1. Introduction

Dissemination of precise optical clocks based on optical transitions in laser cooled atoms and ions [1] enables wider usage of these frequency references for metrology applications such as fundamental physics tests, and remote comparison of frequency references ([2] and references therein). In addition, applications in other fields such as geodesy and astronomy [3], sensing [4], deep space navigation [5], as well as emerging applications such as super GPS and time and frequency dissemination from the ‘cloud’ will directly benefit from precise frequency dissemination. Accurate Optical Frequency Dissemination (OFD) has been widely demonstrated within the last two decades with extension of dissemination lengths from 100s of km [6–8] to 1840 km [9] with promising record of fractional instability 2 × 10⁻¹⁵ with 1 s averaging time.

Current OFD schemes require a dark fibre link or dedicated research fibre networks as well as bi-directional amplifier(s) to compare the return clock with that of the original and track the slow phase noise of the link and cancel it by phase modulation [7] or a fibre stretcher [10]. With increasing interest in, and demand for, the practical availability of such precise clocks, a key advance in the dissemination technology is required so that these clocks can be transmitted over existing installed fibre optics communication systems and networks. If this step can be made, a new class of end users and applications will benefit from these optical references. To this end, several successes have been reported using a real optical communication link for precise frequency dissemination [11–13]. In these demonstrations, the bi-directionality of the link was enabled using optical add-drop multiplexers and bi-directional amplifiers. In addition, since the launch power is limited by stimulated Brillouin scattering (SBS), to extend the dissemination length and compensate for higher noise and loss of a network fibre, inline repeaters were used [11]. In each repeater, an additional low noise laser is phase locked to the incoming signal as a regenerator and stabilizer for the next segment. While such demonstrations reflect the fact that a bi-directional precise dissemination may be implemented in a real data network with live data traffic, there remain major challenges in making a deployable dissemination scheme. The needs for a bi-directional link and amplifier as well as an all-optical stabilization scheme are at odds with present network architectures. These would require considerable and un-economic modifications for implementation of a bi-directional dissemination scheme.

In this paper, we introduce and demonstrate a novel dissemination scheme for high-fidelity optical carriers using coherent communication techniques, achieving moderate fractional instabilities (~10⁻¹⁴). The scheme is unidirectional, more resilient to the launch power for SBS suppression [14,15], and is deployable in a real telecommunications optical fibre network. We demonstrate a dissemination scheme with 10 Gb/s Binary Phase Shift Keying (BPSK) modulation and unidirectional, round-trip transmission over 124 km of field-installed optical fibre between Cork City and town of Clonakilty (50 km south west of Cork) using an ultra-narrow linewidth laser source as high-fidelity optical carrier. With Allan deviation measurements, a fractional instability of ~3.3 × 10⁻¹⁴ has been achieved for 1 s averaging time without bi-directional phase compensation. This is the first attempt, to the best of our knowledge, to demonstrate a dissemination scheme based on coherent communication techniques which is fully deployable in current optical fibre coherent systems and networks. The current demonstration shows fractional instabilities of approximately 10⁻¹⁴, essentially confirming that the technique allows for a modulated data signal to be used to transfer frequency information to the same fidelity as CW signals. However, as is the case for CW signals, low frequency fluctuations in fibre length should be compensated. This may be performed using the conventional bidirectional technique [6–13]; however, it is conceivable that the data modulation may enable alternative unidirectional approaches to be investigated as discussed in section 3.4. The paper is arranged as follows: in Section 2 the principle of operation and experimental arrangement are described; performance measurements and discussion are presented in Section 3, and conclusion is drawn in Section 4.

2. Principle of operation and experimental arrangement

The basic diagram of the scheme is shown in Fig. 1. The system is divided in three main building blocks. At the transmitter side, the CW high-fidelity carrier is phase modulated and then launched through the optical fibre link (denoted as the link). At the receiver, first the carrier is recovered from the transmitted signal by demodulating it with the regenerated data signal. This is done in a two-stage process: firstly, the electrical data at the receiver is regenerated using optical/electrical (O/E) conversion and feed-forward based homodyne coherent detection [16]. Then, the residual modulation and additional noise is suppressed by optical injection-locking of recovered carrier to a stable CW local semiconductor laser. The recovered carrier after phase noise cancellation and stabilization can be re-modulated and lau-nched into the next carrier dissemination link. It is worth noting that BPSK modulation with Pseudo-Random Binary Sequence (PRBS) data broadens the signal by the order of the bit rate, which increases the SBS threshold [15]. The increase in SBS threshold enables higher launch powers than for CW bi-directional dissemination systems and reduces the complexity and cost of inline amplification requirements. This is an important feature of our scheme.

 

Fig. 1 Block diagram of proposed OFD system based on coherent communication link.

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The detailed experimental arrangement for the high-fidelity carrier dissemination over installed fibre is shown in Fig. 2 which consists of the three sections of Fig. 1. The transmitter section (in Cork City) is followed by the installed fibre link (Cork City-Clonakilty-Cork City), and the receiver section (in Cork City) is further broken down into a carrier recovery section, a laser injection locking section, and lastly an analysis section. The latter includes the frequency instability, optical linewidth, and RF spectrum measurements. The transmitter consists of an ultra-stable CW fibre laser followed by a Mach-Zehnder modulator (MZM). We used a commercial ultra-narrow linewidth DFB fibre laser (Koheras Adjustic E15 model from NKT Photonics) in this work. The laser system was a bench top module with active wavelength control without additional stabilized cavity or referencing to an atomic clock. The optical linewidth of the laser was measured to be ~1.9 kHz using the self-heterodyne technique with a fibre delay of 77.2 km.

 

Fig. 2 Experimental arrangement for the dissemination scheme deployable to a real fibre optics network. List of acronyms: AOM: Acousto-Optic Modulator, MZM: Mach-Zehnder Modulator, BPF: Band-pass filter, CRU: Clock Recovery Unit, DI: Delayed interferometer, Diff. Encd. Differential Encoder, PC: Polarization controller, DCF: Dispersion compensating fibre, SMF: Single-mode fibre.

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The electrical signal to drive the MZM was generated from a pattern generator giving a Pseudo-Random Binary Sequence (PRBS length: 2⁷-2³¹), with bit-rate 10.709 Gb/s. To create phase-modulation, a modulator driver generating a Vπ signal at the modulator, which was DC biased at null, created a binary phase-shift keyed (BPSK) modulation [17], depicted in the eye diagram (I) in Fig. 2. There is a π phase shift between ‘zero’ and one bits in this modulation format which creates a carrier-less signal when time averaged. The BPSK signal was launched ( + 5 dBm power) to the optical fibre pair running from Cork City to the town of Clonakilty on different on-going and return paths with a round-trip length of 124 km. The optical fibre pair (two different fibre strands in a bundle of 16 strands) used is a commercial link installed by British Telecom (BT) and access to their infrastructure was given to us for this work. The average insertion loss of the link was measured to be 0.21 dB/km with total loss of 26.8 dB, including the fibre connectors. At the receiver, the optical signal was first pre-amplified (EDFA1 + 10 dBm), filtered and dispersion compensated with a dispersion compensating fibre (DCF) and additional single-mode fibre (SMF) of ~2 km length and total loss of 8.3 dB. The signal was then amplified to the power of + 13 dBm, followed by the second band-pass filter.

At the receiver, the carrier-recovery section generates the original data pattern (inverted or same logic) electronically and phase modulates the BPSK signal with this generated pattern [16]. Note that re-modulating the BPSK signal with the same (or inverted) data causes all bits to have phase shifts of 0 or 2π, (or all π), resulting in cancellation of the phase modulation, so recovering the original carrier. For this purpose, the incoming optical signal is split into two paths. In path (1) (Fig. 2) the BPSK optical signal is demodulated by conversion to an intensity modulated signal using the 1-bit delay interferometer (DI) (eye diagram (III) shown in Fig. 2). The outputs of the DI were split so that a tap is used for clock-recovery which is required for optical/electrical/optical (OEO) carrier-recovery circuit. The clock-recovery was carried out using a commercial unit (Centellax TR1C1-A) that generates a sine-wave from the Non-Return to Zero (NRZ) signal. Using a pair of same couplers and delay elements both DI output ports were time synchronized with similar intensity before being detected using balanced photo-diode detectors for the OEO circuit. The photo-current signal drives a differential encoder (after a fan out/limiting amplifier) to generate the inverted or same data pattern electronically (50% probability). The encoder output signal (eye diagram (IV) in Fig. 2) drives a second MZM via a driver amplifier to re-modulate the optical signal with this pattern. A fine tunable delay element and a polarization controller in path (2) are used to match the timing of the optical signal arriving at the MZM to its electrical signal in path (1) and to match the polarization state of the optical input signal. It is worth noting that the recovered carrier has amplitude transitions caused by null-transitions of the MZM during π phase shifts [18] (eye diagram (V) in Fig. 2). The recovered carrier passes through a coupler (10% tap, injection monitor) and a polarization controller (to match the polarization state) before being injected to the cavity of a stable CW single-mode laser (slave laser) through a circulator (port 1). To minimize optical feedback to the slave laser, the circulator is placed before the laser, and port 2 of the circulator is spliced to slave laser’s pigtailed fibre. The local (slave) laser was a single-mode CW “digital” DFB quantum well laser where a single mode performance was obtained by etching features into the ridge of a Fabry-Pérot cavity [18–20].

The output of the slave laser (port 3 of the circulator) was used for fractional instability and optical linewidth measurements. The RF spectrum of the slave laser was also monitored to confirm the regime of stable injection-locking. All the frequency instability measurements were carried out by measuring the frequency error of the beat note between the signal under test and the frequency shifted version of the transmitter laser source (self-referenced) at Tyndall (Cork City), shown in Fig. 2 bottom right. For this purpose, a tap of slave laser’s light was mixed with a frequency shifted version of the original fibre laser’s light (using an acousto-optic modulator) through a coupler to generate a beating signal at 30.0 MHz on a 125MHz ultra-low noise photo-receiver (New Focus 1811). The electrical signal was measured on a dead-time free counter (Keysight 53230A) for long- term stability analysis. The 10.0 MHz reference signal from an oven-stabilized microwave atomic clock (counter’s reference) was synchronized to the third harmonic from a commercial function generator (HP 8116A) to drive the acousto-optic modulator (AOM) at 30.0 MHz. The short and long-term stability of the self-heterodyne beat note (short delay) for high-fidelity lasers was not limited by RF signal synchronized to the 10 MHz reference confirming no additional noise contributed from the 30 MHz driving signal.

In Fig. 3(a), the optical spectra of the BPSK signal (dashed-black), recovered carrier (solid-blue), and injection-locked laser (solid-red) are shown. As can be seen, the BPSK spectrum is a broad shape with no carrier at the fibre laser’s emission wavelength. However, in the carrier-recovery circuit, when the optical delay between the optical and electrical signals is optimized a single-mode spectrum with ~18 dB side-mode suppression ratio (SMSR) was observed (Fig. 3(a), solid-blue). The side modes in the spectrum correspond to the amplitude modulation caused by null transitions of the MZMs which is observed in the eye diagram V (recovered carrier) in Fig. 2. As can be seen, this modulation was completely suppressed when the recovered carrier was stably injection-locked to the slave laser (Fig. 3(a), solid-red). When this occurred, the optical linewidth of the slave laser was decreased from MHz range to that of the original fibre laser with no observable broadening after transmission [21]. We also confirmed stable injection-locking by observing a clean RF spectrum with no amplitude fluctuations coming from frequency beating or nonlinear dynamical instabilities. The eye diagrams of the BPSK signal before transmission, after transmission, and after dispersion compensation is shown in Figs. 3(b)-(d).

 

Fig. 3 (a). Optical spectra of the BPSK modulated signal (dashed-black), recovered carrier (solid-blue), and injection-locked laser (solid-red). (b) The eye diagram of 10 Gbps BPSK at the transmitter. (c) After the 124 km field-installed BT optical fibre link (Cork-Clonakilty). (c) After dispersion compensation at the receiver.

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3. Measurement results and discussions

3.1 Optical signal to noise ratio and OEO delay mismatch

We analyzed the robustness of the dissemination system against Optical Signal to Noise Ratio (OSNR) deterioration. For this purpose, a variable optical attenuator and EDFA2 in constant power mode (Fig. 2) were used (EDFA1 and DCF in Fig. 2 were removed) for back-to-backmeasurements (no transmission). The measured optical linewidth of the injection-locked laser against OSNR is shown in Fig. 4(a). We see that the linewidth of the laser remains similar to the fibre laser for OSNRs ≥28 dB. When the OSNR deteriorated below this value, an abrupt increase in the linewidth of up to 100 kHz was observed. We measured the linewidth of the recovered carrier (before injection-locking) and similar linewidths were measured. We believe that the main limitation is from the balanced detector’s photo-current before the OEO circuit. This was confirmed by measuring the OSNR tolerance of single-detection which was ~3 dB worse than the balanced detection. In the clock-recovery circuit, any noise in the electrical signal’s amplitude driving the MZM is directly transferred to the phase-noise of the recovered carrier. This limit can be extended by adding an RF amplifier before the differential encoder or another EDFA (cascaded) before the balanced detector [16].

 

Fig. 4 (a). OSNR tolerance of linewidth of self-homodyne high-fidelity carrier receiver (Back-to-Back). (b) Fractional instability as a function of time delay between the optical and electrical signal at the carrier recovery circuit.

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We also studied the performance of the receiver when the delay between the electrical and optical signals in the second MZM is detuned from its optimum point. For this purpose, we measured short term stability (Allan deviation) for 10 μs gate time (zero dead-time) and 300,000 samples (3 seconds total measurement time). The fractional instability for 10 μs and 1 ms (sample averaged) gate times are depicted in Fig. 4(b). The injection ratio was kept constant for all the delay values (~-40 dB). No significant change was observed in the fractional instabilities for both gate times once the signal detuning remained < 50 ps (bit duration ~93 ps). The SMSR of the optical spectrum was decreased from ~18 dB to ~6 dB before any noticeable increase in the fractional instability observed, confirming excellent tolerance of optical injection-locking with power fluctuations of the recovered carrier.

As the delay was changing, we also monitored the RF spectrum of the beat note (30 MHz) showing some increase in the SNR without any visible change in the linewidth. This confirmed that the origin of instability is not the broadening in the beat note, pointing to some other cause of the increase in Allan deviation. The time trace of frequency data (1 or 10 μs gate time) measured from the counter for the delay detuning around half bit duration (negative or positive) showed some form of high speed frequency switching. Looking at the histogram of raw frequency data, we observed side-bands around the main lobe evenly distributed ~100 kHz with similar Gaussian-like distributions unlike smaller delays which only showed one symmetric distribution. Note that at these delays, the optical spectrum showed a poor SMSR and a narrow peak with a broad pedestal, indicating incomplete carrier recovery. This modulation might be a result of complex dynamical switching of slave laser’s optical field at the boundary of locked and unlocked states.

3.2 Optical injection-locking in noise suppression

It has been shown that injection-locking can suppress the unwanted side bands separated by the bit rate frequency shown in the optical spectrum of recovered carrier (Fig. 3(a)). Here, wepresent a more detailed performance analysis of optical injection-locking in suppressing unwanted amplitude modulation caused by MZM operation, shown in Figs. 5(a)-(d). The RF spectra of the recovered carrier (blue) and injection-locked laser (red) are shown in large span (a), (c) and zoomed (b), (d) for two PRBS lengths (2⁷-1, 2¹⁵-1). Note that the finite length of PRBS data pattern imposes an additional periodicity on the modulation which manifests as low frequency spur tones. For example, for the shortest PRBS (2⁷-1) and bit rate 10.7 GHz, spur tones are created every ~84 MHz, seen in Figs. 5(a) and 5(b). As can be seen, the spur lines present in the recovered carrier were completely suppressed after injection-locking. We increased the length to 15 bits (Fig. 5(c)) reducing the spur spacing to ~330 kHz and we note that these lines are still suppressed through optical injection. This confirmed the injection-locking process acted as a very effective limiter, not only suppressing the bit-rate range amplitude modulations as seen in Fig. 3(a) but also the PRBS related “slow” spur tones down to the sub-MHz range. Study of noise suppression for longer PRBS lengths were limited by the RF spectrum analyser, but the results presented above clearly demonstrates optical injection as an effective amplitude limiter [22].

 

Fig. 5 (a). RF spectra of recovered carrier (blue) and injection-locked laser (red). (a) For 10 Gb/s BPSK PRBS length 2⁷-1, full span. (b) Same as (a), zoomed. (c), (d) for 10 Gb/s BPSK PRBS length 2¹⁵-1.

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It has been demonstrated that low injection levels (<-30 dB or lower) helps for suppression of high-speed phase noise [23–25]. The OEO carrier recovery and injection-locking scheme has also shown to be effective as a phase regenerator for high frequency phase noise [26]. We also studied the performance of injection-locking in phase noise suppression of recovered carrier. For this purpose, the RF spectrum of the beat-note between the injection-locked laser and original fibre laser (before modulation at the transmitter) was analyzed. Note that the amplitude of the beat note between two optical fields is contributed by both the optical fields’ intensity and their phase noises. In the absence of significant intensity modulation in the optical field of the injection-locked laser (Fig. 5), no intensity fluctuations in fibre laser and negligible phase noise of fibre laser, the RF spectrum of the beat-note indicates the phase-noise of the injection-locked laser. The spectra for recovered carrier (blue) and injection-locked laser (red) normalized to the RF peak power are shown in Fig. 6(a) for PRBS 15 (~330 kHz). It can be seen that some improvement in noise suppression (< 10 dB) after injection-locking was observed. However, the injection-locking was not able to complet-ely suppress the residual phase-noise unlike amplitude noise. To quantify the spectral contribution of this residual phase noise, we compared the percentage of increase in Allan deviation of the recovered carrier, shown in Fig. 6(b). For each transmission length, the base case (reference to calculate the percentage of increase in Allan deviation) was the shortest PRBS (2⁷-1). For Back to Back, we reference to shortest PRBS in back to back transmission and for the field-installed fibre we refer to that of shortest PRBS with transmission over the fibre. As expected, the Allan deviation increased with longer PRBS length (closer spur tones in frequency). However, when the recovered carrier was injection-locked, the percentage increase dropped by a factor of two. Note that for Back-to-Back we observed higher percentage increase. This confirms that the contribution of PRBS side-bands to the phase-noise is more significant as the beating tone is much narrower because of the fact that the two laser lights are coherent. It is worth noting that reducing the frequency of spur tones (longer PRBS length) limits the performance of injection-locking in suppressing these lines.

 

Fig. 6 RF spectra of the beating signal (30 MHz) for the recovered carrier before (blue) and after (red) injection-locking. PRBS length: 2¹⁵-1. (b). Percentage change of Allan deviation (10 μs and 1 ms gate times) for longest PRBS length (2³¹-1) before and after injection-locking compared to shortest PRBS length (7 bits) after transmission. The Back-to-Back cases were also reference to shortest PRBS in Back-to-Back.

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3.3 Fractional instability measurements

For frequency stability measurements, the counter was set to the continuous measurement mode (dead-time free) and Π-type (non-over lapping) averaging. For short term stability, the gate time was set to 1 ms with total measurement time of 10 minutes (600,000 samples). For long term stability measurements, we set the gate time to 1 s and the measurements were taken overnight for > 12 hours over which time we observed stable performance of the setup including the carrier recovery and injection-locking. The main limitation to longer measurement time arose from polarization drift occurring during transmission and sensitivity of MZM at the carrier recovery circuit to the polarization of incoming light. This drift affected the power of recovered carrier and hence the stability of injection-locking process. This can be mitigated using active polarization control using commercial components [27]. The logged data from the counter was then post processed using the classic (non-overlapping) Allan deviation formula [28]:

Where $\sigma (\tau )$ is the Allan deviation, $\overline{y_l}$ is the i_th averaged sample at the gate time, and M is the total number of samples. The fractional Allan deviation was then obtained by dividing the Allan deviation by the measured optical frequency using a calibrated optical spectrum analyzer with wavelength accuracy of ± 0.01 nm (1.25 GHz) and resolution bandwidth of 0.02nm (2.5 GHz). The $\sigma -\tau$ results are shown in Fig. 7(a) for several scenarios: Cork-Clonakilty link (red filled triangles), a 20 km SMF link in the lab (blue-filled circles) and Back to Back measurements (black-filled squares) where no link between the transmitter and receiver existed. The beating signal from the fractional instability setup between the received carrier after 124 km transmission and the original laser was measured to be ~2.8 kHz.

 

Fig. 7 (a). $\sigma -\tau$ measurements for unidirectional link different scenarios and two fibe lasers as the high-fidelity optical carrier. (b) Frequency error data for Cork-Clonakilty link using Koheras laser (1 s averaging time). (c) Statistical distribution of data in 7(b).

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For the Cork-Clonakilty link, the fractional instability of ~3.3 × 10⁻¹⁴ was achieved for 1 s averaging time. We observed a better performance over 20 km lab transmission (blue-filled circles) compared to the Cork-Clonakilty fibre; however, their performances match very well for averaging time > 200 s. Detailed spectral analysis of the noise contributions from the laser or the link requires access to the ~Hz linewidth laser and a dynamic (FFT) analyzer to measure sub Hz phase noise; this will be carried out in a separate study. The Back-to-Back case showed the best performance for both short term and long term ranges with fractional instability of few parts in 10⁻¹⁵. The long-term stability of the Back-to-Back case might be affected by the noise of transmitter/receiver sections gated by the external 10.7 GHz RF oscillator driving pattern generator. This RF source was operating independently from our 10 MHz reference source from the counter. The significant difference in performance is associated with the limited coherence length of the optical carrier, confirming the kHz range optical linewidth. With these observations, it was confirmed that the long-term performance of the Cork-Clonakilty link is dominated by the laser phase-noise rather than the fibre link. This means the results should be significantly improved by further stabilizing the lasers’s cavity similar to the laser system reported in [11].

A recorded time-trace for the long term stability (Cork-Clonakilty link) measurement from the counter as well as statistical distribution of frequency errors are shown in Fig. 7 (b), (c). The random nature of the data with symmetric distribution over the mean frequency was confirmed in Fig. 7(b). The average frequency of the beat note was measured to be 29,999,993.82078 ± 0.00002 Hz.

3.4 Discussion

While the system ran stably > 12 hours despite polarization drift from the link fibre, the results so far are limited in several aspects. Firstly, the fractional instability for the field-installed optical fibre is limited by the high-fidelity source rather than the link, confirming the limit of laser’s coherence length. We expect to have significantly improved results for short and long-term stability with the use of stabilized cavity fibre lasers providing sub Hertz linewidth [11]. With such optical references for coherent transmitter; we would expect to see the long-term drift of the transmission link due to environmental effects.

The next challenge is to investigate the possibility of injection-locking process as an active filter to compensate the slow phase variation of the recovered carrier due to the link refractive index change. While very low injection levels can suppress the high-speed residual phase noise of the injected signal to some degree, it can contribute to higher noise level at lower frequencies [29]. In our measurements, we also observed a similar behavior: when the injection ratio went below −50 dB, the spur tones at Fig. 6(a) were suppressed better, but the fractional instability showed increase in averaging time in the order of seconds. We propose a cascaded injection-locking scheme where the high frequency amplitude and phase-noise is suppressed during the first injection-locking stage to a semiconductor laser. Then, using a high Q long-cavity stable laser for second injection-locking stage the slower (sub kHz range) noise can be suppressed.

4. Conclusion

We have proposed and demonstrated a novel and practical (unidirectional) scheme for dissemination of high-fidelity optical carriers based on coherent communication techniques for phase modulated signals. The scheme involves BPSK modulation of an optical carrier at the transmitter, followed by self-homodyne coherent detection and optical injection-locking at the receiver. Using commercially available optical components, we implemented a 10 Gb/s system using an ultra-narrow linewidth laser source, transmitted over a field-installed optical fibre between Cork and Clonakilty (124 km). The properties of injection-locking for noise suppression as well as short and long term stability of the recovered carrier were analyzed. The true Allan deviation measurements show fractional instabilities of few parts in 10⁻¹⁴ for 1 s averaging (gate) time. Future work will focus on using cavity stabilized laser or carrier envelope offset (CEO) mode-locked lasers to remove the residual phase instability in the launched carrier which plays a limit on the phase noise (fractional instability) of the carrier dissemination. This will be developed further to a transportable test bed to enable extensive trailing with optical atomic clocks. The system described enables the high-fidelity dissemination of optical carriers at near zero cost since the OEO carrier recovery scheme does not affect the underlined data impressed on the carrier up to at least 10 Gb/s line rates. Consequently, the carrier dissemination and the data transmission utilizing the same launched beam are independent aspects of the system where the data is recoverable without affecting the carrier. The scheme is fully compatible and deployable with current installed telecommunication networks. This economic feature has tremendous implications for the widespread deployment of “network friendly” high-fidelity carrier dissemination systems.