Fiber-optic resonator sensors based on comb synthesizers

Invited Paper Fiber-optic resonator sensors based on comb synthesizers G. Gagliardi * Consiglio Nazionale delle Ricerche-Istituto Nazionale di Ottica (INO) via Campi Flegrei 34, Complesso. A. Olivetti 80078 Pozzuoli (Naples), Italy. ABSTRACT Over the past several years, fiber-optic resonators have been successfully used as mechanical probes by virtue of their intrinsic sensitivity to length changes. In a recent work, we devised a diode-laser system for strain interrogation of a high-finesse fiber Bragg-grating cavity, achieving a 10-13 resolution in the infrasonic and acoustic frequency ranges, thanks to the exceptional stability of an optical frequency comb (OFC). A Pound-Drever-Hall (PDH) frequency locking technique is implemented for low-noise and wide dynamic range readout of the sensor keeping the interrogating laser always linked to the OFC reference. In this way, the low-frequency strain noisefloor is free from laser noise and possibly limited by thermodynamic phase fluctuations or other thermal effects in the fiber. Keywords: Diode laser, strain sensor, fiber Bragg-grating, Fabry-Pèrot resonator, frequency locking 1. INTRODUCTION Fiber-optic sensors are widespread tools for monitoring static and dynamic local deformations inside mechanical structures and materials, in environments as diverse as ocean depths, geothermal wells and aircrafts 1-3. Strain resolution ranging between 10-9 ε Hz -1/2 and 10-6 ε Hz -1/2 has been demonstrated using standard fiber sensors, such as fiber Bragg gratings (FBGs) 4. Higher resolutions with passive sensors can be obtained using fiber-optic resonators combined to laser frequency modulation techniques but mostly at acoustic frequencies 5, 6. However, measuring quasi-static deformations below the 10-9 level is challenging since, in the infrasonic range, the achievable resolution is usually hampered by low-frequency noise and thermal drifts in the interrogation unit. In the last decade, the invention of optical frequency-comb (OFC) synthesizers has allowed unprecedented accuracy and precision in spectroscopy experiments as well as measurements of fundamental physical constants 7, 8. Originally devised for metrological applications, OFCs have recently been proposed as infrared light sources for broadband, high-sensitivity molecular spectroscopy as well as for wide-band refractometry, absolute distance determination and imaging applications 9-11. Owing to their amazing frequency stability, OFC serve as ultra-stable references for laser interrogation in the yet unexplored infrasonic frequency range. In this work, we describe details and limitations of the system by which, in a recent work, we interrogated a fiber Bragg-grating (FBG) resonator strain sensor using a comb-stabilized laser demonstrating sub-pε detection 12. The OFC provides a phase-coherent link between the laser and a radio-frequency oscillator referenced to the primary time standard, leading to an almost laser-frequency noise free interrogation system. The achieved laser stability unveils sensitivity limitations due to fundamental noise sources of thermal nature in the fiber. *gianluca.gagliardi@ino.it; phone 39 081 8675423; fax 39 081 8675420; www.ino.it Laser Resonators, Microresonators, and Beam Control XIV, edited by Alexis V. Kudryashov, Alan H. Paxton, Vladimir S. Ilchenko, Lutz Aschke, Kunihiko Washio, Proc. of SPIE Vol. 8236, 82361E 2012 SPIE CCC code: 0277-786X/12/$18 doi: 10.1117/12.906226 Proc. of SPIE Vol. 8236 82361E-1

2. EXPERIMENTAL DETAILS AND RESULTS The experimental apparatus has already been described in detail elsewhere 11. The optical part is entirely based on telecom fibers. Therefore, the system is compact and no element needs free-space alignment. The strain sensor is a 13- cm-long Fabry-Pérot fiber cavity (FPFC) formed by two identical 99-% FBGs as end reflectors. The strain interrogation & readout unit relies on an OFC that serves as a time and frequency reference. The comb comes from a 80-fs pulse mode-locked Er-fiber laser whose repetition rate (250 MHz) and carrier-envelope offset frequency (20 MHz) are phase locked to the 25 th and 2 nd harmonics of an ultra-stable 10-MHz quartz oscillator (OCXO), respectively. An extendedcavity diode laser emitting around 1560 nm is phase locked to the nearest comb tooth with a loop bandwidth > 1 MHz and a frequency offset from the tooth given by a 30-MHz local oscillator. As a result, the laser reproduces the long and short-term frequency stability of the comb and its emission spectrum is narrowed down to the tooth linewidth (Fig. 1). Thereby, an extremely-low frequency noise level, in the range of few tens of Hz/ Hz, can be obtained for the laser. This is particularly true in the infrasonic range where the OCXO ensures a long-term fractional stability better than 10-13. 0-10 -20 Signal (dbm) -30-40 -50-60 -70-80 -8-6 -4-2 0 2 4 6 8 Laser offset frequency - 30 (MHz) Figure 1. Beat note signal between the laser and the optical comb in locked condition (resolution bandwidth 1 Hz). Servo bumps at about 1.5 MHz represent the unity-gain frequency of the phase-lock loop. In Fig. 2, we show the fluctuations of the laser-comb frequency offset values over a 30-min time when the phase lock is activated. The data exhibit a fairly Gaussian distribution with a standard deviation of 60 mhz. A Pound-Drever-Hall (PDH) locking scheme is realized to keep the laser resonant with the FBG resonator and exploit its sensitivity enhancement 12. For this purpose, sidebands are first created by an electro-optic phase modulator at 28 MHz and two secondary carriers (SCs) are analogously generated at a higher frequency using a widely-tunable synthesizer. The electronic scheme used for this purpose is illustrated in Fig. 3. Beat signals at 28 MHz are detected and demodulated in a RF mixer to obtain dispersive-like error signals around the SC resonances. In Fig. 4, the cavity modes as seen by the laser carrier and SCs are shown along with their PDH signals. A multiplier chain is also employed to increase the tuning range of the SC (up to 320 MHz). In this way, one of the SCs may serve as a probe to track resonance frequency shifts caused by deformations of the sensor, in totally passive operation, without affecting the laser-comb lock. Indeed, the SC can be tuned and locked to the cavity modes while the laser carrier frequency is kept stable by the OFC. The PDH lock loop is based on a three-stage proportional-integrative amplifier acting on the analog modulation input of the SC synthesizer and has a bandwidth of about 40 khz. Mechanical perturbations in the intra-cavity fiber are seen as proportional changes of the cavity resonance position and translated into laser frequency changes by the locking loop. The correction signal used for locking thus contains the strain information within the servo action bandwidth. Proc. of SPIE Vol. 8236 82361E-2

30000000.20 0.5 h measurement 60 Laser-comb offset frequency (Hz) 30000000.15 30000000.10 30000000.05 30000000.00 29999999.95 29999999.90 29999999.85 29999999.80-200 0 200 400 600 800 1000 1200 1400 1600 Time (s) 50 40 30 20 10 σ = 60 mhz 0 29999999.8 29999999.9 30000000.0 30000000.1 30000000.2 Offset-lock frequency (Hz) Figure 2. On the left:. Countings of the laser-comb offset frequency obtained by a precision counter when the phase lock is on. On the right: histogram of the countings with a center of 30 MHz and a σ = 60 mhz To estimate the strain resolution, we cause a known deformation in the sensor by applying a voltage to a PZT actuator attached to the fiber. The servo voltage readout is acquired by a data acquisition board and fast-fourier transformed (FFT) for spectral analysis. The PZT calibration signal allows us to convert the FFT plot in strain spectral density units. Diode Laser 40 MHz SINT 8 28 MHz Σ E O M Figure 3.. Schematic of the phase modulation unit: a fiber-coupled electro-optic modulator (EOM) generates sidebands for the PDH error signal generation and creates secondary carriers (SCs) from a tunable sinthesizers. Proc. of SPIE Vol. 8236 82361E-3

0,3 cavity reflected power PDH signal 320 MHz -28 0,2 Signal (V) 0,1 secondary carrier carrier 0,0-0,1 0,0 312,5 625,0 937,5 1250,0 1562,5 Laser frequency scan (MHz) Figure 4. Reflected power spectrum of the fiber cavity sensor along a laser frequency scan (upper trace) with the corresponding error signals (bottom trace). The strain noise spectra in the infrasonic range are shown in Fig. 5. Here, we applied a sinusoidal perturbation at 2 Hz to the PZT attached to the intra-cavity fiber for calibration. The average noise floor has a minimum of 350 fε rms / Hz at 5 Hz. It is worth noting that the electronic noise of the interrogation system (basically, noise from the servo and photodetector) is quite far from the resolution limit. In principle, the strain performance may be limited by the residual phase noise of the comb, due to the OCXO clock. Indeed, the clock stability is rigidly transferred to the comb RR (x 25) and then to the optical domain multiplying by the tooth number (~ 10 6 ). Nevertheless, the quartz oscillator has a phase noise curve that does not resemble the experimental strain spectrum and its conversion to strain units provides a noise level that is about 1 order of magnitude lower than the measured strain resolution in the 0.01-3 Hz interval. Therefore, the experimental spectra exhibit an unexpected noise content if compared to the estimate based on comb stability. Thermally-induced phase fluctuations in the fiber may be considered. A few theoretical models have been proposed to explain their physical nature but they have some disagreement 13, 14. This fundamental noise source has been confirmed experimentally only in the acoustic range for long-fiber interferometers and, for high audio frequencies, in the frequencynoise spectrum of fiber lasers 14, 15. No attempt to extend observations to low frequencies has been reported so far. We believe that our system can be an important step to observe thermodynamic noise in fibers also in the low-frequency range. Moreover, it would be interesting to compare theoretical predictions with phase (strain) noise of fiber-optic resonators, such as Bragg-grating Fabry-Pérot cavities, eventually considering other related effects. Proc. of SPIE Vol. 8236 82361E-4

1E-8 1E-9 Strain noise (ε Hz -1/2 ) 1E-10 1E-11 1E-12 1E-13 1E-14 1E-15 1E-16 0.01 0.1 1 10 Fourier frequency (Hz) Figure 5. Low-frequency FFT spectrum recorded when the laser is stabilized by the phase lock to the OFC (red line) and in the free-running condition (blue). The sharp peak at 2 Hz is due to a strain-calibration signal applied to the PZT. The black trace is the dark electronic noise. The dashed line corresponds to the detection limit calculated from the shotnoise level (200-μW incident power). 3. CONCLUSIONS We have devised an interrogation system that led to unprecedented resolution level in strain detection both in the audio and infrasonic frequency ranges. The use of an optical comb dramatically reduces contributions of laser frequency jitter that usually mask other effects, particularly in the low-frequency operation. This makes it possible to measure strain signals below the pε level even in the infrasonic frequency range. Also, the experimental findings provide evidence of extra noise that cannot be explained only in terms of limitations from the interrogation unit. The strain resolution is believed to be very close to limit set by thermodynamic phase fluctuations. However, a review of current theories of thermal phase noise in optical fibers is mandatory for a better description of this system. Particularly, a complete model of phase noise in optical fiber resonators should consider different thermally-induced noises as well as the effect of insulating boundary conditions around the fiber. In general, new experiments are necessary to confirm dominant physical mechanisms in cases of particular interest. A more quantitative understanding of thermally-induced phase noise can be performed using fiber optic cavities with different lengths and materials in well-controlled thermodynamic conditions. REFERENCES [1] Reitze D., Chasing gravitational waves, Nat. Photonics 2, 582-585 (2008 [2] Niklès M., Distributed fibre sensors: Depth and sensitivity, Nat. Photonics 4, 431-432 (2010). [3] Jones M., Structural-health monitoring: A sensitive issue, Nat. Photonics 2, 153-+ (2008). [4] Rao Y. J., In-fibre Bragg grating sensors, Meas. Sci. Technol. 8, 355-375 (1997). Proc. of SPIE Vol. 8236 82361E-5

[5] Chow J. H, McClelland D. E., Gray M. B., Littler I. C. M., Demonstration of a passive sub-picostrain fiber strain sensor, Opt. Lett. 30 (15), 1923-1925 (2005). [6] Gagliardi G., De Nicola S., Ferraro P., De Natale P., Interrogation of fiber Bragg-grating resonators by polarization-spectroscopy laser-frequency locking, Opt. Express 15 (7), 3715-3728 (2007). [7] Maddaloni P., Malara P., Gagliardi G., and De Natale P., Absolute frequency measurement of molecular transitions by a direct link to a comb generated around 3-µm, Opt. Express 16 (11), 8242-8249, 2008 [8] Udem T., Reichert J., Holzwarth R., Hansch T. W., Absolute Optical Frequency Measurement of the Cesium D 1 Line with a Mode-Locked Laser, Phys. Rev. Lett. 82, 3568-3571 (1999). [9] Zhang J., Lu Z.H., and Wang L.J., Precision measurement of the refractive index of air with frequency combs Opt. Lett. 30, 3314-3316, 2005 [10] Bernhardt B. et al., Cavity-enhanced dual-comb spectroscopy, Nat. Photonics 4 (1), 55-57 (2010). [11] Gagliardi G. et al., Probing the ultimate limit of fiber-optic strain sensing, Science 330 (6007), 1081-1084 (2010). [12] Drever R. W. P. et al., Laser phase and frequency stabilization using an optical resonator, Appl. Phys. B 31 (2), 97-105 (1983). [13] Wanser K. H., Electron. Lett., Fundamental phase noise limit in optical fibres due to temperature fluctuations 28, 53-54 (1992). [14] Foster S. et al., Fundamental thermal noise in distributed feedback fiber lasers, IEEE J. Quantum Electron. 43 (5), 378-384 (2007). [15] Wanser K. H., Kersey A. D, Dandridge,A., Intrinsic Thermal Phase Noise Limit in Optical Fiber Interferometers, Opt. Photonics News 4 (12), 37-38 (1993). Proc. of SPIE Vol. 8236 82361E-6