Motivated by the necessity of a high-quality stray light control in the
detection of the gravitational waves in space, the spot size of a flat top beam
generated by the clipping of the Gaussian beam(GB) is studied. By adopting the
mode expansion method (MEM) approach to simulating the beam, a slight variant
of the definition of the mean square deviation (MSD) spot size for the MEM beam
is proposed and this enables us to quickly estimate the spot size for arbitrary
propagation distance. Given that the degree of clipping is dependent on the
power ratio within the surface of an optical element, the power ratio within
the MSD spot range is used as a measure of spot size. The definition is then
validated in the cases of simple astigmatic Gaussian beam and nearly-Gaussian
beam profiles. As a representative example, the MSD spot size for a top-hat
beam in a science interferometer in the detection of gravitational waves in
space is then simulated. As in traditional MSD spot size analysis, the spot
size is divergent when diffraction is taken into account. A careful error
analysis is carried out on the divergence and in the present context, it is
argued that this error will have little effect on our estimation. Using the
results of our study allows an optimal design of optical systems with top-hat
or other types of non-Gaussian beams. Furthermore, it allows testing the
interferometry of space-based gravitational wave detectors for beam clipping in
optical simulations. The present work will serve as a useful guide in the
future system design of the optical bench and the sizes of the optical
components.
