Cordierite-based optical resonators with extremely low thermal expansion

Applications for ultra-stable lasers outside controlled laboratory environments require compact and robust optical resonators with reduced sensitivity to temperature fluctuations. The low thermal expansion coefficient (CTE) and the high stiffness make cordierite-based ceramics, such as NEXCERA, attractive for vibration insensitive room-temperature resonators. We revisit the effective CTE of resonators with spacers and mirrors made of different materials and use finite element simulations to analyze the impact of a CTE mismatch in a cordierite-based resonator with mirrors made of ultra-low expansion (ULE) glass or fused silica (FS). This enabled us to determine the CTE of a cordierite spacer from the measured effective CTE of a resonator. We confirm a six-fold larger CTE slope of cordierite around the zero-crossing temperature than in ULE glass. The steep CTE slope, in combination with the large stiffness, makes cordierite-based resonators far less sensitive to CTE mismatch with FS mirrors, thereby eliminating the need for additional compensation rings. We further consider the so far neglected case, where the CTE of the spacer is larger than that of the mirror, and propose resonator designs in which the thermal length change of the spacer is fully or partially compensated by the deflection of the mirrors. This results in a cordierite-based resonator with ULE mirrors whose effective CTE can be close to zero over a temperature range of several tens of Kelvin. We are extending our concept to resonators based on crystalline materials with high stiffness and low isothermal length change, such as silicon, enabling compact and robust room-temperature resonators for terrestrial and space-born applications.