Broadband parametric multicasting via four-mode phase-sensitive interaction

doi:10.1364/OE.20.019363

Broadband parametric multicasting via four-mode phase-sensitive interaction

Zhi Tong, Andreas O. J. Wiberg, Evgeny Myslivets, Bill P. P. Kuo, Nikola Alic, and Stojan Radic »View Author Affiliations

Optics Express, Vol. 20, Issue 17, pp. 19363-19373 (2012)
http://dx.doi.org/10.1364/OE.20.019363

View Full Text Article

Acrobat PDF (1151 KB)

Journal Search
Article Lookup

Article Tools

Citations

Alert me when this article is cited
Export Citation/Save

Article Navigation

▸ Article Outline
– Abstract
1. Introduction
2. Four-mode PS replication principle
3. Experimental architecture
4. Results and discussion
5. Conclusion
– References and links

Article Tools
Full Text
Article Info
References
Cited By
Figures
Metrics
Download PDF

Viewing Equations in the
HTML Article

Optimal Viewing Recommendations

Full Text
Article Info
References (31)
Cited By
Figures (7)
Metrics

Abstract

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.

1. Introduction

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

C. M. Caves, “Quantum limits on noise in linear amplifiers,” Phys. Rev. D Part. Fields 26(8), 1817–1839 (1982). [CrossRef]

–4

Z. Tong, C. Lundström, P. A. Andrekson, M. Karlsson, and A. Bogris, “Ultra-low noise, broadband phase-sensitive amplifiers and their applications,” IEEE J. Sel. Top. Quantum Electron. 18(2), 1016–1032 (2012). [CrossRef]

] and direct regeneration of all-optical phase-modulated signals [5

K. Croussore, C. Kim, and G. Li, “All-optical regeneration of differential phase-shift keying signals based on phase-sensitive amplification,” Opt. Lett. 29(20), 2357–2359 (2004). [CrossRef] [PubMed]

–8

C. Lundström, Z. Tong, M. Karlsson, and P. A. Andrekson, “Phase-to-phase and phase-to-amplitude transfer characteristics of a nondegenerate-idler phase-sensitive amplifier,” Opt. Lett. 36(22), 4356–4358 (2011). [CrossRef] [PubMed]

]. Nearly all work reported to date has focused on one- [5

R. Slavík, F. Parmigiani, J. Kakande, C. Lundström, M. Sjödin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Grüner-Nielsen, D. Jakobsen, S. Herstrøm, R. Phelan, J. O'Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4(10), 690–695 (2010). [CrossRef]

] and two-mode [3

Z. Tong, C. Lundström, P. A. Andrekson, C. J. McKinstrie, M. Karlsson, D. J. Blessing, E. Tipsuwannakul, B. J. Puttnam, H. Toda, and L. Grüner-Nielsen, “Towards ultrasensitive optical links enabled by low-noise phase-sensitive amplifiers,” Nat. Photonics 5(7), 430–436 (2011). [CrossRef]

] 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.

Fig. 1 Input schematics of (a) one-mode, (b) two-mode, and (c) four-mode phase-sensitive processes. MI: modulation instability, PC: phase conjugation, BS: Bragg scattering.

In principle, PS process relying on χ⁽³⁾-mixer [9

C. J. McKinstrie, S. Radic, and M. G. Raymer, “Quantum noise properties of parametric amplifiers driven by two pump waves,” Opt. Express 12(21), 5037–5066 (2004). [CrossRef] [PubMed]

,10

C. J. McKinstrie, S. J. van Enk, M. G. Raymer, and S. Radic, “Multicolor multipartite entanglement produced by vector four-wave mixing in a fiber,” Opt. Express 16(4), 2720–2739 (2008). [CrossRef] [PubMed]

] 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

], 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 [11

E. Desuvire, Erbium-Doped Fiber Amplifiers (John Wiley and Sons, 1994), Chap. 2.

]) improvement over conventional EDFA-amplified system [12

P. A. Andrekson, “Phase sensitive fiber optic parametric amplifiers,” in European Conference on Optical Communications (ECOC), paper Th.11.LeCervin.1 (2011).

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

C.-S. Brès, A. O. J. Wiberg, B. P. P. Kuo, N. Alic, and S. Radic, “Wavelength multicasting of 320Gb/s channel in self-seeded parametric amplifier,” IEEE Photon. Technol. Lett. 21(14), 1002–1004 (2009). [CrossRef]

,14

R. Slavík, J. Kakande, F. Parmigiani, L. Grüner-Nielsen, D. Jakobsen, S. Herstrøm, P. Petropoulos, and D. J. Richardson, “All-optical phase-regenerative multicasting of 40 Gbit/s DPSK signal in a degenerate phase sensitive amplifier,” in European Conference on Optical Communications (ECOC), paper Mo.1.A2 (2010).

]. 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

C. J. McKinstrie and S. Radic, “Phase-sensitive amplification in a fiber,” Opt. Express 12(20), 4973–4979 (2004). [CrossRef] [PubMed]

]. 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

C. J. McKinstrie and S. Radic, “Phase-sensitive amplification in a fiber,” Opt. Express 12(20), 4973–4979 (2004). [CrossRef] [PubMed]

–17

C. J. McKinstrie, M. Karlsson, and Z. Tong, “Field-quadrature and photon-number correlations produced by parametric processes,” Opt. Express 18(19), 19792–19823 (2010). [CrossRef] [PubMed]

]. 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

R. Tang, J. Lasri, P. S. Devgan, V. Grigoryan, P. Kumar, and M. Vasilyev, “Gain characteristics of a frequency nondegenerate phase-sensitive fiber-optic parametric amplifier with phase self-stabilized input,” Opt. Express 13(26), 10483–10493 (2005). [CrossRef] [PubMed]

–20

J. Kakande, C. Lundström, P. A. Andrekson, Z. Tong, M. Karlsson, P. Petropoulos, F. Parmigiani, and D. J. Richardson, “Detailed characterization of afiber-optic parametric amplifier in phase-sensitive and phase-insensitive operation,” Opt. Express 18(5), 4130–4137 (2010). [CrossRef] [PubMed]

]. 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

Z. Tong, C. J. McKinstrie, C. Lundström, M. Karlsson, and P. A. Andrekson, “Noise performance of optical fiber transmission links that use non-degenerate cascaded phase-sensitive amplifiers,” Opt. Express 18(15), 15426–15439 (2010). [CrossRef] [PubMed]

,17

C. J. McKinstrie, M. Karlsson, and Z. Tong, “Field-quadrature and photon-number correlations produced by parametric processes,” Opt. Express 18(19), 19792–19823 (2010). [CrossRef] [PubMed]

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

B. P. P. Kuo, E. Myslivets, N. Alic, and S. Radic, “Wavelength multicasting via frequency comb generation in a bandwidth-enhanced fiber optical parametric mixer,” J. Lightwave Technol. 29(23), 3515–3522 (2011). [CrossRef]

,22

E. Myslivets, B. P. P. Kuo, N. Alic, and S. Radic, “Generation of wideband frequency combs by continuous-wave seeding of multistage mixers with synthesized dispersion,” Opt. Express 20(3), 3331–3344 (2012). [CrossRef] [PubMed]

]. 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?

Fig. 2 Concept of two-pump seeded broadband multicasting [21

] relying on (a) phase-insensitive and (b) four-mode phase-sensitive processes. DF-HNLF: dispersion flattened highly-nonlinear-fiber.

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 [22

], 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.

Fig. 3 Simulated output spectra of an example broadband parametric multicaster with (a) PI input, (b) 4-mode (power equalized) PS input possessing maximum CE (PS amplification) and (c) minimum CE (PS de-amplification, 90-degree phase shift for all input sidebands). Insets show zoomed-in spectra of Figs. (a)–(c). Calculated CE spectra under three different conditions are shown in (d).

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

,16

,17

C. J. McKinstrie, M. Karlsson, and Z. Tong, “Field-quadrature and photon-number correlations produced by parametric processes,” Opt. Express 18(19), 19792–19823 (2010). [CrossRef] [PubMed]

]. However, this scheme is limited by the inherent 6-dB NF [23

C. J. McKinstrie, M. Yu, M. G. Raymer, and S. Radic, “Quantum noise properties of parametric processes,” Opt. Express 13(13), 4986–5012 (2005). [CrossRef] [PubMed]

] and the correlated noise generated at the sidebands [16

,17

C. J. McKinstrie, M. Karlsson, and Z. Tong, “Field-quadrature and photon-number correlations produced by parametric processes,” Opt. Express 18(19), 19792–19823 (2010). [CrossRef] [PubMed]

], 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

J. Kakande, R. Slavík, F. Parmigiani, A. Bogris, D. Syvridis, L. Grüner-Nielsen, R. Phelan, P. Petropoulos, and D. J. Richardson, “Multilevel quantization of optical phase in a novel coherent parametric mixer architecture,” Nat. Photonics 5(12), 748–752 (2011). [CrossRef]

,24

R. Weerasuriya, S. Sygletos, S. K. Ibrahim, R. Phelan, J. O’Carroll, B. Kelly, J. O’Gorman, and A. D. Ellis, “Generation of frequency symmetric signals from a BPSK input for phase sensitive amplification,” in Optical Fiber Communications Conference (OFC), paper OWT6 (2010).

], high-repetition-rate pulse generation [25

R. Slavík, F. Parmigiani, L. Grüner-Nielsen, D. Jakobsen, S. Herstrøm, P. Petropoulos, and D. J. Richardson, “Stable and efficient generation of high repetition rate (>160 GHz) subpicosecond optical pulses,” IEEE Photon. Technol. Lett. 23(9), 540–542 (2011). [CrossRef]

] and parametric comb generation with preserved phase fidelity [26

Z. Tong, A. O. J. Wiberg, E. Myslivets, B. P. P. Kuo, N. Alic, and S. Radic, “Spectral linewidth preservation in parametric frequency combs seeded by dual pumps,” Opt. Express 20(16), 17610–17619 (2012). [CrossRef]

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) [27

Z. Tong, A. Bogris, M. Karlsson, and P. A. Andrekson, “Full characterization of the signal and idler noise figure spectra in single-pumped fiber optical parametric amplifiers,” Opt. Express 18(3), 2884–2893 (2010). [CrossRef] [PubMed]

], 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.

Fig. 4 Experimental setup. LD: laser diode, PC: polarization controller, MZM: Mach-Zehnder modulator, PM: phase modulator, PS: phase shifter, OP: optical processor, TDL: tunable delay line, WDM: wavelength-division multiplexer.

Fig. 5 (a) Output spectrum of the phase-modulated comb at point 'A', as marked in Fig. 4, and input spectra of (b) the phase-insensitive, (c) the two-mode phase-sensitive, and (d) the four-mode phase-sensitive multicasters at point 'B'. Each pump power was 100-mW in Figs. (b)–(d).

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 [28

W. Mao, P. A. Andrekson, and J. Toulouse, “Investigation of a spectrally flat multi-wavelength DWDM source based on optical phase- and intensity-modulation,” in Optical Fiber Communications Conference (OFC), paper MF78 (2004).

]. 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 [8

]. 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 [29

E. Myslivets, C. Lundström, J. M. Aparicio, S. Moro, A. O. J. Wiberg, C.-S. Bres, N. Alic, P. A. Andrekson, and S. Radic, “Spatial equalization of zero dispersion wavelength profiles in nonlinear fibers,” IEEE Photon. Technol. Lett. 21(24), 1807–1809 (2009). [CrossRef]

]. 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) [26

]. The injection locking process allowed for strict preservation of higher-order tone linewidth [26

], 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.

Fig. 6 Measured output spectra of (a) the phase-insensitive, (b) the two-mode phase-sensitive, (c) the four-mode amplification, and (d) the four-mode de-amplification processes in the multicasting setup. The shadowed part in each figure corresponds to output copies surrounding the pumps.

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 [6

]. The mixer should be operated in saturation regime to avoid the phase-to-amplitude transfer.

Fig. 7 (a) High resolution spectra subset for different cases, and (b) measured conversion efficiency of each copy for different input schemes.

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 [30

S. Radic, “Parametric signal processing,” IEEE J. Sel. Top. Quantum Electron. 18(2), 670–680 (2012). [CrossRef]

] 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 [31

Z. Tong, C. Lundström, M. Karlsson, M. Vasilyev, and P. A. Andrekson, “Noise performance of a frequency nondegenerate phase-sensitive amplifier with unequalized inputs,” Opt. Lett. 36(5), 722–724 (2011). [CrossRef] [PubMed]

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

C. J. McKinstrie, M. Karlsson, and Z. Tong, “Field-quadrature and photon-number correlations produced by parametric processes,” Opt. Express 18(19), 19792–19823 (2010). [CrossRef] [PubMed]

,19

M. Vasilyev, “Distributed phase-sensitive amplification,” Opt. Express 13(19), 7563–7571 (2005). [CrossRef] [PubMed]

] 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.

5. Conclusion

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.

Acknowledgments

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.

References and links

1.	C. M. Caves, “Quantum limits on noise in linear amplifiers,” Phys. Rev. D Part. Fields 26(8), 1817–1839 (1982). [CrossRef]
2.	J. A. Levenson, K. Bencheikh, D. J. Lovering, P. Vidakovic, and C. Simonneau, “Quantum noise in optical parametric amplification: a means to achieve noiseless optical functions,” Quantum Semiclass. Opt. 9(2), 221–237 (1997). [CrossRef]
3.	Z. Tong, C. Lundström, P. A. Andrekson, C. J. McKinstrie, M. Karlsson, D. J. Blessing, E. Tipsuwannakul, B. J. Puttnam, H. Toda, and L. Grüner-Nielsen, “Towards ultrasensitive optical links enabled by low-noise phase-sensitive amplifiers,” Nat. Photonics 5(7), 430–436 (2011). [CrossRef]
4.	Z. Tong, C. Lundström, P. A. Andrekson, M. Karlsson, and A. Bogris, “Ultra-low noise, broadband phase-sensitive amplifiers and their applications,” IEEE J. Sel. Top. Quantum Electron. 18(2), 1016–1032 (2012). [CrossRef]
5.	K. Croussore, C. Kim, and G. Li, “All-optical regeneration of differential phase-shift keying signals based on phase-sensitive amplification,” Opt. Lett. 29(20), 2357–2359 (2004). [CrossRef] [PubMed]
6.	R. Slavík, F. Parmigiani, J. Kakande, C. Lundström, M. Sjödin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Grüner-Nielsen, D. Jakobsen, S. Herstrøm, R. Phelan, J. O'Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4(10), 690–695 (2010). [CrossRef]
7.	J. Kakande, R. Slavík, F. Parmigiani, A. Bogris, D. Syvridis, L. Grüner-Nielsen, R. Phelan, P. Petropoulos, and D. J. Richardson, “Multilevel quantization of optical phase in a novel coherent parametric mixer architecture,” Nat. Photonics 5(12), 748–752 (2011). [CrossRef]
8.	C. Lundström, Z. Tong, M. Karlsson, and P. A. Andrekson, “Phase-to-phase and phase-to-amplitude transfer characteristics of a nondegenerate-idler phase-sensitive amplifier,” Opt. Lett. 36(22), 4356–4358 (2011). [CrossRef] [PubMed]
9.	C. J. McKinstrie, S. Radic, and M. G. Raymer, “Quantum noise properties of parametric amplifiers driven by two pump waves,” Opt. Express 12(21), 5037–5066 (2004). [CrossRef] [PubMed]
10.	C. J. McKinstrie, S. J. van Enk, M. G. Raymer, and S. Radic, “Multicolor multipartite entanglement produced by vector four-wave mixing in a fiber,” Opt. Express 16(4), 2720–2739 (2008). [CrossRef] [PubMed]
11.	E. Desuvire, Erbium-Doped Fiber Amplifiers (John Wiley and Sons, 1994), Chap. 2.
12.	P. A. Andrekson, “Phase sensitive fiber optic parametric amplifiers,” in European Conference on Optical Communications (ECOC), paper Th.11.LeCervin.1 (2011).
13.	C.-S. Brès, A. O. J. Wiberg, B. P. P. Kuo, N. Alic, and S. Radic, “Wavelength multicasting of 320Gb/s channel in self-seeded parametric amplifier,” IEEE Photon. Technol. Lett. 21(14), 1002–1004 (2009). [CrossRef]
14.	R. Slavík, J. Kakande, F. Parmigiani, L. Grüner-Nielsen, D. Jakobsen, S. Herstrøm, P. Petropoulos, and D. J. Richardson, “All-optical phase-regenerative multicasting of 40 Gbit/s DPSK signal in a degenerate phase sensitive amplifier,” in European Conference on Optical Communications (ECOC), paper Mo.1.A2 (2010).
15.	C. J. McKinstrie and S. Radic, “Phase-sensitive amplification in a fiber,” Opt. Express 12(20), 4973–4979 (2004). [CrossRef] [PubMed]
16.	Z. Tong, C. J. McKinstrie, C. Lundström, M. Karlsson, and P. A. Andrekson, “Noise performance of optical fiber transmission links that use non-degenerate cascaded phase-sensitive amplifiers,” Opt. Express 18(15), 15426–15439 (2010). [CrossRef] [PubMed]
17.	C. J. McKinstrie, M. Karlsson, and Z. Tong, “Field-quadrature and photon-number correlations produced by parametric processes,” Opt. Express 18(19), 19792–19823 (2010). [CrossRef] [PubMed]
18.	R. Tang, J. Lasri, P. S. Devgan, V. Grigoryan, P. Kumar, and M. Vasilyev, “Gain characteristics of a frequency nondegenerate phase-sensitive fiber-optic parametric amplifier with phase self-stabilized input,” Opt. Express 13(26), 10483–10493 (2005). [CrossRef] [PubMed]
19.	M. Vasilyev, “Distributed phase-sensitive amplification,” Opt. Express 13(19), 7563–7571 (2005). [CrossRef] [PubMed]
20.	J. Kakande, C. Lundström, P. A. Andrekson, Z. Tong, M. Karlsson, P. Petropoulos, F. Parmigiani, and D. J. Richardson, “Detailed characterization of afiber-optic parametric amplifier in phase-sensitive and phase-insensitive operation,” Opt. Express 18(5), 4130–4137 (2010). [CrossRef] [PubMed]
21.	B. P. P. Kuo, E. Myslivets, N. Alic, and S. Radic, “Wavelength multicasting via frequency comb generation in a bandwidth-enhanced fiber optical parametric mixer,” J. Lightwave Technol. 29(23), 3515–3522 (2011). [CrossRef]
22.	E. Myslivets, B. P. P. Kuo, N. Alic, and S. Radic, “Generation of wideband frequency combs by continuous-wave seeding of multistage mixers with synthesized dispersion,” Opt. Express 20(3), 3331–3344 (2012). [CrossRef] [PubMed]
23.	C. J. McKinstrie, M. Yu, M. G. Raymer, and S. Radic, “Quantum noise properties of parametric processes,” Opt. Express 13(13), 4986–5012 (2005). [CrossRef] [PubMed]
24.	R. Weerasuriya, S. Sygletos, S. K. Ibrahim, R. Phelan, J. O’Carroll, B. Kelly, J. O’Gorman, and A. D. Ellis, “Generation of frequency symmetric signals from a BPSK input for phase sensitive amplification,” in Optical Fiber Communications Conference (OFC), paper OWT6 (2010).
25.	R. Slavík, F. Parmigiani, L. Grüner-Nielsen, D. Jakobsen, S. Herstrøm, P. Petropoulos, and D. J. Richardson, “Stable and efficient generation of high repetition rate (>160 GHz) subpicosecond optical pulses,” IEEE Photon. Technol. Lett. 23(9), 540–542 (2011). [CrossRef]
26.	Z. Tong, A. O. J. Wiberg, E. Myslivets, B. P. P. Kuo, N. Alic, and S. Radic, “Spectral linewidth preservation in parametric frequency combs seeded by dual pumps,” Opt. Express 20(16), 17610–17619 (2012). [CrossRef]
27.	Z. Tong, A. Bogris, M. Karlsson, and P. A. Andrekson, “Full characterization of the signal and idler noise figure spectra in single-pumped fiber optical parametric amplifiers,” Opt. Express 18(3), 2884–2893 (2010). [CrossRef] [PubMed]
28.	W. Mao, P. A. Andrekson, and J. Toulouse, “Investigation of a spectrally flat multi-wavelength DWDM source based on optical phase- and intensity-modulation,” in Optical Fiber Communications Conference (OFC), paper MF78 (2004).
29.	E. Myslivets, C. Lundström, J. M. Aparicio, S. Moro, A. O. J. Wiberg, C.-S. Bres, N. Alic, P. A. Andrekson, and S. Radic, “Spatial equalization of zero dispersion wavelength profiles in nonlinear fibers,” IEEE Photon. Technol. Lett. 21(24), 1807–1809 (2009). [CrossRef]
30.	S. Radic, “Parametric signal processing,” IEEE J. Sel. Top. Quantum Electron. 18(2), 670–680 (2012). [CrossRef]
31.	Z. Tong, C. Lundström, M. Karlsson, M. Vasilyev, and P. A. Andrekson, “Noise performance of a frequency nondegenerate phase-sensitive amplifier with unequalized inputs,” Opt. Lett. 36(5), 722–724 (2011). [CrossRef] [PubMed]

OCIS Codes
(190.4380) Nonlinear optics : Nonlinear optics, four-wave mixing
(190.4975) Nonlinear optics : Parametric processes

ToC Category:
Nonlinear Optics

History
Original Manuscript: May 30, 2012
Revised Manuscript: July 11, 2012
Manuscript Accepted: August 3, 2012
Published: August 9, 2012

Citation
Zhi Tong, Andreas O. J. Wiberg, Evgeny Myslivets, Bill P. P. Kuo, Nikola Alic, and Stojan Radic, "Broadband parametric multicasting via four-mode phase-sensitive interaction," Opt. Express 20, 19363-19373 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-17-19363

Sort: Author | Year | Journal | Reset

References

C. M. Caves, “Quantum limits on noise in linear amplifiers,” Phys. Rev. D Part. Fields26(8), 1817–1839 (1982). [CrossRef]
J. A. Levenson, K. Bencheikh, D. J. Lovering, P. Vidakovic, and C. Simonneau, “Quantum noise in optical parametric amplification: a means to achieve noiseless optical functions,” Quantum Semiclass. Opt.9(2), 221–237 (1997). [CrossRef]
Z. Tong, C. Lundström, P. A. Andrekson, C. J. McKinstrie, M. Karlsson, D. J. Blessing, E. Tipsuwannakul, B. J. Puttnam, H. Toda, and L. Grüner-Nielsen, “Towards ultrasensitive optical links enabled by low-noise phase-sensitive amplifiers,” Nat. Photonics5(7), 430–436 (2011). [CrossRef]
Z. Tong, C. Lundström, P. A. Andrekson, M. Karlsson, and A. Bogris, “Ultra-low noise, broadband phase-sensitive amplifiers and their applications,” IEEE J. Sel. Top. Quantum Electron.18(2), 1016–1032 (2012). [CrossRef]
K. Croussore, C. Kim, and G. Li, “All-optical regeneration of differential phase-shift keying signals based on phase-sensitive amplification,” Opt. Lett.29(20), 2357–2359 (2004). [CrossRef] [PubMed]
R. Slavík, F. Parmigiani, J. Kakande, C. Lundström, M. Sjödin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Grüner-Nielsen, D. Jakobsen, S. Herstrøm, R. Phelan, J. O'Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics4(10), 690–695 (2010). [CrossRef]
J. Kakande, R. Slavík, F. Parmigiani, A. Bogris, D. Syvridis, L. Grüner-Nielsen, R. Phelan, P. Petropoulos, and D. J. Richardson, “Multilevel quantization of optical phase in a novel coherent parametric mixer architecture,” Nat. Photonics5(12), 748–752 (2011). [CrossRef]
C. Lundström, Z. Tong, M. Karlsson, and P. A. Andrekson, “Phase-to-phase and phase-to-amplitude transfer characteristics of a nondegenerate-idler phase-sensitive amplifier,” Opt. Lett.36(22), 4356–4358 (2011). [CrossRef] [PubMed]
C. J. McKinstrie, S. Radic, and M. G. Raymer, “Quantum noise properties of parametric amplifiers driven by two pump waves,” Opt. Express12(21), 5037–5066 (2004). [CrossRef] [PubMed]
C. J. McKinstrie, S. J. van Enk, M. G. Raymer, and S. Radic, “Multicolor multipartite entanglement produced by vector four-wave mixing in a fiber,” Opt. Express16(4), 2720–2739 (2008). [CrossRef] [PubMed]
E. Desuvire, Erbium-Doped Fiber Amplifiers (John Wiley and Sons, 1994), Chap. 2.
P. A. Andrekson, “Phase sensitive fiber optic parametric amplifiers,” in European Conference on Optical Communications (ECOC), paper Th.11.LeCervin.1 (2011).
C.-S. Brès, A. O. J. Wiberg, B. P. P. Kuo, N. Alic, and S. Radic, “Wavelength multicasting of 320Gb/s channel in self-seeded parametric amplifier,” IEEE Photon. Technol. Lett.21(14), 1002–1004 (2009). [CrossRef]
R. Slavík, J. Kakande, F. Parmigiani, L. Grüner-Nielsen, D. Jakobsen, S. Herstrøm, P. Petropoulos, and D. J. Richardson, “All-optical phase-regenerative multicasting of 40 Gbit/s DPSK signal in a degenerate phase sensitive amplifier,” in European Conference on Optical Communications (ECOC), paper Mo.1.A2 (2010).
C. J. McKinstrie and S. Radic, “Phase-sensitive amplification in a fiber,” Opt. Express12(20), 4973–4979 (2004). [CrossRef] [PubMed]
Z. Tong, C. J. McKinstrie, C. Lundström, M. Karlsson, and P. A. Andrekson, “Noise performance of optical fiber transmission links that use non-degenerate cascaded phase-sensitive amplifiers,” Opt. Express18(15), 15426–15439 (2010). [CrossRef] [PubMed]
C. J. McKinstrie, M. Karlsson, and Z. Tong, “Field-quadrature and photon-number correlations produced by parametric processes,” Opt. Express18(19), 19792–19823 (2010). [CrossRef] [PubMed]
R. Tang, J. Lasri, P. S. Devgan, V. Grigoryan, P. Kumar, and M. Vasilyev, “Gain characteristics of a frequency nondegenerate phase-sensitive fiber-optic parametric amplifier with phase self-stabilized input,” Opt. Express13(26), 10483–10493 (2005). [CrossRef] [PubMed]
M. Vasilyev, “Distributed phase-sensitive amplification,” Opt. Express13(19), 7563–7571 (2005). [CrossRef] [PubMed]
J. Kakande, C. Lundström, P. A. Andrekson, Z. Tong, M. Karlsson, P. Petropoulos, F. Parmigiani, and D. J. Richardson, “Detailed characterization of afiber-optic parametric amplifier in phase-sensitive and phase-insensitive operation,” Opt. Express18(5), 4130–4137 (2010). [CrossRef] [PubMed]
B. P. P. Kuo, E. Myslivets, N. Alic, and S. Radic, “Wavelength multicasting via frequency comb generation in a bandwidth-enhanced fiber optical parametric mixer,” J. Lightwave Technol.29(23), 3515–3522 (2011). [CrossRef]
E. Myslivets, B. P. P. Kuo, N. Alic, and S. Radic, “Generation of wideband frequency combs by continuous-wave seeding of multistage mixers with synthesized dispersion,” Opt. Express20(3), 3331–3344 (2012). [CrossRef] [PubMed]
C. J. McKinstrie, M. Yu, M. G. Raymer, and S. Radic, “Quantum noise properties of parametric processes,” Opt. Express13(13), 4986–5012 (2005). [CrossRef] [PubMed]
R. Weerasuriya, S. Sygletos, S. K. Ibrahim, R. Phelan, J. O’Carroll, B. Kelly, J. O’Gorman, and A. D. Ellis, “Generation of frequency symmetric signals from a BPSK input for phase sensitive amplification,” in Optical Fiber Communications Conference (OFC), paper OWT6 (2010).
R. Slavík, F. Parmigiani, L. Grüner-Nielsen, D. Jakobsen, S. Herstrøm, P. Petropoulos, and D. J. Richardson, “Stable and efficient generation of high repetition rate (>160 GHz) subpicosecond optical pulses,” IEEE Photon. Technol. Lett.23(9), 540–542 (2011). [CrossRef]
Z. Tong, A. O. J. Wiberg, E. Myslivets, B. P. P. Kuo, N. Alic, and S. Radic, “Spectral linewidth preservation in parametric frequency combs seeded by dual pumps,” Opt. Express20(16), 17610–17619 (2012). [CrossRef]
Z. Tong, A. Bogris, M. Karlsson, and P. A. Andrekson, “Full characterization of the signal and idler noise figure spectra in single-pumped fiber optical parametric amplifiers,” Opt. Express18(3), 2884–2893 (2010). [CrossRef] [PubMed]
W. Mao, P. A. Andrekson, and J. Toulouse, “Investigation of a spectrally flat multi-wavelength DWDM source based on optical phase- and intensity-modulation,” in Optical Fiber Communications Conference (OFC), paper MF78 (2004).
E. Myslivets, C. Lundström, J. M. Aparicio, S. Moro, A. O. J. Wiberg, C.-S. Bres, N. Alic, P. A. Andrekson, and S. Radic, “Spatial equalization of zero dispersion wavelength profiles in nonlinear fibers,” IEEE Photon. Technol. Lett.21(24), 1807–1809 (2009). [CrossRef]
S. Radic, “Parametric signal processing,” IEEE J. Sel. Top. Quantum Electron.18(2), 670–680 (2012). [CrossRef]
Z. Tong, C. Lundström, M. Karlsson, M. Vasilyev, and P. A. Andrekson, “Noise performance of a frequency nondegenerate phase-sensitive amplifier with unequalized inputs,” Opt. Lett.36(5), 722–724 (2011). [CrossRef] [PubMed]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

Click here to see a list of articles that cite this paper