Abstract 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 mode. We conclude that for ‘effective’ bond lines with 6 µm width, and the beam size chosen to guarantee 1 ppm clipping loss when centered, the beam can be rotated by roughly 1∘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. 
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                    This content will become publicly available on August 1, 2026
                            
                            Quantum-limited imaging of a nanomechanical resonator with a spatial mode sorter
                        
                    
    
            We explore the use of a spatial mode sorter to image a nanomechanical resonator, with the goal of studying the quantum limits of active imaging and extending the toolbox for optomechanical force sensing. In our experiment, we reflect a Gaussian laser beam from a vibrating nanoribbon and pass the reflected beam through a commercial spatial mode demultiplexer (Cailabs Proteus). The intensity in each demultiplexed channel depends on the mechanical modeshapes and encodes information about their displacement amplitudes. As a concrete demonstration, we monitor the angular displacement of the ribbon’s fundamental torsion mode by illuminating in the fundamental Hermite-Gauss mode ( ) and reading out in the mode. We show that this technique permits readout of the ribbon’s torsional vibration with a precision near the quantum limit. Our results highlight new opportunities at the interface of quantum imaging and quantum optomechanics. 
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                            - Award ID(s):
- 2239735
- PAR ID:
- 10632713
- Publisher / Repository:
- APS
- Date Published:
- Journal Name:
- Physical Review Research
- Volume:
- 7
- Issue:
- 3
- ISSN:
- 2643-1564
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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