In this paper, we establish the sharp critical and subcritical trace Trudinger–Moser Adams inequalities on half-spaces prove existence of their extremals through method based Fourier rearrangement, harmonic extension scaling invariance. These (Theorems 1.1 1.2) 1.4, 1.5, 1.10 1.11) can be considered as borderline case Sobolev first higher orders half-spaces. Furthermore, an application, show le...

Heavily doped semiconductors have emerged as tunable low-loss plasmonic materials at mid-infrared frequencies. In this article we investigate nonlinear optical phenomena associated with high concentration of free electrons. We use a hydrodynamic description to study electron dynamics in heavily up third-order terms, which are usually negligible for noble metals. find that cascaded third-harmoni...

Harmonic comb states have proven to be ubiquitous in mid-IR quantum cascade lasers. We report here on robust, pure, self-starting harmonic mode locking Copper-based double-metal THz Different orders can excited the same laser cavity depending pumping condition, and stable combs spanning more than 600 GHz at 80 K are reported. Such devices RF injected, free running coherence is assessed by means...

We study the rational harmonic mode-locking (RHML) order dependent pulse shortening force and dynamic chirp characteristics of a gain-saturated semiconductor optical amplifier fiber laser (SOAFL) under dark-optical-comb injection, and discuss the competition between mode-locking mechanisms in the SOAFL at high-gain and strong optical injection condition at higher RHML orders. The evolutions of ...

Careful monitoring of harmonically bound (or as a limiting case, free) masses is the basis of current and future gravitational wave detectors, and of nanomechanical devices designed to access the quantum regime. We analyze the effects of stochastic localization models for state vector reduction, and of related models for environmental decoherence, on such systems, focusing our analysis on the n...

High harmonics driven by two-color counterrotating circularly polarized laser fields are a unique source of bright, circularly polarized, extreme ultraviolet, and soft x-ray beams, where the individual harmonics themselves are completely circularly polarized. Here, we demonstrate the ability to preferentially select either the right or left circularly polarized harmonics simply by adjusting the...

Nonlinear optical phenomena on rough self-affine metal surfaces are theoretically studied. Placing nonlinearly polarizable molecules on such surfaces results in strong enhancement of optical nonlinearities. A quasistatic approximation is used to calculate local-enhancement factors for the second and third harmonic generation, degenerate four-wave mixing, and nonlinear Kerr effect. The calculati...

We theoretically investigate the possible increase of the second harmonic generation (SHG) efficiency in silicon compatible waveguides by considering an asymmetrical plasmonic slot waveguide geometry and a χ((2)) nonlinear polymer infiltrating the slot. The needed phase matching condition is satisfied between the fundamental waveguide mode at the fundamental frequency (FF) and second-order wave...

Novel table-top sources of extreme-ultraviolet light based on high-harmonic generation yield unique insight into the fundamental properties of molecules, nanomaterials or correlated solids, and enable advanced applications in imaging or metrology. Extending high-harmonic generation to high repetition rates portends great experimental benefits, yet efficient extreme-ultraviolet conversion of cor...