Short and Long Range Screening of Optical Singularities

Abstract

Screening of topological charges (singularities) is discussed for paraxial optical fields with short and with long range correlations. For short range screening the charge variance in a circular region with radius $R$ grows linearly with $R$, instead of with $R^2$ as expected in the absence of screening; for long range screening it grows faster than $R$: for a field whose autocorrelation function is the zero order Bessel function J_{0}, the charge variance grows as R ln R$. A J_{0} correlation function is not attainable in practice, but we show how to generate an optical field whose correlation function closely approximates this form. The charge variance can be measured by counting positive and negative singularities inside the region A, or more easily by counting signed zero crossings on the perimeter of A. \For the first method the charge variance is calculated by integration over the charge correlation function C(r), for the second by integration over the zero crossing correlation function Gamma(r). Using the explicit forms of C(r) and of Gamma(r) we show that both methods of calculation yield the same result. We show that for short range screening the zero crossings can be counted along a straight line whose length equals P, but that for long range screening this simplification no longer holds. We also show that for realizable optical fields, for sufficiently small R, the charge variance goes as R^2, whereas for sufficiently large R, it grows as R. These universal laws are applicable to both short and pseudo-long range correlation functions.

References in corpus (11)

• Percolation model for nodal domains of chaotic wave functions
• Random wave functions and percolation
• SLE description of the nodal lines of random wave functions
• Correlations and screening of topological charges in gaussian random fields
• Distribution of nearest distances between nodal points for the Berry function in two dimensions
• The morphology of nodal lines-random waves versus percolation
• Signed zeros of Gaussian vector fields-density, correlation functions and curvature
• Role of mean free path in spatial phase correlation and nodal screening
• Screening of charged singularities of random fields
• The distribution of extremal points of Gaussian scalar fields
• The Statistics of the Points Where Nodal Lines Intersect a Reference Curve

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