April 1, 2009 / Vol. 34, No. 7 / OPTICS LETTERS
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Atmospheric transfer of optical and radio frequency clock signals B. Sprenger, J. Zhang, Z. H. Lu,* and L. J. Wang Max-Planck Research Group, Institute of Optics, Information and Photonics, University Erlangen-Nuremberg, Günther-Scharowsky-Straße 1, Bau 24, 91058 Erlangen, Germany *Corresponding author:
[email protected] Received November 3, 2008; revised December 19, 2008; accepted February 16, 2009; posted February 25, 2009 (Doc. ID 103637); published March 19, 2009 The phase instability induced during the transfer of radio frequency and optical clock signals through the turbulent atmosphere was measured in a rooftop experiment. Radio frequency intensity modulation of a laser to transmit signals over 100 m results in an Allan deviation of 1.31⫻ 10−10 at 1 s. Optical transfer is more accurate at 1.68⫻ 10−13 at 1 s. As a consequence, fiber links are more suitable for the transfer of optical frequencies over very long distances while free space transmission might find applications in short distances of less than 1 km. © 2009 Optical Society of America OCIS codes: 010.3310, 060.2605.
Accurate long distance distribution of atomic clock and optical clock signals has important applications in many fields including intercomparison of clocks, time dissemination, searches for the time variations of fundamental constants, very long baseline interferometry (VLBI) in radio astronomy, sensitive gravity wave searches in the NASA Deep Space Network (DSN), and accelerator physics. One common way to distribute these highly stable phase coherent signals is via fiber links [1–10]. This can be done either by transmitting a radio frequency by rf modulation of the optical carrier or by directly transmitting the stabilized optical frequency. The optical frequency can be converted into rf at the remote end with an optical frequency comb. Currently the fiber transmission phase instability can be lowered to the level of 10−17 at 1 s with a 32 km actively stabilized fiber link [8]. This instability is much smaller than the currently available best optical clock signal at a stability of 10−15 at 1 s and would be enough for optical clocks intercomparison. There are situations, however, where the two sites for clock comparison have no direct fiber link but are close enough to establish a direct free space line-of-sight link. In this case, it might be more convenient and cost effective to transfer the clock signals through the atmosphere instead of establishing a new fiber link. In comparison to fiber network transmission, atmospheric transmission has additional problems. Temperature and pressure fluctuations at various scales cause the refractive index of the air to be a random function of time and space. This turbulent effect destroys the spatial coherence of a laser beam as it propagates through the atmosphere, which severely affects the stability of the transferred optical signals. In addition, the detection system will exhibit temporal fading associated with the scintillation-induced optical amplitude fluctuations, which might be converted into phase fluctuations by amplitude to phase modulation conversion. Consequently, it is important to quantify the performance limitations air turbulence imposes on atmospheric transmission of coherent signals. To our knowledge, there has been no 0146-9592/09/070965-3/$15.00
prior work on the measurement of phase noise disturbance in optical beam transmission through the atmosphere. In this Letter, we report a rooftop experiment to accurately measure these properties. The results also could be useful for time transfer by laser link (T2L2) [11,12], light detection and ranging (LIDAR), and free space optical communication. Figure 1(a) shows the experimental setup to study the passive instability of the transfer of clock signals through atmosphere. The experiment is carried out on the rooftop of the building that houses the authors’ institution. It consists of a Mach–Zehnder interferometer with a 1550 nm diode laser (Tunics PRI 1550) as the light source. The laser output power is 5.5 mW. The line-
Fig. 1. (Color online) (a) Experimental setup. The output from a 1550 nm diode laser is separated into two beams by a beam splitter. One beam goes through an AOM, and its first order diffracted light is recombined with the other beam, which is reflected by a retroreflector. The beat signal is detected by a fast photodiode. The results are analyzed by an rf spectrum analyzer, an FFT analyzer, and a frequency counter. The path-length difference of the interferometer can be varied by changing the positions of the retroreflector for up to 100 m. (b) Linear increase of noise bandwidth with distance. Distances from 10 to100 m. The slope is roughly 250 Hz per meter. © 2009 Optical Society of America
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width of the laser is 150 kHz, thus easily allowing its coherence length to exceed the round trip distance of the rooftop 共⬃100 m兲. The output of the laser is sent through a short-length single mode fiber and is collimated with a collimator upon exiting the fiber to an intensity 1 / e2 diameter of 7 mm. The collimated beam is split into two beams by a beam splitter. One beam goes through a 165 MHz acousto-optic modulator (AOM), and the first order of the diffracted light is used as the reference. The other beam transmits on the rooftop over distances of up to 50 m and is reflected by a 63.5 mm gold-coated retroreflector. Measurements are taken at times of the day without wind or precipitation. After 50 m the beam waist expands to about 13 mm. There is visible beam sway of a few millimeters at a rate of a few hertz in most atmospheric conditions. The two beams are focused and recombined on a fast photodiode. The output signal is analyzed using an rf spectrum analyzer as well as a frequency counter. All electronic instruments are referenced to a rubidium atomic clock (Stanford Research Systems FS725). For optical frequency transfer, the beat noise shown on the rf spectrum analyzer (HP 4195A) at 165 MHz has a 3 dB bandwidth of about 25 kHz (resolution bandwidth 1 kHz, sweep time 3 s) with the retroreflector 50 m away under fair weather conditions. This noise is dominated by the amplitude fluctuation of the swaying beam, and it increases with the distance almost linearly with a slope of ⬃250 Hz per meter. These data are shown in Fig. 1(b). It is difficult to deduce the phase noise from this measurement. To overcome this problem, a frequency counter (Agilent 53181A) with a gate time of 1 s is used to analyze the zero-crossings of the beat signals, thus suppressing the effect of the amplitude fluctuations. These data are used to calculate the Allan deviation [13], which is a common metric used to characterize clock signal stability as well as a histogram showing the frequency fluctuation within a 1 s gate time as shown in Fig. 2.
Fig. 2. (Color online) Allan deviation of optical beat signal over 100 m at 165 MHz. Two dashed curves act as guides to the eye. One has −1/2 dependence. The other one has −1 dependence. Inset, histogram of beat signal (black squares) with Gaussian fit (solid curve), FWHM= 70.5 Hz.
The underlining noise processes can be inferred by checking the Allan deviation slopes [14]. The measured Allan deviation shows a −1/2 dependence if the samples are averaged from 1 to 500 s, showing a white frequency noise character. After 500 s, it shows −1 dependence, implying that white phase noise is dominating. The 1 s instability of 1.68⫻ 10−13 corresponds to a 1 s linewidth of 32.4 Hz with the optical carrier frequency at 193 THz. This agrees reasonably well with the histogram width of 70.5 Hz (taken at a 1 s gate time). The result is about 1 order of magnitude worse than that of a 7 km fiber transmission, showing much worse phase incursion due to air turbulence. Note that the linewidth of the laser does not affect the measurement results due to common-mode rejection. In the experiment we also measure the atmospheric transfer instability of rf clock signals caused by air turbulence. In this case, the laser is amplitude modulated at 80 MHz by modulating the diode laser’s current with a frequency synthesizer (Rhode & Schwarz SMH), and the reference beam is blocked. The resulting 80 MHz signal on the photodiode is mixed with an 81 MHz reference signal from another frequency synthesizer (HP 8656B) to increase the resolution of the frequency counter; both are locked to the same rubidium clock. The mixer output, after low pass filtering, is analyzed using a frequency counter. Additionally, we also look at the beat signal with a high-resolution fast Fourier transform (FFT) spectrum analyzer (Stanford Research Systems SR760). In this case, the 80 MHz signal is mixed down to 10 kHz with the same HP 8656B frequency synthesizer so that the signal can be detected by the FFT spectrum analyzer. Since no optical interference is needed for rf transfer, the amplitude noise due to beam sway is not very significant in this case. The 10 kHz output from the mixer is analyzed using the FFT spectrum analyzer at the highest resolution of 0.476 mHz. The frequency counter result is used to calculate the Allan deviation for rf transmission. The result (shown in Fig. 3) is 1.31⫻ 10−10 at 1 s, which is about 3 orders of
Fig. 3. (Color online) Allan deviation of an 80 MHz rf signal transmitted over 100 m of free space. Inset, spectrum of beat signal measured over 30 min (black squares) with Gaussian fit (red curve), FWHM= 1.05 mHz.
April 1, 2009 / Vol. 34, No. 7 / OPTICS LETTERS
magnitude worse than that of the optical transmission 共1.68⫻ 10−13 at 1 s) shown in Fig. 2. The frequency spectrum (measured over 30 min) is shown in the inset of Fig. 3. RF frequency dissemination is less precise due to its lower carrier frequency, a fact that has also been observed in fiber network experiments [4–6]. However, the absolute degradation factor reported here might not be correct due to the fact that our rf results are close to the measurement limit of the current setup. The limit on the Allan deviation measurement is the stability of the two frequency synthesizers used, which also depends on the stability of the rubidium reference clock. To test this, a direct 1 MHz beat signal is generated using the two frequency synthesizers and then analyzed. The result is only slightly better than the rf transfer experiment. Hence, the result shown in Fig. 3 is merely the upper bound of the instability incurred during atmospheric transfer of rf signals. Further testing would require a more stable reference than the rubidium clock. Based on our measurement results, and in comparison with other groups’ fiber link results, we conclude that for accurate long distance frequency dissemination a fiber network is preferable. A few tens of meters in the turbulent air induce as much phase noise as many kilometers of fibers. However, with some averaging the results can still be quite promising for short distance applications. A passive stability of 1.34⫻ 10−15 is reached after just over half an hour of averaging. For most applications this accuracy may be quite adequate. To further improve the transmission stability, an active phase-compensated link would be required. To accomplish this, several technical issues need to be solved. First, atmospheric conditions have a large effect on amplitude noise. Pressure and temperature variations can cause the beam to sway drastically. Current measurements are taken at windless times of the day without too much sunshine to minimize heat currents from the roof. To achieve phase-locking, a feedback-control scheme would be necessary to compensate for the beam sway in real time. Second, the wavefront distortion caused by atmospheric turbulence also needs to be compensated [15]. In addition, the current setup with the retroreflector causes a 40 mm spacing between the outgoing and the incoming beams. If the paths do not overlap, accurate compensation of the phase noise cannot be achieved, as reported by Williams et al. [10]. To compensate the phase noise, we will need to exactly overlap the optical paths of the outgoing and the returning beams. This can be achieved by centering the optical beam to the optical center of the cornercube retroreflector or by using a cat-eye retroreflector.
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In conclusion, we measured the phase instability induced by atmospheric turbulence when both rf and optical clock signals are transferred through the atmosphere. For a round trip distance of 100 m, the rf instability is 1.31⫻ 10−10 while the optical signal instability is much less at 1.68⫻ 10−13. Based on this finding, we conclude that a free space high-stability frequency dissemination link of up to 1 km is feasible. However, for longer distances a fiber link would be preferable. Additional efforts are needed to establish an active phase-lock free space link, and atmospheric conditions, such as temperature, wind, fog, and precipitation, need to be taken into consideration. References 1. L.-S. Ma, P. Jungner, J. Ye, and J. L. Hall, Opt. Lett. 19, 1777 (1994). 2. J. Ye, J.-L. Peng, R. J. Jones, K. W. Holman, J. L. Hall, D. J. Jones, S. A. Diddams, J. Kitching, S. Bize, J. C. Bergquist, L. W. Hollberg, L. Robertsson, and L.-S. Ma, J. Opt. Soc. Am. B 20, 1459 (2003). 3. K. W. Holman, D. D. Hudson, J. Ye, and D. J. Jones, Opt. Lett. 30, 1225 (2005). 4. C. Daussy, O. Lopez, A. Amy-Klein, A. Goncharov, M. Guinet, C. Chardonnet, F. Narbonneau, M. Lours, D. Chambon, S. Bize, A. Clairon, G. Santarelli, M. E. Tobar, and A. N. Luiten, Phys. Rev. Lett. 94, 203904 (2005). 5. F. Narbonneau, M. Lours, S. Bize, A. Clairon, G. Santarelli, O. Lopez, Ch. Daussy, A. Amy-Klein, and Ch. Chardonnet, Rev. Sci. Instrum. 77, 064701 (2006). 6. S. M. Foreman, K. W. Holman, D. D. Hudson, D. J. Jones, and J. Ye, Rev. Sci. Instrum. 78, 021101 (2007). 7. I. Coddington, W. C. Swann, L. Lorini, J. C. Bergquist, Y. Le Coq, C. W. Oates, Q. Quraishi, K. S. Feder, J. W. Nicholson, P. S. Westbrook, S. A. Diddams, and N. R. Newbury, Nat. Photonics 1, 283 (2007). 8. S. M. Foreman, A. D. Ludlow, M. H. G. de Miranda, J. E. Stalnaker, S. A. Diddams, and J. Ye, Phys. Rev. Lett. 99, 153601 (2007). 9. N. R. Newbury, P. A. Williams, and W. C. Swann, Opt. Lett. 32, 3056 (2007). 10. P. A. Williams, W. C. Swann, and N. R. Newbury, J. Opt. Soc. Am. B 25, 1284 (2008). 11. E. Samain and P. Fridelance, Metrologia 35, 151 (1998). 12. D. E. Smith, M. T. Zuber, X. Sun, G. A. Neumann, J. F. Cavanaugh, J. F. McGarry, and T. W. Zagwodzki, Science 311, 53 (2006). 13. D. W. Allan, Proc. IEEE 54, 221 (1966). 14. D. W. Allan, IEEE Trans. Ultrason. Ferroelectr. Freq. Control UFFC-34, 647 (1987). 15. K. L. Baker, E. A. Stappaerts, D. Gavel, J. Tucker, D. A. Silva, S. C. Wilks, S. S. Olivier, and J. Olsen, Proc. SPIE 5553, 269 (2004).
