Diffraction of conic and Gaussian beams by a spiral phase plate

Abstract

An analytical expression for the spatial spectrum of the conic wave diffracted by a spiral phase plate (SPP) with arbitrary integer singularity of order n is obtained. Conic wave diffraction by the SPP is equivalent to plane-wave diffraction by a helical axicon. A comparison of the conic wave and Gaussian beam diffraction on a SPP is made. It is shown that in both cases a light ring is formed, with the intensity function growing in proportion to ${\rho }^{2n}$ at small values of radial variable ρ and decreasing as $n^2{\rho }^{-4}$ at large ρ. By use of direct e-beam writing on the resist, a 32 level SPP of the 2nd order and diameter $5\text{\hspace{0.17em} mm}$ is manufactured. By use of this SPP, a He–Ne laser beam is transformed into a beam with phase singularity and ringlike intensity distribution. A four-order binary diffractive optical element (DOE) with its transmittance proportional to a linear superposition of four angular harmonics is also manufactured. With this DOE, simultaneous optical trapping of several polystyrene beads of diameter $\text{5 \hspace{0.17em} μm}$ is performed.

© 2006 Optical Society of America

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