1. Introduction

Dissemination of timing and frequency signal are important to precision scientific and engineering applications such as metrology, optical-microwave frequency standard, optical communication, radar, and navigation [1–3]. Recently, optical free-space links have become an attractive option for dissemination of timing and frequency signals as it can provide higher flexibility than fiber links [4–6]. In the past decade, there are some important works to demonstrate the disseminations of frequency signals via optical free-space links [7–16]. In some of these frequency dissemination experiments, atmospheric transfers of radio-frequency (RF), optical frequency, and optical frequency comb (OFC) signals with ultra-low timing deviation have been achieved, where kinds of phase compensation schemes ranging from two-way time-frequency transfer (TWTFT) [11–13] to active optical/microwave phase delay line [14–16], were proposed to suppress the turbulence-affected timing fluctuation over free-space optical link.

In these beforementioned works of free-space frequency dissemination, usually, the transferred frequency signal with active phase compensation have high stability. However, we can only recover the disseminated frequency signal between specific sites using the currently-used free-space frequency transfer schemes, while for satellite link or fiber link, we can disseminate time-frequency signal to an arbitrary point in the area where the transmission link is covered. This kind of multiple-access frequency dissemination can benefit for the application of time-frequency synchronization between multiple stations, for example, radar, astronomy, navigation, etc. In the past few years, there are some prior experiments to demonstrate the multiple-access frequency disseminations via fiber links, in which ultra-low noise extractions of RF signal [17–19], optical frequency signal [20, 21], time signal [22, 23], and OFC [24] at arbitrary point of fiber links have been achieved. This kind of multiple-access frequency dissemination can provide a flexibility of reproduction of ultra-sable timing-frequency signal at arbitrary section of a fiber link without design of any independent signal dissemination, while for free-space link, it is still a problem that multiple-access frequency dissemination cannot be realized with currently-used atmospheric frequency transfer techniques.

In this paper, we demonstrate a free-space-based multiple-access frequency dissemination with a frequency comb using passive phase conjunction correction. In our experiment, we first deployed a 60-m long free-space OFC transmission link with our before-used frequency transfer setup [16], and then reproduced a stable radio-frequency signal at the middle point in the entire free-space pathway, where the middle point was chosen arbitrarily. The experiment result shows that the root-mean-square (RMS) timing fluctuation of the reproduced 2 GHz microwave signal at the middle point of the 60 m free-space link was ~224 fs within 5000 s in a normal environment, and the relative fractional frequency instability of the transmission link in a normal outdoor environment is on the order of 8 × 10⁻¹⁴ at 1 s and 1 × 10⁻¹⁶ at 1000 s.

2. Experimental setup for free-space-based multiple-access frequency dissemination

In a multiple-access dissemination of timing and frequency signal with an ultra-low timing fluctuation at a point in the free-space link, the biggest problem is that the air turbulence introduces excess phase noise or timing jitter into the reproduced frequency signal at an arbitrary point in the frequency transmission link [25,26], which indicates the stability of the direct reproduced frequency signal at any point of the free-space link is deteriorated. Therefore, to reduce the stability deterioration in a multiple-access atmospheric frequency transfer, the timing fluctuation affected by turbulence should be suppressed. In the before-presented multiple-access frequency transfer via fiber link, a phase correction technique were proposed with bidirectional phase compensation, in which the timing fluctuations of the reproduced signals at arbitrary point of fiber links have been suppressed. Therefore, based on the phase correction idea, we proposed a free-space-based multiple-access frequency dissemination scheme with a femtosecond OFC using a passive phase correction technique.

Figure 1 shows the experimental setup of our free-space-based multiple-access frequency dissemination with an OFC. In our previous comb-based frequency transfer experiments, an Er: fiber mode-locked laser (MLL) was used as the OFC source, and disseminated from the transmitter to the receiver with a passive phase conjunction correction technique [16]. Here, the comb-based frequency transmission link is rebuilt, where the frequency signal is transferred from transmitter and receiver with the phase conjunction correction. In this frequency transmission link, an Er: fiber MLL with repetition frequency of 100 MHz and center wavelength of 1550 nm, is tightly locked to an Rb clock referenced RF source (Agilent, E4421B) with a phase-locked loop (PLL) at 2 GHz. A laser pulse beam with optical power of 60 mW generated from the laser is directly launched into free-space. With the help of a half-reflecting mirror (HM) on the receiver and a mirror on the transmitter, the laser light travels three times over the optical free-space link between transmitter and receiver (see Fig. 1). On the receiver, part of the laser beam which travels the free-space link once and the other part of the beam which travels the free-space link three times are both detected by two high-speed photodiodes (PD2 and PD3) respectively. By mixing the third harmonic of the microwave detected by PD1 and fundamental signal of the microwave detected by PD2, a clean and stable microwave signal at the lower sideband is achieved because of the natural elimination of timing fluctuation with the down-converting function of the mixer. This process realizes a stable frequency transfer from transmitter to receiver, which has been demonstrated in our previous report [16]. After this, to achieve a multiple-access frequency dissemination in this paper, we arbitrarily chose a point of the optical free-space link to reproduce the comb frequency signal. In the arbitrary section of the rebuilt free-space frequency transmission link, we coupled three beams on the laser travel path at three nodes a, b, and c via three partially reflecting mirrors (10:90). Three high-speed photodiodes (PD4, PD5, and PD6) and three band-pass filters (BF4, BF5, and BF6) were used to extract the three microwave signals V_a, V_b, and V_c, respectively. Here, V_a is the extracted second harmonic signal of MLL, and V_b and V_c are the extracted fundamental frequency signals of MLL. After the extraction, V_a is mixed with V_b via a RF mixer, and its higher sideband is extracted via a band-pass filter (BF7) to produce a new intermediate signal V_d. Next, by mixing the new intermediate signal V_d and V_c, and extracting its lower sideband signal, a clean and stable microwave signal at the lower sideband is achieved because of the natural elimination of timing fluctuation with the up-converting and down-converting function of the mixers. Note that, for the recovered microwave signal at this arbitrary point in the free-space link, the timing fluctuation affected by turbulence is eliminated naturally by the passive phase conjunction correction scheme. The mechanism of the elimination of the timing fluctuation in the multiple-access frequency dissemination will be explained in detail below.

 

Fig. 1 Experimental setup of free-space-based multiple-access frequency transfer with OFC by using passive phase conjunction correction. PD: photodiode, HM: half-reflecting mirror, PI: proportional-integral controller, BPF: band-pass filter. V₁… V_n, are harmonics of the OFC.

Download Full Size | PDF

As shown in Fig. 1, we assume the frequency-stabilized OFC has a fundamental frequency V₁, second harmonic frequency V₂, and third harmonic frequency V₃ in RF domain; the initial phase of the fundamental frequency signal is φ₀. Accordingly, the initial phases of the second harmonic are 2φ₀. We also assume the air turbulence introduces a phase fluctuation φ_p to the transmitted signal between the transmitter and receiver, a phase fluctuation φ_p1 between the transmitter and arbitrary point, and a phase fluctuation φ_p2 between the receiver and arbitrary point, at the fundamental frequency over a one-trip free-space link. Naturally we have φ_p = φ_p1 + φ_p2. In this case, on the arbitrary point, the phase delay of the second harmonic signal V_a coupled from a is given by φ_a = 2φ₀ + 2φ_p1, the phase delay of fundamental frequency signal V_b coupled from b is given by φ_b = φ₀ + φ_p + φ_p2, and the phase delay of fundamental frequency signal V_c coupled from c is given by φ_c = φ₀ + 2φ_p + φ_p1, respectively. With mixing V_a and V_b, and extracting its higher sideband, a new intermediate signal V_d is produced, and its phase delay, therefore, is given by φ_d = φ_a + φ_b = 3φ₀ + 2φ_p + φ_p1. Next, by mixing V_d and V_c, and extracting its lower sideband, a final microwave signal V_out is produced, and its phase delay, therefore, is given by φ_out = φ_d-φ_c = 2φ₀. Note that, for the recovered microwave signal V_out at this arbitrary point, the phase fluctuation affected by turbulence is eliminated naturally by the passive phase conjunction correction scheme. To verify this multiple-access frequency dissemination technique with passive phase conjunction correction, an actual OFC-based multiple-access frequency transfer experiment has been conducted.

Our frequency transmission link was located at the top floor of the engineering building of our university. The distance between the transmitter and receiver was 60 meters, and the middle point of the transmission link was arbitrarily chosen as the multiple-access frequency dissemination point, in which a stable RF frequency has been extracted. In this multiple-access frequency transfer experiment, we chose 1 GHz as the fundamental frequency V₁ (10th harmonic of the OFC), and accordingly the frequency of V₂ is 2 GHz (20th harmonic of the OFC). With the passive phase correction technique described above, a clean and stable 2 GHz RF signal should be extracted on the arbitrary point. To estimate the timing fluctuation and stability of the resulting 2 GHz RF signal, we mixed it with a frequency reference signal which was coupled from the transmitter via a 30-m long fiber link, to produce a DC error output and sent it to a digital voltage meter (Keysight, 34461A), for data recording and analysis. To compare the qualities of the transmitted frequency signals with and without timing fluctuation suppression, a direct link was also designed (Fig. 1). In this direct link setup, a 2 GHz microwave was extracted from PD4 and BF4, and directly mixed with the reference signal.

3. Experimental results and discussion

Our multiple-access frequency transfer experiment was conducted in a normal night. We believe the quality of the frequency extracted at the arbitrary point should be improved significantly when compared to the uncorrected direct link. Because the passive phase conjunction correction can suppress the additional timing fluctuations caused by turbulence, Here, we measured the timing drifts and relative frequency stabilities of the reproduced OFC signals with and without phase conjunction correction. The timing drift results are shown in Fig. 2. Here, Curve (i) and (ii) are the measured timing drift of the transferred 2 GHz RF signal without and with timing fluctuation suppression. It can be calculated that the RMS timing fluctuation without and with timing fluctuation suppression are 1.3 ps and 224 fs within 5000 s, respectively. In addition, the 30-m short fiber could introduce a few extra phase noise. Therefore, we tested the timing fluctuation of the reference signal coupled from the fiber, by comparing it to the RF reference on the transmitter (see Fig. 1). The measured residual timing drift can be treated as the measurement floor of our multiple-access frequency transfer experiment. Curve (iii) shows the residual timing drift of the reference signal coupled form the short fiber, and its RMS timing drift is approximately 45 fs within 5000 s.

 

Fig. 2 Timing fluctuation results for free-space-based multiple-access frequency transfer. Curve (i): Without timing fluctuation suppression. (ii): With timing fluctuation suppression. Curve (iii): The result for the 30-m long short fiber link as a measurement floor. Sample rate is 1 point/second for all curves.

Download Full Size | PDF

To evaluate the stability of the multiple-access frequency transfer, we calculated the Allan Deviation of the transferred 2 GHz frequency signal at the arbitrary point. Figure 3 demonstrates the instability results of the transferred RF signal. Curve (i) and (ii) shown in Fig. 3 are the relative Allan Deviations without and with timing fluctuation suppression. These curves show the instability of the multiple-access frequency transmission link without timing fluctuation suppression is 8 × 10⁻¹³ at 1 s and 4 × 10⁻¹⁶ at 1000 s, and the instability of the transmission link with timing fluctuation suppression is 8 × 10⁻¹⁴ at 1 s and 1 × 10⁻¹⁶ at 1000 s, respectively. We also demonstrates the instability measurement floor as Curve (iii) that is obtained directly from the short fiber link. Note that, curve (iii) is merely the lower bound of instability incurred during the multiple-access frequency transfer experiment. This is because it was measured with the short fiber link, and most of the turbulence and vibration effects were cancelled out. By comparing Curve (i) and Curve (ii), we find that the instability of the transferred signal at the arbitrary point with phase correction is reduced more at short-term scale (1 s) than long-term scale (1000 s). We believe this is because the most of timing fluctuation affected by turbulence is within short-term scale (less than few hertz). The improvement of Curve (ii) also proves that the phase conjunction correction can effectively eliminate the residual timing fluctuation of the multiple-access frequency transmission link. When comparing the instability of our transfer result and that of a commercial Cs clock (5071A) [27] or H-master clock (MHM-2010) [28], we find that the instability of the multiple-access frequency transmission link is lower than those of the clocks. Therefore, we believe that disseminating a Cs or H-maser clock signal at arbitrary point over a short free-space link is feasible with the atmospheric comb-based multiple-access frequency transfer technique proposed in this paper.

 

Fig. 3 Instability results for free-space-based multiple-access frequency transfer, (i) Relative Allan deviation between transferred microwave and reference signal without timing fluctuation suppression; (ii) Relative Allan deviation with timing fluctuation suppression; (iii) Allan deviation for a short link as measurement floor.

Download Full Size | PDF

4. Conclusions

We have demonstrated a free-space-based multiple-access frequency dissemination with OFC by using passive phase conjunction correction. The RMS timing fluctuation for a 2 GHz frequency signal extracted at middle point over a 60-m long free-space link was measured to be approximately 224 fs within 5000 s with a fractional frequency instability on the order of 8 × 10⁻¹⁴ at 1 s and of 1 × 10⁻¹⁶ at 1000 s. The achieved instability demonstrates that the proposed multiple-access frequency transfer setup with passive phase conjunction correction promises a high flexibility of timing and frequency dissemination at arbitrary point of a free-space transmission link. For instance, the proposed setup can be used to transfer a Cs or H-master clock signal at arbitrary point over a free-space transmission link. In the future, we will attempt to build a free-space-based multiple-access frequency dissemination link with a lower short-time timing fluctuation and a longer distance by using a higher power OFC and higher frequency harmonic.