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We report on the linear and nonlinear optical response of metamaterials evoked by first and second order multipoles. The analytical ground on which our approach bases permits for new insights into the functionality of metamaterials. For the…

Parametric oscillation is a fundamental concept that underlies nonlinear wave-matter interactions, leading to generation or amplification of new frequency components. Using a temporal modulation generated by the heterodyne interference of a…

Optics · Physics 2020-01-10 Xuexue Guo , Xingjie Ni

In this Letter, we provide experimental evidence of nonlinear wave propagation in a triangular lattice of repulsive magnets supported by an elastic foundation of thin pillars and we interpret all the individual features of the nonlinear…

Pattern Formation and Solitons · Physics 2021-03-22 Weijian Jiao , Stefano Gonella

We present exact electromagnetic solitary pulses that can be experimentally obtained within nonlinear left-handed metamaterials. The effect of pulse decoherence on the modulation instability of partially incoherent electromagnetic waves is…

Materials Science · Physics 2009-11-11 M. Marklund , P. K. Shukla , L. Stenflo , G. Brodin

Hyperbolic plasmonic metamaterials provide numerous opportunities for designing unusual linear and nonlinear optical properties. We show that the modal overlap of fundamental and second-harmonic light in an anisotropic plasmonic…

The discovery of second harmonic generation in 1961 marked the birth of nonlinear optics, unlocking a range of applications from frequency conversion to quantum light generation. Yet, phase matching in bulk nonlinear crystals remains a key…

Generation of second-harmonic waves is one of the universal nonlinear phenomena that have found numerous technical applications in many modern technologies, in particular, in photonics. This phenomenon also has great potential in the field…

Mesoscale and Nanoscale Physics · Physics 2024-03-01 K. O. Nikolaev , S. R. Lake , G. Schmidt , S. O. Demokritov , V. E. Demidov

Dielectric metasurfaces have shown prominent applications in nonlinear optics due to strong field enhancement and low dissipation losses at the nanoscale. Chalcogenide glasses are one of the promising materials for the observation of…

We study the nonlinear process of second harmonic generation in photonic time-crystals, materials with refractive index that varies abruptly and periodically in time, and obtain the phase matching condition for this process. We find…

The second harmonic generation is one of the most important applications of nonlinear effect, which has attracted great interests in nonlinear optics and microwave in the past decades. To the best of our knowledge, however, generating the…

This paper concerns the scattering problem for a nonlinear medium of compact support, $D$, with second-harmonic generation. Such a medium, when probed with monochromatic light beams at frequency $\omega$, generates additional waves at…

Analysis of PDEs · Mathematics 2024-01-03 Fioralba Cakoni , Narek Hovsepyan , Matti Lassas , Michael S. Vogelius

Nonlinear metamaterials (NLMMs) have been predicted to support new and exciting domains in the manipulation of light, including novel phase matching schemes for wave mixing. Most notable is the so-called nonlinear-optical mirror, in which a…

Optics · Physics 2015-05-28 Alec Rose , Da Huang , David R. Smith

Due to the deep sub-wavelength unit cell in metamaterials, the quasi-static approximation is usually employed to describe the propagation. By making pairs of resonators, we highlight that multiple scattering also occurs at this scale and…

Applied Physics · Physics 2019-03-20 Simon Yves , Thomas Berthelot , Mathias Fink , Geoffroy Lerosey , Fabrice Lemoult

We analyze nonlinear properties of microstructured materials with negative refraction, the so-called left-handed metamaterials. We demonstrate that the hysteresis-type dependence of the magnetic permeability on the field intensity allows…

The extraordinary properties of nonlinear optical propagation processes in double-domain positive/negative index metamaterials are reviewed. These processes include second harmonic generation, three- and four-wave frequency mixing, and…

Optics · Physics 2012-04-02 Alexander K. Popov , Vladimir M. Shalaev

We employ transformation optics to optimize the generic nonlinear wave interaction of second-harmonic generation from a pair of touching metallic wires. We demonstrate a 10 orders of magnitude increase in the second-harmonic scattering…

We develop a quantitative mathematical theory that offers new perspectives on nonlinear harmonic generation in plasmonic structures arising from symmetry breaking. Focusing on second harmonic generation--the most fundamental process and the…

Analysis of PDEs · Mathematics 2026-05-04 Hongyu Liu , Zhi-Qiang Miao , Jingfeng Yao , Chengxun Yuan , Guang-Hui Zheng

Plasmonic waveguides provide an integrated platform to develop efficient nanoscale ultrafast photonic devices. Theoretical models that describe nonlinear optical phenomena in plasmonic waveguides, usually, only incorporate bulk…

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,…

Optics · Physics 2009-11-11 A. K. Popov , Vladimir M. Shalaev

We present experimental results on the observation of a bulk second-order nonlinear susceptibility derived from both free-space and integrated measurements in silicon nitride. Phase-matching is achieved through dispersion engineering of the…