Temperature compensation of the difference frequency between modes of orthogonal polarization in anisotropic dielectric resonators

A new method to construct frequency-temperature compensated oscillators based on anisotropic dielectric resonators is presented. The method relies on the anisotropic fractional Temperature Coefficients of Frequency (TCF) of orthogonally polarized modes. We show that it is possible to design a resonator with transverse electric and magnetic modes at different frequencies, but with the same TCF in units Hz/K, resulting in temperature compensation of the difference frequency. The principle was verified near room temperature, and between 50 to 77 K, by measuring the difference frequency of two microwave oscillators frequency locked to orthogonally polarized whispering gallery modes. Curvature of the compensation points was measured to be 8×10^-8 K^-2 near room temperature, and 1 to 3×10^-8 K^-2 between 50 and 77 K. This technique, enables the design of temperature compensate oscillators at any temperature and does not require dielectric, paramagnetic or mechanical compensation techniques. Considering the above parameters, it is possible to construct oscillators with fractional frequency instability at τ = 1 s, of order 10^-13 at room temperature and 10^-15 at solid nitrogen temperature.