No abstract

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. This enables us to quickly estimate the spot size for arbitrary propagation distances. 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. This work will serve as a useful guide in the future system design of the optical bench and the sizes of the optical components.

No abstract

In space-based gravitational wave detection, the estimation of far-field wavefront error of the distorted beam is the precondition for the noise reduction. Zernike polynomials is used to describe the wavefront error of the transmitted distorted beam. The propagation of a laser beam between two telescope apertures is calculated numerically. Far-field wavefront error is estimated with the absolute height of the peak-to-valley phase deviation between distorted Gaussian beam and a reference distortion-free Gaussian beam. The results show the pointing jitter is strongly related to the wavefront error. Furthermore, when jitter decreases 10 times from 100 to 10 nrad, wavefront error reduces for more than an order of magnitude. In the analysis of multi-parameter minimization, the minimum of wavefront error tends to Z[5,3] Zernike in some parameter ranges. Some Zernikes have a strong correlation with wavefront error of the received beam. When the aperture diameter increases at Z[5,3] Zernike, wavefront error is not monotonic and has oscillation. Nevertheless, wavefront error almost remains constant with the arm length increasing from 10-1 Mkm to 103 Mkm. When the arm length decreases for three orders of magnitude from 10-1 Mkm to 10-4 Mkm, wavefront error has only an order of magnitude increasing. In the range of 10-4 Mkm to 103 Mkm, the lowest limit of the wavefront error is from 0.5 fm to 0.015 fm, at Z[5,3] Zernike and 10 nrad jitter.