A new kind of laser beam called the decentered elliptical Hermite–Gaussian beam (DEHGB) is defined by use of a tensor method. The propagation formula of the DEHGB passing through a nonsymmetrical paraxial optical system is derived through vector integration. The derived formula can be easily reduced to the propagation formula of an aligned elliptical Hermite–Gaussian beam and that of a decentered elliptical Gaussian beam under certain conditions. By use of this formula, the propagation characteristics of the DEHGB through free space are presented graphically. As application examples, we construct a generalized laser array using the DEHGB as the fundamental mode. We also obtain the decentered elliptical flattened Gaussian beam by expressing it as superposition of a series of DEHGBs by using polynomial expansion.
© 2003 Optical Society of America
Original Manuscript: September 4, 2002
Revised Manuscript: February 3, 2003
Manuscript Accepted: February 3, 2003
Published: June 1, 2003
Yangjian Cai and Qiang Lin, "Decentered elliptical Hermite–Gaussian beam," J. Opt. Soc. Am. A 20, 1111-1119 (2003)