Self-referencing photothermal common-path interferometry to measure absorption of Si3N4 membranes for laser-light sails

Laser-light sails are a spacecraft concept wherein lightweight "sails" are propelled by high-intensity lasers. We investigated the near-infrared absorption of free-standing membranes of stoichiometric silicon nitride (Si$_3$N$_4$), a candidate sail material. To resolve the small but non-zero optical loss, we used photothermal common-path interferometry (PCI), for which we developed a self-referencing modality where a PCI measurement is performed twice: once on a bare membrane, and a second time with monolayer graphene deposited on the membrane. The graphene increases the absorption of the sample by orders of magnitude, such that it can be measured by ellipsometry, without significantly affecting the thermal properties. We measured the absorption coefficient of Si$_3$N$_4$ to be (1.5-3) $\times$ 10$^{-2}$ cm$^{-1}$ at 1064 nm, making it a suitable sail material for laser intensities as high as ~10 GW/m$^2$. By comparison, silicon-rich "low stress" SiN$_x$ (x~1), with a measured absorption coefficient of approximately 8 cm$^{-1}$, is unlikely to survive such high laser intensities. Our self-referencing technique enables testing of low-loss membranes of various materials for laser sails and other applications.