We investigate high fidelity channel replication approaching the idealized notion of channel cloning with negligible excess noise and distortion. Previously proposed cloning architectures require that the channel carriers to be externally seeded, limiting their ultimate usefulness, whereas the self-seeded approach limits the channel number and signal-to-noise ratio. Specifically, when a single channel is replicated, the noise figure (NF) remains above the well-known 3-dB limit, and multi-channel replication by a dual-pump driven parametric mixer faces a theoretical NF limit of 6-dB. On the other hand, large-channel-count cloning is of particular importance as it allows for rate scaling in generalized signal processing. Recognizing the limits of conventional architectures that rest on homogeneous parametric mixers, we here propose multi-stage, dispersion-managed parametric mixers in multi-mode phase-sensitive architecture to clone the input signal to a substantial number of channels. In particular, when the new mixer is operated in four-mode phase-sensitive architecture, a 17-copy-count channel cloning with maximum NF less than 6-dB and a record-low NF of 2-dB was experimentally implemented and demonstrated in this paper.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
The ability to clone an arbitrarily modulated channel to multiple spectral copies has both practical and fundamental implications . Its use in optical fiber communication is readily understood in terms of multicasting and broadcasting functions. Specifically, the wavelength division multiplexing (WDM) represents a natural interface for channel cloning since it provides simultaneous transmission of spectrally-distinct, parallel channels over a single fiber waveguide . A channel replicator was recognized early as an essential component in the WDM networks since it can aid both routing and switching within the physical layer for network contention resolution . The importance of channel replication is reinforced with the introduction of streaming multimedia services where a multi-channel replication clones a single source signal to multiple destinations, exploiting the primary topology of WDM networks . Ideally, any channel replication should possess low complexity, instantaneous response and scalability , in addition to preserving the input signal-to-noise ratio (SNR) .
Past attempts to achieve scalable channel replication have relied on conventional optoelectronic devices [7,8]. However, the conversion between electrical and optical domains is inevitably bandwidth-, and channel-count- restricted. Consequently, considerable research efforts have been made towards achieving all-optical signal replication to overcome this electronic bottleneck and improve the overall efficiency . As an example, semiconductor optical amplifier (SOA) has been identified as a potential candidate [6,10]; however, the physics behind the channel replication through SOA is subject to the carrier density dynamics that limits the conversion bandwidth .
In contrast, motivated by the broad conversion bandwidth, the nearly instantaneous response and the full transparency with respect to modulation format, nonlinear processes, including self-phase modulation, cross-phase modulation and four-wave mixing, (FWM) [1,12], have been investigated to be used for channel replication. However, most of these approaches require the channel carriers to be externally seeded [10,13], limiting its ultimate utility.
Recognizing these limitations, self-seeded parametric mixers have been developed for broadband channel replication [3,6,14]. In particular, the advent of dispersion-synthesized parametric mixer [15–17] made the construction of scalable and efficient multi-channel replication achievable for the first time. In particular, parametric mixer-based multi-channel replication contributes substantially to all-optical signal processing, such as photonic-assisted analog-to-digital conversion (ADC)  and filter-less microwave channelization , in addition to the well-known applications such as broadcasting/multicasting.
The noise performance of the channel replication is of critical importance in all known applications, and particularly so in signal processing architectures. Until recently, the lowest reported noise figure (NF) of a single-channel conversion was 3.7 dB , and in the case of multi-channel, dual-pump driven parametric replication [15,16], the theoretical NF limit of 6-dB was recognized .
In this paper, we describe the physical architecture capable of near-noiseless replication using a new class of noise-managed parametric mixers operated in multi-mode phase-sensitive (PS) setting. In particular, the new approach of four-mode PS parametric mixer minimizes the excess noise added to the newly replicated channel copies, approaching, for the first time, sub-3-dB NF over 7 signal channels, while sub-6-dB NF over 17 signal channels in the presented experimental demonstration.
The paper is structured as followed. Section II introduces the theory of the dual-pump driven single-mode channel replication and PS multi-mode channel cloning, including the mathematical derivation of non-degenerate and degenerate scenarios. The experiments of the proposed PS four-mode channel cloning scheme are implemented and described in detail in Section III, including the rigorous characterization results of NF and bit-error rate (BER) performance. Section V summarizes this contribution.
2. Operating principle
The PS parametric process, which amplifies the in-phase quadrature but de-amplifies the out-of-phase quadrature component, has been extensively studied in noiseless amplification  and phase squeezing . Consequently, to achieve the near-ideal channel cloning, which is the main goal of our investigation, the parametric mixer is operated in a PS multi-mode architecture.
In the previously reported work [14–17], replication was implemented using a PI process. As illustrated in Figs. 1(a) and 1(b), the PS two- and four-mode processes only have one signal (see the purple S1) at the input of the parametric device, implying that the conversion efficiency (CE) that characterizes the channel replication is not dependent on the phases of the input waves, whereas the SNR is degraded by the noise coupling between the distinct channels. Correspondingly, the input and output SNRs of the multi-channel replication in the PI parametric mixer are defined asEquation (2) clearly manifests that the output SNR of the PI channel replication is degraded by the signal copy number , leading to the NF quantum limit of 3-dB and 6-dB for the PI two- and four-mode parametric processes, respectively. In particular, the theory also applies to the PI dispersion-less parametric mixer for broadband high-order wave mixing, as shown in Fig. 1(c), where S1, P1 and P2 are the input signal and pumps, while all the other waves are the high-order pumps and signals created by the parametric effects. Each wave contributes equally to the noise coupling here, implying that the NF of the PI signal replication in the dispersion-less parametric mixer scales up with copy number .
In contrast to the idealized dispersion-less mixer, our past investigations indicate that the normally-dispersive parametric mixer with localized noise coupling leads to a 6-dB SNR degradation for dual-pump driven PI broadband channel replication , which is denoted as in Eq. (3).
Instead of NF scaling up with copy number in the dispersion-less mixer, the dispersion-managed parametric mixer driven by two pumps in the PI scenario has a quantum limit NF of 6-dB, calculated by Eqs. (3) and (1). Furthermore, when four frequency-locked and phase-correlated signal waves are present at the input of the normally dispersive mixer, and utilized to seed the PS process, shown as the S1 to S4 in Fig. 1(d), the corresponding output SNR of one replica copy is
The 12-dB CE improvement relative to the PI device ( as compared to Eqs. (2) and (3)) originates from the interferometric addition of the four input beams. Conversely, due to the localized noise coupling, the uncorrelated noise associated with the input waves adds incoherently and accumulates to 6 dB ().
In contrast to the aforementioned PI input SNR definition, which is based on a single input signal wave (as expressed in Eq. (1)), it is our preference to use a more rigorous NF definition relying on the combined power of the four input signals
Compared to the PI one-mode scheme in normally-dispersive parametric mixer (where NF quantum limit is 6 dB, defined by Eqs. (1) and (3)), the PS four-mode architecture (where NF is calculated with Eqs. (4) and (5)) leads to the 0-dB NF for multi-channel replication, justifying the original notion of noiseless channel cloning.
We can generalize the conclusion to even higher-order PS multi-mode (>4) operations. For example, regarding the PS architecture with input N pumps and 2N signals, the input and output SNRs are derived asEqs. (6) and (7) leads to the noiseless channel cloning with high count copy throughput.
Here, we note that the above conclusion only applies to the non-degenerate PI one-mode and PS multi-mode configurations. Correspondingly, in the non-degenerate PI one-mode scenario with multiple pumps, the input signal wave is offset from the middle of the two pumps (as shown in Figs. 1(b) and 1(c)). While our recent investigation on the degenerate PS one- and three-mode architectures indicates a different theory for the final localized noise coupling state .
Figures 1(e) and 1(f) shows the schematic of degenerate PS one- and three-mode processes. When the nonlinear interactions are constrained in the input waves for amplification (e.g. no high-order pumps and signals), the NF is theoretically 0-dB, since all the internal modes are occupied by the input signals, and no excess noise is induced by the nonlinear process.
Take the five-wave model as an example (as shown in Fig. 1(f)), the PS three-mode amplifier (with two pumps and three signals at the input of the parametric device) has 0-dB NF. On the other hand, when the parametric device has only one signal and two pumps at the input (see Fig. 1(g), S1 and P1/P2) in the five-wave model, two more sideband signals are generated (see Fig. 1(g) S2 and S3). Hence, each input signal contributes evenly to the noise coupling, leading to a three-fold noise coupling, calculated as
In contrast, when the PS one-mode architecture is employed in the multi-channel replication (output pumps and signal channels >5), the theory needs to be re-derived. Reference  has demonstrated corresponding numerical simulation and experimental results, supporting the hypothesis that the degenerate PS one-mode architecture for multi-channel replication with high-count copy number (>5) has a quantum limit of 3-dB, instead of the 4.77-dB NF in the five-wave model. Here, we will provide the thorough analytical derivation.
The theoretical final state of localized noise coupling for the degenerate PS channel replication/cloning is shown in Fig. 1(h), where the degenerate signal wave in the middle of the two pumps can be considered as two waves sharing the same frequency. In the central noise coupling, the signal S1 contributes a field of and noise power of (where ). Whereas the sideband signal S2 or S3 interacts with the sideband noise coupling, in addition to contributing a field of and noise power of to the central noise coupling. Therefore, the output SNR of the degenerate PS one-mode multi-channel replication can be deduced as
We note that, the noise term of is induced by the doubled excess noise from S2 and S3, and correspondingly, the degenerate PS one-mode channel replication has a quantum limit NF of 3-dB, defined by the Eqs. (8) and (10). While regarding the degenerate PS three-mode channel replication, we can obtain
Note that, the PS three-mode architecture has a gain improvement compared to the degenerate PS one-mode scenario, corresponding to ~7.66 dB multi-mode interferometric addition induced gain. Relying on Eqs. (11) and (12), we can obtain the theoretical NF quantum limit for the degenerate PS three-mode channel cloning is 0.126 dB, which is also close to the noiseless performance, further corroborating the superiority of the PS multi-mode architecture for the channel cloning with high count copy number.
The PS three- and four-mode channel cloning have been theoretically investigated using the numerical simulations in [24,25], and the corresponding results support that the noiseless channel cloning can be implemented by the dispersion-synthesized noise-managed parametric mixer in the PS multi-mode architecture. In addition to the theoretical investigation, we experimentally implemented the PS three-mode channel cloning with sub-3-dB NF over 5 signal copies. The PS four-mode architecture has been experimentally exploited in the PS amplifier [26,27]. However, the noiseless performance has not been straightly validated, and most of the past demonstrations focused on the signal amplification with no extra replicated signal channels. Here, we extended the experimental investigation into the PS four-mode channel cloning for ultra-low noise performance and high count channel number. Next, we proceed to the experimental implementation and results.
3. Experimental configuration
The experimental architecture shown in Fig. 2 consists of four essential partitions: the reference comb, the pump recovery, the parametric mixer and the phase-locked loop (PLL).
In the first module, to create an optical frequency reference comb for channel replication, a narrow-linewidth (< 5-kHz) external-cavity-laser at 1549.3-nm was utilized as a master laser, injecting continuous wave (CW) output into a tandem of a Mach-Zehnder modulator (MZM) and two phase modulators (PMs). A 25-GHz harmonic tone from a radio-frequency (RF) oscillator was amplified and then employed to drive the modulators, defining the reference comb with 25-GHz frequency grid. The monitored equalized spectrum of the reference comb is shown in Fig. 3(a), obtained by tuning the MZM bias and aligning the phase delays of the RF signals into the corresponding PMs. Subsequently, the reference comb was amplified by an Erbium-doped fiber amplifier (EDFA) to 21 dBm, and then launched into a four-port programmable optical processor (OP). Two comb lines with 400-GHz spacing (1547.7 and 1550.9 nm) were selected by the OP as pump seeds with correlated phase characteristics, while four tones at 1546.9, 1548.5, 1550.1 and 1551.7 nm were derived as the signal carriers for the PS four-mode scheme. Additionally, the OP power-balanced and phase-manipulated the four signals, and then de-multiplexed the input six waves into three fiber branches.
In the upper and lower fiber branch of the pump recovery module in Fig. 2, filtered pump seeds were employed to injection-lock two distributed-feedback (DFB) slave lasers, in order to endow the pump waves with inherent narrow linewidth of the master laser and high output power of the slave laser. Next, the power of the two pumps were further boosted by high power EDFAs to 33 dBm, narrowly filtered in respective branches and subsequently combined with the input four signals by wavelength division multiplexers (WDMers). Here, we note that the path length difference of the fiber in the three branches was engineered to be less than 1 cm, allowing the pumps and signals to interact with maximum coherence.
Next, the six waves (two pumps and four signals) were launched into a three-stage dispersion-engineered parametric mixer. The first fiber section, a 105-m long highly nonlinear fiber (HNLF, i.e. HNLF1), characterized by a zero dispersion wavelength of 1597 nm, a nonlinear coefficient of 22 km−1W−1, and a dispersion slope of 0.018 ps/nm2/km, induces positive chirp to the dual-pump defined sinusoid wave and creates multiple frequency tones. In addition, HNLF1 was longitudinal strained in sections with different tension force to elevate the Brillouin threshold . Subsequently, a 6-m single-mode fiber (SMF) was used to compensate for the nonlinear chirp induced in the HNLF1 and compresses the corresponding pulses in time domain to enhance the peak power intensity, and to effectively increase the nonlinear figure of merit (defined as the product of nonlinear coefficient, optical peak power and interaction length) of the final mixer section. The efficient broadband mixing was accomplished in a 230-m dispersion flattened HNLF (HNLF2), characterized by a peak dispersion of −0.2 ps/nm/km, and dispersion fluctuation less than 1-ps/nm/km over 100-nm.
The parametric mixer has previously been validated as an efficient platform for broadband multi-channel replication in the PI regime [15–17]. However, in the PS four-mode scheme, the device inherently behaves as an interferometer, and therefore, a digital PLL (DPLL) was developed to track and compensate for the ambient-induced phase and power fluctuations. The principle of the DPLL was theoretically and experimentally demonstrated in . As shown in Fig. 2, a small fraction of the power at the mixer output was utilized by DPLL, to track and compensate for the phase fluctuations. The remaining part of the output power was launched into a tunable optical filter to extract a specific channel copy for subsequent NF and BER measurements. In contrast to the PS operation, only the 1550.1-nm signal carrier was extracted by the OP for the PI channel replication. Note that in the PI operation, the DPLL was not utilized.
The feasibility of the DPLL-stabilized channel cloning has been indicated by the time-transient power evolution of three monitored channels in . Figure 3(b) shows the output spectrum of the channel replication/cloning under the PI and DPLL-stabilized PS operations, both obtained at individual input signal power of −18 dBm. We note that the PS channel cloning exhibits 3-dB spectral flatness over 20 replicated channels (as shown in Fig. 3(c), i.e. the expanded spectrum plot of the central 20 copies), with the maximum channel output power of 1 dBm. Moreover, Fig. 3(b) validates that the PS cloning possesses a 12-dB CE improvement compared to the PI counterpart.
To further corroborate the advantage of the PS multi-mode channel cloning, the NFs of the central 17 channels under the PI and PS operations were calibrated with the RIN subtraction method [30,31], and are shown as blue and red curves, respectively, in Fig. 4(a). In case of the PI channel replication, the lowest NF over 17 replicas was 8.15 dB. We attribute the discrepancy between the measured PI NF from the quantum limit of 6-dB to the Brillouin-scattering limited mixer length, responsible for the inadequate localization of noise coupling. In sharp contrast, the four-mode PS channel replication offers a 6-dB NF benefit, as clearly demonstrated in the red curve of Fig. 4(a).
We note that the lowest NF of 2-dB corresponds to the signal wave at 1548.5 nm; whereas regarding the newly generated replicas, the lowest NF is 2.85 dB at 1553.3 nm. Most importantly, there are 7 copies having NFs lower than 3 dB, and additionally, all the 17 replicas possess lower than 6-dB NFs. To the best of our knowledge, these results correspond to the highest copy number with sub-3-dB NF for channel replication.
To further highlight the advantages of the PS four-mode parametric mixer, replicated channels were characterized by the BER measurements , where the evaluation was implemented with a 10-Gbit/s NRZ OOK data sequence. As specifically shown in Fig. 2, two pumps are regenerated by the injection locking in the upper and lower fiber branches of the pump recovery block, while the OOK data modulation is implemented in the middle fiber branch, where amplitude modulator is inserted for the BER validation. Figure 4(b) compares the BER curves of eight replicated channels under the PI one-mode and PS four-mode scenarios, illustrating the PS operation has a 1.9-dB receiver sensitivity improvement compared to the single channel (at 1550.1 nm) amplification by an EDFA, possessing a NF of 4.1 dB. Here, the total power of the input optical signal(s) into the parametric mixer (or EDFA for single channel amplification) was maintained at −34 dBm, implying that the power of each input signal for PS operation is −40 dBm. Most importantly, we note that multiple channels were successfully replicated with significantly improved BER receiver sensitivities compared to the single channel amplification, as demonstrated in Fig. 4(b).
In this paper we have theoretically and experimentally reported a near-noiseless channel cloning based on a PS multi-mode architecture using a parametric mixer. The experimental results presented in this paper support the original hypothesis that the parametric mixer can replicate multiple channels over a wide bandwidth, while simultaneously maintaining a low noise level. In addition, the DPLL stabilized operation has provided the first practical, environment-invariant PS four-mode operation, as manifested by the record-low NFs and significant BER improvements over the PI equivalent. Even though substantial work remains with respect to engineering an optimized, wide-band PS four-mode mixer, the measured results presented here indicate that near-noiseless channel replication can indeed be achieved. The realization of such practical channel cloning modules is expected to qualitatively change wide-ranging applications in signal processing, channel distribution and remote sensing.
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