Study of the behaviour of the light field orbital angular momentum upon astigmatic mode conversion

We consider the behaviour of the orbital angular momentum of the light field as a superposition of Hermite–Gaussian beams upon astigmatic mode conversion. An analytical expression is obtained for the orbital angular momentum of such fields. Expressions are found for various linear combinations of Hermite–Gaussian beams. The astigmatic mode conversion of the initial light fields that are equivalent from the point of view of the orbital angular momentum is shown to lead to significantly different final results.