Bessel–Gaussian Shifted Paraxial Beams: I

We have considered a new family of localized solutions of a parabolic (paraxial wave) equation that generalizes the well-known Bessel–Gaussian beams and includes asymmetric and noncoaxial Bessel–Gaussian beams as subfamilies. The Fourier spectra of these solutions have been found, and their expansions into nonshifted Bessel–Gaussian beams have been obtained.