserve their propagation constants while being spatially separated. This global matching of the propagation constants, in conjunction with the adiabatic modification of the refractive index landscape along the propagation direction, results in the negligible modal cross-talk and low scattering losses in the sorter. We show that a properly optimized SUSY mode sorter outperforms a standard asymmetric Y-splitter by reducing the cross-talk by at least two orders of magnitude. Moreover, the SUSY sorter is capable of sorting either transverse-electric or transverse-magnetic polarized modes and operates in a broad range of wavelengths. At the telecommunication wavelength, the 300-µm-long SUSY sorter provides the cross-talk of -35 dB and a broad operation bandwidth. The design proposed here paves the way toward efficient signal manipulation in integrated photonic devices.

Distributed feedback lasing based on a negative-index metamaterial waveguide.

This Letter lays the foundation of a new type of distributed feedback (DFB) laser whose optical feedback is due to the evanescent coupling between an active positive-index material (PIM) waveguide and a lossy negative-index metamaterial (NIM) waveguide. Active PIM-NIM coupled-mode equations are presented and solved to characterize the dispersion relation, resonant optical gain, and lasing. The photonic bandgap of this grating-less DFB laser does not depend on a Bragg wavenumber, but depends on the difference between the wavenumbers of the PIM and NIM waveguides; controlling this wavenumber difference allows for single-mode lasing and, ultimately, single-mode broadband lasing.

Nanoscale orbital angular momentum beam instabilities in engineered nonlinear colloidal media.

Colloidal media with well-defined optical properties have been widely used as model systems in many fundamental and applied studies of light-matter interactions in complex media. Recent progress in the field of engineered nanoscale optical materials with fundamentally new physical properties opens new opportunities for tailoring the properties of colloids. In this work, we experimentally demonstrate the evolution of the optical vortex beams of different topological charges propagating in engineered nano-colloidal suspension of negative polarizability with saturable nonlinearities. Due to the high power of the incident beam, the modulation instability leads to an exponential growth of weak perturbations and thus splits the original vortex beam into a necklace beam consisting of several bright spots. At a fixed power, the number of observed bright spots is intrinsically determined by the topological charge of the incident beam and agrees well with the predictions of our linear stability analysis and numerical simulations. Besides contributing to the fundamental science of light-matter interactions in engineered soft-matter media, this work opens new opportunities for dynamic optical manipulation and transmission of light through scattering media as well as formation of complex optical patterns and light filamentation in naturally existing colloids such as fog and clouds.

Reconfiguring structured light beams using nonlinear metasurfaces.

Ultra-compact, low-loss, fast, and reconfigurable optical components, enabling manipulation of light by light, could open numerous opportunities for controlling light on the nanoscale. Nanostructured all-dielectric metasurfaces have been shown to enable extensive control of amplitude and phase of light in the linear optical regime. Among other functionalities, they offer unique opportunities for shaping the wave front of light to introduce the orbital angular momentum (OAM) to a beam. Such structured light beams bring a new degree of freedom for applications ranging from spectroscopy and micromanipulation to classical and quantum optical communications. To date, reconfigurability or tuning of the optical properties of all-dielectric metasurfaces have been achieved mechanically, thermally, electrically or optically, using phase-change or nonlinear optical materials. However, a majority of demonstrated tuning approaches are either slow or require high optical powers. Arsenic trisulfide (As2S3) chalcogenide glass offering ultra-fast and large χ(3)nonlinearity as well as a low two-photon absorption coefficient in the near and mid-wave infrared spectral range, could provide a new platform for the realization of fast and relatively low intensity reconfigurable metasurfaces. Here, we design and experimentally demonstrate an As2S3 chalcogenide glass based metasurface that enables reshaping of a conventional Hermite-Gaussian beam with no OAM into an OAM beam at low intensity levels, while preserves the original beam's amplitude and phase characteristics at high intensity levels. The proposed metasurface could find applications for a new generation of optical communication systems and optical signal processing.

Supersymmetry-guided method for mode selection and optimization in coupled systems.

Single-mode operation of coupled optical systems, such as optical-fiber bundles, lattices of photonic waveguides, or laser arrays, requires an efficient method to suppress unwanted super-modes. Here, we propose a systematic supersymmetry-based approach to selectively eliminate modes of such systems by decreasing their lifetime relative to the lifetime of the mode of interest. The proposed method allows to explore the opto-geometric parameters of the coupled system and to maximize the relative lifetime of a selected mode. We report a 10-fold increase in the relative lifetime of the fundamental modes of large one-dimensional coupled arrays in comparison to simple "head-to-tail" coupling geometries. The ability to select multiple supported modes in one- and two-dimensional arrays is also demonstrated.

Supercharge optical arrays.

We introduce the notion of a supercharge optical array synthesized according to supersymmetric charge operators. Starting from an arbitrary array, mathematical supersymmetry transformation can be used systematically to create a zero-energy physical state below the ground state of the super-partner array. This zero mode, which is pinned deep in the mid-gap of the corresponding supercharge array owing to the square-root spectral relationship between a supercharge and a super-Hamiltonian array, is shown to be protected because of the chiral symmetry inherent to a supercharge array. A supercharge array can be used in practical applications to design a discrete optical system of waveguides or coupled resonators where the mid-gap zero mode facilitates robust light dynamics in either spatial or time domain.

Focus issue introduction: synergy of structured light and structured materials.

Structured light beams, such as optical vortices, vector beams, and non-diffracting beams, have been recently studied in a variety of fields, such as optical manipulations, optical telecommunications, nonlinear interactions, quantum physics, and 'super resolution' microscopy.. Their unique physical properties, such as annular intensity profile, helical wavefront and orbital angular momentum, give rise to a plethora of new, fundamental light-matter interactions and device applications. Recent progress in nanostructured materials, including metamaterials and metasurfaces, opened new opportunities for structured light generation on the microscale that exceed the capabilities of bulk-optics approaches such as computer generated holography and diffractive optics. Furthermore, structured optical fields may interact with matters on the subwavelength scale to yield new physical effects, such as spin-orbital momentum coupling. This special issue of Optics Express focuses on the state-of-the-art fundamental research and emerging technologies and applications enabled by the interplay of "structured light" and "structured materials".

Experimental Demonstration of Demagnifying Hyperlens.

The emergence of optical metamaterials opens new opportunities for spatial pattern compression from the micro- to nanoscale. By exploiting strongly anisotropic optical properties of engineered nanostructures, we realize the first experimental demonstration of demagnifying hyperlens enabling optical patterning below the diffraction limit. We show that the diffraction-limited features on a mask can be demagnified to form the subwavelength patterns on the photoresist using visible light.

Probing metamaterials with structured light.

Photonic metamaterials and metasurfaces are nanostructured optical materials engineered to enable properties that have not been found in nature. Optical characterization of these structures is a challenging task. We report a reliable technique that is particularly useful for characterization of phase properties introduced by small and spatially inhomogeneous samples of metamaterials and metasurfaces. The proposed structured light, or vortex based interferometric method is used to directly visualize phase changes introduced by subwavelength-thick nanostructures. In order to demonstrate the efficiency of the proposed technique, we designed and fabricated several metasurface samples consisting of metal nano-antennas introducing different phase shifts and experimentally measured phase shifts of the transmitted light. The experimental results are in good agreement with numerical simulations and with the designed properties of the antenna arrays. Due to the presence of the singularity in the vortex beam, one of the potential applications of the proposed approach based on structured light is step-by-step probing of small fractions of the micro-scale samples or images.

Structuring Light by Concentric-Ring Patterned Magnetic Metamaterial Cavities.

Ultracompact and tunable beam converters pose a significant potential for modern optical technologies ranging from classical and quantum communication to optical manipulation. Here we design and demonstrate concentric-ring patterned structures of magnetic metamaterial cavities capable of tailoring both polarization and phase of light by converting circularly polarized light into a vector beam with an orbital angular momentum. We experimentally illustrate the realization of both radially and azimuthally polarized vortex beams using such concentric-ring patterned magnetic metamaterials. These results contribute to the advanced complex light manipulation with optical metamaterials, making it one step closer to realizing the simultaneous control of polarization and orbital angular momentum of light on a chip.

High-Efficiency All-Dielectric Metasurfaces for Ultracompact Beam Manipulation in Transmission Mode.

Metasurfaces are two-dimensional structures enabling complete control on light amplitude, phase, and polarization. Unlike plasmonic metasurfaces, silicon structures facilitate high transmission, low losses, and compatibility with existing semiconductor technologies. We experimentally demonstrate two examples of high-efficiency polarization-sensitive dielectric metasurfaces with 2π phase control in transmission mode (45% transmission efficiency for the vortex converter and 36% transmission efficiency for the beam steering device) at telecommunication wavelengths. Silicon metasurfaces are poised to enable a versatile platform for the realization of all-optical circuitry on a chip.

Nonlinear parity-time-symmetric transition in finite-size optical couplers.

Parity-time-symmetric (PT-symmetric) optical waveguide couplers offer a great potential for future applications in integrated optics, such as ultracompact reconfigurable all-optical signal processing. Here, we predict a nonlinearly triggered transition from a full to a broken PT-symmetric regime in finite-size systems described by smooth permittivity profiles and, in particular, in a conventional discrete waveguide directional coupler configuration with a rectangular profile. For these systems, we show that this phase transition occurs in PT-symmetric couplers, regardless of the details of their geometry, therefore suggesting a practical route for experimental realization of such systems.

Necklace beam generation in nonlinear colloidal engineered media.

Modulational instability is a phenomenon that reveals itself as the exponential growth of weak perturbations in the presence of an intense pump beam propagating in a nonlinear medium. It plays a key role in such nonlinear optical processes as supercontinuum generation, light filamentation, rogue waves, and ring (or necklace) beam formation. To date, a majority of studies of these phenomena have focused on light-matter interactions in self-focusing Kerr media existing in nature. However, a large and tunable nonlinear response of a colloidal suspension can be tailored at will by judiciously engineering the optical polarizability. Here, we analytically and numerically show the possibility of necklace beam generation originating from spatial modulational instability of vortex beams in engineered soft-matter nonlinear media with different types of exponential nonlinearity.

Spinning light on the nanoscale.

Light beams with orbital angular momentum have significant potential to transform many areas of modern photonics from imaging to classical and quantum communication systems. We design and experimentally demonstrate an ultracompact array of nanowaveguides with a circular graded distribution of channel diameters that coverts a conventional laser beam into a vortex with an orbital angular momentum. The proposed nanoscale beam converter is likely to enable a new generation of on-chip or all-fiber structured light applications.

Broadband Spin and Orbital Momentum Modulator Using Self-Assembled Nanostructures.

The structural symmetry of solids plays an important role in defining their linear and nonlinear optical properties. The quest for versatile, cost-effective, large-scale, and defect-free approaches and materials platforms for tailoring structural and optical properties on demand is underway since decades. A self-assembled spherulite material comprised of synthesized molecules with large dipole moments aligned azimuthally, forming a vortex polarity with spontaneously broken symmetry, is experimentally demonstrated. This unique self-assembled structure enables new linear and nonlinear light-matter interactions, including generating optical vortex beams with complex spin states and on-demand topological charges at the fundamental, doubled, and tripled frequencies. This work will likely enable numerous applications in areas such as high-dimensional quantum information processing with large capacity and high security, spatiotemporal optical vortices, and a novel optical manipulation and trapping platform.

Twisting light with hyperbolic metamaterials.

We propose a novel, miniaturized astigmatic optical element based on a single biaxial hyperbolic metamaterial that enables the conversion of Hermite-Gaussian beams into vortex beams carrying an orbital angular momentum and vice versa. As an example, we design a biaxial anisotropic metamaterial that introduces a π/2 phase shift between two orthogonal components of a Hermite-Gaussian beam due to the optical path difference and at the same time astigmatically focuses these orthogonal components such that they recombine in a symmetric Laguerre-Gaussian beam. We design the proposed device using an array of silver nanowires in an MgF(2) matrix. The advantages of the proposed approach over the existing bulk optics based techniques include compactness and therefore, compatibility with ultra-compact opto-electronic circuits, potential re-configurability and an increased tolerance to misalignment.

Twisted light in a nonlinear mirror.

Opposite directionality of the Poynting vector and the wave vector, an inherent property of negative index metamaterials (NIMs), was predicted to enable backward phase-matching condition for a second harmonic generation (SHG) process. As a result, such a nonlinear negative index slab acts as a nonlinear mirror. In this Letter, we predict that SHG with structured light carrying orbital angular momentum (OAM) and propagating in NIMs results in a possibility of generating a backward propagating beam with simultaneously doubled frequency, OAM, and reversed rotation direction of the wavefront. These results may find applications in high-dimensional communication systems, quantum information processing, and optical manipulation on a nanoscale.