A passive optical resonator is a special sensor used for measurement of lengths on the nanometer and sub-nanometer scale. A？stabilized optical frequency comb can provide an ultimate reference for measuring the wavelength of a tunable laser locked to the optical resonator. If we lock the repetition and offset frequencies of the comb to a high-grade radiofrequency (RF) oscillator its relative frequency stability is transferred from the RF to the optical frequency domain. Experiments in the field of precise length metrology of low-expansion materials are usually of long-term nature so it is required that the optical frequency comb stay in operation for an extended period of time. The optoelectronic closed-loop systems used for stabilization of combs are usually based on traditional analog electronic circuits processing signals from photodetectors. From an experimental point of view, these setups are very complicated and sensitive to ambient conditions, especially in the optical part, therefore maintaining long-time operation is not easy. The research presented in this paper deals with a novel approach based on digital signal processing and a software-defined radio. We describe digital signal processing algorithms intended for keeping the femtosecond optical comb in a long-time stable operation. This need arose during specialized experiments involving measurements of optical frequencies of tunable continuous-wave lasers. The resulting system is capable of keeping the comb in lock for an extensive period of time (8 days or more) with the relative stability better than 1.6 × 10 ？11.
References
[1]
Diddams, S.A.; Udem, T.; Bergquist, J.C.; Curtis, E.A.; Drullinger, R.E.; Hollberg, L.; Itano, W.M.; Lee, W.D.; Oates, C.W.; Vogel, K.R.; et al. An optical clock based on a single trapped 199Hg+ ion. Science 2001, 293, 825–828.
[2]
Hall, J.L.; Ye, J. Optical frequency standards and measurement. IEEE Trans. Instrum. Meas. 2003, 52, 227–231.
[3]
Ludlow, A.D.; Zelevinsky, T.; Campbell, G.K.; Blatt, S.; Boyd, M.M.; de Miranda, M.H.G.; Martin, M.J.; Thomsen, J.W.; Foreman, S.M.; Ye, J.; et al. Sr lattice clock at 1 × 10？16 fractional uncertainty by remote optical evaluation with a Ca clock. Science 2008, 319, 1805–1808.
[4]
Cundiff, S.T. Phase stabilization of ultrashort optical pulses. J. Phys. D Appl. Phys. 2002, 35, R43–R59.
Tang, D.Y.; Zhao, L.M. Generation of 47-fs pulses directly from an erbium-doped fiber laser. Opt. Lett. 2007, 32, 41–43.
[7]
Diddams, S.A. Optical Clocks and Frequency Synthesis Using Femtosecond Lasers. In Holey Fibers and Photonic Crystals/Polarization Mode Dispersion/Photonics Time/Frequency Measurement and Control, Proceedings of the Digest of the LEOS Summer Topical Meetings, Vancouver, BC, Canada, 14–16 July 2003. TuC3.1/45–TuC3.1/46.
[8]
Diddams, S.A. Low-Noise Microwave and Optical Waveform Synthesis with Femtosecond Laser Frequency Combs. Proceedings of the 20th Annual Meeting of the IEEE Lasers and Electro-Optics Society (LEOS), Lake Buena Vista, FL, USA, 21–25 October 2007; pp. 731–732.
Rosenband, T.; Hume, D.B.; Schmidt, P.O.; Chou, C.W.; Brusch, A.; Lorini, L.; Oskay, W.H.; Drullinger, R.E.; Fortier, T.M.; Stalnaker, J.E.; et al. Frequency ratio of Al+ and Hg+ single-ion optical clocks; Metrology at the 17th decimal place. Science 2008, 319, 1808–1812.
[11]
iMaser？ 3000 Smart Active Hydrogen Maser Clock Specifications. Available online: http://www.t4science.com/documents/iMaser_Clock_Spec1.pdf (accessed on 26 December 2013).
[12]
Time & Frequency References. Available online: http://www.symmetricom.com/products/ (accessed on 26 December 2013).
[13]
Best, R.E. Phase-locked Loops: Design, Simulation and Applications; McGraw-Hill: New York, USA, 2003. ISBN:0-07-14120-8.
[14]
MenloSystems—Products. Available online: http://www.menlosystems.com/products/ (accessed on 26 December 2013).
[15]
Kumm, M.; Klingbeil, H.; Zipf, P. An FPGA-based linear all-digital phase-locked loop. IEEE Trans. Circuits Syst. I 2010, 57, 2487–2497.
[16]
？í？ek, M.; ？íp, O.; ？míd, R.; Hrabina, J.; Mikel, B.; Lazar, J. Digital Approach to Stabilizing Optical Frequency Combs and Beat Notes of CW Lasers. Proceedings of the SPIE 8916, Sixth International Symposium on Precision Mechanical Measurements, Guiyang, China, 8–12 August 2013; Volume 8916.
[17]
Cip, O.; Smid, R.; Cizek, M.; Buchta, Z.; Lazar, J. Study of the thermal stability of Zerodur glass ceramics suitable for a scanning probe microscope frame. Cent. Eur. J. Phys. 2012, 10, 447–453.
[18]
Bellini, M.; Hansch, T.W. Phase-locked white-light continuum pulses: Toward a universal optical frequency-comb synthesizer. Opt. Lett. 2000, 25, 1049–1051.
[19]
Holzwarth, R.; Udem, T.; Hansch, T.W.; Knight, J.C.; Wadsworth, W.J.; Russell, P.S.J. Optical frequency synthesizer for precision spectroscopy. Phys. Rev. Lett. 2000, 85, 2264–2267.
[20]
Reichert, J.; Holzwarth, R.; Udem, T.; Hansch, T.W. Measuring the frequency of light with mode-locked lasers. Opt. Commun. 1999, 172, 59–68.
[21]
Villa, M.; Tian, F.; Cofrancesco, P.; Halamek, J.; Kasal, M. High-resolution digital quadrature detection. Rev. Sci. Instrum. 1996, 67, 2123–2129.
[22]
Widrow, B.; Kollar, I. Quantization Noise: Round Off Error in Digital Computation, Signal Processing, Control and Communications; Cambridge University Press: New York, NY, USA, 2008.
[23]
FFT Benchmark Methodology. Available online: http://www.fftw.org/speed/method.html (accessed on 29 October 2013).
[24]
Smid, R.; Cizek, M.; Buchta, Z.; Lazar, J.; Cip, O. Evaluation of Fabry-Perot Cavity Length by the Stabilized Optical Frequency Comb and Acetylene Absorption. Proceedings of the 2011 Joint Conference of the IEEE International Frequency Control and the European Frequency and Time Forum (FCS), San Fransisco, CA, USA, 2–5 May 2011; pp. 1–4.
[25]
Smid, R.; Jezek, J.; Buchta, Z.; Cizek, M.; Mikel, B.; Lazar, J.; Cip, O. Monitor of Mirror Distance of Fabry-Perot Cavity by the Use of Stabilized Femtosecond Laser Comb. Proceedings of the 17th Slovak-Czech-Polish Optical Conference on Wave and Quantum Aspects of Contemporary Optics, Liptovsky Ján, Slovakia, 6–10 September 2010; Volume 7746.
[26]
Smid, R.; Cip, O.; Buchta, Z.; Jezek, J.; Mikel, B.; Cizek, M.; Lazar, J. Precise Monitoring of Ultra Low Expansion Fabry-Perot Cavity Length by the Use of a Stabilized Optical Frequency Comb. Proceedings of the 2010 IEEE International Frequency Control Symposium (FCS), Newport Beach, CA, USA, 1–4 June 2010; pp. 480–484.
