Light structuring via nonlinear total angular momentum addition with flat optics.

Non-contact microcrack detection via nonlinear Lamb wave mixing and laser line arrays

We experimentally demonstrate an optics-based half-adder of two 4-phase-shift-keying (4-PSK) data channels using nonlinear wave mixing. The optics-based half-adder has two 4-ary phase-encoded inputs (i.e., SA and SB) and two phase-encoded outputs (i.e., Sum and Carry). The input quaternary base numbers {0,1,2,3} are represented by 4-PSK signals A and B with four phase levels. Along with the original signals A and B, the phase-conjugate signal copies A* and B*and phase-doubled signal copies A2 and B2 are also generated to form two signal groups SA(A, A*, A2) and SB(B, B*, B2). All of the above signals in the same signal group are (a) prepared in the electrical domain with a frequency spacing of Δf and (b) generated optically in the same IQ modulator. When combined with a pump laser, group SA mixes with group SB in a periodically poled lithium niobate nonlinear (PPLN) device. At the output of the PPLN device, both the Sum (A2B2) and the Carry (AB + A*B*) are simultaneously generated with four phase levels and two phase levels, respectively. In our experiment, the symbol rates can be varied between 5 Gbaud and 10 Gbaud. The experimental results show that (i) the measured conversion efficiency of two 5-Gbaud outputs is approximately -24 dB for Sum and approximately -20 dB for Carry, and (ii) the measured optical signal-to-noise ratio (OSNR) penalty of the 10-Gbaud Sum and Carry channels is <10 dB and <5 dB, compared with that of the 5-Gbaud channels at the BER of 3.8 × 10-3.

Optical vortex beams are made to interact via degenerate two-wave mixing in a Kerr-like nonlinear medium. Vortex mixing is shown to occur inside the medium, leading to exchange of topological charge and cascaded generation of vortex beams. A mean-field model is developed and is shown to account for the selection rules of the topological charges observed after the wave-mixing process. Fractional charges are demonstrated to follow the same rules as for integer charges.

Integrated photonics, characterized by miniaturization and dense on-chip integration, facilitates various photonic applications, such as optical communications, optical computing, and optical sensing. Due to the enhanced mode field intensity and nonlinear optical interaction efficiency, integrated photonics serves as a competitive platform for nonlinear optics. In this chapter, we summarize the transparent window, refractive index, and nonlinear refractive index of the common nonlinear integrated media. The integrated nonlinear photonics exhibits tremendous potential in a wide range of emerging applications. The progress and applications of integrated nonlinear photonics are reviewed, mainly focusing on the generation of supercontinuum (SC), optical frequency comb (OFC), and nonlinear wave mixing. Current challenges and future prospectives of this field are further discussed.

We describe the second- and third-order nonlinear response of monolayer transition metal dichalcogenides, demonstrating their potential for phase-matched nonlinear wave mixing thanks to their atomic-layer thickness implying a surface-like nonlinear interaction.

Topological quantum plasmas provide a groundbreaking platform for high-efficiency terahertz generation through nonlinear wave mixing. A comprehensive theoretical framework is presented by combining quantum hydrodynamics with Maxwell’s equations to demonstrate that Dirac fermions in materials like graphene and topological insulators exhibit a giant third-order nonlinear susceptibility enhanced by linear band dispersion, Berry phase effects, and spin-momentum locking. The predicted terahertz emission efficiency exceeds conventional semiconductor plasmas by 2–3 orders of magnitude, reaching enhancement factors of 25–1250 times across different Dirac materials. The analysis reveals that the combination of quantum plasmon dispersion and intrinsic Dirac fermion nonlinearity enables exceptional spectral tunability through pump frequency and chemical potential control. This work establishes topological quantum plasmas as a superior platform for compact, efficient on-chip terahertz sources, providing a transformative pathway to bridge the longstanding ‘THz gap’ in photonic technology.

We analyse how light-induced coherent population oscillations and ground-state Zeeman coherence in an atomic medium with degenerate two-level transitions can modify spectra of applied cw resonant radiation at the sub-mW power level. The use of mutually coherent optical fields and heterodyne detection schemes allows spectral resolution at a kHz level, well below the laser linewidth. We find that ground-state Zeeman coherence may facilitate nonlinear wave mixing, while coherent population oscillations are responsible for phase and amplitude modulation of the applied fields. Conditions for the generation of new optical fields by nonlinear wave mixing in degenerate two-level atomic media are formulated.

Nonlocal metasurfaces—metasurfaces with an engineered momentum-dependent (spatially-dispersive) response—represent an emerging direction in the field of flat optics, with applications ranging from optical computing to ultra-compact imaging systems. In this talk, we present our recent efforts on this exciting topic at the frontier of the field of metasurfaces. We broadly discuss how nonlocal designs afford new degrees of freedom that enable functionalities and performance metrics unattainable using local metasurfaces and conventional optics. As a relevant example, we present our recent work on nonlocal metasurfaces for space compression ("spaceplates"), with a focus on their bandwidth performance, physical bounds, and optimal designs.

Research on topological photonics has considerably grown, transferring condensed matter concepts of topological insulators with the discovery of the integer Quantum-Hall effect into the realm of photonics. Today, nanophotonics, which is related to light manipulation with subwavelength objects, offers new opportunities to address light properties. New degrees of freedom in the design of optical components are attained by considering the response of topological nanostructures. So far, optical metasurfaces, made of subwavelength arrangements of nanostructures, have relied on resonant phase scattering occurring in Mie resonators or ultrathin pillars. Full wavefront control requires finding sets of nanostructures that can provide 2π optical phase retardation on the incoming beam. Ultimately, and despite all the efforts in understanding the physical mechanisms leading to optimal designs, including powerful optimization methods, metasurface designs often require witless numerical parameter searches. Relying on symmetry-breaking arguments and topological properties of the associated non-Hermitian matrices representing the metasurfaces, we provide new guidelines for achieving 2π phase coverage in transmission and reflection. This framework allows us to unravel the physical principles underlying Huygens metasurfaces, showing that it exploits degeneracies of transmission- or reflection-matrices Zeros, so-called exceptional points, corresponding to transmissionless and reflectionless states. Overall, symmetry-breaking leading to a displacement of a Zero-Pole pair with its branch cut crossing the real axis, provides a very intuitive design approach for achieving full resonant phase scattering. Encircling EPs and/or zeros in the nanostructure parameter space to provide full 2π-phase are considered, entrusting metasurfaces and flat optics with additional light modulation schemes. Our results explain the importance of topological defects and how they can be manipulated for achieving realistic and insightful metasurface designs.

Revolutionary optical imaging enabled by vectorial and flat optics marks a transformative paradigm that unites subwavelength photonic engineering, full‐vector light‐field control (amplitude, phase, and polarization), and planar optical architectures. Conventional imaging systems, constrained by curved‐optics geometry and scalar diffraction theory, face intrinsic trade‐offs among spatial resolution, field of view (FOV), and system compactness. By harnessing flat optical elements such as metasurfaces and catenary‐phase devices together with vectorial manipulation, this emerging field transcends those limitations. The review highlights three fundamental breakthroughs: (1) Abrupt phase shifts in subwavelength scale enabling ultrathin, wide‐FOV planar imaging; (2) Evanescent–propagating wave conversion under appropriate near‐field coupling conditions, and vectorial optical synthetic apertures achieving far‐field super‐resolution beyond the diffraction limit; (3) Computational optics that integrates sensing and computing in a unified physical platform. These advances enable intelligent, programmable imaging systems that transcend the limitations of traditional optics, with applications spanning biomedical nanoscopy, remote sensing, and quantum information.

Nonlinear laser wave mixing in a common graphite furnace atomizer is presented as a zeptomole-level, sub-Doppler, high-resolution atomic absorption spectrophotometric method. A nonplanar three-dimensional wave-mixing optical setup is used to generate the signal beam in its own space. Signal collection is efficient and convenient using a template-based optical alignment. The graphite furnace atomizer offers advantages including fast and convenient introduction of solid, liquid, or gas analytes, clean atomization environment, and minimum background noise. Taking advantage of the unique features of the wave-mixing optical method and those of the graphite furnace atomizer, one can obtain both excellent spectral resolution and detection sensitivity. A preliminary concentration detection limit of 0.07 parts-per-quadrillion and a preliminary mass detection limit of 0.7 ag or 8 zmol are determined for rubidium using a compact laser diode as the excitation source.

A commonly accepted picture of the transition dipole structure of colloidal semiconductor quantum dots is the so-called 2D degenerate dipole. Optical transitions in CdSe-ZnS quantum dot occur primarily for the low energy state for which the total spin angular momentum projection axis is J=±1. These transitions involve X+iY and X-iY combinations of the (hole) Bloch functions along the QD "X" and "Y" axis; in a spherical approximation, there are equal dipole strengths along two orthogonal axes in the QD frame resulting in a 2D degenerate dipole. This 2D dipole model has been used by Bawendi et al.[1] in their studies of quantum dot emission properties and Enderlein et al.[2] in their studies of quantum dot radiation patterns, and also provides a useful prototype of the complicated dipole structure for chiral nanosystems. Despite reliance on this model, a definitive study demonstrating the dipole structure of CdSe-ZnS quantum dots has not yet been performed. However, as demonstrated by Efros[3], transitions between the |1Se > z electron state and |1Se3/2 > hole state contain projections along the quantum dot Z-axis. During excitation, this transition is forbidden; however, non-radiative energy transfer can make this transition allowed during emission. This 3rd dipole component can, in principle, produce a noticeable effect in the observed linear polarization anisotropy of the light emitted from the quantum dot and observed interference patterns.

We demonstrate optical pattern recognition between two independent 5-Gbaud QPSK inputs using nonlinear wave mixing. The output constellation symbols correspond to the different pattern recognition cases, where the upper-right symbol represents the matched cases.

Photonic spin Hall effect (SHE) refers to the transverse separation of spin photons in refraction and reflection phenomena. The photonic SHE has been investigated in various optical systems including air–glass interfaces, interfaces containing 2D materials, random media, etc. Here, the spin–orbit coupling (SOC) in nonlinear uniaxial crystals is investigated, and the SHE of second‐harmonic photons is demonstrated theoretically and experimentally. The generation and evolution processes of nonlinear spin photons within the crystal are visualized by the derived four wave coupling equations and wavevector‐varying Berry phases. For a focused fundamental beam, two cascaded SOCs occurring in the fundamental and second‐harmonic fields are connected by the nonlinear wave mixing near the focal position. Thus the SHE of nonlinear photons depends on the focal position, different strongly from linear photons whose SHE is independent of the focal position. Similar to the focal‐position‐dependent SHE, the focal‐position‐dependent optical vortex generations are also demonstrated for the nonlinear fields. Finally, a high‐speed modulation scheme for the SHE is proposed based on an electro‐optical polarization controller, which routes nonlinear spin photons into different destinations. These findings deepen the understanding of spin–orbit coupling in nonlinear systems and facilitate the development of spin multiplexed electrooptic devices.

Silicon nitride is widely used in integrated photonics for optical nonlinear wave mixing due to its low optical losses combined with relatively high nonlinear optical properties and a wide‐range transparency window. It is known that a higher concentration of Si in silicon‐rich nitride (SRN) magnifies both the nonlinear response and optical losses, including nonlinear losses. To address the trade‐off, four‐wave mixing (FWM) is implemented in over a hundred SRN waveguides prepared by plasma‐enhanced chemical vapor deposition in a wide range of SRN refractive indices varying between 2.5 and 3.2 (measured in the C‐band). It is determined that SRN with a refractive index of about 3 maximizes the FWM efficiency for continuous‐wave operation, indicating that the refractive index of SRN is indeed a crucial optimization parameter for nonlinear optics applications. The FWM efficiency is limited by large nonlinear optical losses observed in SRN waveguides with indices larger than 2.7, which are not related to two‐photon absorption. Finally, the third‐order susceptibility and the nonlinear refractive index are estimated for multiple SRN refractive indices, and, specifically, the nonlinearities as large as and are estimated in a waveguide with an SRN refractive index of 3.2.