  We achieved a 0.5 Hz optical beat note line width with ~ 0.1 Hz/s frequency
drift at 972 nm between two external cavity diode lasers independently
stabilized to two vertically mounted Fabry-Perot (FP) reference cavities.
Vertical FP reference cavities are suspended in mid-plane such that the
influence of vertical vibrations to the mirror separation is significantly
suppressed. This makes the setup virtually immune for vertical vibrations that
are more difficult to isolate than the horizontal vibrations. To compensate for
thermal drifts the FP spacers are made from Ultra-Low-Expansion (ULE) glass
which possesses a zero linear expansion coefficient. A new design using Peltier
elements in vacuum allows operation at an optimal temperature where the
quadratic temperature expansion of the ULE could be eliminated as well. The
measured linear drift of such ULE FP cavity of 63 mHz/s was due to material
aging and the residual frequency fluctuations were less than 40 Hz during 16
hours of measurement. Some part of the temperature-caused drift is attributed
to the thermal expansion of the mirror coatings. High-frequency thermal
fluctuations that cause vibrations of the mirror surfaces limit the stability
of a well designed reference cavity. By comparing two similar laser systems we
obtain an Allan instability of 2*10-15 between 0.1 and 10 s averaging time,
which is close to the theoretical thermal noise limit.
