Graphic comparisons between Hermite-Gaussian modes and Laguerre-Gaussian modes

The Hermite-Gaussian modes and Laguerre-Gaussian modes are briefly described. The three-dimensional plots of Hermite-Gaussian modes and Laguerre-Gaussian modes in the plane z=0 are drawn. For the sake of revealing the relation among the various modes of Hermite-Gaussian and Laguerre-Gaussian, contour maps for modal orders varying from (0, 0) to (2, 2) are plotted. The characteristics of the mode order number and the peak value, the change of peak value, the extending area and the symmetry are obtained, respectively. The similarities and differences of the characteristics can also be acquired through the comparisons. The minimum modes of Hermite-Gaussian and Laguerre-Gaussian are consistent, which can be described both in images and formulas. The differences between the electric (magnetic) field and averaged Poynting vector have relationship with the mode. The image of amplitude intensity of the cross-sectional image changes along with the increase of transmission distance. The waist of the beam and peak value also have some connections with the transmission distance.