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Abstract
Herein, we verify that a Raman/EDFA hybrid amplifier can improve the stability of fiber-optic time and frequency synchronization systems compared to the Er3+-doped fiber amplifier (EDFA), owing to its higher gain and lower noise figure (NF) performance. We studied the variation law of Raman gain efficiency for a fiber Raman amplifier (FRA) as a function of pump power and input signal power, designed a bidirectional Raman/EDFA hybrid amplifier, and proved that equivalent NF below 0 dB can be obtained. Finally, hybrid amplifiers were compared to EDFAs in a free-running frequency synchronization system. The transfer stabilities reached 1.9678 × 10−13/1 s and 2.0248 × 10−13/1 s when FRA + EDFA and EDFA + FRA configurations were used, respectively, both exhibiting better performance than the stability of 3.0905 × 10−13/1 s obtained by EDFA.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Time and frequency standards significantly contribute to a broad range of avenues involving commercial applications and scientific research (e.g., metrology, navigation, and telecommunication). Fiber-optic networks have afforded promising approaches to realize more accurate comparison techniques than satellite-based systems. When the time and frequency signals either be transmitted either separately [1,2] or at the same time [3], different kinds of optical amplifiers, such as the Er3+-doped fiber amplifier (EDFA) [4,5], fiber Raman amplifier (FRA) [6], fiber Brillouin amplifier [7,8], and optical injection locking amplifier [9,10] have been used to extend stable comparison lengths for regional applications or transoceanic international applications. The advantage of the fiber Brillouin and optical injection locking amplifiers is their characteristically high gain for small signals, but the small bandwidth characteristics limit their use in systems in which time and frequency are transmitted simultaneously.
EDFA is one of the most commonly used amplifiers for optical fiber links and can cover C + L band transmission. The distributed FRA has been investigated, and the bandwidth can reach approximately 6 THz. Therefore, both the EDFA and FRA can be used in the relay system for a synchronous transmission of time and frequency signals (e.g. 1 pulse per second and 2.4 GHz). The noise of the EDFA comes from amplified spontaneous emission (ASE) noise, and the power of the ASE can be estimated as $ASE = 2{n_{sp}}({G - 1} )hv{B_{ref}}$ [11], where ${n_{sp}}$ represents the Er3+ inversion parameter, G denotes the gain of the amplifier, h is the Planck’s constant, v is the frequency of the light, and ${B_{ref}}$ denotes the optical bandwidth. Therefore, to reduce the ASE noise of the amplifiers, the length of the fiber link between amplifiers needs to be limited to avoid the use of EDFAs with very high gain. However, in our experiment, limited by power supply and other factors, the amplifiers were placed in some fixed places, which inevitably resulted in long-distance optical fiber transmission. In this case, the EDFA inevitably introduced a lot of ASE noise and reduced the performance of the time and frequency synchronization system, even though no useful signal was received at the remote side. Moreover, the minimum noise figure (NF) of the EDFA is 3 dB [12], which means that the signal-to-noise ratio (SNR) of the signal was bound to deteriorate, even though the power was compensated. The FRA is regarded as a promising amplifier to realize ultra-long haul fiber-optic transmission and is capable of exhibiting an equivalent NF below 0 dB [13,14]. However, a small gain can be obtained with very high pump power (approximately a few hundred mW) fed into the fiber. Therefore, by combining the low noise of the FRA and the high gain of the EDFA, we fabricated a Raman/EDFA hybrid bidirectional amplifier with high gain, low noise, and wide bandwidth to attain fiber-optic time and frequency synchronization systems.
In Section 2 of this paper, we present the modeling and experimental research on FRA using the dispersion compensation fiber (DCF) or single-mode fiber (SMF) as the gain medium, focusing on the Raman gain efficiency as a function of the input signal and pump power. Section 3 proposes a bidirectional Raman/EDFA hybrid amplifier based on the bidirectional transmission characteristics of the time and frequency transfer system and presents our analysis of the gain and noise of the hybrid amplifier. Finally, different structures of relay systems (EDFA, Raman + EDFA, and EDFA + Raman hybrid amplifiers) are employed in a free-running frequency transmission system in Section 4.
2. Raman amplification in an optical fiber
Figure 1 presents a schematic diagram of the distributed FRA with a 1455 nm laser as the co-directional pump and the DCF or SMF as the gain medium. In addition to producing gain for the signal, the FRA resulted in noise accumulation, which corrupted the transmitted information. The two most important types of noise are spontaneous Raman scattering (SpRS) and double-Rayleigh backscattering (DRB) noise [14,15]. SpRS is generated along with the fiber and then amplified by the Raman pump, whose characteristics are similar to the ASE noise in the EDFA. Therefore, some studies also call this SpRS noise in FRA as ASE noise [14,16,17]. The signal is amplified and scattered randomly when the light transmits along with the fiber. Some of the backscattered light is captured to produce a single Rayleigh backscattering (SRB) noise [18]. The SRB noise is also amplified by the pump and backscattered randomly to generate DRB noise. At the receiver of the system, the DRB noise is the sum of several lights with different time delays in contrast with the signal, producing multiple-path interference (MPI) in Raman-amplified systems.
Fig. 1. Schematic diagram of Raman amplifier and the noise generate in optical fiber. OSA: optical spectrum analyzer, DCF: dispersion compensated fiber, SMF: single-mode fiber.
Referring to papers [14] and [15], the FRA shown in Fig. 1 is modeled, as expressed below, to analyze the power changes of the pump (${P_p}$), signal (${P_s}$), and noise (${P_{ASE}}$, ${P_{SRB}}$, and ${P_{DRB}}$) along with the fiber:
Here, + and – denote the forward and backward propagation of light in the fiber, respectively. $\alpha$ represents the attenuation coefficient for light. ${g_R}$ is the Raman gain efficiency from the pump to the signal light. $\gamma$ denotes the Rayleigh backscattering coefficients for light. $[{1 + \eta (T )} ]h{v_{ASE}}{B_{ref}}$ represents spontaneous Raman scattering, where $\eta (T )\approx 0.14$ at the Raman gain peak when $T = 25{}^ \circ C$[14], h is the Planck’s constant, and ${B_{ref}}$ is the bandwidth of the ASE noise.
In the experiment, a Lumentum-S36-2774-DH-500 laser was used as the Raman pump, a 14.86 km DCF or a 41.68 km SMF, was used as the gain medium for measuring the signal output power as a function of the different input signals or pump power. After applying the test data to Eqs. (1)–(6), we found out that the Raman gain efficiency ${g_R}$ was not a constant, and instead followed the variation law, as shown in Fig. 2.
Fig. 2. Raman gain efficiency as a function of different pump power and input signal power. Here, the up-triangles and down-triangles denote the measured data, which the up-triangles correspond to the use of DCF as gain medium and down-triangles correspond to the SMF been used. The blue and red curves are obtained by fitting the measured data.
Figure 2(a) shows the Raman gain efficiency as a function of the pump power for the FRA based on the DCF and SMF. Here, the attenuation of DCF was approximately 7.7 dB, the attenuation of the SMF was approximately 8.66 dB, and the input signal power was −31.34 dBm. Figure 2(b) shows the Raman gain efficiency as a function of the input signal power when the effective Raman pump power was set to 212.6 mW. The results show that, regardless of employing the DCF or SMF as the gain medium, the Raman gain efficiency decreases with the increase in pump power or input signal power.
It is common knowledge that the Raman gain efficiency depends on the relative state of polarization (SOP) of the pump and signal. It achieves a maximum for the parallel and minimum for the orthogonal polarization [19]. The data for Fig. 2(a) and Fig. 2(b) were measured on two different days, and the SOPs of the output light of the lasers may change every time when they were turned on. Due to the lack of equipment, such as a polarization analyzer, we failed to adjust the relative SOP of the pump and signal to the same angle in all the tests. This caused a difference in the Raman gain efficiency between Fig. 2(a) and Fig. 2(b) though under the same input signal and pump power. For instance, when the pump was set to 212.6 mW and the input signal was approximately −30 dBm, the measured Raman gain efficiencies based on the DCF were 3.69 ${[{W \cdot \textrm{km}} ]^{\textrm{ - }1}}$ in Fig. 2(a) and 2.92 ${[{W \cdot \textrm{km}} ]^{\textrm{ - }1}}$ in Fig. 2(b), respectively. But the data for each individual line in Fig. 2 were obtained in one test within a short time and the SOPs remained unchanged during the measurement, so the measured variation law of Raman gain efficiency as a function of pump power and input signal power is reliable.
3. Raman/EDFA hybrid bidirectional amplifier
The configuration of our Raman/EDFA hybrid bidirectional amplifier and amplification process of the desired signal, ASE noise, and DRB noise is shown in Fig. 3. The hybrid bidirectional amplifier is composed of three parts. The first part is a one-way EDFA consisting of a 6 m Fibercore I-12(980/1250) HC Er3+-doped fiber (EDF), a 980 nm pump, and two isolators for amplifying the input signal from the right side. The second part is an FRA composed of DCF and a 1455 nm Raman pump for amplifying the signals from both directions. In time and frequency synchronization systems, DCF is typically to compensate for the dispersion effect induced by the fiber link; it is also an ideal Raman gain medium, owing to its small effective areas. The third part is also a one-way EDFA as part one, but is used to amplify the signal from the left side. The purpose of using two unidirectional EDFAs with isolators is to avoid spontaneous lasing [8]. Two wavelength-division multiplexers (WDMs) are used to separate/combine the signals amplified by the two EDFAs. The band covered by (A) channel of WDM is 1553.72∼1550.52 nm while that covered by (B) channel is 1550.52∼1547.32 nm.
Fig. 3. Schematic diagram of Raman/EDFA hybrid bidirectional amplifier and the noise generate in the system. DCF: dispersion compensated fiber, EDF: Er3+-doped fiber, WDM: wavelength division multiplexer.
Because the hybrid bidirectional amplifier is composed of three parts, we modeled and analyzed the amplification process of the desired signals and noise in these parts.
3.1 Mathematical model of EDFA for the first part of the hybrid bidirectional amplifier
The EDFA pumped by a 980 nm laser can be modeled as a two-level model of Giles and Desurvire [20]. The Er3+ population densities on the energy levels 4I13/2 and 4I15/2 are denoted as ${n_2}(z )$ and ${n_1}(z )$, where z represents the position on the fiber:
Here, ${n_t}(z )$ represents the Er3+ density per unit volume. The values of $R(z )$, ${W_{12}}(z )$, and ${W_{21}}(z )$ can be calculated as
In the Giles and Desurvire model, the power of the pump ${P_p}(z )$, signal ${P_{{\lambda _2}}}(z )$, and ASE noise ${P_{ASE4}}(z )$ are given as
Here, + and – denote the forward and backward propagation of light, respectively. ${\Gamma _p}$ and ${\Gamma _s}$ denote the pump over-lap factor and signal over-lap factor, respectively. $\sigma _s^{(a )}$ and $\sigma _s^{(e )}$ denote the signal absorption cross-section and signal emission cross-section, respectively. $\sigma _p^{(a)}$ denotes the pump absorption cross-section. ${v_p}$ and ${v_s}$ denote the pump frequency and signal frequency, respectively. h is the Planck constant, ${B_{ref}}$ is the bandwidth of the ASE noise, and A is the fiber effective area.
3.2 Mathematical model of FRA for the second part of the hybrid bidirectional amplifier
The second part of the hybrid amplifier is shown in Fig. 3. It consists of a DCF pumped by a 1455 nm pump with a power of $P_p^ +$ and the signals and noise are amplified along with the DCF. Drawing from the analytical methods mentioned previously [14,15], the mathematical model of the FRA becomes:
Here, + and – also denote the propagating direction of light. ${P_{{\lambda _1}}}$ and ${P_{{\lambda _2}}}$ denote the power of the amplified signal lights from the left and right sides, respectively. ${P_{ASE1}}$ and ${P_{ASE2}}$ are the powers of amplified SpRS noise produced by the FRA and transmit only in the opposite direction. ${P_{ASE4}}$ is the ASE noise originating from the EDFA in the first part and is also amplified by the FRA. ${P_{SRB}}$ and ${P_{DRB}}$ represent the SRB and DRB scattered from the signals at wavelength ${\lambda _1}$ or ${\lambda _2}$.
3.3 Mathematical model of EDFA for the third part of the hybrid bidirectional amplifier
For the EDFA in the third part, it will amplify the signal, DRB, and ASE noise output from the FRA forward direction, simultaneously. Therefore, the updated Giles and Desurvire model for the third part becomes:
Here the Eqs. (35)–(36) denote the amplified progress of the ASE noise originating from the FRA and DRB of the signal input from the left side.
3.4 Gain and NF of the hybrid bidirectional amplifier
Conceptually, the gain and noise figure in distributed amplifiers are usually referred to as the net gain (${G_{net}}$) and the equivalent noise figure ($N{F_{eq}}$). They correspond to the gain and NF that a lumped amplifier placed at the end of the transmission span would need, in the absence of the distributed amplifier, to provide the same gain and the same noise as the distributed fiber amplifier in consideration. In the above analysis, the value of $N{F_{eq}}$ is estimated by measuring the ASE noise, which is typically much broader, and DRB noise, which typically has the same spectrum as the signal. Thus, a general expression for the equivalent NF of the hybrid amplifier can be written as [21]
Here, ${P_{ASE}}$ is the power of the ASE noise measured in the OSA resolution bandwidth ${B_{opt}}$, ${P_{DRB}}$ is the power of DRB noise, ${B_{el}}$ is the electrical filter bandwidth, and ${B_{sig}}$ is the optical signal bandwidth, $hv$ is the OSA resolution bandwidth.
As Eq. (37) shows, ${G_{net}}$, ${P_{ASE}}$, and ${P_{DRB}}$ should be known to calculate the $N{F_{eq}}$ of the hybrid amplifier. ${G_{net}}$ and ${P_{ASE}}$ can be measured directly by an optical spectrum analyzer, but it is impossible to determine the power of ${P_{DRB}}$ from the spectrometer for the Rayleigh scattering noise at the same frequency as the signal light. Eqs. (7)–(36) provide a method to calculate the DRB noise power in the hybrid amplifier according to the measured signal power values before and after amplification.
Figure 4 shows the measured ${G_{net}}$ and $N{F_{eq}}$ of the Raman/EDFA hybrid bidirectional amplifier as a function of the input signal power. Here, the wavelengths of the signals were ${\lambda _1}\textrm{ = }1550.92$ nm and ${\lambda _2}\textrm{ = }1550.12$ nm, respectively. The effective Raman 1455 nm pump power was set to 212.6 mW and the 980 nm pump power of the two EDFAs was 46 mW. The electrical filter bandwidth ${B_{el}}\textrm{ = }1$ GHz and the optical signal bandwidth ${B_{sig}}\textrm{ = }5$ KHz. The Rayleigh scattering coefficient $\gamma$ was set to $5 \times {10^{\textrm{ - }4}}$ $k{m^{ - 1}}$.
Fig. 4. ${G_{net}}$ and $N{F_{eq}}$ of the Raman/EDFA hybrid bidirectional amplifier as a function of the input signal power. The triangles denote the measured results, while the curves are obtained by fitting the measured data. The FRA + EDFA denotes that the signal is amplified by FRA first and then by EDFA, which means that the signal is input from the left side and output from the right side of the hybrid amplifier, as shown in Fig. 3. In contrast, the EDFA + FRA represents the signal is amplified by the EDFA first and then by the FRA, which means that the signal is input from the right side and output from the left side of the hybrid amplifier.
As shown in Fig. 4(a), the ${G_{net}}$ of the hybrid amplifier is inversely proportional to the input signal power. The gain of FRA + EDFA is larger than that of EDFA + FRA as the FRA has a better amplification effect on a small signal. Regarding the NF results, we observe that the smaller the input signal power, the lower the $N{F_{eq}}$. When the input signal power is lower than approximately −20 dBm, $N{F_{eq}}$ is less than 3 dB, which is the theoretical minimum NF for the EDFA.
Figure 5 shows the measured ${G_{net}}$ and $N{F_{eq}}$ of the Raman/EDFA hybrid bidirectional amplifier as a function of the effective Raman pump power. The input signal power was set to −30 dBm.
Fig. 5. ${G_{net}}$ and $N{F_{eq}}$ of the Raman/EDFA hybrid bidirectional amplifier as a function of Raman pump power. The triangles denote the measured results, while the curves are obtained by fitting the measured data.
The gain of the hybrid amplifier is proportional to the Raman pump power, and the FRA + EDFA showed a better performance than the EDFA + FRA. With the increase in the Raman pump power, a slow improvement in $N{F_{eq}}$ for FRA + EDFA was observed, while rapid deterioration was observed for the EDFA + FRA.
In general, the Raman/EDFA hybrid bidirectional amplifier can provide high gain in both positive and negative directions. At the same time, it can not only break through the minimum NF limit of the EDFA, which is 3 dB, but also reduces the NF to below 0 dB, which implies that the SNR of the signal can be improved by the amplifier.
4. Performance verification of the hybrid amplifier in the frequency synchronization system
A free-running frequency synchronization system was carried out to verify the advantage of the Raman/EDFA hybrid amplifier, as shown in Fig. 6. No techniques, such as the phase-lock-loop [1] were employed to improve the SNR of the received RF signal. In the experiment, a 2.4 GHz RF signal was generated by Agilent E8267D and was divided into two signals by an electrical coupler for transmission and reference, respectively. The transmission RF signal modulated one laser diode (LD) through a Mach–Zehnder modulator (MZM). The output optical power of the LD with a 1550.12 nm center wavelength was 6.71 dBm after MZM. A variable optical attenuator was used to replace the power attenuation introduced by the optical fiber link, as it was easily affected by temperature and vibration. The output power was adjusted to −25 dBm at point a. Three kinds of relay systems were used to compensate the light power to 0 dBm at point b before being received by the photodetector (PD). As no need for bidirectional amplification at the same time in the free-running system, the structures of the three kinds of relay systems are shown in Fig. 6(b), Fig. 6(c), and Fig. 6(d). In Fig. 6(b), the relay system was composed of a 14.86 km DCF and an EDFA. In Fig. 6(c), a 1455 nm Raman pump laser and a 1442:1550 nm WDM were used with the DCF to form an FRA. Here, the light was amplified by the FRA and then by the EDFA which simulate the signal light input from the left side of the hybrid amplifier shown in Fig. 3. Compared to Fig. 6(c), the order of the FRA and EDFA in Fig. 6(d) was reversed to simulate the signal light input from the right side of the hybrid amplifier. As an inherent part of the frequency synchronization system, the DCF can not only compensate for the dispersion of the optical fiber link but also result in optical signal power attenuation. Although the variable optical attenuator was used in the system instead of the optical fiber link, we retained the DCF in Fig. 6(b) to maintain the same attenuation as that in Fig. 6(c) and 6(d). After a manual phase shifter MPS-DC4.2G-180-S, the demodulated 2.4 GHz RF signal (${S_2} = B\cos ({\omega _\textrm{0}}t + {\varphi _0} + \Delta \varphi \textrm{ + }{\varphi _{phase}}$) from the PD was mixed with the reference 2.4 GHz signal (${S_1} = A\cos ({\omega _\textrm{0}}t + {\varphi _0})$) by mixer. Here, $\Delta \varphi$ denotes the additional phase introduced during the transmission, ${\varphi _{phase}}$ denotes the phase added by the manual phase shifter. A Keysight 34465 A was used to transmit the down conversion signal mixing from ${S_1}$ and ${S_2}$ to the voltage value:
Here, the D denotes the voltage offset caused by the mixer. The additional phase $\Delta \varphi$ can be obtained by:
Fig. 6. Free-running frequency synchronization system and the structure of the three relay systems. LD: laser diode, MZM: Mach-Zehnder modulator, VOA: variable optical attenuator, PD: photodiode, EC: electrical coupler, DCF: dispersion compensated fiber, EDFA: Er3+-doped fiber amplifier.
And then we obtained the Allan deviation representing the stability of the system.
As shown in Eq. (39), the value of D and ${{AB} / 2}$ are important factors to obtain the additional phase $\Delta \varphi$. In the experiment, the whole phase range of $[{0\quad 2\pi } ]$ was traversed by the manual phase shifter to get the maximum (${V_{\max }} = D + {{AB} / 2}$) and minimum (${V_{\min }} = D - {{AB} / 2}$) voltage. Then the two factors can be calculated by:
Then the phase of the manual phase shifter was set to a suitable fixed value, which has no effect on judging the change of the additional phase $\Delta \varphi$.
The experimental Allan deviations, that denote the frequency instabilities of the free-running system based on the three relay systems, are shown in Fig. 7. The results illustrate that, compared to the EDFA alone, the Raman/EDFA hybrid amplifiers effectively improved the frequency stability of the system, regardless of the order of the FRA and EDFA. The measured result of $\sigma ({\tau \textrm{ = }1\;s} )= 3.0905 \times {10^{ - 13}}$ when the attenuation was compensated by the EDFA alone while the stabilities of the free-running system with EDFA + FRA and FRA + EDFA were $\sigma ({\tau \textrm{ = }1\;s} )= 2.0248 \times {10^{ - 13}}$ and $\sigma ({\tau \textrm{ = }1\;s} )= 1.9678 \times {10^{ - 13}}$, respectively.
Fig. 7. Frequency stability performance of the free-running system based on different relay systems: EDFA (triangles red solid line), EDFA + FRA (squares pink solid line) and FRA + EDFA (blue dotted line).
The DCF in the relay system was sensitive to random changes in temperature and mechanical vibration and caused phase jitter of the optical transmitted signal. The Allan deviation deteriorated when the average time exceeded approximately 200 s, as our test system functioned in the absence of compensation.
5. Conclusion
We demonstrate that Raman/EDFA hybrid amplifiers are suitable for optical amplification in time and frequency synchronization systems, owing to their higher gain and lower NF characteristics, compared to the traditional EDFA. A bidirectional Raman/EDFA hybrid amplifier was designed and the combination of modeling and experimental measurements proved that the amplifier has high gain and low noise performance. In addition, the study verifies that the Raman gain efficiency was not constant but decreased with an increase in the input signal light power or Raman pump power.
Funding
Youth Research and Innovation Program of Beijing University of Posts and Telecommunications (2017RC13); National Natural Science Foundation of China (61531003, 61690195, 61701040).
Disclosures
The authors declare no conflicts of interest.
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