Freak Waves in the Linear Regime: A Microwave Study

Abstract

Microwave transport experiments have been performed in a quasi-two-dimensional resonator with randomly distributed conical scatterers. At high frequencies, the flow shows branching structures similar to those observed in stationary imaging of electron flow. Semiclassical simulations confirm that caustics in the ray dynamics are responsible for these structures. At lower frequencies, large deviations from Rayleigh's law for the wave height distribution are observed, which can only partially be described by existing multiple-scattering theories. In particular, there are "hot spots" with intensities far beyond those expected in a random wave field. The results are analogous to flow patterns observed in the ocean in the presence of spatially varying currents or depth variations in the sea floor, where branches and hot spots lead to an enhanced frequency of freak or rogue wave formation.

Systematic study of rogue wave probability distributions in a fourth‐order nonlinear Schrödinger equation

“…and convolving the c 2 distribution of the mean intensity with the Rayleigh distribution around the mean intensity, we can obtain as in the linear case [Höhmann et al, 2010] a K-distribution for the total distribution of wave heights…”

Extreme events in complex linear and nonlinear photonic media

“…Intuitively, one may link the onset of a rogue wave to a resonant interaction of two or three solitary waves that may appear in the medium. However, large amplitude events may also appear in a purely linear regime [1,2,4,6]; a typical example is the generation of caustic surfaces in wave propagation [13,14].Propagation of electrons or light in a weakly scattering medium is a well-studied classical problem related to Anderson localization and caustic formation. Recent experiments in the optical regime [15] have shown clearly both the theoretically predicted light localization features as well as the localizing role of (focusing) nonlinearity in the propagation [15][16][17][18][19][20].…”

“…Thus, destructive wave interference due to disorder leads to Anderson localization that may be enhanced by self-focusing nonlinearity. In the purely linear regime propagation in two dimensions in a weakly random medium has shown that branching effects appear through the generation of caustic surfaces [13,14], while linear rogue waves have been observed with microwaves [4].In this work we focus on an entirely different regime of wave propagation, in strongly scattering optical media that consist of Luneburg-type lenses randomly embedded in the bulk of glasses. Spherical or cylindrical Luneburg lenses (LLs) have very strong focusing properties directing all parallel rays impinging on them to a single spot on the opposite side surface.…”

“…By the central limit theorem and the simple random wave prediction for the probability distribution of wave intensities I, the intensities have to follow the Rayleigh law, meaning a distribution type  P(I)  e I where  I  E 2 (E is the electric field) is normalized to one [1,2,4,14,18]. However, when extreme events appear, the intensities distribution deviates from simple exponential and long tails appear [1,2,4,8], clearly seen in both our experimental Fig. 1(d) and numerical results Fig.…”

“…Since sailors are well known story makers these monster, destructive waves that were in naval folklore perhaps for thousands of years penetrated the realm of science only recently and after quantitative observations [1,2]. Since then, they seem to spring up in many other fields including optics [3][4][5][6][7], BEC and matter waves, finance, etc [8][9][10][11][12]. Unique 2 features of rogue waves, contrary to other solitary waves, are both their extreme magnitude but also their sudden appearance and disappearance.…”