Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 1202.5763

Rogue waves statistics in the framework of one-dimensional Generalized Nonlinear Schrodinger Equation

Dmitry Agafontsev·Vladimir Zakharov
View original source ↗Read source document ↗Export metadata ↓

Abstract

We measure evolution of spectra, spatial correlation functions and probability density functions (PDFs) of waves appearance for a set of one-dimensional NLS-like equations of focusing type, namely for the classical integrable Nonlinear Schrodinger equation (1), nonintegrable NLS equation accounting for dumping (linear dissipation, two- and three-photon absorption) and pumping terms (2) and generalized NLS equation accounting for six-wave interactions, dumping and pumping terms (3). All additional terms beyond the classical NLS equation are small. As initial conditions we choose seeded by noise modulationally unstable solutions of the considered systems in the form of (a) condensate for systems (1)-(3) and (b) cnoidal wave for the classical NLS equation (1). We observe 'strange' results for the classical NLS equation (1) with condensate initial condition including peak at zeroth harmonic in averaged over ensemble spectra, non-decaying spacial correlation functions and a 'breathing' region on the PDFs for medium waves amplitudes where frequency of waves appearance oscillates with time, while the far-tails of the PDFs remain Rayleigh ones. Addition of small dumping and pumping terms in model (2) breaks integrability that results in absence of the peak at zeroth harmonic in spectra, spacial correlation functions decaying to zero level and strictly Rayleigh PDFs for waves amplitudes. For the classical NLS equation (1) with cnoidal wave initial condition PDFs turn out to be significantly different from Rayleigh ones with 'fat tails' in the region of large amplitudes where higher waves appear more frequently, while for generalized NLS equation with six-wave interactions, dumping and pumping terms (3) we demonstrate absence of non-Rayleigh addition to the PDFs for zeroth six-wave interactions coefficient and increase of non-Rayleigh addition with six-wave interactions term.

Explore related subjects

physics.optics

Keep this discovery

BibTeXRIS

Dmitry Agafontsev, Vladimir Zakharov. 2012-02-26. Rogue waves statistics in the framework of one-dimensional Generalized Nonlinear Schrodinger Equation. https://arxiv.org/abs/1202.5763

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Two-step high-accuracy microwave frequency measurement and time-frequency analysis based on optical frequency combs

Broadband microwave frequency measurement and time-frequency analysis are crucial for applications such as electronic warfare. However, when it comes to ultra wideband signal analysis, traditional electronic methods have high analysis accuracy, but intrinsic electronic bottlenecks limit their real-time analysis. Here, we propose and experimentally demonstrate a two-step microwave frequency measurement and time-frequency analysis method based on optical frequency combs. The system first performs coarse frequency localization over the 0-40 GHz range using stimulated-Brillouin-scattering-assisted frequency-to-time mapping (FTTM) and dual-comb channelized reception. The dual-comb is then reapplied for downconverting the signal under test, followed by digital signal processing to achieve high-accuracy unambiguous frequency extraction. Experimental results show that the system achieves mean single-tone frequency measurement errors of less than 10 kHz over 0-40 GHz. We further experimentally measure multi-tone, linearly frequency-modulated, and V-shaped frequency-modulated signals, demonstrating the proposed method's capability for analyzing complex signals.

physics.optics↗
arXiv2026

A Two-Mirror Faceted Projection System for EUV Lithography

We propose an all-reflective two-mirror projection system for extreme ultraviolet (EUV) lithography operating at exposure wavelengths of $13.5$~nm (Mo/Si) and $11.2$~nm (Ru/Be), delivering a fourfold ($4\times$) demagnification of the periodic mask pattern at a numerical aperture approaching unity ($\mathrm{NA}_{\max} \approx 0.993$). In contrast to conventional EUV projection objectives that incorporate 6--10 aspheric mirrors with an overall optical throughput of less than $15\%$, the proposed design redirects each accepted discrete spatial diffraction order scattered by the mask onto the wafer via a dedicated pair of planar mirror facets. The number of reflections is strictly fixed at two for all accepted orders, retaining $50$--$60\%$ of the power leaving the mask in each accepted order. We derive a spatial geometry providing rigorous optical path length equalization across all diffraction orders, thereby removing order-dependent propagation phase shifts. Individually optimized 30-bilayer Bragg multilayer coatings are designed for each facet using the transfer matrix method combined with global evolutionary optimization algorithms. The architecture is generalized to a three-dimensional vector formulation with a two-dimensionally periodic mask. Utilizing inverse lithography technology, Fourier parameterization, and a differentiable electromagnetic modal waveguide solver, we solve the synthesis problem for binary absorber masks (La absorber on a Ru/Be/Sr multilayer mirror). We demonstrate simulated aerial images of sub-10-nm features on the wafer (isolated peaks with a full width at half maximum (FWHM) of approximately $5.4$~nm and line pairs with a critical dimension of $6$~nm) and find that the two peaks remain resolved for the tested wafer defocus values from $0$ to $5$~nm along the $z$-axis.

physics.optics↗
arXiv2026

Antimony for broadband nanophotonics across the ultraviolet, visible and infrared

Semimetal elemental antimony (Sb) nanostructures show great potential for applications where nanophotonic properties play a key role, such as phase-change optical memories, non-linear optical elements, photothermal therapy agents, photodetectors and photocatalysts. However, designing advanced Sb-based photonic devices critically requires an accurate and reliable knowledge of the optical response of bulk and nanoscale Sb. Herein, we report for the first time a fully consistent and accurately measured dielectric function for Sb nanoscale films in a wide spectral range from the ultraviolet to the far infrared (4 - 0.04 eV, i.e. ~ 0.3 - 30 $\mu$m), surpassing previous reports that explored a limited spectral range. It is found that the Sb spectral response is driven exclusively by giant interband transitions in the visible up to mid infrared (4 - 0.4 eV, i.e. ~ 0.3 - 3 $\mu$m), and that their contribution dominates over that of free carriers down to 0.12 eV (i.e. ~ 10 $\mu$m). Such spectral response enables Sb nanostructures to display spectrally selective and tunable nanophotonic resonances. First, we showcase interband plasmonic resonances in the visible-to-near infrared for Sb nanogratings. Second, we report giant refractive index dielectric resonances in the mid infrared for nanostructured Sb/dielectric/metal resonant cavities. These findings open a pathway to optimized planar Sb nanoscale designs enabling a tailored light-matter interaction, which will be useful for integrated data, telecom, medical, optoelectronic and energy conversion devices operating in a broad spectral range.

physics.optics↗