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An optical vortex appears as a black circular spot in the transverse cross section of a light beam, owing to a helical phase ramp of modulus 2π. Such fields are ubiquitous throughout physics; even the nonlinear Schrödinger equation has solutions with such modes,1 which may be written in cylindrical coordinates as E(r,θ,z) = A(r)exp(±iθ)exp(iβz).
© 1995 Optical Society of America
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