Density and correlation functions of vortex and saddle points in open billiard systems

Höhmann, R.; Kuhl, Ulrich; Stöckmann, H.‐J.; Urbina, Juan Diego; Dennis, Mark R.

doi:10.1103/physreve.79.016203

Cited by 22 publications

(26 citation statements)

References 52 publications

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“…The biggest difference is in the g Q (r), where the first peak turns out to be narrower than in theory, as well as significantly shifted towards lower distances. This is in contrast with what was observed for out-of-plane fields in microwaves billiards [21], where excellent agreement was found. The origin of the observed discrepancies with respect to g(r) and g Q (r) lies in the vector nature of the light.…”

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confidence: 99%

Spatial Distribution of Phase Singularities in Optical Random Vector Waves

et al. 2016

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Phase singularities are dislocations widely studied in optical fields as well as in other areas of physics. With experiment and theory we show that the vectorial nature of light affects the spatial distribution of phase singularities in random light fields. While in scalar random waves phase singularities exhibit spatial distributions reminiscent of particles in isotropic liquids, in vector fields their distribution for the different vector components becomes anisotropic due to the direct relation between propagation and field direction. By incorporating this relation in the theory for scalar fields by Berry and Dennis, we quantitatively describe our experiments.PACS numbers: 02.40.Xx Finding correlations in chaotic systems is the first step towards understanding. Many are the fields where such predictions could be exploited, from weather forecast to economic modeling [1,2]. The study of random phenomena is a topic of great interest and inspiration for many branches of physics as well. In electromagnetism, for example, random wave fields have been a topic of intense studies since decades, an outstanding example being Anderson localization of light [3]. More recently the scientific interest on random wave fields has continued intensively, ranging from useful techniques as noninvasive imaging with speckle correlation [4] to fascination concerning the observation of rogue waves in optical fields [5,6]. Zooming into the structure of a random wave field, attention has been pointed to deep-subwavelength dislocations known as phase singularities [7].Phase singularities are locations in which the phase of a scalar complex field is not defined. In two-dimensional fields these locations are points in the plane. Although they are just a discrete set of points, phase singularities can describe the basic properties of the field in which they arise. For this reason they are widely studied in wave fields [8][9][10][11][12][13][14], as well as in many areas of physics, where they are better-known as topological defects in nematics [15] or as vortices in superfluids [16].For a single frequency phase singularities are fixed in space, and their spatial distribution in a scalar field of monochromatic random waves has been analytically modeled by Berry and Dennis [17]. The hallmark of such a distribution is a clear pair correlation, reminiscent of that of particles in liquids. By realizing random waves ensembles in microwave billiards [18][19][20], the correlation of phase singularities was tested for a field perpendicular to the plane of the billiard, showing excellent agreement with the theoretical expectations [21]. For such a field and in that geometry indeed scalar theory was appropriate. However, electromagnetic waves are vectorial in nature, and in a different framework it was already demonstrated how the presence of a spin degree of freedom can affect the correlation properties of a random field [22,23].Here, we show how the vectorial nature of light affects the distribution of its phase singularities. By mapping the in-...

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Spatial Distribution of Phase Singularities in Optical Random Vector Waves

et al. 2016

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“…Their position is also independent of the global phase (see Ref. [29] for a more detailed discussion of these features).…”

Section: Nodal Domain Dependence On Global Phasementioning

confidence: 98%

Nodal domains in open microwave systems

et al. 2007

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Nodal domains are studied both for real ψR and imaginary part ψI of the wavefunctions of an open microwave cavity and found to show the same behavior as wavefunctions in closed billiards. In addition we investigate the variation of the number of nodal domains and the signed area correlation by changing the global phase ϕg according to ψR +iψI = e iϕg (ψ). This variation can be qualitatively, and the correlation quantitatively explained in terms of the phase rigidity characterising the openness of the billiard.

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“…To gain insight into the spatial distribution of the singularities that underpin the general structure of the flowfield, we determine their pair correlation, which tells us how the points are distributed spatially with respect to each other. For isotropic random waves, it is known that this function is liquid-like [27], which has been verified experimentally [13,18,31]. Fig.…”

Section: Restriction To a 2d Light Fieldmentioning

confidence: 56%

Poynting singularities in the transverse flow-field of random vector waves

et al. 2020

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In order to utilize the full potential of tailored flows of electromagnetic energy at the nanoscale, we need to understand its general behaviour given by its generic representation of interfering random waves. For applications in on-chip photonics as well as particle trapping, it is important to discern the topological features in the flow field between the commonly investigated cases of fully vectorial light fields and their 2D equivalents. We demonstrate the distinct difference between these cases in both the allowed topology of the flow-field and the spatial distribution of its singularities, given by their pair correlation function g(r). Specifically, we show that a random field confined to a 2D plane has a divergence-free flow-field and exhibits a liquid-like correlation, whereas its freely propagating counterpart has no clear correlation and features a transverse flow-field with the full range of possible 2D topologies around its singularities.

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Density and correlation functions of vortex and saddle points in open billiard systems

Cited by 22 publications

References 52 publications

Spatial Distribution of Phase Singularities in Optical Random Vector Waves

Spatial Distribution of Phase Singularities in Optical Random Vector Waves

Nodal domains in open microwave systems

Poynting singularities in the transverse flow-field of random vector waves

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