Freak waves spotted in microwave cavity
Hamish Johnston - physicsworld.com
Sep 23, 2009
http://physicsworld.com/cws/article/news/40463
Freak waves towering as much as 30 m above the surrounding seas have long been reported by mariners, and recent satellite studies have shown that they are more common that previously expected. Now, a team of physicists in Germany and the US has gained important insights into the possible origins of such waves by scattering microwaves in the laboratory.
The work suggests that rogue waves can emerge from linear interactions between waves – contradicting some theories, which assume that non-linear interactions are required.
The team in Germany injected microwaves into a cavity comprising two parallel metal plates. The distance between the plates was much less than the wavelength of the microwaves, making the waves "quasi 2D" – just like ocean waves. Scattering from random currents was simulated by placing a number of metal cones in random positions in the cavity.
The team monitored the microwave intensity throughout the cavity and noticed the emergence of "hot spots", where the intensity was five or more times greater than background levels. The team counted the number of such freak waves that occurred over a finite time and discovered that they were many orders of magnitude more common than if they resulted from the random superposition of plane waves in the cavity. Random superposition had earlier been thought to govern the formation of freak waves in the ocean..
The experiment is also the first to establish that freak waves can be generated via simple linear interactions between waves – the microwaves in the cavity only interact linearly.
Covering the recent paper:
Freak waves in the linear regime: A microwave study
Höhmann et al.
September 4, 2009
Abstract
Microwave transport experiments have been performed in a quasi-two-dimensional resonator with randomly distributed scatterers, each mimicking an r−2 repulsive potential. Analysis of both stationary wave fields and transient transport shows large deviations from Rayleigh’s law for the wave height distribution, which can only partially be described by existing multiple-scattering theories. At high frequencies, the flow shows branching structures similar to those observed previously in stationary imaging of electron flow. Semiclassical simulations confirm that caustics in the ray dynamics are likely to be responsible for the observed structures. Particular conspicuous features observed in the stationary patterns are “hot spots” with intensities far beyond those expected in a random wave field. Reinterpreting the flow patterns as ocean waves in the presence of spatially varying currents
or depth variations in the sea floor, the branches and hot spots lead to enhanced frequency of freak or rogue wave formation in these regions.
Fig. 1: Photograph of the set-up for one of the two scattering arrangements used. The platform has width 260mm and length 360mm. Each cone has diameter 25 mm and height 15mm. The probe antenna is fixed in a top plate located 20mm above the bottom (not shown) and can be scanned in two horizontal dimensions to map the field distribution within the scattering arrangement. (link to image in article provided by physicsworld.com)
Some interesting points:
Scanning tunneling microscopy studies of electron flow through a high-mobility two-dimensional electron gas (2DEG) by Topinka et al. [1] exhibited intricate branching patterns of fractal appearance. This behavior was in contrast to the simple random wave prediction for the probability distribution of wave heights ..
For quasi-two-dimensional systems with parallel top and bottom plates separated by a distance d, the electromagnetic wave equations reduce to a single, scalar equation for the perpendicular component E_l_(x, y, z) of the electric field. Furthermore, we can separate the z coordinate, E_l_(x, y, z) = E(x, y) cos(nπz/d), where n is the transverse quantum number, resulting in a two-dimensional wave equation for E(x, y)..
The number of active modes depends on frequency.
In this open system, we observe exponential decay of the wave intensity with distance from the source caused by escape of the waves from the scattering setup as well as by absorption.
The present results provide strong evidence in favor of the conjecture [1, 2] that correlated random potentials are responsible for these features.
To avoid the complication of mixing of up to five different modes, most of the experiments have been performed between 7.5 and 15 GHz, where only the first two modes n = 0 and 1 are propagating. In this regime, however, the wave lengths are large compared to the size of the scatterers, and interpretation of the cones in terms of a classical particle potential loses its justification. In fact, a measurement with a single cone shows that each cone scatters the waves isotropically with a cross-section of
several mm depending slightly on frequency.
We note that all corrections to Rayleigh contained in such multiple-scattering expressions are essentially finite wave length effects, disappearing in the limit of short wave length (high frequency or large γ). This is not the case with smooth potentials, which semiclassically deflect the flow; indeed the effect of classical caustics becomes more pronounced at short wave lengths [2].
- Optical rogue wave - hot-spot.jpg (13.65 KB) Viewed 206 times
Fig. 3: A “hot spot”, observed at a frequency of 8.85GHz. The experimental probability density for observing
such a hot spot is one to two orders of magnitude larger than expected from multiple scattering theory.
Looking into the details, we find that there are just two regions (and another one at the border of significance) that are responsible for these deviations, one of them shown in Fig. 4. Each of these “hot spots” exists only in a limited frequency window about 500MHz in width, and the range of incoming wave directions able to excite each hot spot is only about 20 degrees wide. If the
frequency ranges containing these hot spots are omitted from the analysis, the resulting intensity distribution is in full agreement with the predictions from Eq. (2), see Fig. 3.
For the study of time-dependent waves, such as those found in the sea, we must superimpose waves with different frequencies, entering from different directions. To this end we concentrate on one hot spot found at 9.5GHz near the center of our scattering arrangement.
Fixing the probe position, we always find a Rayleigh law for the distribution of intensities in a time sequence, P_loc(I) = s−1 e−I/s (4) but with the time-averaged value s = <I> depending on position. This is nothing but a manifestation of the central limit theorem.
In the experiment, we observe events of this magnitude or greater with a probability of 1.3 · 10−9. Thus, such events are still quite rare, but the probability is enhanced by 5 orders of magnitude compared with Eq. (7), and by 15 orders of magnitude compared to the Rayleigh distribution!
Simply by varying the frequency, we are able to study both ray dominated branching behavior of flow in a potential landscape, as well as the diffractive multiple scattering regime. The interpretation of the hot spots in this latter regime has to remain speculative for the moment, in view of the small number of such hot spots showing up in the experiments. However, the narrow angular acceptance of each hot spot, the visually obvious branching behavior at the higher frequencies, and particularly the fact
that the observed deviations from Rayleigh statistics get stronger rather than weaker at shorter wavelengths, all support the hypothesis that ray refraction, as opposed to resonance, for example, is responsible for these extreme events.
There is a lot to say about this paper, and rogue waves in general. For now, I'd just like to wonder out loud what it is the authors would define "resonance" as, and how they think it differs from caustic dynamics in the ray model (or even path integrals). The term resonance is ill defined in physics; it usually does not include the concept of "partial coherence", which can change the picture dramatically.
regards,
T.Roc
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