Model of a microtoroidal magnetometer

Abstract

We present a model of a cavity optomechanical magnetic field sensor based on a microtoroidal resonator. The magnetic field induced expansion of a magnetostrictive material is transduced onto the physical structure of a highly compliant optical microresonator. The resulting motion is read out optically with ultra-high sensitivity. According to our theoretical model sensitivities of up to 750 fT/ √ Hz may be possible. The simultaneous presence of high-quality mechanical and optical resonances in microtoroids greatly enhances both the response to the magnetic field and the measurement sensitivity.

Optomechanical Magnetometry with a Macroscopic Resonator

“…Estimates based on Ref. [30] indicate that sensitivities in the range of femtotesla may be obtainable with a full optimization.…”

Sensitivity and performance of cavity optomechanical field sensors

“…where the actuation constant c act determines the strength of the coupling. act c depends on the material properties of the transduction medium, and it is determined for the case of a magnetostrictive material in [20]. The minimum detectable field is then simply found by substituting this relationship into (37):…”

“…The magnetometer demonstrated in [19] was based on lithographically fabricated optical microtoroidal resonators coupled to the magnetostrictive material Terfenol-D. High quality optical and mechanical resonances are present in microtoroids, and Terfenol-D stretches significantly at room temperature under applied magnetic fields resulting in experimental sensitivities in the range of one hundred nT•Hz -1/2 . Theoretical sensitivities in the pT Hz -1/2 range predicted for an optimized geometry of this construction [19,20]. Furthermore, a combination of lithographic fabrication and fiber or waveguide coupling, makes these devices amenable to expansion into arrays.…”

“…Here, we elaborate in detail on the eigenmode based method for the calculation of the predicted sensitivity of general cavity optomechanical field sensors presented in [21]. Furthermore, we compare the performance achievable by cavity optomechanical magnetometers presented in [19,20] to other types of magnetometers.…”

Modelling of cavity optomechanical magnetometers

“…The mechanical response changes the path length of the optical cavity to which the magnetostrictive material is attached, allowing the magnetic field to be read out optically from the shift of the optical resonance [10]. While significant successes have been achieved in experimental demonstrations of optomechanical magnetometers [7,8], modelling and sensitivity-prediction for these devices have been somewhat ad hoc [11,12]. Better modelling techniques are needed to both enhance understanding of previous experimental results and for design of future magnetometers.…”