Abstract

Polarization-insensitive conversion of return-to-zero (RZ) ON-OFF keying (RZ-OOK) to RZ binary phase-shift keying (RZ-BPSK) has been achieved by cross-phase modulation (XPM) in a nonlinear birefringent fiber. This work presents a theoretical analysis of the dependence of format conversion on pump-probe detuning, and the pump state-of-polarization (SOP) that can fluctuate unpredictably in a realistic system. An investigation of the impact of pump polarization fluctuation on receiver sensitivity and receiver optimal threshold for the converted RZ-BPSK probe is also carried out. It was found that although the desired XPM-induced n phase shift can be achieved by launching both the RZ-OOK pump and the probe along the same birefringent axis of the fiber, the phase shift degrades to π/3 if the SOP of the RZ-OOK pump unpredictably switches to the other axis of the fiber, resulting in a large receiver sensitivity penalty fluctuation of 14 dB. By contrast, launching the probe at 45° relative to the birefringent axes can reduce the polarization-dependent receiver sensitivity penalty fluctuation to about 2 dB as the SOP of the RZ-OOK pump is swept over the Poincaré sphere. These conclusions are in good agreement with recently published experimental results.

© 2009 Optical Society of America

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References

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  1. A. H. Gnauck and P. J. Winzer, "Optical phase-shift-keyed transmission," J. Lightwave Technol. 23, 115-130 (2005).
    [CrossRef]
  2. K. Mishina, A. Maruta, S. Mitani, T. Miyahara, K. Ishida, K. Shimizu, T. Hatta, K. Motoshima, and K.-I. Kitayama, "NRZ-OOK-to-RZ-BPSK modulation-format conversion using SOA-MZI wavelength converter," J. Lightwave Technol. 24, 3751-3758 (2006).
    [CrossRef]
  3. W. Astar, A. S. Lenihan, and G. M. Carter, "Performance of DBPSK in a 5 × 10 Gb/s mixed modulation format Raman/EDFA WDM system," IEEE Photon. Technol. Lett. 17, 2766-2768 (2005).
    [CrossRef]
  4. W. Astar and G. M. Carter, "10 Gbit/s RZ-OOK to RZ-BPSK format conversion using SOA and synchronous pulse carver," Electron. Lett. 44, 369-370 (2008).
    [CrossRef]
  5. Cishuo Yan, Yikai Su, Lilin Yi, Lufeng Leng, Xiangqing Tian, Xinyu Vu, and Yue Tian, "All-optical format conversion from NRZ to BPSK using a single saturated SOA," IEEE Photon. Technol. Lett. 18, 2368-2370 (2006).
    [CrossRef]
  6. H. Jiang, He Wen, Liuyan Han, Yili Guo, and Hanyi Zhang, "All-optical NRZ-OOK to BPSK format conversion in an SOA-based nonlinear polarization switch," IEEE Photon. Technol. Lett. 19, 1985-1987 (2007).
    [CrossRef]
  7. K. Mishina, S. Kitagawa, and A. Maruta, "All-optical modulation format conversion from on-off-keying to multiple-level phase-shift-keying based on nonlinearity in optical fiber," Opt. Express 15, 8444-8453 (2007), http://www.opticsexpress.org/abstract.cfm?uri=OE-15-13-8444.
    [CrossRef] [PubMed]
  8. W. Astar, C.-C. Wei, Y.-J. Chen, J. Chen, and G. M. Carter, "Polarization-insensitive, 40 Gb/s wavelength and RZ-OOK-to-RZ-BPSK modulation format conversion by XPM in a highly nonlinear PCF," Opt. Express 16, 12039-12049 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-16-12039.
    [CrossRef] [PubMed]
  9. S. Kumar, A. Selvarajan, and G. Anand, "Nonlinear propagation of two optical pulses of two different frequencies in birefringent fibers," J. Opt. Soc. Am. B 11, 810-817 (1994).
    [CrossRef]
  10. G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, San Diego, CA, 2001), Chap. 7.
  11. D. Marcuse, "Derivation of analytical expressions for the bit-error probability in lightwave systems with optical amplifiers," J. Lightwave Technol. 8, 1819-1826 (1990).
    [CrossRef]
  12. E. W. Weisstein, "Noncentral Chi-Squared Distribution." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/NoncentralChi-SquaredDistribution.html.
  13. Q1. S. Stein, "Unified analysis of certain coherent and noncoherent binary communications systems," IEEE.Trans. Info. Theory 10, 43-51 (1964).
    [CrossRef]
  14. K.-P. Ho, Phase-Modulated Optical Communication System (Springer, 2005), Appendix 3.A.

2008 (2)

2007 (2)

H. Jiang, He Wen, Liuyan Han, Yili Guo, and Hanyi Zhang, "All-optical NRZ-OOK to BPSK format conversion in an SOA-based nonlinear polarization switch," IEEE Photon. Technol. Lett. 19, 1985-1987 (2007).
[CrossRef]

K. Mishina, S. Kitagawa, and A. Maruta, "All-optical modulation format conversion from on-off-keying to multiple-level phase-shift-keying based on nonlinearity in optical fiber," Opt. Express 15, 8444-8453 (2007), http://www.opticsexpress.org/abstract.cfm?uri=OE-15-13-8444.
[CrossRef] [PubMed]

2006 (2)

Cishuo Yan, Yikai Su, Lilin Yi, Lufeng Leng, Xiangqing Tian, Xinyu Vu, and Yue Tian, "All-optical format conversion from NRZ to BPSK using a single saturated SOA," IEEE Photon. Technol. Lett. 18, 2368-2370 (2006).
[CrossRef]

K. Mishina, A. Maruta, S. Mitani, T. Miyahara, K. Ishida, K. Shimizu, T. Hatta, K. Motoshima, and K.-I. Kitayama, "NRZ-OOK-to-RZ-BPSK modulation-format conversion using SOA-MZI wavelength converter," J. Lightwave Technol. 24, 3751-3758 (2006).
[CrossRef]

2005 (2)

W. Astar, A. S. Lenihan, and G. M. Carter, "Performance of DBPSK in a 5 × 10 Gb/s mixed modulation format Raman/EDFA WDM system," IEEE Photon. Technol. Lett. 17, 2766-2768 (2005).
[CrossRef]

A. H. Gnauck and P. J. Winzer, "Optical phase-shift-keyed transmission," J. Lightwave Technol. 23, 115-130 (2005).
[CrossRef]

1994 (1)

1990 (1)

D. Marcuse, "Derivation of analytical expressions for the bit-error probability in lightwave systems with optical amplifiers," J. Lightwave Technol. 8, 1819-1826 (1990).
[CrossRef]

1964 (1)

Q1. S. Stein, "Unified analysis of certain coherent and noncoherent binary communications systems," IEEE.Trans. Info. Theory 10, 43-51 (1964).
[CrossRef]

Anand, G.

Astar, W.

W. Astar, C.-C. Wei, Y.-J. Chen, J. Chen, and G. M. Carter, "Polarization-insensitive, 40 Gb/s wavelength and RZ-OOK-to-RZ-BPSK modulation format conversion by XPM in a highly nonlinear PCF," Opt. Express 16, 12039-12049 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-16-12039.
[CrossRef] [PubMed]

W. Astar and G. M. Carter, "10 Gbit/s RZ-OOK to RZ-BPSK format conversion using SOA and synchronous pulse carver," Electron. Lett. 44, 369-370 (2008).
[CrossRef]

W. Astar, A. S. Lenihan, and G. M. Carter, "Performance of DBPSK in a 5 × 10 Gb/s mixed modulation format Raman/EDFA WDM system," IEEE Photon. Technol. Lett. 17, 2766-2768 (2005).
[CrossRef]

Carter, G. M.

W. Astar and G. M. Carter, "10 Gbit/s RZ-OOK to RZ-BPSK format conversion using SOA and synchronous pulse carver," Electron. Lett. 44, 369-370 (2008).
[CrossRef]

W. Astar, C.-C. Wei, Y.-J. Chen, J. Chen, and G. M. Carter, "Polarization-insensitive, 40 Gb/s wavelength and RZ-OOK-to-RZ-BPSK modulation format conversion by XPM in a highly nonlinear PCF," Opt. Express 16, 12039-12049 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-16-12039.
[CrossRef] [PubMed]

W. Astar, A. S. Lenihan, and G. M. Carter, "Performance of DBPSK in a 5 × 10 Gb/s mixed modulation format Raman/EDFA WDM system," IEEE Photon. Technol. Lett. 17, 2766-2768 (2005).
[CrossRef]

Chen, J.

Chen, Y.-J.

Gnauck, A. H.

Hatta, T.

Ishida, K.

Jiang, H.

H. Jiang, He Wen, Liuyan Han, Yili Guo, and Hanyi Zhang, "All-optical NRZ-OOK to BPSK format conversion in an SOA-based nonlinear polarization switch," IEEE Photon. Technol. Lett. 19, 1985-1987 (2007).
[CrossRef]

Kitagawa, S.

Kitayama, K.-I.

Kumar, S.

Leng, Lufeng

Cishuo Yan, Yikai Su, Lilin Yi, Lufeng Leng, Xiangqing Tian, Xinyu Vu, and Yue Tian, "All-optical format conversion from NRZ to BPSK using a single saturated SOA," IEEE Photon. Technol. Lett. 18, 2368-2370 (2006).
[CrossRef]

Lenihan, A. S.

W. Astar, A. S. Lenihan, and G. M. Carter, "Performance of DBPSK in a 5 × 10 Gb/s mixed modulation format Raman/EDFA WDM system," IEEE Photon. Technol. Lett. 17, 2766-2768 (2005).
[CrossRef]

Marcuse, D.

D. Marcuse, "Derivation of analytical expressions for the bit-error probability in lightwave systems with optical amplifiers," J. Lightwave Technol. 8, 1819-1826 (1990).
[CrossRef]

Maruta, A.

Mishina, K.

Mitani, S.

Miyahara, T.

Motoshima, K.

Selvarajan, A.

Shimizu, K.

Stein, S.

Q1. S. Stein, "Unified analysis of certain coherent and noncoherent binary communications systems," IEEE.Trans. Info. Theory 10, 43-51 (1964).
[CrossRef]

Su, Yikai

Cishuo Yan, Yikai Su, Lilin Yi, Lufeng Leng, Xiangqing Tian, Xinyu Vu, and Yue Tian, "All-optical format conversion from NRZ to BPSK using a single saturated SOA," IEEE Photon. Technol. Lett. 18, 2368-2370 (2006).
[CrossRef]

Tian, Xiangqing

Cishuo Yan, Yikai Su, Lilin Yi, Lufeng Leng, Xiangqing Tian, Xinyu Vu, and Yue Tian, "All-optical format conversion from NRZ to BPSK using a single saturated SOA," IEEE Photon. Technol. Lett. 18, 2368-2370 (2006).
[CrossRef]

Tian, Yue

Cishuo Yan, Yikai Su, Lilin Yi, Lufeng Leng, Xiangqing Tian, Xinyu Vu, and Yue Tian, "All-optical format conversion from NRZ to BPSK using a single saturated SOA," IEEE Photon. Technol. Lett. 18, 2368-2370 (2006).
[CrossRef]

Vu, Xinyu

Cishuo Yan, Yikai Su, Lilin Yi, Lufeng Leng, Xiangqing Tian, Xinyu Vu, and Yue Tian, "All-optical format conversion from NRZ to BPSK using a single saturated SOA," IEEE Photon. Technol. Lett. 18, 2368-2370 (2006).
[CrossRef]

Wei, C.-C.

Winzer, P. J.

Yan, Cishuo

Cishuo Yan, Yikai Su, Lilin Yi, Lufeng Leng, Xiangqing Tian, Xinyu Vu, and Yue Tian, "All-optical format conversion from NRZ to BPSK using a single saturated SOA," IEEE Photon. Technol. Lett. 18, 2368-2370 (2006).
[CrossRef]

Yi, Lilin

Cishuo Yan, Yikai Su, Lilin Yi, Lufeng Leng, Xiangqing Tian, Xinyu Vu, and Yue Tian, "All-optical format conversion from NRZ to BPSK using a single saturated SOA," IEEE Photon. Technol. Lett. 18, 2368-2370 (2006).
[CrossRef]

Electron. Lett. (1)

W. Astar and G. M. Carter, "10 Gbit/s RZ-OOK to RZ-BPSK format conversion using SOA and synchronous pulse carver," Electron. Lett. 44, 369-370 (2008).
[CrossRef]

IEEE Photon. Technol. Lett. (3)

Cishuo Yan, Yikai Su, Lilin Yi, Lufeng Leng, Xiangqing Tian, Xinyu Vu, and Yue Tian, "All-optical format conversion from NRZ to BPSK using a single saturated SOA," IEEE Photon. Technol. Lett. 18, 2368-2370 (2006).
[CrossRef]

H. Jiang, He Wen, Liuyan Han, Yili Guo, and Hanyi Zhang, "All-optical NRZ-OOK to BPSK format conversion in an SOA-based nonlinear polarization switch," IEEE Photon. Technol. Lett. 19, 1985-1987 (2007).
[CrossRef]

W. Astar, A. S. Lenihan, and G. M. Carter, "Performance of DBPSK in a 5 × 10 Gb/s mixed modulation format Raman/EDFA WDM system," IEEE Photon. Technol. Lett. 17, 2766-2768 (2005).
[CrossRef]

J. Lightwave Technol. (3)

J. Opt. Soc. Am. B (1)

Opt. Express (2)

Trans. Info. Theory (1)

Q1. S. Stein, "Unified analysis of certain coherent and noncoherent binary communications systems," IEEE.Trans. Info. Theory 10, 43-51 (1964).
[CrossRef]

Other (3)

K.-P. Ho, Phase-Modulated Optical Communication System (Springer, 2005), Appendix 3.A.

E. W. Weisstein, "Noncentral Chi-Squared Distribution." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/NoncentralChi-SquaredDistribution.html.

G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, San Diego, CA, 2001), Chap. 7.

Supplementary Material (2)

» Media 1: AVI (704 KB)     
» Media 2: AVI (1726 KB)     

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Figures (5)

Fig. 1.
Fig. 1.

RZ-OOK-to-RZ-BPSK format conversion in a birefringent fiber.

Fig. 2.
Fig. 2.

With Φ = π , (a) (Media 1)the effective phase shift with L|∆K|≫2π as a function of ψ 2 , and (b) (Media 2) the effective phase shift for the best scenario (ψ 2 = π/4) as a function of L|∆K|.

Fig. 3.
Fig. 3.

Maximum and minimum effective phase shifts as functions of Φ (Eq. (12)).

Fig. 4.
Fig. 4.

(a) The optimal thresholds, and (b) the sensitivities as functions of ϕeff .

Fig. 5.
Fig. 5.

(a) The optimal thresholds, and (b) the sensitivity penalty as functions of Φ.

Equations (29)

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d A mp dz = ( A mp 2 + 2 A np 2 + 2 3 A mq 2 + 2 3 A nq 2 ) A mp + j γ 3 A mp * A mq 2 e j 2 Δ β mpq z
+ j 2 γ 3 A np * A nq A mq e j ( Δ β mpq + Δ β npq ) z + j 2 γ 3 A np A nq * A mq e j ( Δ β mpq Δ β npq ) z ,
d A 1 p dz = ( A 1 p 2 + 2 3 A 1 q 2 ) A 1 p ,
d A 2 p dz = ( 2 A 1 p 2 + 2 3 A 1 q 2 ) A 2 p + j 2 γ 3 A 1 A 1 q * A 2 q e j ( Δ β 1 pq Δ β 2 pq ) z .
A 1 x ( z ) = A 1 x ( 0 ) exp [ j γ P 1 3 ( 2 + cos 2 ψ 1 ) z ] ,
A 1 y ( z ) = A 1 y ( 0 ) exp [ j γ P 1 3 ( 2 + sin 2 ψ 1 ) z ] .
A 2 x ( L ) = A 2 x ( 0 ) [ cos ( kL 2 ) + j μ x sin ( kL 2 ) ] exp [ j ( 3 γ P 1 2 j γ P 1 3 sin 2 ψ 1 j ΔK 2 ) L ] ,
A 2 y ( L ) = A 2 y ( 0 ) [ cos ( kL 2 ) + j μ y sin ( kL 2 ) ] exp [ j ( 3 γ P 1 2 j γ P 1 3 cos 2 ψ 1 + j ΔK 2 ) L ] ,
k = 4 9 γ 2 P 1 2 sin 2 ( 2 ψ 1 ) + [ γ P 1 cos ( 2 ψ 1 ) + ΔK ] 2 ,
μ x = 1 k [ γ P 1 cos ( 2 ψ 1 ) + ΔK + 2 γ P 1 3 tan ψ 2 sin ( 2 ψ 1 ) e j Δ θ ] ,
μ y = 1 k [ γ P 1 cos ( 2 ψ 1 ) ΔK + 2 γ P 1 3 cos ψ 2 sin ( 2 ψ 1 ) e j Δ θ ] ,
ϕ eff = cos 1 ( A 2 x ( 0 ) A 2 x ( L ) cos ϕ x + A 2 y ( 0 ) A 2 y ( L ) cos ϕ y A 2 x ( 0 ) 2 + A 2 y ( 0 ) 2 ) ,
ϕ eff = cos 1 ( cos 2 ψ 2 cos ( Φ ( 1 + 2 cos 2 ψ 1 ) 3 ) + sin 2 ψ 2 cos ( Φ ( 1 + 2 sin 2 ψ 1 ) 3 ) ) ,
ΔK = 1.02 × 10 6 × ( 1 λ 1 1 λ 2 ) + 7.04 × 10 2 × In λ 1 λ 2 ,
i DB ( t ) = p = x , y E p ( t ) + E p ( t T ) 2 + n p ( t ) + n p ( t T ) 2 2 ,
i AMI ( t ) = p = x , y E p ( t ) E p ( t T ) 2 + n p ( t ) n p ( t T ) 2 2 .
ξ = p = x , y E p ( t ) ± E p ( t T ) 2 2 σ n 2 .
p v ( v ) = 4 ρ s ρ s v ξ e 2 ρ s v ξ 2 I 1 ( 2 ξ ρ s v )
p V DB in ( v ) = 2 ρ s v e 2 ρ s ( 1 + v ) I 1 ( 4 ρ s v ) ,
p V AMI in ( v ) = 4 ρ s 2 v e 2 ρ s v ,
p V DB out ( v ) = 2 ρ s v sec ( ϕ eff 2 ) e 2 ρ s [ cos 2 ( ϕ eff 2 ) + v ] I 1 ( 4 ρ s v cos ( ϕ eff 2 ) ) ,
p V AMI out ( v ) = 2 ρ s v csc ( ϕ eff 2 ) e 2 ρ s [ sin 2 ( ϕ eff 2 ) + v ] I 1 ( 4 ρ s v sin ( ϕ eff 2 ) ) ,
P e in = 1 Q 1 ( 2 ρ s , 2 ρ s h ) + 1 2 e ρ s + 2 ρ s h Q 1 ( 2 ρ s , 2 2 ρ s h )
1 8 e 2 ρ s 2 ρ s h h I 1 ( 4 ρ s h ) + 1 8 e 2 ρ s 2 ρ s h n = 1 n ( 2 h ) n I n ( 4 ρ s h ) ,
P e out = e ρ s ( 1 + 2 h ) n = 0 ( a n 4 a n 1 a n 2 + 8 m = 0 n 1 a m ) × cot n 1 ( ϕ eff 2 ) I n 1 ( ρ s sin ( ϕ eff 2 ) ) ,
= e ρ s [ 1 + cos 2 ( ϕ eff 2 ) + 2 h ] m = 0 ( a ˜ n + 4 m = 0 n 1 ( 2 n m 1 ) a ˜ m m = 1 n 1 m = 0 m 1 a ˜ m )
× ( cos ( ϕ eff 2 ) 2 h ) n 1 I n 1 ( 4 ρ s cos ( ϕ eff 2 ) ) ,
a m = 1 8 δ 0 , m + 1 8 l = 1 m ( 1 ) n l l ! ( m 1 l 1 ) ( 4 ρ s h ) l ,
a ¯ m = 1 8 δ 0 , m + 1 8 l = 1 m 1 l ! ( m 1 l 1 ) ( ρ s sin 2 ( ϕ eff 2 ) ) l ,

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