A differential-frequency measurement technique has been devised to reduce the spurious contributions of temperature fluctuations to determinations of physical quantities from readings of optical resonator and interferometric sensors. The technique is applicable mainly to sensors in the form of whispering-gallery mode (WGM) optical resonators. The evanescent electromagnetic fields of such resonators interact with their environments, such that their resonance frequencies change in response to environmental changes (e.g., a change in the index of refraction of the surrounding medium) that one seeks to measure. The resonance frequencies also vary significantly with temperature, with consequent introduction of errors and uncertainties and, hence, effective loss of sensitivity to changes in quantities other than temperature that one seeks to determine.
The present differential-frequency measurement technique involves the use of two spatially overlapping resonator modes: a transverse electric (TE) mode and a transverse magnetic (TM) mode. The resonance frequencies of both modes change by different amounts in response to the environmental change that one seeks to determine. However, the resonance frequencies of the two modes change by nearly the same amount in response to a change in temperature: for a typical TE/TM pair of modes of a typical WGM resonator made of fused silica, the difference between the temperature-induced changes in resonance frequencies is only about 10–5× the changes themselves, as illustrated in the upper part of the figure.
Hence, by using the change in the difference between their resonance frequencies (instead of the change in either resonance frequency alone) as the measurement quantity, one effectively reduces the undesired temperature sensitivity to about 10–5× the temperature sensitivity of either mode considered alone. This choice of the measurement quantity also reduces the sensitivity to the environmental change of interest, but not so much as to make the sensor unusable: typically, the sensitivity to the environmental change of interest does not vary so much × that of either mode considered alone, as illustrated in the lower part of the figure. The net effect is that the ratio between the desired measurement signal and the undesired temperature-induced signal is 105 times that attainable through measurement of the resonance frequency of a single TM or TE mode.
This work was done by Thanh M. Le, Nan Yu, and Lute Maleki of Caltech, Anatoliy A. Savchenkov of OEWaves Inc., and William H. Steier of the University of Southern California for NASA’s Jet Propulsion Laboratory.
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