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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 15 — Jul. 19, 2010
  • pp: 15426–15439
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Noise performance of optical fiber transmission links that use non-degenerate cascaded phase-sensitive amplifiers

Zhi Tong, C. J. McKinstrie, Carl Lundström, Magnus Karlsson, and Peter A. Andrekson  »View Author Affiliations


Optics Express, Vol. 18, Issue 15, pp. 15426-15439 (2010)
http://dx.doi.org/10.1364/OE.18.015426


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Abstract

Based on semi-classical theory, the noise performance of a multi-span fiber optical transmission system employing a cascaded phase-insensitive amplifier (PIA) and phase-sensitive amplifiers (PSAs) is investigated. Compared with the pure-PIA and pure-PSA based in-line amplification schemes, the copier + PSA scheme is found to improve the system NF by up to 6 and 3 dB, respectively, in an optimized long-haul fiber link. In addition, this cascaded configuration will significantly relax the requirement for accurate phase- and wavelength-locking which is rigorously needed in the pure-PSA configuration. This scheme is also modulation-format independent. As a proof of concept, the NF of a fiber parametric amplifier based copier + PSA cascade with inter-stage attenuation representing the fiber link is measured, which shows a 1.8-dB total NF improvement over the conventional EDFA cascade.

© 2010 OSA

1. Introduction

As is well known, phase-sensitive amplifiers (PSAs) have the potential to realize noiseless amplification [1

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

], which is a highly attractive characteristic for high-sensitivity photo-detection [2

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]

] as well as high-speed optical communications [3

3. M. V. Vasilyev, “Phase-sensitive amplification in optical fibers,” in Frontiers in Optics, Technical Digest (Optical Society of America, 2005), paper FThB1.

]. To date, most PSA experiments have been based on parametric processes in nonlinear crystals [4

4. J. A. Levenson, I. Abram, Th. Rivera, and P. Grangier, “Reduction of quantum noise in optical parametric amplification,” J. Opt. Soc. Am. B 10(11), 2233–2238 (1993). [CrossRef]

] or optical fibers [5

5. D. Levandovsky, M. Vasilyev, and P. Kumar, “Amplitude squeezing of light by means of a phase-sensitive fiber parametric amplifier,” Opt. Lett. 24(14), 984–986 (1999). [CrossRef] [PubMed]

]. Phase-sensitive (PS) fiber optical parametric amplifiers (FOPAs) have attracted more attention due to their high gain (partly thanks to the use of highly nonlinear fibers, HNLFs) and their compatibility with fiber communication systems. Basically two types of PS-FOPAs have been studied so far: the frequency degenerate (signal and idler frequencies are identical) and non-degenerate (frequencies are different) cases. Degenerate PSAs are more straightforward to realize [6

6. W. Imajuku, A. Takada, and Y. Yamabayashi, “Low-noise amplification under the 3dB noise figure in high-gain phase-sensitive fibre amplifier,” Electron. Lett. 35(22), 1954–1955 (1999). [CrossRef]

,7

7. W. Imajuku and A. Takada, “Error-free operation of in-line phase-sensitive amplifier,” Electron. Lett. 34(17), 1673–1674 (1998). [CrossRef]

], however, the inherent single-channel property limits their potential applications. For example, non-degenerate PSA schemes can realize exponential gain [3

3. M. V. Vasilyev, “Phase-sensitive amplification in optical fibers,” in Frontiers in Optics, Technical Digest (Optical Society of America, 2005), paper FThB1.

] and multi-channel amplification [8

8. R. Tang, P. S. Devgan, V. S. Grigoryan, P. Kumar, and M. Vasilyev, “In-line phase-sensitive amplification of multi-channel CW signals based on frequency nondegenerate four-wave-mixing in fiber,” Opt. Express 16(12), 9046–9053 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-12-9046. [CrossRef] [PubMed]

] without suffering the guided acoustic-wave Brillouin scattering, which makes them more promising in practical WDM systems, though rigorous phase- and frequency-locking among the pump, signal and idler waves is required.

In this paper, we derive the noise formulas of a multi-span fiber optical transmission system employing the aforementioned cascaded copier + PSA scheme for in-line amplification based on a semi-classical theory, which can be shown to be consistent with the quantum theory in the large-photon-number limit. The result shows that the cascaded PSA scheme can improve the system SNR by up to 6 dB and 3 dB compared to the pure-PIA and pure-PSA cases, respectively, in an optimized multi-span, long-haul transmission link, while this NF benefit will decrease or even disappear for a short-distance link. This big improvement relies on taking advantage of the correlated idler wave generated by the copier. The result implies that the cascaded copier + PSA scheme might be more promising for a long-haul transmission system than a pure-PSA link. As a proof of concept, the NF of a PI- and PS-FOPA cascade, with inter-stage attenuation representing the fiber link, is measured, which shows a 1.8-dB total NF improvement over a cascaded EDFA scheme.

2. Semi-classical theory

A complete noise analysis of a copier + PSA cascaded system should be based on quantum theory [16

16. C. J. McKinstrie, M. Yu, M. G. Raymer, and S. Radic, “Quantum noise properties of parametric processes,” Opt. Express 13(13), 4986–5012 (2005), http://www.opticsinfobase.org/oe/abstract.cfm?uri=OE-13-13-4986. [CrossRef] [PubMed]

18

18. C. J. McKinstrie, M. G. Raymer, S. Radic, and M. Vasilyev, “Quantum mechanics of phase-sensitive amplification in a fiber,” Opt. Commun. 257(1), 146–163 (2006). [CrossRef]

]. However, a semi-classical description with satisfying accuracy is usually easier to grasp for the engineer. In this section, we will demonstrate how to model the noise characteristics of a non-degenerate, cascaded PSA amplified system in a semi-classical way.

3. NF derivation for an m-span fiber link with cascaded copier + PSA inline amplification

Here, a PI-FOPA is used as the copier in the first span (amplifier + fiber), to amplify the signal as well as to generate the conjugated idler [9

9. R. Tang, J. Lasri, P. S. Devgan, V. S. 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), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-13-26-10483. [CrossRef] [PubMed]

,13

13. M. V. Vasilyev, “Distributed phase-sensitive amplification,” Opt. Express 13(19), 7563–7571 (2005), http://www.opticsinfobase.org/oe/abstract.cfm?uri=OE-13-19-7563. [CrossRef] [PubMed]

]. After the first span, the phase- and wavelength-locked signal, idler and pump waves will be input to the following parametric amplifiers, where non-degenerate PS amplification can be achieved. However, to achieve optimal PSA performance (highest gain and lowest NF), several practical issues need to be addressed: (i) The pump power and phase (propagated along the fiber as a pilot tone) must be regenerated with very low phase and intensity noise. This might be realized by using injection locking with a high performance slave laser [23

23. A. Takada and W. Imajuku, “In-line optical phase-sensitive amplifier employing pump laser injection locked to input signal light,” Electron. Lett. 34(3), 274–276 (1998). [CrossRef]

,24

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, paper OWT6 (2010).

]. (ii) The relative phase between the pump, signal and idler should be precisely manipulated to get the maximal PS gain, thus requiring perfect dispersion and dispersion slope compensation plus accurate phase-shifting. The simplest method is to use a piece of SMF with proper length [9

9. R. Tang, J. Lasri, P. S. Devgan, V. S. 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), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-13-26-10483. [CrossRef] [PubMed]

]. However, for WDM applications, per-channel phase control is needed. Liquid-crystal [25

25. G. Baxter, S. Frisken, D. Abakoumov, H. Zhou, I. Clarke, A. Bartos, and S. Poole, “Highly programmable wavelength selective switch based on liquid crystal on silicon switching elements,” in Optical Fiber Communication Conference, paper OTuF2 (2009).

] or MEMS [26

26. G. Zhou and F. S. Chau, “Nondispersive optical phase shifter array using microelectromechanical systems based gratings,” Opt. Express 15(17), 10958–10963 (2007), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-17-10958. [CrossRef] [PubMed]

] based frequency-resolved phase shifters might be good choices in such a situation. (iii) Polarization tracking and adaptive control are required at the input of each FOPA since parametric amplification is highly polarization-dependent [27

27. C. J. McKinstrie, H. Kogelnik, R. Jopson, S. Radic, and A. Kanaev, “Four-wave mixing in fibers with random birefringence,” Opt. Express 12(10), 2033–2055 (2004), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-12-10-2033. [CrossRef] [PubMed]

]. (iv) Phase locking might be required for recombining the regenerated pump and the signal/idler wave before the PSAs, as shown in Fig. 2, to cancel the slowly-varying phase-errors induced by environmental fluctuations or temperature changes. Of course the system performance will be much better if the above functions can be integrated together.

By assuming that the aforementioned four requirements have all been fulfilled, in the following we will analyze the noise performance of both Type A and B transmission systems with m transparent spans (fiber loss is exactly compensated by the amplifier gain).

3.1 Type A link

Subsequently, for two spans, m = 2, we have the IO relation as

[As,2Ai,2*]=L^A,2L^A,1[As0+nsni*].
(7)

<Iout,2>=R0(GT)2|As0|2Bo=R0|As0|2Bo,<ΔIout,22>=4R02|As0|2[3+(2|μ2|21)T2|μ2|2T2T]hvΔf/2.
(9)

Now extending the above analysis to an m-span system, we have the IO relation as

[As,mAi,m*]=L^A,mL^A,2L^A,1[As0+nsni*].
(10)

<Iout,m>=R0(GT)m|As0|2Bo=R0|As0|2Bo,<ΔIout,m2>4R02|As0|2[3T+i=2m(Gi1+Ti12)Ti1(1T)]hvΔf/2.
(13)

By combining Eqs. (8) and (13) and assuming T << 1, we obtain the approximate NF formula

NFA,m52+m2.
(14)

3.2 Type B link

<Iout,1>=R0GT|As0|2Bo=R0|As0|2Bo,<ΔIout,12>=4R02GT|As0|2[T(2G1)+(1T)(2G1)]hvΔf/2.
(16)

By using Eq. (4), we obtain the signal NF of the first span as NFB,1=2G1, which will reduce to NFB,1=2G when the gain is large.

When m = 2, we have the IO relation as

[As,2Ai,2*]=L^B,2L^B,1[As0+nsni*].
(17)

<Iout,2>=R0(GT)2|As0|2Bo=R0|As0|2Bo,<ΔIout,22>=4R02GT|As0|2[2G+2|μ2|22|μ2|2T1]hvΔf/2.
(18)

After the second span, the maximal signal and idler gains will be the same in the following PSAs. Assuming that the copier gain is much larger than 1 (i.e. |μ1||ν1|) and following the procedure described in Section 3.1, we have

<Iout,m>=R0(GT)m|As0|2Bo=R0|As0|2Bo,<ΔIout,m2>4R02|As0|2[2G+i=2m(Gi1+Ti12)Ti2(1T)]hvΔf/2.
(19)

Therefore the approximate NF formula (at the maximal PSA gain) can be derived as

NFB,m3G2+mG2.
(20)

4. Comparison and discussion

We should emphasize that in the above discussions we only considered the fundamental amplified quantum noise. In fact other noise contributions exist in FOPAs [32

32. 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), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-3-2884. [CrossRef] [PubMed]

] such as the pump transferred noise and Raman phonon-seeded excess noise, as previously mentioned. The former contribution can be effectively suppressed by using a clean pump as well as a lower signal power, while the latter one can be canceled by adopting a cross-polarized pump-signal/idler scheme [13

13. M. V. Vasilyev, “Distributed phase-sensitive amplification,” Opt. Express 13(19), 7563–7571 (2005), http://www.opticsinfobase.org/oe/abstract.cfm?uri=OE-13-19-7563. [CrossRef] [PubMed]

]. In a properly designed FOPA, it is reasonable to assume the excess NF induced by these two noise sources will be less than 1 dB.

5. Experimental proof of concept

As a proof of concept, we measured the NF of a PI-FOPA + attenuator (ATT) + PS-FOPA + ATT cascade to resemble the two-span copier + PSA amplified transmission link. Figure 4
Fig. 4 Experimental setup. NFA: Noise figure analyzer; ESA: Electrical spectrum analyzer; OSA: Optical spectrum analyzer; PC: Polarization controller; VOA: Variable optical attenuator. Inset (a) shows the principal scheme and inset (b) shows the output optical spectrum.
shows the experimental setup. A 60-mW low-noise DFB laser (1554.4 nm) was used as the pump laser, which was phase-modulated to suppress stimulated Brillouin scattering. After an 8.5 W EDFA booster followed by two cascaded 2-nm filters, the amplified pump was combined with signal by a 10-dB coupler representing the transmission fiber loss. Two spools (50 m and 500 m each) of highly nonlinear fibers (HNLF, parameters are λ0 = 1552 nm, γ = 11.8 W−1km−1 and S0 = 0.02 ps/nm2ּkm) were used as the PIA and PSA, respectively. In between the two stages, another SMF-based 10 dB coupler (SMF length = 7 m) was inserted as the mid-stage attenuator as well as the signal/idler/noise monitor. In the linear regime, this 10dB coupler can be viewed as a 50 km transmission fiber with dispersion compensation. We connected the 10% port to the PSA input. A 20 dB coupler was spliced after the PSA to monitor the output spectrum, and two cascaded filters were used to effectively filter out the residual pump and the amplified noise. By choosing this setup, no phase-locked loops are needed, which makes it possible to measure the NF in a more stable condition. Finally the amplified signal and idler were properly attenuated and then detected by the NF analyzer. The detected signal and noise components were separated by a bias-T, and then measured by a current meter and electrical spectrum analyzer, respectively. After carrying out calibration for shot noise and subtracting laser relative-intensity-noise (RIN) [30

30. Z. Tong, A. Bogris, C. Lundström, C. J. McKinstrie, M. Vasilyev, M. Karlsson, and P. A. Andrekson, “Modeling and measurement of noise figure in a cascaded non-degenerate phase-sensitive parametric amplifier,” to appear in Opt. Express .

,33

33. M. Movassaghi, M. K. Jackson, V. M. Smith, and W. J. Hallam, “Noise figure of erbium-doped fiber amplifiers in saturated operation,” J. Lightwave Technol. 16(5), 812–816 (1998). [CrossRef]

], the NF can be obtained from the following equation
NF=1G+Pin(SoutSin)2hvIout2,
(23)
where Pin is the input signal power, Sout and Sin are the noise power spectral density measured at the input and output of the amplifier, respectively, and Iout is the detected output signal photocurrent. According to Eq. (20), the NF of a transparent amplifier + ATT cascade can be easily derived by measuring Sout, Sin and Iout at a proper signal-power level and then replacing the net gain G with 0 dB in Eq. (23). We chose 894.7 MHz as the central frequency to measure the noise power spectral density, with 2-MHz resolution bandwidth and 3-Hz video bandwidth. In most cases, the NF measurement error is within ± 0.4 dB. The output noise spectrum of the PSA is shown in inset (b) of Fig. 4, which clearly shows that the PSA gain changes with the relative phase.

In our setup, 10-dB average PIA gain was achieved in the first (copier) stage to realize transparent amplification, which leads to well equalized signal and idler inputs to the PSA. The maximal PSA gain at 1561.7 nm is larger than 16 dB. The average input signal power is −19.4 dBm to reduce the pump-noise transfer. Figure 5
Fig. 5 Measured PSA gain and NF spectra of different cascaded amplification cases.
shows the measured copier, PSA gain spectra as well as the NF spectra of the copier + ATT cascade (representing the one-span link) and the copier + ATT + PSA + ATT cascade (representing the two-span link. At the peak PSA gain around 1561.7 nm, NFPIA + ATT + PSA is very close or even slightly lower than NFPIA + ATT, indicating the noise benefit from the PSA stage. The total NF degradation close to the pump is due to the strong pump residual ASE noise-induced measurement errors. For comparison, we also measured the NF of an EDFA + ATT + EDFA + ATT cascade (total NF is about 8.8 dB). The NF as well as the net gain of the EDFA + ATT part was almost equal to that of the copier + ATT case (with about 6 dB NF and 0 dB net gain, respectively), while the second EDFA had a 4.5 dB NF. The results show that under the above conditions, the cascaded FOPA has a 1.8-dB NF advantage over the conventional cascaded EDFA scheme, which is consistent with the theoretical predictions. Larger benefits can be expected for larger PSA span numbers, however, pump power and phase regeneration is then required.

6. Conclusion

Appendix A: NF derivation of the pure-PIA link

[As,mAi,m*]=L^A,PIAmL^A,PIA2L^A,PIA1[As0+nsni*],[As,mAi,m*]=L^B,PIAmL^B,PIA2L^B,PIA1[As0+nsni*].
(24)

Appendix B: NF derivation of the pure-PSA link

For the pure non-degenerate case, the IO relations become slightly different since the signal and idler are no longer the same wave. We have
[As,mAi,m*]=L^A,PSAmL^A,PSA2L^A,PSA1[As0+nsAi0*+ni*],
(31)
[As,mAi,m*]=L^B,PSAmL^B,PSA2L^B,PSA1[As0+nsAi0*+ni*],
(32)
for the Type A and Type B configurations, respectively. By noting that |μ2|2+|ν2|2=[(|μ2|+|ν2|)2+(|μ2||ν2|)2]/2, and only considering the signal wave, we have
<ΔIout,m2>=4R02|As0|2[1T+(Gm+Tm2)Tm+i=1m1(Gi+Ti2)Ti(1T)]hvΔf/2,
(33)
for a Type A link, and
<ΔIout,m2>=4R02|As0|2[(Gm+Tm2)Tm+i=1m(Gi+Ti2)Ti1(1T)]hvΔf/2,
(34)
for a Type B link. Moreover, since both signal and idler waves should be taken into account in the non-degenerate PSA case, a factor of 2 (3 dB) should be multiplied to the input SNR [13

13. M. V. Vasilyev, “Distributed phase-sensitive amplification,” Opt. Express 13(19), 7563–7571 (2005), http://www.opticsinfobase.org/oe/abstract.cfm?uri=OE-13-19-7563. [CrossRef] [PubMed]

,34

34. P. L. Voss, K. G. Köprülü, and P. Kumar, “Raman-noise-induced quantum limits for χ(3) nondegenerate phase-sensitive amplification and quadrature squeezing,” J. Opt. Soc. Am. B 23(4), 598–610 (2006). [CrossRef]

], while the output SNR remains identical, which will give the ‘real’ PSA NF in the high gain regime [13

13. M. V. Vasilyev, “Distributed phase-sensitive amplification,” Opt. Express 13(19), 7563–7571 (2005), http://www.opticsinfobase.org/oe/abstract.cfm?uri=OE-13-19-7563. [CrossRef] [PubMed]

]. Thus by combing Eq. (4) and assuming T << 1, we have

NFAs,mm+2, NFBs,mmG.
(35)

Acknowledgements

The research leading to these results received funding from the European Communities Seventh Framework Programme FP/2007-2013 under grant agreement 224547 (STREP PHASORS), and also from the Air Force Office of Scientific Research, Air Force Material Command, USAF, under grant number FA8655-09-1-3076. Z. Tong would like to thank Dr. Per-Olof Hedekvist for help with error analysis, Dr. Michael Vasilyev for enlightening help, Dr. Adonis Bogris, Dr. Andrew Ellis and Dr. Stylianos Sygletos for fruitful discussions.

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2.

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Z. Tong, A. Bogris, C. Lundström, C. J. McKinstrie, M. Vasilyev, M. Karlsson, and P. A. Andrekson, “Modeling and measurement of noise figure in a cascaded non-degenerate phase-sensitive parametric amplifier,” to appear in Opt. Express .

31.

T. Torounidis and P. Andrekson, “Broadband single-pumped fiber-optic parametric amplifiers,” IEEE Photon. Technol. Lett. 19(9), 650–652 (2007). [CrossRef]

32.

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), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-3-2884. [CrossRef] [PubMed]

33.

M. Movassaghi, M. K. Jackson, V. M. Smith, and W. J. Hallam, “Noise figure of erbium-doped fiber amplifiers in saturated operation,” J. Lightwave Technol. 16(5), 812–816 (1998). [CrossRef]

34.

P. L. Voss, K. G. Köprülü, and P. Kumar, “Raman-noise-induced quantum limits for χ(3) nondegenerate phase-sensitive amplification and quadrature squeezing,” J. Opt. Soc. Am. B 23(4), 598–610 (2006). [CrossRef]

OCIS Codes
(060.2320) Fiber optics and optical communications : Fiber optics amplifiers and oscillators
(190.4380) Nonlinear optics : Nonlinear optics, four-wave mixing

ToC Category:
Fiber Optics and Optical Communications

History
Original Manuscript: April 19, 2010
Revised Manuscript: June 22, 2010
Manuscript Accepted: June 28, 2010
Published: July 6, 2010

Citation
Zhi Tong, C. J. McKinstrie, Carl Lundström, Magnus Karlsson, and Peter A. Andrekson, "Noise performance of optical fiber transmission links that use non-degenerate cascaded phase-sensitive amplifiers," Opt. Express 18, 15426-15439 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-15-15426


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  31. T. Torounidis and P. Andrekson, “Broadband single-pumped fiber-optic parametric amplifiers,” IEEE Photon. Technol. Lett. 19(9), 650–652 (2007). [CrossRef]
  32. 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), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-3-2884 . [CrossRef] [PubMed]
  33. M. Movassaghi, M. K. Jackson, V. M. Smith, and W. J. Hallam, “Noise figure of erbium-doped fiber amplifiers in saturated operation,” J. Lightwave Technol. 16(5), 812–816 (1998). [CrossRef]
  34. P. L. Voss, K. G. Köprülü, and P. Kumar, “Raman-noise-induced quantum limits for χ(3) nondegenerate phase-sensitive amplification and quadrature squeezing,” J. Opt. Soc. Am. B 23(4), 598–610 (2006). [CrossRef]

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