Twisted light in a nonlinear mirror

We show that unique optical properties of metamaterials open unlimited prospects to “engineer” light itself. For example, we demonstrate a novel way of complex light manipulation in few-mode optical fibers using metamaterials highlighting how unique properties of metamaterials, namely the ability to manipulate both electric and magnetic field components, open new degrees of freedom in engineering complex polarization states of light. We discuss several approaches to ultra-compact structured light generation, including a nanoscale beam converter based on an ultra-compact array of nano-waveguides with a circular graded distribution of channel diameters that coverts a conventional laser beam into a vortex with configurable orbital angular momentum and 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. Such beam converters is likely to enable a new generation of on-chip or all-fiber structured light applications. We also present our initial theoretical studies predicting that vortex-based nonlinear optical processes, such as second harmonic generation or parametric amplification that rely on phase matching, will also be strongly modified in negative index materials. These studies may find applications for multidimensional information encoding, secure communications, and quantum cryptography as both spin and orbital angular momentum could be used to encode information; dispersion engineering for spontaneous parametric down-conversion; and on-chip optoelectronic signal processing.

In recent years, considerable research has been carried out relative to the electromagnetic (EM) propagation and refraction characteristics in metamaterials with emphasis on the origins of negative refractive index. Negative refractive index may be introduced in metamaterials via different methods; one such is the con- dition whereby the Poynting vector of the EM wave is in opposition to the group velocity in the material. Alternatively, negative refractive index also occurs when the group and phase velocities in the medium are in opposition. The latter phenomenon has been extensively investigated in the literature, including recent work involving chiral metamaterials with material dispersion up to the first order. This paper examines the pos- sible emergence of negative refractive index in dispersive chiral metamaterials with material dispersion up to the second order. The motivation is to determine if using second- as opposed to first-order dispersion may lead to more practical negative index behavior. A spectral approach combined with a slowly time-varying phasor analy- sis is applied, leading to the analytic derivation of EM phase and group velocities, and the resulting phase and group velocities and the corresponding phase and group indices are evaluated by selecting somewhat arbitrary dispersive parameters. The results indicate the emergence of negative index (via negative phase indices along with positive group indices, as reported in the literature) or negative index material (NIM) behavior over infor- mation bandwidths in the low RF range. The second-order results are not significantly better than those for first-order results based on the theoretical analysis; however, greater parametric flexibility exists for the second-order system leading to the higher likelihood of achieving NIM over practical frequency bands. The velocities and indices computed using the Lorentzian and Condon models yield an NIM bandwidth around 200 − 400 Mrad∕sec, about 2 orders of magnitude higher than that for the parametric approach; more impor- tantly, NIM is found not to occur in the first order when using practical models. © 2015 Society of Photo-Optical

Optical vortices are a new kind of laser beam and receiving more and more attention currently.The complex amplitudes of optical vortices comprise a helical term exp (il),with l being the topological charge and the azimuthal angle.Each photon in optical vortices carries the orbital angular momentum (OAM) with a value of lħ,where ħ is the Planck's constant divided by 2.The topological charge l is the eigenvalue of optical vortices,and determines the helical wavefront distribution,thus also known as OAM state.Moreover,such an OAM state can be an infinite integer state. And vortices with various OAM states are orthogonal to each other,making it possible to be employed in high capacity data-transmission system.In addition,the above unique features contribute to their widely applications in lots of areas such as optical tweezers and spanners,rotation detection,quantum entanglement,etc.In these applications,detecting OAM states is basic,and greatly significant.Recently researchers have developed lots of approaches to detecting the OAM states,including the methods of interference,diffraction gratings,metasurface,etc.Of such approaches,the scheme of diffraction gratings is the simplest and most widely used,where one or more diffraction gratings are employed. When optical vortices propagate through such gratings,the OAM states are acquired immediately through capturing and analyzing the distinct OAM-related diffraction patterns.In this review,we focus on the techniques of detecting OAM states through diffraction gratings,which have been demonstrated by our group and other researchers.Some of the main detection gratings,including double-slit,triangle aperture and slit,angular slit,cylindrical lens,graduallychanging-period grating,annular grating,are introduced.In addition,schemes like composite fork grating,Dammann vortex grating and integrated Dammann grating,are presented to detect the OAM state for coaxial multiplexed vortices. Besides diagnosing OAM state,measuring the intensity proportion of each OAM channel,known as OAM spectrum, in multiplexed vortices is also necessary in some cases.Therefore we also introduce the ways to measure the OAM spectrum,e.g.the OAM mode sorter,the gray-scale algorithm.

Light with helical phase structures, carrying quantized orbital angular momentum (OAM), has many applications in both classical and quantum optics, such as high-capacity optical communications and quantum information processing. Frequency conversion is a basic technique to expand the frequency range of the fundamental light. The frequency conversion of OAM-carrying light gives rise to new physics and applications such as up-conversion detection of images and generation of high dimensional OAM entanglements. Quasi-phase matching (QPM) nonlinear crystals are good candidates for frequency conversion, particularly due to their high-valued effective nonlinear coefficients and no walk-off effect. Here we report the first experimental second-harmonic generation (SHG) of an OAM-carried light with a QPM crystal, where a UV light with OAM of 100 ℏ is generated. OAM conservation is verified using a specially designed interferometer. With a pump beam carrying an OAM superposition of opposite sign, we observe interesting interference phenomena in the SHG light; specifically, a photonics gear-like structure is obtained that gives direct evidence of OAM conservation, which will be very useful for ultra-sensitive angular measurements. Besides, we also develop a theory to reveal the underlying physics of the phenomena. The methods and theoretical analysis shown here are also applicable to other frequency conversion processes, such as sum frequency generation and difference-frequency generation, and may also be generalized to the quantum regime for single photons.

Optical vortex beams, carrying orbital angular momentum (OAM), are of great interest for applications in optical communications, particle manipulation, and quantum information processing. However, achieving high‐efficiency generation and manipulation of vortex beams with a single compact element, particularly in the visible range, remains challenging. Here, we demonstrate laser‐written geometric phase fork gratings in silica glass that enable simultaneous generation and propagation control of vortex beams with an efficiency up to 98.4% at 515 nm. By tailoring the phase‐gradient period and topological charge ( l = 1–100), we achieve tunable control over the vortex beam's topological charge, diameter, and diffraction position. The fabricated gratings maintain high efficiency across a broad spectral range from 450 to 690 nm. Furthermore, we demonstrate spin–orbit coupling between incident vortices and fork gratings, verifying that the output OAM values follow the expected addition rule l out = l in ± l fork . In addition, the fork gratings exhibit excellent thermal stability (up to 800°C) and optical damage threshold (close to pristine silica glass). These results establish nanopore‐based geometric‐phase fork gratings as a scalable, broadband, high‐performance platform with outstanding thermal and optical tolerance for next‐generation OAM photonics.

Second harmonic generation and optical parametric amplification in negative-index metamaterials (NIMs) are studied. The opposite directions of the wave vector and the Poynting vector in NIMs results in a "backward" phase-matching condition, causing significant changes in the Manley-Rowe relations and spatial distributions of the coupled field intensities. It is shown that absorption in NIMs can be compensated by backward optical parametric amplification. The possibility of distributed-feedback parametric oscillation with no cavity has been demonstrated. The feasibility of the generation of entangled pairs of left- and right-handed counter-propagating photons is discussed.

Light orbital angular momentum (OAM) has been recognized as a new promising resource for classical and quantum information applications. In contrast to the spin angular momentum, the OAM is an inherently multidimensional. Thus, the information can be encoded in the higher-dimensional OAM alphabets. Recently, Marrucci et al. have invented a new device named q-plate (QP), made of liquid crystal cell patterned in such a way to introduce a topological charge q at the transverse plane, which is able to generate a well-defined values of photon OAM. My research has been aimed at investigating the physics of the QP, of the optical fields that it generates and of its possible applications for optical communication and quantum information. We studied both theoretically and experimentally a novel set of non-orthogonal but over-complete paraxial modes, named Hypergeometric-Gaussian modes, that is typically associated with OAM-carrying optical fields. We have also found the light propagation kernel inside the QP and we have shown analytically that if small losses due to reflection, absorption, and scattering are neglected, the QP can convert the photon spin into OAM with up to 100 \% efficiency. We implemented a technique to control the QP optical retardation by tuning the QP temperature. At the optimal temperature, the QP can generate a beam with up to 97\% efficiency. Moreover, the OAM state generated by QP can be rotated easily in the 2D OAM Hilbert space by proper manipulation of the input polarization state, a fact which opens a new way of beam shape controlling in MHz scale. We also performed a novel way to encode and read two bits information on the 4D OAM space by using only one QP. Finally, we experimentally demonstrated the transfer of quantum information from spin to OAM and vice versa, including the case of bi-photon states having quantum correlations. Furthermore, by exploiting these quantum information transfer devices, we demonstrated the Hong-Ou-Mandel effect and the optimal quantum cloning with OAM-carrying photons.

Twisted light with orbital angular momentum (OAM) has been extensively studied for applications in quantum and classical communications, microscopy, and optical micromanipulation. Ejecting high angular momentum states of a whispering gallery mode (WGM) microresonator through a grating-assisted mechanism provides a scalable, chip-integrated solution for OAM generation. However, demonstrated OAM microresonators have exhibited a much lower quality factor (Q) than conventional WGM resonators (by >100×), and an understanding of the limits on Q has been lacking. This is crucial given the importance of Q in enhancing light-matter interactions. Moreover, though high-OAM states are often desirable, the limits on what is achievable in a microresonator are not well understood. Here, we provide insight on these two questions, through understanding OAM from the perspective of mode coupling in a photonic crystal ring and linking it to coherent backscattering between counter-propagating WGMs. In addition to demonstrating high-Q (105 to 106), a high estimated upper bound on OAM ejection efficiency (up to 90%), and high-OAM number (up to l = 60), our empirical model is supported by experiments and provides a quantitative explanation for the behavior of Q and the upper bound of OAM ejection efficiency with l. The state-of-the-art performance and understanding of microresonator OAM generation opens opportunities for OAM applications using chip-integrated technologies.

Wide bandgap semiconductors such as gallium nitride (GaN) are essential constituents of future optical circuits, as their optical response can accommodate a broad wavelength range while suppressing two-photon absorption and free-carrier absorption effects that are encountered with silicon (Si) structures. Their direct wide bandgap is also favourable for the incorporation of active elements. Furthermore, nonlinear optical processes can be harnessed by exploiting the higher-order susceptibility tensors of the crystal structure to achieve advanced light control modalities, enabling all-optical processing and the generation of entangled photon states. We will report on nonlinear frequency conversion from the telecom range via second harmonic generation (SHG) and third harmonic generation (THG) in suspended gallium nitride slab photonic crystal (PhC) cavities on silicon, under continuous-wave resonant excitation. Genetic optimization is applied to sweep parameter space for the highest cavity quality factors, and simultaneously accounting for power in-coupling. While there is a clear trade-off theoretically between coupling efficiency and Q-factor for a given cavity design, the upper limit on the Q-factor that is imposed by loss channels, given the disorder figure of current fabrication technology, makes room for introducing improved far-field coupling to enhance nonlinear processes without sacrificing the experimentally achievable light confinement. Far-field coupling is addressed through various PhC cavity designs, which enable the excitation of the fundamental mode with a Gaussian beam. Optimized two-dimensional PhC cavities with increased far-field coupling have been characterized with quality factors as high as 44′000, approaching the computed theoretical values. The strong enhancement in light confinement has enabled second harmonic generation (SHG) under continuous-wave excitation, with up-conversion from both 1300 nm and 1550 nm wavelength bands, confirmed by spectral and power dependence measurements. At 1550 nm, normalized SHG conversion efficiency as large as 2.4×10−3 W−1 are measured as well as simultaneous THG. SHG emission power of up to 0.74 nW has been detected without saturation

We present in this work the design of second harmonic generation process in χ <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(2)</sup> nonlinear waveguides by a new time domain simulator. The presented Hertzian potential formulation (HPF) is applied to quasi-phase-matched GaAs/AlGaAs nonlinear waveguide with dielectric discontinuities. With the introduction of the presented rigorous time domain method it is possible to represent the physical phenomena such as light propagation and second harmonic generation (SHG) process inside a nonlinear optical device with a good convergent solution and low computational cost. We first check the convergence of the HPF approach by comparing the numerical results with experimental ones for a GaAs/AlGaAs nonlinear waveguide with a fundamental mode at λ <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">FU</inf> =1.955 μm coupled to a coprapagating second-harmonic SH mode (λ <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">SH</inf> =9.775 μm) through an appropriate nonlinear susceptibility coefficient. Then we apply the modelling to a GaAs/AlGaAs ridge waveguide with λ <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">FU</inf> =1.55 μm and λ <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">SH</inf> =0.775 μm by evaluating the second harmonic conversion efficiency versus the waveguide length. The model is generic and can be applied also to periodic microwave waveguides.

The non-linear optical process of laser harmonic generation (HG) enables the creation of high quality pulses of UV or even X-ray radiation, which have many potential uses at the frontiers of experimental science, ranging from lensless microscopy to ultrafast metrology and chiral science. Although many of the promising applications are enabled by generating harmonic modes with orbital angular momentum (OAM), independent control of the harmonic frequency and OAM level remains elusive. Here we show, through a theoretical approach, validated with 3D simulations, how unique 2-D harmonic progressions can be obtained, with both frequency and OAM level tuned independently, from tailored structured targets in both reflective and transmissive configurations. Through preferential selection of a subset of harmonic modes with a specific OAM value, a controlled frequency comb of circularly polarised harmonics can be produced. Our approach to describe HG, which simplifies both the theoretical predictions and the analysis of the harmonic spectrum, is directly applicable across the full range of HG mechanisms and can be readily applied to investigations of OAM harmonics in other processes, such as OAM cascades in Raman amplification, or the analysis of harmonic progressions in nonlinear optics.

Optical vortex beams are profiled as helical wavefronts with a phase singularity carrying an orbital angular momentum (OAM) associated with their spatial distribution. The transverse intensity distribution of a conventional optical vortex has a strong dependence on the carried topological charge. However, perfect optical vortex (POV) beams have their transverse intensity distribution independent of their charge. Such “size-invariant” POV beams have found exciting applications in optical manipulation, imaging, and communication. In this paper, we investigate the use of POV modes in the efficient generation of high-dimensional quantum states of light. We generate heralded single photons carrying OAM using spontaneous parametric downconversion (SPDC) of POV beams. We show that the heralding efficiency of the SPDC single photons generated with a POV pump is greater than that with normal optical vortex beams. The dimensionality of the two-photon OAM states is increased with POV modes in the pump and projective measurements using Bessel–Gaussian vortex modes that give POV, instead of Laguerre–Gaussian modes.

The nonlinear process of second harmonic generation (SHG) in monolayer (1L) transition metal dichalcogenides (TMD), like WS2, strongly depends on the polarization state of the excitation light. By combination of plasmonic nanostructures with 1L-WS2 by transferring it onto a plasmonic nanoantenna array, a hybrid metasurface is realized impacting the polarization dependency of its SHG. Here, we investigate how plasmonic dipole resonances affect the process of SHG in plasmonic-TMD hybrid metasurfaces by nonlinear spectroscopy. We show that the polarization dependency is affected by the lattice structure of plasmonic nanoantenna arrays as well as by the relative orientation between the 1L-WS2 and the individual plasmonic nanoantennas. In addition, such hybrid metasurfaces show SHG in polarization states, where SHG is usually forbidden for either 1L-WS2 or plasmonic nanoantennas. By comparing the SHG in these channels with the SHG generated by the hybrid metasurface components, we detect an enhancement of the SHG signal by a factor of more than 40. Meanwhile, an attenuation of the SHG signal in usually allowed polarization states is observed. Our study provides valuable insight into hybrid systems where symmetries strongly affect the SHG and enable tailored SHG in 1L-WS2 for future applications.

Robust high-order optical vortices are much in demand for applications in optical manipulation, optical communications, quantum entanglement and quantum computing. However, in numerous experimental settings, a controlled generation of optical vortices with arbitrary orbital angular momentum remains a challenge. Here, we present a concept of “optical vortex ladder” for the stepwise generation of optical vortices through Sisyphus pumping of pseudospin modes in photonic graphene. The ladder is applicable in various lattices with Dirac-like structures. Instead of conical diffraction and incomplete pseudospin conversion under conventional Gaussian beam excitations, the vortices produced in the ladder arise from non-trivial topology and feature diffraction-free Bessel profiles, thanks to the refined excitation of the ring spectrum around the Dirac cones. By employing a periodic “kick” to the photonic graphene, effectively inducing the Sisyphus pumping, the ladder enables tunable generation of optical vortices of any order even when the initial excitation does not involve any orbital angular momentum. The optical vortex ladder stands out as an intriguing non-Hermitian dynamical system, and, among other possibilities, opens a pathway for applications of topological singularities in beam shaping and wavefront engineering.

Point of zero charge of a corundum-water interface probed with optical second harmonic generation (SHG) and atomic force microscopy (AFM): New approaches to oxide surface charge