Frequency splitting of polarization eigenmodes in microscopic Fabry–Perot cavities

Manuel Uphoff,Stephan Ritter,Manuel Brekenfeld,Gerhard Rempe

doi:10.1088/1367-2630/17/1/013053

Manuel Uphoff, Stephan Ritter + Show 2 more

Open Access

https://doi.org/10.1088/1367-2630/17/1/013053

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Abstract

We study the frequency splitting of the polarization eigenmodes of the fundamental transverse mode in CO2 laser-machined, high-finesse optical Fabry–Perot cavities and investigate the influence of the geometry of the cavity mirrors. Their highly reflective surfaces are typically not rotationally symmetric but have slightly different radii of curvature along two principal axes. We observe that the eccentricity of such elliptical mirrors lifts the degeneracy of the polarization eigenmodes. The impact of the eccentricity increases for smaller radii of curvature. A model derived from corrections to the paraxial resonator theory is in excellent agreement with the measurements, showing that geometric effects are the main source of the frequency splitting of polarization modes for the type of microscopic cavity studied here. By rotating one of the mirrors around the cavity axis, the splitting can be tuned. In the case of an identical differential phase shift per mirror, it can even be eliminated, despite a nonvanishing eccentricity of each mirror. We expect our results to have important implications for many experiments in cavity quantum electrodynamics, where Fabry–Perot cavities with small mode volumes are required.

Highlights

Fabry–Perot resonators entered the scene of physics more than a century ago and have continued to play an important role ever since
We study the dependence of the frequency splitting of the polarization eigenmodes on the properties of CO2 laser-machined mirrors in a hybrid cavity setup (figure 4(a))
For every fibre mirror characterized in this way, we have verified that the polarization eigenmodes are aligned with the principal axes of the CO2 laser-machined structure, with the mode assigned to the minor axis always being lower in frequency

Summary

Introduction

Fabry–Perot resonators entered the scene of physics more than a century ago and have continued to play an important role ever since. Examples range from cavity-enhanced polarimetry [30,31,32] and cavity ring-down spectroscopy [33, 34] to applications in quantum information processing, such as the efficient and coherent coupling of atomic states to the polarization of single photons [35] The latter requires degeneracy of the polarization eigenmodes, which has been achieved for Fabry–Perot cavities built from superpolished mirror substrates [36]. We find good quantitative agreement between experimental data and a theoretically derived analytic relation between surface geometry and induced frequency splitting This confirms that for mirrors machined with a CO2 laser, their ellipticity is the dominant reason for the splitting of polarization modes. We demonstrate that for cavities with two elliptical mirrors, the amount of frequency splitting can be further controlled by rotating one of the mirrors

Fabrication of fibre mirrors

Theoretical model

Experimental results

Control by fibre rotation

Conclusion

Rx x Re