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Tunable fiber Fabry-Perot cavities with high passive stability

Carlos Saavedra, Deepak Pandey, Wolfgang Alt, Hannes Pfeifer, and Dieter Meschede

Open Access Open Access

Abstract

We present three high finesse tunable monolithic fiber Fabry-Perot cavities (FFPCs) with high passive mechanical stability. The fiber mirrors are fixed inside slotted glass ferrules, which guarantee an inherent alignment of the resonators. An attached piezoelectric element enables fast tuning of the FFPC resonance frequency over the entire free-spectral range for two of the designs. Stable locking of the cavity resonance is achieved for sub-Hertz feedback bandwidths, demonstrating the high passive stability. At the other limit, locking bandwidths up to tens of kilohertz, close to the first mechanical resonance, can be obtained. The root-mean-square frequency fluctuations are suppressed down to ∼2% of the cavity linewidth. Over a wide frequency range, the frequency noise is dominated by the thermal noise limit of the system’s mechanical resonances. The demonstrated small footprint devices can be used advantageously in a broad range of applications like cavity-based sensing techniques, optical filters or quantum light-matter interfaces.

© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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Supplementary Material (1)

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Supplement 1       Extended fabriction and characterization details

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Figures (6)
Fig. 1.
Fig. 1. Designs and components of the three FFPCs. The optical cavities are formed by concave dielectric mirrors on the opposing end-facets of the optical fibers (diameters exaggerated by a factor of 2) at the center of the structures. The fibers are glued into the glass ferrules, which are in turn glued to piezoelectric elements for tuning the cavity resonances.

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Fig. 2.
Fig. 2. Setup for characterizing FFPCs. The reflected and transmitted laser light power from the FFPC is monitored by the two photodiodes (PD) while the FFPC length $L_{\textrm{cavity}}$ is scanned. The waveplates ($\lambda /2$ and $\lambda /4$) before the input fiber are used to investigate the polarization mode splitting of the cavity. The calibration of scan time $t_{\textrm{scan}}$ to frequency is achieved by modulating sidebands onto the laser tone using an electro-optic modulator (EOM). BS represents a non-polarizing beam splitter. (sketch uses [22])

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Fig. 3.
Fig. 3. (a) Reflected and transmitted power fraction in an exemplary cavity scan of the half slot FFPC with Lorentzian and dispersive fit [2]. (b) Scan of the full free spectral range (FSR) for full slot and triple slots FFPCs. Detailed FFPC properties are listed in Table 1.

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Fig. 4.
Fig. 4. (a) Schematic of the PDH-locking setup for investigating the feedback bandwidth and stability of monolithic FFPCs. The closed feedback system consists of the FFPC device $(S)$, the PDH mixer setup $(M)$, and the feedback controller $(C)$. The input to the PI-controller is the PDH error signal $e$. The output voltage $u$ is applied to the piezo. The gain of the PI-controller can be adjusted to explore different locking bandwidths. To measure the frequency response of the closed-loop circuit a frequency sweep signal $d$ from the electrical network analyser (ENA) can be added to $e$. (b) The plots show the magnitude and phase of the full system ($CSM$) transfer function for the maximum achieved bandwidths (dash-dotted vertical lines) of the three designs listed in Table 1. Sketch uses [22].

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Fig. 5.
Fig. 5. (a) Magnitude of the closed-loop-gain ($CSM(\nu$)) for the three FFPCs with small locking bandwidths (LBW). The intersections of the measured transfer functions with the unity gain line are the values corresponding to the low LBW. (b) Measurements of the frequency noise spectral density $S_\nu$ for the triple slot FFPC for three different LBWs. The off resonance noise curve corresponds to the detection noise limit, measured when the cavity is unlocked and far-off resonance.

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Fig. 6.
Fig. 6. Analysis of the measured FFPC frequency noise induced by mechanical resonances of the system for the full slot FFPC. (a) The measured $S_\nu$ are compared with the laser frequency noise and with the expected noise from thermally excited mechanical resonances of the system. The $S_\nu$ approaches the expected thermal noise limit near the mechanical resonances. Without a low-pass filter, excess electrical noise is coupled to the cavity through the piezoelectric element for some of the modes. (b) Displacement fields of the mechanical resonances included in the model. The two most prominent resonances, I and V, correspond to a bending mode (no piezoelectric coupling) and a longitudinal stretching mode (piezoelectrically coupled) of the structure.

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Tables (1)

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Table 1. Overview of the optical and locking characteristics of the three FFPCs

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Equations (1)

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C S M ( ν ) = − A A + 1 , A = e d .

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