We introduce the generalized Helmholtz–Gauss (gHzG) beam and analyze its propagation through optical systems described by matrices with real and complex elements. The transverse mathematical structure of the gHzG beam is form invariant under paraxial transformations and reduces to those of ordinary HzG and modified HzG beams as special cases. We derive a closed-form expression for the fractional Fourier transform of gHzG beams.
© 2006 Optical Society of America
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