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.