Optical frequency multicasting with significantly enhanced signal-to-noise-ratio (SNR) is demonstrated over wide wavelength range. High-fidelity multicasting relies on a four-mode phase-sensitive (PS) parametric process. Four-mode seeding was used to drive dual-pump, multistage mixer and achieve high-efficiency frequency comb generation and signal replication assisted by field interference. New PS mixer was measured to possess near 12-dB of spectrally uniform optical SNR advantage over conventional, phase-insensitive (PI) parametric multicaster. In signal attenuation regime, PS operation was measured with better than 10dB over the entire mixer band, indicating highly controllable PS interference. The role of the new PS mixer in near-noiseless signal replication is elaborated.
© 2012 OSA
Commercial introduction of coherent fiber optical links has renewed interest in low-noise laser sources, precise phase manipulation and optical parametric phase-sensitive (PS) processes. In contrast to conventional, phase-insensitive amplifier (PIA), PS mixer is capable of deterministic noiseless amplification [1–4] and direct regeneration of all-optical phase-modulated signals [5–8]. Nearly all work reported to date has focused on one- [5,6] and two-mode [3,4,8] PS processes, primarily due to practical difficulties associated with multi-mode parametric interaction. The conventional PS process, illustrated in Figs. 1(a) and 1(b), involves one and two waves, respectively: in case of one-mode PS, signal and idler frequencies are identical; two-mode PS requires two input waves.
In principle, PS process relying on χ(3)-mixer [9,10] may be seeded by four input modes if two frequency-degenerate pumps are accompanied by the input field comprised of four phase-referenced sidebands, as shown in Fig. 1(c). While this PS architecture is more complex and poses practical implementation challenges, it offers considerable advantages over its one- / two-mode counterparts. With recently demonstrated copier-PSA topology [3,4], four-mode PS amplifier (PSA) can be realized when four sidebands are generated by a dual-pump parametric phase-insensitive (PI) amplifier (copier) and launched into subsequent PSA stage. As a consequence, four-mode phase-sensitive amplification in optical link can support 9-dB link noise-figure (NF, defined as the input-to-output signal SNR ratio, assuming that input signal is shot-noise limited ) improvement over conventional EDFA-amplified system .
Separately, the four-mode parametric seeding concept can be implemented in two-pump cascaded four-wave-mixing (FWM) configuration, leading to broadband phase-sensitive frequency copying and multicasting [13,14]. However, the above instances were considered only theoretically, with no experimental demonstrations to date. An absence of experimental results has left the basic question unanswered: what is the viable gain and noise performance of a four-mode PS device? Specifically, can optical signal be replicated without excess noise that is necessarily accumulated in conventional amplification or phase-insensitive mixing process?
In attempt to answer this, we constructed and investigated four-mode seeded multicaster capable of replicating large number of signal replicas. The new device was used to demonstrate the first, to the best of our knowledge, broadband frequency multicasting based on four-mode seeded PS interactions. More than 100 copies were generated with considerably improved optical SNR (with respect to standard PI mixer) over a 160-nm bandwidth.
The experimental architecture was used to characterize the PS amplification and de-amplification properties associated with high-count signal replication. In order to make quantitative comparison to conventional PI multicasting, we have measured 12-dB of nearly uniform conversion efficiency (CE) and signal copy OSNR increase with PS multicasting. A controlled CE decrease was demonstrated and measured to be in excess of 12-dB over the entire operational bandwidth. PS multicasting mixer exhibited behavior predicted by non-classical four-field constructive and destructive interferences [10,15]. Furthermore, comparisons with multicasters based on a two-mode PS process and a four-input PI process were also conducted. The results unambiguously point to quantitative benefits of four-mode PS process in wideband optical signal processing that cannot be matched by single- and dual-mode mixers.
The remaining paper is organized in multiple sections describing principle, construction and characterization of four-mode PS mixer. In Section 2, the principle of a broadband parametric multicasting with four-mode PS process is introduced and illustrated theoretically. This section also describes generation of phase-locked pump / sideband (signal) waves via injection locking. Section 3 describes the experimental construction of the mixer. The Section 4 reports on characterization of PS amplification and de-amplification and provides comparison among different signal input conditions; the last section concludes the paper.
2. Four-mode PS replication principle
Under undepleted pump assumption, PS process can be interpreted as coherent superposition of output fields that are seeded by each input mode independently. This formulation is readily described in semi-classical matrix form [10,15–17]. The constructive and destructive summation, governed by the input phase relation, corresponds to well-known PS amplification and deamplification, respectively. Intuitively, the coherent field addition within the mixer is expected to lead to considerable gain improvement over that in PI process. As an example, in two-mode PS case, constructive interference between two balanced output modes results in a 6-dB gain increase over the PI case [18–20]. Similarly, by assuming seeding by six frequency- and phase-locked waves in which two pumps are surrounded by four equalized signal sidebands, as shown in Fig. 1(c), it should be possible to increase PS gain further. By using six locked seeds as the input into dispersion-engineered nonlinear mixer and by ensuring that balanced input-output response for each sideband is maintained, a 12-dB PS gain improvement can be expected over the single-input PI scenario. More importantly, the output SNR will be increased directly with gain, provided that the input noise at distinct sidebands is fully uncorrelated [16,17].
The four-mode PS scheme can be generalized if two-pump driven four-photon mixing (FPM) cascade is used to generate higher-order frequency tones, as shown in Fig. 2 . In principle, this approach allows for broadband frequency signal replication (multicasting) as long as the phase matching condition in high-order mixer is well controlled [21,22]. The main concern for this type of signal multicasting relates to the efficiency of PS process over a wide bandwidth in presence of finite intra-mixer dispersion. In other words, is it possible to have effective PS constructive (or destructive) interactions for all output copies simultaneously in case when phase matching condition varies across the wide operational band?
To answer this question, we have performed numerical study by implementing nonlinear Schrödinger (NLS) description of PS multicaster. This approach was justified as no analytical solution of many-wave FPM process are known to exist to this date. While NLS model was capable of addressing pump saturation effects, we have investigated small-signal operation only (i.e. the case that signal has much lower power with respect to the pump), as the pump-depletion regime is beyond the scope of the current report.
The results of theoretical study are shown in Figs. 3(a) –3(c). Representative simulation of the output spectra generated by PI and four-mode PS processes (incorporating amplification and de-amplification) are shown, respectively. Copy deamplification was achieved by introducing 90-degree phase shift to the input signal fields, with dramatic results to the output multicasting gain and SNR. While wideband representation prevents resolving individual signal copies from the pump tones, their power level can be clearly distinguished. Insets shown in Figs. 3(a)–3(c) serve to indicate distinct copy and pump tones in case of PI and PS operational modes. The conversion efficiencies (CE), defined as the power ratio between the output copy and a single input sideband, are plotted in Fig. 3(d) for PI and constructive/destructive PS cases. The simulation was carried out with pump wavelengths fixed at 1547.7 and 1550.9 nm, guaranteeing a 400-GHz frequency comb pitch. The signal input was 1548.5 nm in the PI case; the identical signal-pump frequency separation of 100GHz was kept in PS configuration by placing the input sidebands at 1546.9, 1548.5, 1550.1 and 1551.7 nm, respectively. Pumps and signals were launched into a multi-stage, highly-nonlinear-fiber (HNLF) mixer. The mixer sections were composed of front-end conventional HNLF, mid-stage made of short standard single-mode-fiber (SMF) used to compress the temporal pulse width, and the third stage, dispersion-flattened HNLF required to obtain a flat and wide FPM spectrum [21,22], as shown in Fig. 2. The first HNLF section was 105-m long, with a 1555-nm zero-dispersion-wavelength (ZDW), 0.025-ps/nm2/km dispersion slope and 20-W−1km−1 nonlinear coefficient. The mid-stage SMF was 5.9-m long, and was selected to achieve maximum pulse compression and increase the efficiency of the third-stage mixer. The third fiber section was a 240-m long HNLF with a parabolic (flattened) dispersion profile , with peak dispersion value of 0.01-ps/nm/km and absolute dispersion variation of less than 1-ps/nm/km over the 1450 ̶ 1650-nm range (mostly in the normal dispersion regime). Launched powers for each pump was 27.8 and −20 dBm for each signal. All optical waves in simulations were assumed to be co-polarized, HNLF sections were assumed to possess negligible birefringence. Raman effect was not taken into account in simulations. The approximation is supported by the fact that frequency generation is governed by spectrally localized process: four coherently-interacting modes occupy a narrow bandwidth, over which the Raman induced gain asymmetry is negligible. As a result, Raman effect does not compromise PS interaction appreciably, even though the overall CE profile is modified.
The comparison with PI performance, shown in Fig. 3(a), it is clear that PS amplification (de-amplification) profile, shown in Figs. 3(b)–3(c) provides more than 11-dB CE gain (attenuation) advantage. More importantly, the CE gain contrast associated with PS operation can be achieved over the entire mixer bandwidth by optimizing the input sideband/pump phases. We note that 12-dB differential gain can only be attributed to the constructive PS field summation corresponding to 4-mode seeding: adding four balanced optical waves with independent (uncorrelated) phases in PI case leads only to a 6-dB power increase. Moreover, the results shown in Fig. 3 prove that an efficient PS interactions can be maintained for large copy count across large bandwidth. The latter requires that the phase relations between six input-waves are maintained by practical means such as phase-locked control. Detailed investigations on optimal phase relation and phase-to-amplitude transfer function will be the future topic.
3. Experimental architecture
One of the most challenging aspects of realizing four-mode PS device relies on generation of six low-noise optical waves with strictly referenced (locked) frequency- and phase-relations. As mentioned earlier, it is possible to produce these waves via parametric 'copier', i.e. a dual-pump PI amplifier [3,4,16,17]. However, this scheme is limited by the inherent 6-dB NF  and the correlated noise generated at the sidebands [16,17], significantly limiting the output SNR improvement expected from PS mixer. An alternative technique is capable of circumventing the above problem: it is sufficient to create an optical comb via RF phase modulation and then select out the required lines to seed four-mode PS mixer. This method eliminates inherent noise contribution associated with ‘copier’ scheme and overcomes the practical limit associated with frequency limits imposed on RF oscillators. Indeed, the phase modulator maps the fundamental RF frequency to multiple tones that enable pump-pump and modal frequency pitch to be considerably higher. Unfortunately, this technique also requires narrow-band filtering to select the specific frequency tone, leading to the loss in carrier SNR. To recover the SNR of the seed, the injection locking is introduced immediately after the tones are selected. The approach guarantees simultaneous SNR recovery and preservation of phase relation between all modes generated by the phase modulator. We note that similar schemes have been reported recently and have been implemented in phase-sensitive amplification [6,7,24], high-repetition-rate pulse generation  and parametric comb generation with preserved phase fidelity .
The experimental schematic is shown in Fig. 4 . A narrow-linewidth (< 5-kHz) external-cavity-laser (ECL) used as the master laser (centered at 1549.3 nm) was followed by an amplitude modulator and two concatenated phase modulators to generate spectrally flat, 25GHz-pitch optical comb over narrow band (5nm) , as shown in Fig. 5(a) . The amplitude modulator was used to spectrally equalize generated comb. Next, two comb lines with 400-GHz (1547.7 and 1550.9 nm) spacing were selected as the pump seeds, while four tones were picked as the signal sidebands with a 75-GHz offset to the closest pump line. The practical challenge with this topology was posed by simultaneous multi-frequency narrow-band filtering and wave de-multiplexing. This work used a four-port programmable optical processor to implement filtering and separate the pump and signal waves. Filtered pump seeds were subsequently employed to injection-lock two distributed-feedback (DFB) slave lasers (characterized by 700-kHz linewidth and 20-dBm output). It should be emphasized that, based on this method, both pump / signal frequencies and their spacing can be flexibly tuned with recovered SNR level, only limited by the original phase-modulated bandwidth. The injection locking guaranteed that the phase noise of the slave laser strictly follows that of the master laser. Of equal importance, the amplitude noise is mainly determined by the slave laser itself (with modified relaxation-oscillation frequency depending on the injection ratio), implying that both low phase and amplitude noise can be obtained at the same time with the described approach. After injection locking, the slave laser indeed exhibits more than 62-dB OSNR at 20-dBm output, ensuring superior noise performance in the ensuing parametric mixing.
Subsequently, the output of each slave laser was amplified by a high-power EDFA to 27.8 dBm and then narrowly filtered to avoid the residual pump noise injection into the mixer . Finally, the two pumps were combined with four equalized signal sidebands possessing a −17-dBm input power and launched into a 3-stage HNLF cascade. Polarization controllers were used to align the input waves to achieve maximal comb generation efficiency. In practice, an electro-optic modulator can be added in the signal branch (following the optical processor block) to imprint information on all sidebands simultaneously, as previously implemented in . Consequently, an efficient PS interaction can be realized with signals possessing finite modulation bandwidth.
The fiber cascade consisted of three sections. The first stage was 105-m long conventional HNLF with 1554 nm average zero dispersion wavelength, 0.021 ps/nm2/km dispersion slope and 22 W−1km−1 nonlinear coefficient. This section was longitudinally strained to increase the Brillouin threshold (HNLF1) to about 30-dBm . The second section was 4-m SMF as the pulse compressor [21,22], and final mixer stage was 240-m dispersion-flattened HNLF possessing small normal dispersion with spectral variation not exceeding 1-ps/nm/km over the full comb band (HNLF2). Dispersion of the HNLF2 was precisely adjusted by applying spatially constant tension to shift the HNLF into the normal dispersion region, which effectively suppressed modulation-instability amplified noise [21,22]. Stimulated Brillouin scattering was negligible in all experiments due to the fiber straining in HNLF1 and efficient spectral broadening in HNLF2.
PS multicaster structure shown in Fig. 4 allows newly generated copies to fluctuate in time due to the phase alterations induced by variation in path-lengths between the pump and the signal branches. These path-length variations were caused by the environmental changes such as temperature and acoustic vibrations (with a time scale of millisecond). Typically, a phase-locked loop is required in PS setup to stabilize the output power over long time periods (i.e. longer than a minute), as reported previously with one- and two-mode experiments [3–8]. Phase locking becomes considerably more difficult in a four-mode PS configuration, owing to the more complex phase relations between pumps and signals, and was not pursued in this work, as it only required gain characterization measurements of PS multicasting performance. Indeed, the inherent stability of the PS mixer was sufficient to repeatedly perform amplification (deamplification) measurements. We note that this would not be sufficient in case when long term stability would need to be guaranteed by measured error-data metrics. According to the simulations described in Section 2, the maximum (minimum) PS gain through the entire bandwidth can be achieved at the same time by optimizing the input phases. Consequently, PS amplification and deamplification can be accurately measured by capturing the maximal and minimal output spectra from the optical spectral analyzer without implementing feedback phase controls.
We describe the results of these measurements in subsequent section.
4. Results and discussion
The output spectrum of the concatenated modulators, corresponding to access point 'A' in Fig. 4, is shown in Fig. 5(a), indicating a flat-top, but narrow optical comb. The input spectra used in two distinct multicasting schemes (i.e. PI, two- and four-mode PS processes) at access point 'B', are shown in Figs. 5(b)–5(d). Narrow filtering provided by WDM elements after high-power EDFAs, ensured no appreciable ASE leakage from the amplified pumps to the neighboring sidebands. Pump and signal input powers are kept that same in different schemes. The output spectra after the HNLF cascade, obtained at access point 'C', are shown in Fig. 6 . A wideband parametric comb consisting of high-count higher-order pump tones was created over span exceeding 200-nm, characterized by more than 35-dB optical SNR (within 0.1-nm resolution bandwidth) . The injection locking process allowed for strict preservation of higher-order tone linewidth , critically important feature in case when phase coherence properties must be preserved to guarantee low-noise creation of the signal copies. Since a capture of the entire 200-nm-wide comb spectrum does not allow for spectral resolution necessary for pump-copy distinction, multicast signal replicas are recognized in Fig. 6 as “shadowed” region surrounding the pumps: from this level, one can clearly distinguish the significant CE difference between PI and four-mode PS multicasting.
For more details, the zoomed-in output spectra under different input conditions, which are PI, two-mode PS amplification, four-mode PS amplification, four-mode PS de-amplification, and four-input with independent pump phases, respectively, are juxtaposed together (as shown in Fig. 7(a) ). The last scheme has exactly the same input spectrum as that shown in Fig. 5(d), but with un-correlated phase relations between the pump and signal waves (by simply turning off the injection locking seeds), and thus is a PI process since the newly created idler photons are independent with respect to the input fields. Assuming that the parametric multicaster has an even gain spectrum, the four-input PI case will give a 6-dB power improvement over the conventional one-input PI case, owing to the optical power aggregation rather than the field interference. As an example, in Fig. 7(a) a four-mode PS input gives 12.6-dB and 5.1-dB gain advantages over its PI and two-mode PS counterparts, respectively, for the 1579.8-nm copy, while the four-input PI scheme shows similar CE as the two-mode PS one. It should be underlined that the background noise levels in all cases were kept unchanged, implying substantial SNR improvement enabled by the PS processes. These results are in good accordance with the above theoretical analysis, whereas the deviations from the ideal values (i.e. 12.6-dB vs. 12-dB, 5.1-dB vs. 6-dB) are possibly due to the un-equalized CE spectrum of the parametric mixer. In addition, for the same copy, an approximately 25-dB gain curve between the optimal amplification and the de-amplification is noted as well, clearly showing the potential of efficient multicasting / regeneration of binary phase-shift-keying (or differential phase-shift-keying) signals . The mixer should be operated in saturation regime to avoid the phase-to-amplitude transfer.
Furthermore, the output CE of each copy was measured over more than 160-nm band for various schemes, as shown in Fig. 7(b). The asymmetric CE fluctuations originate with nonlinear interactions in presence of small, but spatially fluctuating dispersion. In very good agreement with simulation results reported in Section 2, uniform CE difference (both in amplification and deamplification case) between PS and PI scheme can be seen across the entire mixer band. We note that approximately 12-dB CE advantage over the one-input PI scheme (or 6-dB over the four-input PI scheme) is maintained in practice over such a wide wavelength range, revealing perfectly-preserved coherence among the interacting waves. This observation is critical as it points to practically realizable path for broadband optical signal processing with a large copy count  such as signal replication, multicasting and phase regeneration. Another interesting phenomenon that deserves attention is the improvement in output sideband symmetry: PS interaction is superior to that of PI regime, as shown in Fig. 7(b), and particularly so at long-wavelength section of the spectrum. This may be explained, at least qualitatively, by the excess PS gain seen by the weaker input sideband(s) during the parametric process .
While this report was focused on gain performance of four-mode PS mixer, we note that system performance of such mixer also holds great interest. Indeed, the noise analysis of such a system is rather complex and is well beyond the scope of the present report. We note that presently reported measurements indicate that significant SNR improvement can be expected by comparing the 12-dB gain increase to the unchanged noise level between the PS and PI cases. Even if one takes into the account the total input power budget [16,17,19] that is inherently 6-dB higher in the PS multicasting than that in the PI case, coherent PS interaction still provides 6-dB more output SNR at the same input power. As a result, an effective increase of 6-dB in NF is achieved. A measure of multicaster performance can be obtained by comparing the input and output signal OSNR. In case when the input OSNR of 38-dB corresponds to a shot-noise limited signal at −17-dBm, while output OSNR in excess of 35-dB can be observed from Fig. 6(c) in the 1630–1650 nm region, indicating less than 3-dB OSNR degradation. Consequently, four-mode PS process is expected to be instrumental in constructing ultra-low noise optical signal processors.
Broadband parametric multicasting with qualitative SNR improvement is demonstrated for the first time by implementing a novel four-mode PS seeding scheme. The architecture uses six phase-locked input waves which include two pumps and four sidebands (signals). Key techniques that had to be developed for this experiment include: (1) coherent generation of six waves with strictly-locked phases and frequencies via phase-modulated optical comb generation followed by injection locking; (2) precisely dispersion-synthesized (HNLF) cascade to create spectrally-flat, broadband FWM; (3) spectrally programmable optical processor to precisely control the input wave phases, and (4) efficient and dither-free stimulated-Brillouin-scattering suppression.
When compared to a conventional PI and a two-mode PS multicasting, the new mixer was measured with 12-dB and 6-dB gain / optical-SNR improvement for more than 100 signal copies spread over 160-nm bandwidth. This performance reveals well preserved coherence across all generated signal copies, regardless of their spectral distance from the original signal. A 6-dB gain increase was observed compared to a four-input scheme with independent (uncorrelated) pump phases, further confirming the coherent nature of intra-mixer field-summation. Finally, spectrally uniform de-amplification was observed over the entire operational bandwidth. The results indicate a clear potential for use of four-mode PS mixer in low-noise, wideband optical signal replication and processing.
This work is based in part on research sponsored by the Office of Naval Research (ONR). The authors would like to acknowledge Sumitomo Electric Industries for providing the HNLFs used in this work.
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