Biomedical subjects

Isaac Freund

Publications and source records attributed to Isaac Freund.

9 recordsLinked to original sources

PubMed2006

Diabolo creation and annihilation.

A point of circular polarization embedded in a paraxial field of elliptical polarization is a polarization singularity called a C point. At such a point the major axis a and minor axis b of the ellipse become degenerate. Away from the C point this degeneracy is lifted such that surfaces a and b form nonanalytic cones that are joined at their apex (the C point) to produce a double cone called a diabolo. Typically, during propagation diabolo pairs are created or annihilated. We present rules based on geometry and topology that govern these events, provide initial experimental confirmation, and enumerate the allowed configurations in which diabolos can be created or annihilated.

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PubMed2006

Experimental optical diabolos.

The canonical point singularity of elliptically polarized light is an isolated point of circular polarization, a C point. As one recedes from such a point the surrounding polarization figures evolve into ellipses characterized by a major axis of length a, a minor axis of length b, and an azimuthal orientational angle alpha: at the C point itself, alpha is singular (undefined) and a and b are degenerate. The profound effects of the singularity in alpha on the orientation of the ellipses surrounding the C point have been extensively studied both theoretically and experimentally for over two decades. The equally profound effects of the degeneracy of a and b on the evolving shapes of the surrounding ellipses have only been described theoretically. As one recedes from a C point, a and b generate a surface that locally takes the form of a double cone (i.e., a diabolo). Contour lines of constant a and b are the classic conic sections, ellipses or hyperbolas depending on the shape of the diabolo and its orientation relative to the direction of propagation. We present measured contour maps, surfaces, cones, and diabolos of a and b for a random ellipse field (speckle pattern).

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PubMed2005

Polarization singularity proliferation in three-dimensional ellipse fields.

The classical singularities of elliptically polarized light are points of circular (linear) polarization, characterized by a half-integer (integer) topological index. On average, in any plane of a random ellipse field there is of the order of one each of these classical singularities per coherence area. It is shown that every ellipse in such a field is a multiple singularity characterized by nine different topological indices: Three indices characterize rotations of the principal axis system of the surrounding ellipses, and six indices characterize a one- or two-turn spiral precession of these axes. The nine indices can divide the field into 32,768 different volumes with different structures separated by singular surfaces (grain boundaries) on which an index becomes undefined. This unprecedented proliferation of singularities and structures can occur in other three-dimensional systems in which individual elements are described by unique principal axis systems, for example, liquid crystals, and should be sought in such systems.

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PubMed2004

Polarization singularity democracy: WYSIWYG.

The canonical point singularity of elliptically polarized light is a C point, an isolated point of circular polarization surrounded by a field of polarization ellipses. The defining singular property of a C point is that the surrounding ellipses rotate about the point. It is shown that this rotation is seen only for a particular line of sight (LOS) and, conversely, that there exists a unique LOS for every ellipse along which the ellipse is seen as a singularity. It is also shown that changes in LOS can turn singularities into stationary points and vice versa. The democratic behavior of polarization singularities and stationary points is a consequence of the fundamental "what you see is what you get" property of ellipse fields. Simple experiments are proposed for observing this unusual property of elliptically polarized light.

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PubMed2004

Polarization singularities in optical lattices.

Polarization singularities are shown to be unavoidable features of three-dimensional optical lattices. These singularities take the form of lines of circular polarization, C lines, and lines of linear polarization, L lines. The polarization figures surrounding a C line (L line) rotate about the line with winding number +/-1/2 (+/-1). C and L lines permeate the lattice, meander throughout the unit cell, and form closed loops. Surprisingly, every point in a linearly polarized optical lattice is found to be a singularity about which the surrounding polarization vectors rotate with an integer winding number.

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PubMed2004

Emergent polarization singularities.

Polarization singularities are shown to emerge spontaneously from the incoherent addition of uncorrelated optical fields that individually need not contain singularities. Examples of this phenomenon are given for both vector and ellipse fields. The incoherent addition of vector fields whose singularities have integer winding numbers is shown to yield fields whose singularities have half-integer winding numbers. These findings are used to make predictions about the singularities of the polarized component of the cosmic microwave background.

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PubMed2003

Polychromatic polarization singularities.

Elliptical polarization can appear in only monochromatic optical fields. In polychromatic vector fields the polarization is a Lissajous figure, but in only commensurate fields do the figures have well-defined shapes; in other fields the shapes are undefined. Nonetheless, I show that a given paraxial polychromatic vector field has a coherency ellipse field associated with it that contains polarization singularities and stationary points that are surrogates for the corresponding critical points of the parent optical field.

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PubMed2003

Optical polarization singularities and elliptic stationary points.

Polarization singularities and elliptic stationary points (collectively, elliptic critical points) were measured experimentally via the complex Stokes field S1 + iS2, where S1 and S2 are Stokes parameters. This new, easily implemented method yielded detailed, high-resolution experimental data for all elliptic critical points. These data confirm with high precision the elliptic-field topological sign rule, loop rules, and Stokes singularity relations introduced recently.

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PubMed2003

Lissajous singularities.

Coherent optical Lissajous states are easily created by nonlinear processes such as second-harmonic generation (SHG). Singular properties of such states are discussed and illustrated theoretically with non-phase-matched SHG of an ellipse field containing a C point.

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