Spatial Distribution of Phase Singularities in Optical Random Vector Waves

Abstract

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-...

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

“…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.…”

“…It was recently shown that confinement of light to 2D leads to a fundamental difference in the behaviour of its singularities from those present in the transverse field of a paraxial beam [13,14]. It can be presumed, that such a confinement not only has consequences for singularities in the complex vectorial electromagnetic fields, but also for the singular behaviour exhibited by other physical observables, such as the energy flow.…”

Persistence and Lifelong Fidelity of Phase Singularities in Optical Random Waves

“…But vortices are not a peculiarity of superconductors: light's phase swirls around optical vortices, where it is singular [11]. A multitude of these phase singularities arises in random optical fields, one half swirling in opposite direction to the other, so that they can approach respectively to an arbitrarily small distance [12][13][14][15][16]. It is by letting them move that one can observe creation and/or annihilation of such pairs [17][18][19][20][21][22].…”

“…Figure 1 presents a typical example of our measurements of amplitude and phase of E x . The optical field inside the cavity can be thought of as a random superposition of light waves [28] with transverse electric (TE) polarization [15]. Only the behavior of E x is presented here, without loss of generality as it is representative of the behavior of all in-plane field components [15].…”

“…The optical field inside the cavity can be thought of as a random superposition of light waves [28] with transverse electric (TE) polarization [15]. Only the behavior of E x is presented here, without loss of generality as it is representative of the behavior of all in-plane field components [15]. Figure 1b We pinpoint the position of these singularities with deep sub-wavelength resolution, and simultaneously determine their topological charge, which is always observed to be +1 (light circles) or -1 (dark circles), corresponding to a ±2π change of the phase around the singular point [29].…”