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Optics Express

  • Editor: Michael Duncan
  • Vol. 14, Iss. 11 — May. 29, 2006
  • pp: 4589–4600
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10 Gbps WDM transmission performance limits using in-line SOAs and an optical phase conjugator based on four-wave mixing in SOAs as a mid-span spectral inversion technique

Sub Hur, Yonggyou Kim, Hodeok Jang, and Jichai Jeong  »View Author Affiliations


Optics Express, Vol. 14, Issue 11, pp. 4589-4600 (2006)
http://dx.doi.org/10.1364/OE.14.004589


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Abstract

We have theoretically investigated the transmission performance limits of all semiconductor optical amplifiers (SOA)-based 10 Gb/s wavelength division multiplexing (WDM) systems using in-line SOAs and an optical phase conjugator (OPC) based on four-wave mixing in SOAs as a mid-span spectral inversion technique. With a verified numerical model of SOAs, we have found that the crosstalk from SOAs in OPC is a dominant factor to limit the number of channels in WDM systems. In order to increase the available number of channels, we optimize the input optical power and the injection current to SOAs in OPC with using a reservoir channel in inline SOAs. All SOA-based 10 Gb/s WDM systems using the OPC can transmit 16 channel signals up to 240 km distance with a 3 dB power penalty.

© 2006 Optical Society of America

1. Introduction

In order to increase a transmission distance in optical systems, compensations of the chromatic dispersion are important factors. Dispersion compensating fibers (DCF) with negative dispersion at each fiber span can be normally used for the dispersion compensation. Chirped fiber grating with inverse dispersion also have potential to do such a function. These two dispersion compensating techniques require the accurate information about dispersion of a span, channel wavelength, channel data rate, channel spacing and number of channels [1

1. A. H. Gnauck and R. M. Jopson, “Dispersion compensation for optical fiber systems,” in Optical Fiber Telecommunications III A, I. P. Kaminow and T. L. Koch, eds. (Academic Press, San Diego, 1997).

]. Dispersion tolerant modulation formats may be used for overcoming the dispersion [2

2. T. Ono, Y. Yano, and K. Fukuchi, “Demonstration of high-dispersion tolerance of 20-Gbit/s optical duobinary signal generated by a low-pass filtering method,” OFC 1997, paper ThH1.

]. [3

3. B. Kim, J. Jeong, J. Lee, H. Lee, H. Kim, S. K. Kim, Y. Kim, S. Hwang, Y. Oh, and C. Shim, “Improvement of dispersion tolerance for electrical-binary-signal-based duobinary transmitters,” Opt. Express 13, 5100–5105 (2005). [CrossRef] [PubMed]

]. Moreover, a mid-span spectral inversion (MSSI) technique has been recently attracted for an alternative for the dispersion compensation of competing in price for metro networks.

The MSSI technique enables the dispersion compensation by placing an optical phase conjugator (OPC) which inverts the spectrum and the phase of optical signals distorted by the chromatic dispersion at the middle of a complete transmission link. If phase conjugated optical signals pass through the same amount of dispersion to the end of the link, phase distortion can be recovered to their initial state as exactly the same as the transmitter output. Using the MSSI method, 40 Gb/s transmission is possible over 800 km for 16 channels of on-off-keyed [4

4. S. L. Jansen, S. Spalter, G-D. Khoe, Huug de Waardt, H. E. Escobar, L. Marshall, and M. Sher, “16×40 Gb/s over 800 km of SSMF using mid-link spectral inversion,” IEEE Photon. Technol. Lett. 16, 1763–1765 (2004). [CrossRef]

] and phase-shifted-keyed signals [5

5. S. L. Jansen, D. van den Borne, B. Spinnler, S. Calabro, H. Suche, P. M. Krummrich, W. Sohler, G-D. Khoe, and H. Waardt, “Optical phase conjugation for ultra long-haul phase-shift-keyed transmission,” IEEE J. Lightw. Technol. 24, 54–64 (2006). [CrossRef]

]. Theoretically, the reduction of nonlinear impairments has been shown in [6

6. H. Wei and D. Plant, “Simultaneous nonlinearity suppression and wide-band dispersion compensation using optical phase conjugation,” Opt. Express 12, 1938–1958 (2004). [CrossRef] [PubMed]

]. Other experiments using a difference frequency generation in periodically poled LiNbO3, have been reported so far at 40 Gb/s data rate [7

7. P. Minzioni, I. Cristiani, V. Degiorgio, L. Marazzi, M. Martinelli, C. Langrock, and M. M. Fejer, “Experimental Demonstration of Nonlinearity and Dispersion Compensation in an Embedded Link by Optical Phase Conjugation,” IEEE Photon. Technol. Lett. 18, 995–997 (2006). [CrossRef]

], [8

8. A. Chowdhury, G. Raybon, R.-J. Essiambre, and C. R. Doerr, “WDM CSRZ 40 Gbit/s pseudo-linear transmission over 4800 km using optical phase conjugation,” Electron. Lett. 41,151–152, (2005). [CrossRef]

].

The rest of the paper is organized as follows. In section 2, we describe the modeling of optical components such as OPC, transmitter, receiver and fiber. In section 3, we verify the modeling of optical phase conjugation in WDM channels and optimize the OPC characteristics based on FWM in SOAs. Section 4 shows the transmission performance limits of all SOAs-based 10 Gb/s WDM systems using in-line SOAs and an OPC. Finally, conclusions are given in Section V.

2. OPC, Transmitter, Receiver, and Fiber Models

2.1 OPC model

Fig. 1. Schematic of describing wave propagation on a SOA model based on the timedependent TMM. In every section, the complex pulse envelope was calculated.

Apz+1vgApt=GpAp(z,t)+μp(z,t)
(1)
As,cz+1vgAs,ct=Gs,cAs,c(z,t)+Fs,c{Ap2(z,t)Ac,s(z,t)+2Ap(z,t)Bp(z,t)Bc,s(z,t)}+μs,c(z,t)
(2)
Gp,s,c=(12g̅p,s,ci2αΓp,s,cgp,s,c)(1+w=p,s,c(Aw2+Bw2)PSat)
(3)
Fs,c=(12g̅s,ci2αΓs,cgs,c)hCDP(±Δω)PSat12(1iαCH)(g̅s,cεCH1+gs,cεCH2)hCH(Δω)
12(1iαSHB)g̅s,cεSHBhSHB(Δω)
(4)

where Ai and Bi are normalized slowly varying envelopes of forward and backward fields at section i and index p, s and c present pump, signal, and conjugate waves, respectively. Δω=ωp-ωs is the frequency detuning for pump and signal waves, ḡ is the net gain, g is the material gain, vg is the group velocity, PSat is the saturation power, εSHB is the spectral hole burning parameter, and εCH1 and εCH2 are the carrier heating parameters. The frequency response hyω) (y=CDP, CH, and SHB) of the individual nonlinear processes are given by

hCDP1(Δω)=(1iΔωτ2)(1Δωτs)
hCH1(Δω)=(1iΔωτ2)(1Δωτ1)
hSHB1(Δω)=(1iΔωτ2)
(5)

where τ s is carrier life time,τ 1 is carrier heating lifetime, and τ 2 is hole burning lifetime. In order to model an asymmetric gain profile in SOAs, the gain spectrum was assumed to be cubic and the material gain was approximated to

gi,w(Ni,λw)=a0(NiN0)a1(λwλN)2+a3(λwλN)3
(6)

where index i corresponds to different sections and index w refers to different optical waves. a 0,, a 1 and a 3 are gain constants, and λ N is the gain peak wavelength assumed to shift linearly with carrier density

λN=λoa2(NNo)
(7)

The rate equation in each small section was solved as

Nit=IqVNi(c1+c2Ni+c3Ni2)w=p,s,cvgΓwgw,iSw,i
(8)

2.2 Transmitter model

The output electric field and the chirp parameter of a Mach-Zehnder (MZ) modulator were modeled using the peak voltages applied to two electrodes and the switching voltage of the modulator. The device was biased at the midpoint of its transfer characteristic curve and driven in a push-pull manner. For nonideal devices, the MZ modulator experienced residual chirp and finite extinction ratio [13

13. A. H. Gnauck, S. K. Korotky, J. J. Veselka, J. Nagel, C. T. Kemmerer, W. J. Minford, and D. T. Moser, “Dispersion penalty reduction using an optical modulator with adjustable chirp,” IEEE Photon. Technol. Lett 3, 916–918 (1991). [CrossRef]

].

2.3 Fiber model

The nonlinear Schrödinger equation should be solved in order to consider the nonlinearity, the dispersion, and the loss in a fiber. Because the nonlinear Schrödinger equation is a nonlinear partial differential equation that does not have analytic solutions generally, it was numerically solved using the split-step Fourier method [14

14. G. P. Agrawal, Nonlinear Fiber Optics. 2nd ed. (Academic Press, San Diego, 1995), Chapter 2.

].

2.4 Receiver model

At the receiver, optical pulses were filtered using a fifth-order Bessel-Thomson filter. To accurately calculate receiver sensitivities at the specific bit-error rates (BER), we included the intersymbol interference caused by nonlinear optical fibers and OPCs. Additionally we calculated the various noise components, such as shot noise, signal-spontaneous beat noise, spontaneous-spontaneous beat noise, and thermal noise. The decision threshold was adjusted for obtaining the best BER performance [15

15. S. Kim and J. Jeong, “Transmission performance on frequency response of receivers and chirping shape of transmitters for 10 Gb/s LiNbO3 modulator based lightwave systems,” Optics Commun. 175, 109–123 (2000). [CrossRef]

].

3. Verification of Models and Optimization of OPCs

Fig. 2. Calculated eye diagrams of wavelength converted signals in SOAs with a) large (22dB) and b) small (12 dB) pump-to-probe ratio. In the case of 22 dB, the input signals do not saturate SOAs.

To obtain low crosstalk and high OSNR in transmission systems using the MSSI method, we calculated the receiver sensitivities at 10-9 BER of converted signals while changing the total input optical power and the injection current to an OPC. Figure 3 shows the contour plots of the receiver sensitivities of the worst channel for the total input optical power and the injection current to the OPC. The number of input channels was varied from 2 to 16 and the first wavelength of the converted channel was fixed to 1550.0 nm. For example, the 4 and 16 WDM signals were converted from 1556.4~1558.8 to 1550~1552.4 nm and from 1566~1578 to 1550~1562 nm, respectively. The channel spacing was equally set to 100 GHz. The pump wavelength was placed in a 2 nm wavelength from the last wavelength of the converted channel and the pump power was 13 dBm. Each input optical signal had unequal conversion efficiency, consequently, channels with a high conversion efficiency experienced more crosstalk. Therefore, we found the optimum conditions of the OPC for the channel having the worst receiver sensitivities. The optimum region of BER characteristics means that the phase conjugated signals have the lowest crosstalk and the highest OSNR. It needs to select the largest input power to the OPC in the optimum region to maintain high OSNR in transmission links. With the minimum current in the optimum region, the OPC generates low ASE noise levels. Because the OSNR dominantly affects the phase conjugated signals with the low signal power to SOAs, the optimum injection current increases while reducing signal power. From the contour plots, the optimum injection current and input optical power to the OPC for two channels are 300 mA and -9 dBm, respectively. Using the same procedure, we could find the optimum conditions and the power penalties of the OPC for 4, 8, and 16 channels and then summarized the results in Table 1. The SOA model as an OPC supported for 16 channels with a 1.7 dB power penalty in the worst case. For larger than 16 channels using the OPC, it was impossible to convert all channels without error floors.

Fig. 3. Contour plots of calculated receiver sensitivities for the injection current and total input optical power to OPC with a) 2, b) 4, c) 8, and d) 16 channels. The optimum region of BER characteristics means that the phase conjugated signals have the lowest crosstalk and the highest OSNR.

Table 1. Optimized parameters and power penalties of OPC with different total input optical power to in-line SOAs for different number of channels

table-icon
View This Table

Wavelength dependent conversion efficiency of OPCs based on the FWM in SOAs limits the available number of channels in WDM transmissions. We investigated conversion efficiency of the OPC for 16 channels as shown in Fig. 4. Input optical power to the OPC was varied from 0 to -6 dBm. Optimum injection current to the OPC for 16 channels was used (Table 1). Due to the saturation effect of SOAs, conversion efficiency in the case of high input power (0 dBm) is smaller than that of low input power (-6 dBm). Wavelength dependent conversion efficiency is 7 dB for 16 channels and this will limit the transmission performance of the WDM system using the MSSI technique.

Fig. 4. Conversion efficiency of the OPC for 16 channels. Input power to the OPC was changed from 0 dBm to -6 dBm.

4. Simulation Results

Fig. 5. Transmission configuration using in-line SOAs and an OPC based on FWM in SOAs.

4.1 Eye diagrams after 120 km transmissions

Figure 6 shows the received eye diagrams for the first channel (1550.0 nm) at back-to-back, the first 60 km SSMF, the OPC and the second 60 km SSMF for two input channels. The chromatic dispersion distorts the pulse shape after the first 60 km transmission and the selfphase modulation (SPM) can be negligible due to the low fiber launching power of -10 dBm. The crosstalk between two input channels also affects the converted signals after the OPC. Full dispersion compensation can be obtained by transmitting through the second 60 km SSMF. After the total 120 km transmission, there are a residual distortion of the received eye diagrams due to the dynamic characteristics of SOAs as in-line amplifiers and an OPC.

Fig. 6. Calculated eye diagrams at a) back-to-back, b) first 60 km SMF, c) OPC, and d) second 60 km SMF for two channels. Full dispersion compensation is done after OPC and the second 60 km transmission.

If the difference between input wavelength and output wavelength of the OPC becomes large, the accurate length of the second fiber span should be used. The reason for using the same length of the first and second fiber spans in our paper is that it is difficult to precisely adjust the length of the second fiber spans in the real system design. In the case of large number of channels, the dominant impairment for WDM transmission is the OSNR of converted channels from SOAs.

4.2 Limits of transmission distance with different number of channels

We investigated the performance of transmission systems with in-line SOAs and an OPC as the MSSI technique with changing the number of channels and the transmission distance. Figure 7 shows the average receiver sensitivities at 10-9 BER as a function of transmission distance for different number of channels without using a reservoir channel. We used the optimum conditions of the OPC characteristics for the number of channels in each case. Because the gain profile of SOAs was not flat, we averaged the receiver sensitivities of all the channels at 10-9 BERs after transmissions. Simulations had been performed on systems with a length multiple of 120 km for different number of channels. For comparison, we added the receiver sensitivities of a channel with a 1550.0 nm wavelength. The receiver sensitivity in the back to back case without OPC was -20.52 dBm. As expected, the transmission performance was degraded as the number of channels and the transmission distance was increased. The possible transmission distance for 16 channels was up to 120 km with a 2 dB average power penalty. It was possible to transmit over 480 km for 4 channels with a 2.5 dB average power penalty. Because a reservoir channel was not used, the dominant factors of the transmission performance are OSNR and crosstalk. The OSNR degradation is unaviodable in optical transmission systems but the crosstalk from in-line SOAs and an OPC can be eliminated by injecting a reservoir channel [22

22. K.-P. Ho, S.-K. Liaw, and C. Lin, “Reduction of semiconductor laser amplifier induced distortion and crosstalk for WDM systems using light injection,” Electron. Lett. 32, 2210–2211 (1996). [CrossRef]

].

Fig. 7. Contour plots of calculated receiver sensitivities for transmission distance and number of channels without using a reservoir channel. The possible transmission distance for 16 channels was up to 120 km with a 2 dB average power penalty.

The average receiver sensitivities at 10-9 BER as a function of transmission distance for different number of channels with using a reservoir channel are shown in Fig. 8. The power of the reservoir channel was optimized to obtain the best transmission performance. In the case of 16 channels with a reservoir channel, it was possible to transmit over 240 km with a 3 dB average power penalty. Without using a reservoir channel, it couldn’t transmit up to 240 km distance. In addition to 16 channels, all the channels using a reservoir channel improved the transmission performance. Up to 8 channels, the possible transmission distance was 480 km with a 2 dB average power penalty.

Fig. 8. Contour plots of calculated receiver sensitivities for transmission distance and number of channels with using a reservoir channel. It was possible to transmit over 240 km with 3 dB average power penalty.

5. Conclusion

We investigated the transmission limits of all SOA-based WDM systems using in-line SOAs and an OPC based on FWM in SOAs as a MSSI technique. The input optical power and injection current to the OPC were optimized in the worst channel and a 1.7 dB power penalty existed in the case of 16 input optical signals to the OPC. Using the developed simulation models, it was possible to compensate the chromatic dispersion using an OPC based on the FWM in SOAs as a MSSI technique. With and without using a reservoir channel, we calculated the receiver sensitivities at 10-9 BER of 10 Gb/s WDM signals transmitted over M×60 km for different number of channels. With using a reservoir channel, over 240 km transmission was possible for 16 channels with a 3 dB average power penalty. These results can suggest the possibility to implement the cost-effective optical transmission systems using all SOA-based in-line amplifiers and an OPC.

Acknowledgments

This work was supported in part by the National Research Laboratory Program of Ministry of Science & Technology in South Korea.

References and links

1.

A. H. Gnauck and R. M. Jopson, “Dispersion compensation for optical fiber systems,” in Optical Fiber Telecommunications III A, I. P. Kaminow and T. L. Koch, eds. (Academic Press, San Diego, 1997).

2.

T. Ono, Y. Yano, and K. Fukuchi, “Demonstration of high-dispersion tolerance of 20-Gbit/s optical duobinary signal generated by a low-pass filtering method,” OFC 1997, paper ThH1.

3.

B. Kim, J. Jeong, J. Lee, H. Lee, H. Kim, S. K. Kim, Y. Kim, S. Hwang, Y. Oh, and C. Shim, “Improvement of dispersion tolerance for electrical-binary-signal-based duobinary transmitters,” Opt. Express 13, 5100–5105 (2005). [CrossRef] [PubMed]

4.

S. L. Jansen, S. Spalter, G-D. Khoe, Huug de Waardt, H. E. Escobar, L. Marshall, and M. Sher, “16×40 Gb/s over 800 km of SSMF using mid-link spectral inversion,” IEEE Photon. Technol. Lett. 16, 1763–1765 (2004). [CrossRef]

5.

S. L. Jansen, D. van den Borne, B. Spinnler, S. Calabro, H. Suche, P. M. Krummrich, W. Sohler, G-D. Khoe, and H. Waardt, “Optical phase conjugation for ultra long-haul phase-shift-keyed transmission,” IEEE J. Lightw. Technol. 24, 54–64 (2006). [CrossRef]

6.

H. Wei and D. Plant, “Simultaneous nonlinearity suppression and wide-band dispersion compensation using optical phase conjugation,” Opt. Express 12, 1938–1958 (2004). [CrossRef] [PubMed]

7.

P. Minzioni, I. Cristiani, V. Degiorgio, L. Marazzi, M. Martinelli, C. Langrock, and M. M. Fejer, “Experimental Demonstration of Nonlinearity and Dispersion Compensation in an Embedded Link by Optical Phase Conjugation,” IEEE Photon. Technol. Lett. 18, 995–997 (2006). [CrossRef]

8.

A. Chowdhury, G. Raybon, R.-J. Essiambre, and C. R. Doerr, “WDM CSRZ 40 Gbit/s pseudo-linear transmission over 4800 km using optical phase conjugation,” Electron. Lett. 41,151–152, (2005). [CrossRef]

9.

L. Spiekman and D. Zimmerman, “Optical amplification for metro: EDFA/EDWA amplets & semioconductor technologies,” OFC 2003, paper ThC5.

10.

Y. Kim, H. Lee, S. Kim, J. Ko, and J. Jeong, “Analysis of frequency chirping and extinction ratio of optical phase conjugate signals by four-wave mixing in SOA’s,” IEEE J. Sel. Top. Quantum Electron. 5, 873–879, (1999). [CrossRef]

11.

L. Spiekman, “Semiconductor Optical Amplifiers,” in Optical Fiber Telecommunications IV A, I. Kaminow and T. Li, eds. (Academic Press, San Diego, 2002).

12.

M. A. Summerfield and R. S. Tucker, “Frequency-domain model of multiwave mixing in bulk semiconductor optical amplifiers,” IEEE J. J. Sel. Top. Quantum Electron. 5, 839–850, (1993). [CrossRef]

13.

A. H. Gnauck, S. K. Korotky, J. J. Veselka, J. Nagel, C. T. Kemmerer, W. J. Minford, and D. T. Moser, “Dispersion penalty reduction using an optical modulator with adjustable chirp,” IEEE Photon. Technol. Lett 3, 916–918 (1991). [CrossRef]

14.

G. P. Agrawal, Nonlinear Fiber Optics. 2nd ed. (Academic Press, San Diego, 1995), Chapter 2.

15.

S. Kim and J. Jeong, “Transmission performance on frequency response of receivers and chirping shape of transmitters for 10 Gb/s LiNbO3 modulator based lightwave systems,” Optics Commun. 175, 109–123 (2000). [CrossRef]

16.

A. D’Ottavi, P. Spano, G. Hunziker, R. Paiella, R. Dall’Ara, G. Guekos, and K. J. Vahala, “Wavelength conversion at 10 Gb/s by four-wave mixing over a 30-nm interval,” IEEE Photon. Technol. Lett. 10, 952–954, (1998). [CrossRef]

17.

A. Schiffini, A. Paoletti, P. Griggio, P. Minzioni, G. Contestabile, A. D’Ottavi, and E. Martelli, “4x40 Gbit/s transmission in 500 km long, dispersion-managed link, with in-line all-optical wavelength conversion,” Electron. Lett. 38, 1558–1560 (2002). [CrossRef]

18.

T. Mukai, K. Inoue, and T Saitoh, “Signal gain saturation in two-channel common amplification using a 1.5 µm InGaAsP traveling wave laser amplifier,” Electron. Lett. 23, 396–397 (1987). [CrossRef]

19.

G. P. Agrawal, “Amplifier-induced crosstalk in multichannel coherent lightwave systems,” Electron. Lett. 23, 1175–1177 (1987). [CrossRef]

20.

G. O. Magnus and N. A. Olsson, “Crosstalk between intensity-modulated wavelength-division multiplexed signals in a semiconductor laser amplifier,” J. Quantum Electron. QE-24, 52–59 (1988).

21.

D. F. Geraghty, R. B. Lee, M. Verdiell, M. Ziari, A. Mathur, and K. J. Vahala, “Wavelength conversion for WDM communication systems using four-wave mixing in semiconductor optical amplifiers,” IEEE J. J. Sel. Top. Quantum Electron. 3, 1146–1155, (1997). [CrossRef]

22.

K.-P. Ho, S.-K. Liaw, and C. Lin, “Reduction of semiconductor laser amplifier induced distortion and crosstalk for WDM systems using light injection,” Electron. Lett. 32, 2210–2211 (1996). [CrossRef]

OCIS Codes
(060.2360) Fiber optics and optical communications : Fiber optics links and subsystems
(060.4510) Fiber optics and optical communications : Optical communications

ToC Category:
Fiber Optics and Optical Communications

History
Original Manuscript: March 27, 2006
Revised Manuscript: May 21, 2006
Manuscript Accepted: May 23, 2006
Published: May 29, 2006

Citation
Sub Hur, Yonggyou Kim, Hodeok Jang, and Jichai Jeong, "10 Gbps WDM transmission performance limits using in-line SOAs and an optical phase conjugator based on four-wave mixing in SOAs as a mid-span spectral inversion technique," Opt. Express 14, 4589-4600 (2006)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-11-4589


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References

  1. A. H. Gnauck and R. M. Jopson, "Dispersion compensation for optical fiber systems," in Optical Fiber Telecommunications III A, I. P. Kaminow and T. L. Koch, eds. (Academic Press, San Diego, 1997).
  2. T. Ono, Y. Yano, and K. Fukuchi, "Demonstration of high-dispersion tolerance of 20-Gbit/s optical duobinary signal generated by a low-pass filtering method," OFC 1997, paper ThH1.
  3. B. Kim, J. Jeong, J. Lee, H. Lee, H. Kim, S. K. Kim, Y. Kim, S. Hwang, Y. Oh, and C. Shim, "Improvement of dispersion tolerance for electrical-binary-signal-based duobinary transmitters," Opt. Express 13, 5100-5105 (2005). [CrossRef] [PubMed]
  4. S. L. Jansen, S. Spalter, G-D. Khoe, Huug de Waardt, H. E. Escobar, L. Marshall, and M. Sher, "16×40 Gb/s over 800 km of SSMF using mid-link spectral inversion," IEEE Photon. Technol. Lett. 16, 1763-1765 (2004). [CrossRef]
  5. S. L. Jansen, D. van den Borne, B. Spinnler, S. Calabro, H. Suche, P. M. Krummrich, W. Sohler, G-D. Khoe, and H. Waardt, "Optical phase conjugation for ultra long-haul phase-shift-keyed transmission," IEEE J. Lightw. Technol. 24, 54-64 (2006). [CrossRef]
  6. H. Wei and D. Plant, "Simultaneous nonlinearity suppression and wide-band dispersion compensation using optical phase conjugation," Opt. Express 12, 1938-1958 (2004). [CrossRef] [PubMed]
  7. P. Minzioni, I. Cristiani, V. Degiorgio, L. Marazzi, M. Martinelli, C. Langrock, and M. M. Fejer, "Experimental Demonstration of Nonlinearity and Dispersion Compensation in an Embedded Link by Optical Phase Conjugation," IEEE Photon. Technol. Lett. 18, 995-997 (2006). [CrossRef]
  8. A. Chowdhury, G. Raybon, R.-J. Essiambre, and C. R. Doerr, "WDM CSRZ 40 Gbit/s pseudo-linear transmission over 4800 km using optical phase conjugation," Electron. Lett. 41,151-152, (2005). [CrossRef]
  9. L. Spiekman and D. Zimmerman, "Optical amplification for metro: EDFA/EDWA amplets & semioconductor technologies," OFC 2003, paper ThC5.
  10. Y. Kim, H. Lee, S. Kim, J. Ko, and J. Jeong, "Analysis of frequency chirping and extinction ratio of optical phase conjugate signals by four-wave mixing in SOA's," IEEE J. Sel. Top. Quantum Electron. 5, 873-879, (1999). [CrossRef]
  11. L. Spiekman, "Semiconductor Optical Amplifiers," in Optical Fiber Telecommunications IV A, I. Kaminow and T. Li, eds. (Academic Press, San Diego, 2002).
  12. M. A. Summerfield and R. S. Tucker, "Frequency-domain model of multiwave mixing in bulk semiconductor optical amplifiers," IEEE J. J. Sel. Top. Quantum Electron. 5, 839-850, (1993). [CrossRef]
  13. A. H. Gnauck, S. K. Korotky, J. J. Veselka, J. Nagel, C. T. Kemmerer, W. J. Minford, and D. T. Moser, "Dispersion penalty reduction using an optical modulator with adjustable chirp," IEEE Photon. Technol. Lett 3, 916-918 (1991). [CrossRef]
  14. G. P. Agrawal, Nonlinear Fiber Optics. 2nd ed. (Academic Press, San Diego, 1995), Chapter 2.
  15. S. Kim and J. Jeong, "Transmission performance on frequency response of receivers and chirping shape of transmitters for 10 Gb/s LiNbO3 modulator based lightwave systems," Optics Commun. 175, 109-123 (2000). [CrossRef]
  16. A. D'Ottavi, P. Spano, G. Hunziker, R. Paiella, R. Dall'Ara, G. Guekos, and K. J. Vahala, "Wavelength conversion at 10 Gb/s by four-wave mixing over a 30-nm interval," IEEE Photon. Technol. Lett. 10, 952-954, (1998). [CrossRef]
  17. A. Schiffini, A. Paoletti, P. Griggio, P. Minzioni, G. Contestabile, A. D'Ottavi, and E. Martelli, "4x40 Gbit/s transmission in 500 km long, dispersion-managed link, with in-line all-optical wavelength conversion," Electron. Lett. 38, 1558-1560 (2002). [CrossRef]
  18. T. Mukai, K. Inoue, and T , Saitoh, "Signal gain saturation in two-channel common amplification using a 1.5 μm InGaAsP traveling wave laser amplifier," Electron. Lett. 23, 396-397 (1987). [CrossRef]
  19. G. P. Agrawal, "Amplifier-induced crosstalk in multichannel coherent lightwave systems," Electron. Lett. 23, 1175-1177 (1987). [CrossRef]
  20. G. O. Magnus and N. A. Olsson, "Crosstalk between intensity-modulated wavelength-division multiplexed signals in a semiconductor laser amplifier," J. Quantum Electron. QE-24, 52-59 (1988).
  21. D. F. Geraghty, R. B. Lee, M. Verdiell, M. Ziari, A. Mathur, K. J. Vahala, "Wavelength conversion for WDM communication systems using four-wave mixing in semiconductor optical amplifiers," IEEE J. J. Sel. Top. Quantum Electron. 3, 1146-1155, (1997). [CrossRef]
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