A detailed study of the coherent and the incoherent combinations of two-dimensional off-axis Hermite–Gaussian beams with rectangular symmetry is made. The closed-form propagation formulas of the resulting beam are derived, and the resulting beam quality in terms of the M2 factor and power in the bucket is discussed and compared for the coherent and the incoherent combinations. In addition, it is shown that the resulting astigmatic beam can be symmetrized in the sense of the second-moment definition of beam width. However, the symmetrizing transformation of the resulting astigmatic beams is incomplete, because there exist different irradiance profiles.
© 2000 Optical Society of America
Original Manuscript: August 10, 1999
Revised Manuscript: November 29, 1999
Published: March 10, 2000
Baida Lü and Hong Ma, "Coherent and incoherent off-axis Hermite–Gaussian beam combinations," Appl. Opt. 39, 1279-1289 (2000)