Finite energy Airy-Hermite-Gaussian beam and its paraxial propagation

A new form of laser beam called finite energy Airy-Hermite-Gaussian beam (AHGB) is introduced to describe the out mode of the metal strip waveguide in this paper. In the source plane, this beam can be decomposed into a Hermite-Gaussian function in y-direction and exponentially modified Airy function in x-direction. When the exponential truncation factor is large, the intensity profile in the source plane is an approximate off-axis Hermite-Gaussian distribution. Based on the Collins integral, an analytical expression for the finite energy AHGB passing through a paraxial ABCD optical system has been derived. For special cases, the propagation properties of this kind of beam passing in free space, through a thin lens and a fractional Fourier transformation system are studied and illustrated with numerical calculation. Our results provide an effective and fast way for studying the paraxial propagation properties of the finite energy AHGB.

► A new form of laser beam called finite energy AHGB is introduced.
► An analytical propagation formula for the finite energy AHGB is derived.
► The intensity for the finite energy AHGB is nearly nonspreading in free space.