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Frequency stabilization using WGM reference resonators

Whispering gallery mode resonators (WGMR) possess a unique set of properties which make them very attractive for use as optical frequency reference cavities. Their ultra-high quality factors (often exceeding one billion) facilitate tight locking, while their wide transparency window means that a single cavity could be used for several different wavelengths of laser without needing various expensive mirror coatings. Their small size (often 10 times smaller than a Fabry Pérot cavity) and solid state construction make them particularly suited to portable applications, where acceleration, vibration, and form-factor are of great concern. Figure 1 shows a WGMR frequency reference cavity and one of its typical modes with Q = 5 billion.

 

Figure 1: (Left) A magnesium fluoride (MgF2) resonator is shown, along with its mount, optical input coupler (the metallic cylinder coming in from the left), and wiring for temperature control. (Right) an oscilloscope trace of a typical mode from the cavity.

 

We are currently exploring several different schemes for stabilizing a laser’s frequency with a WGMR cavity. In one such scheme, proposed by our group in 2007 [1], we employ “dual-mode” sensing and active stabilization of the resonator’s temperature, to a precision of about 10 nK – at room temperature! In this arrangement, the differential temperature coefficient of frequency between orthogonally polarized modes in a birefringent crystal allows us to optically measure the temperature of the resonator. We have demonstrated that an active feedback loop based on the error signal from this measurement dramatically stabilizes the resonator’s temperature [2]. More recently we have shown that a single laser can be simultaneously locked to the cavity while it provides an error signal for temperature stabilization [3]. The cavity temperature averages down to 10 nK uncertainty after about 300 seconds, which corresponds to an optical uncertainty of 8.7 × 10 -14. Tests are currently underway to confirm this stability using an external, highly stable optical reference.

Figure 2: (Left) The spacing between orthogonal modes (Δf) is a function of frequency. Therefore, measuring this difference provides means to actively stabilize the cavity’s temperature. (Right) An Allan deviation plot of a typical temperature stabilization run, based on in-loop error-signal residuals.

 

[1] A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, N. Yu, and L. Maleki, “Whispering-gallery-mode resonators as frequency references II, stabilization.,” J. Opt. Soc. Am. B 24, 2988–2997 (2007).

[2] D. V. Strekalov, R. J. Thompson, L. M. Baumgartel, I. S. Grudinin, and N. Yu, “Temperature measurement and stabilization in a birefringent whispering gallery mode resonator,” Opt. Express 19, 14,495–14,501 (2011).

[3] L. Baumgartel, R. Thompson, D. Strekalov, I. Grudinin., “Dual mode frequency stabilization of whispering gallery mode optical reference cavity,” Proceedings of CLEO 2012.