Beam displacement tolerances on a segmented mirror for higher-order Hermite-Gauss modes

Odd-indexed higher-order Hermite-Gauss (HG) modes are compatible with four-quadrant segmented mirrors due to their intensity nulls along the principal axes, which guarantees minimum beam intensity illuminating the bond lines between the segments thus leading to low power loss. However, a misplaced HG beam can cause extra power loss due to the bright intensity spots probing the bond lines. This paper analytically and numerically studies the beam displacement tolerances on a segmented mirror for the HG3,3 mode. We conclude that for 'effective' bond lines with 6 mu m width, and the HG3,3 beam size chosen to guarantee 1 ppm clipping loss when centered, the beam can be rotated by roughly 1 circle or laterally displaced by 4% of its beam size while keeping the total power on the bond lines under 1 ppm. We also demonstrate that the constrained beam displacement parameter region that guarantees a given power loss limit, or the beam displacement tolerance, is inversely proportional to the bond line thickness.