Abstract

The effect of interplay between self-phase modulation (SPM) and group velocity dispersion (GVD), known as the SPM-GVD effect, is analytically and numerically examined in radio-over-fiber transmissions using an optical single sideband with carrier (OSSB+C) signals. To study the effect analytically, we introduce a coupled mode approach considering interactions between the carrier and the fundamental sidebands. During the analyses, we find the effects of SPM-GVD can be divided into two classes: parametric amplification, known as modulation instability (MI), and phase rotation through a dispersive interaction. Numerical analyses assuming a small modulation depth confirm the analytical prediction, while those assuming a large modulation depth show additional transmission penalties. The penalty in the MI case is introduced by gain saturation of the parametric amplification, whereas that in the dispersive case is caused by the dependence of phase rotation on the modulation depth.

© 2014 Optical Society of America

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References

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  1. “Cisco visual networking index: Global mobile data traffic forecast update, 2012–2017,” http://www.cisco.com/en/US/solutions/collateral/ns341/ns525/ns537/ns705/ns827/white_paper_c11-520862.html (2013).
  2. H. Al-Raweshidy and S. Komaki, Radio Over Fiber Technologies for Mobile Communications Networks (Artech House, 2002).
  3. G. J. Meslener, “Chromatic dispersion induced distortion of modulated monochromatic light employing direct detection,” IEEE J. Quantum Electron. QE-20, 1208–1216 (1984).
    [CrossRef]
  4. K. Kitayama, “Highly spectrum efficient OFDM/PDM wireless networks by using optical SSB modulation,” J. Lightwave Technol. 16, 969–976 (1998).
    [CrossRef]
  5. G. H. Smith and D. Novak, “Broad-band millimeter-wave fiber-wireless transmission system using electrical and optical SSB modulation,” IEEE Photon. Technol. Lett. 10, 141–143 (1998).
  6. C. Lim, M. Attygalle, A. Nirmalathas, D. Novak, and R. Waterhouse, “Analysis of optical carrier-to-sideband ratio for improving transmission performance in fiber-radio links,” IEEE Trans. Microwave Theory Technol. 54, 2181–2187 (2006).
    [CrossRef]
  7. C. Lim, A. Nirmalathas, M. Bakaul, K. Lee, D. Novak, and R. Waterhouse, “Mitigation strategy for transmission impairments in millimeterwave radio-over-fiber networks,” J. Opt. Netw. 8, 201–214 (2009).
  8. K. Takano, N. Sakamoto, and K. Nakagawa, “SPM effect on carrier-suppressed optical SSB transmission with NRZ and RZ formats,” Electron. Lett. 40, 1150–1151 (2004).
  9. G. P. Agrawal, Nonlinear Fiber Optics, 4th ed. (Academic, 2007).
  10. F. Ramos and J. Marti, “Frequency transfer function of dispersive and nonlinear single-mode optical fibers in microwave optical systems,” IEEE Photon. Technol. Lett. 12, 549–551 (2000).
  11. P. C. Won, W. Zhang, J. A. R. Williams, and I. Bennion, “Imperfect mitigation of dispersion induced power penalty in high power single-sideband modulated radio-on-fiber links,” in Technical Digest of Quantum Electronics and Laser Science Conference (OSA, 2005), Vol. 3, pp. 1741–1743.
  12. X. Qi, J. Liu, X. Zhang, and L. Xie, “Fiber dispersion and nonlinearity influences on transmissions of AM and FM data modulation signals in radio-over-fiber system,” IEEE J. Quantum Electron. 46, 1170–1177 (2010).
    [CrossRef]
  13. J. Maeda, K. Kusama, and S. Ebisawa, “Effects of fiber nonlinearity on radio-over-fiber transmission of DSB-BPSK signal,” (IEEE, 2010), pp. 716–717.

2010 (1)

X. Qi, J. Liu, X. Zhang, and L. Xie, “Fiber dispersion and nonlinearity influences on transmissions of AM and FM data modulation signals in radio-over-fiber system,” IEEE J. Quantum Electron. 46, 1170–1177 (2010).
[CrossRef]

2009 (1)

2006 (1)

C. Lim, M. Attygalle, A. Nirmalathas, D. Novak, and R. Waterhouse, “Analysis of optical carrier-to-sideband ratio for improving transmission performance in fiber-radio links,” IEEE Trans. Microwave Theory Technol. 54, 2181–2187 (2006).
[CrossRef]

2004 (1)

K. Takano, N. Sakamoto, and K. Nakagawa, “SPM effect on carrier-suppressed optical SSB transmission with NRZ and RZ formats,” Electron. Lett. 40, 1150–1151 (2004).

2000 (1)

F. Ramos and J. Marti, “Frequency transfer function of dispersive and nonlinear single-mode optical fibers in microwave optical systems,” IEEE Photon. Technol. Lett. 12, 549–551 (2000).

1998 (2)

K. Kitayama, “Highly spectrum efficient OFDM/PDM wireless networks by using optical SSB modulation,” J. Lightwave Technol. 16, 969–976 (1998).
[CrossRef]

G. H. Smith and D. Novak, “Broad-band millimeter-wave fiber-wireless transmission system using electrical and optical SSB modulation,” IEEE Photon. Technol. Lett. 10, 141–143 (1998).

1984 (1)

G. J. Meslener, “Chromatic dispersion induced distortion of modulated monochromatic light employing direct detection,” IEEE J. Quantum Electron. QE-20, 1208–1216 (1984).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics, 4th ed. (Academic, 2007).

Al-Raweshidy, H.

H. Al-Raweshidy and S. Komaki, Radio Over Fiber Technologies for Mobile Communications Networks (Artech House, 2002).

Attygalle, M.

C. Lim, M. Attygalle, A. Nirmalathas, D. Novak, and R. Waterhouse, “Analysis of optical carrier-to-sideband ratio for improving transmission performance in fiber-radio links,” IEEE Trans. Microwave Theory Technol. 54, 2181–2187 (2006).
[CrossRef]

Bakaul, M.

Bennion, I.

P. C. Won, W. Zhang, J. A. R. Williams, and I. Bennion, “Imperfect mitigation of dispersion induced power penalty in high power single-sideband modulated radio-on-fiber links,” in Technical Digest of Quantum Electronics and Laser Science Conference (OSA, 2005), Vol. 3, pp. 1741–1743.

Ebisawa, S.

J. Maeda, K. Kusama, and S. Ebisawa, “Effects of fiber nonlinearity on radio-over-fiber transmission of DSB-BPSK signal,” (IEEE, 2010), pp. 716–717.

Kitayama, K.

Komaki, S.

H. Al-Raweshidy and S. Komaki, Radio Over Fiber Technologies for Mobile Communications Networks (Artech House, 2002).

Kusama, K.

J. Maeda, K. Kusama, and S. Ebisawa, “Effects of fiber nonlinearity on radio-over-fiber transmission of DSB-BPSK signal,” (IEEE, 2010), pp. 716–717.

Lee, K.

Lim, C.

C. Lim, A. Nirmalathas, M. Bakaul, K. Lee, D. Novak, and R. Waterhouse, “Mitigation strategy for transmission impairments in millimeterwave radio-over-fiber networks,” J. Opt. Netw. 8, 201–214 (2009).

C. Lim, M. Attygalle, A. Nirmalathas, D. Novak, and R. Waterhouse, “Analysis of optical carrier-to-sideband ratio for improving transmission performance in fiber-radio links,” IEEE Trans. Microwave Theory Technol. 54, 2181–2187 (2006).
[CrossRef]

Liu, J.

X. Qi, J. Liu, X. Zhang, and L. Xie, “Fiber dispersion and nonlinearity influences on transmissions of AM and FM data modulation signals in radio-over-fiber system,” IEEE J. Quantum Electron. 46, 1170–1177 (2010).
[CrossRef]

Maeda, J.

J. Maeda, K. Kusama, and S. Ebisawa, “Effects of fiber nonlinearity on radio-over-fiber transmission of DSB-BPSK signal,” (IEEE, 2010), pp. 716–717.

Marti, J.

F. Ramos and J. Marti, “Frequency transfer function of dispersive and nonlinear single-mode optical fibers in microwave optical systems,” IEEE Photon. Technol. Lett. 12, 549–551 (2000).

Meslener, G. J.

G. J. Meslener, “Chromatic dispersion induced distortion of modulated monochromatic light employing direct detection,” IEEE J. Quantum Electron. QE-20, 1208–1216 (1984).
[CrossRef]

Nakagawa, K.

K. Takano, N. Sakamoto, and K. Nakagawa, “SPM effect on carrier-suppressed optical SSB transmission with NRZ and RZ formats,” Electron. Lett. 40, 1150–1151 (2004).

Nirmalathas, A.

C. Lim, A. Nirmalathas, M. Bakaul, K. Lee, D. Novak, and R. Waterhouse, “Mitigation strategy for transmission impairments in millimeterwave radio-over-fiber networks,” J. Opt. Netw. 8, 201–214 (2009).

C. Lim, M. Attygalle, A. Nirmalathas, D. Novak, and R. Waterhouse, “Analysis of optical carrier-to-sideband ratio for improving transmission performance in fiber-radio links,” IEEE Trans. Microwave Theory Technol. 54, 2181–2187 (2006).
[CrossRef]

Novak, D.

C. Lim, A. Nirmalathas, M. Bakaul, K. Lee, D. Novak, and R. Waterhouse, “Mitigation strategy for transmission impairments in millimeterwave radio-over-fiber networks,” J. Opt. Netw. 8, 201–214 (2009).

C. Lim, M. Attygalle, A. Nirmalathas, D. Novak, and R. Waterhouse, “Analysis of optical carrier-to-sideband ratio for improving transmission performance in fiber-radio links,” IEEE Trans. Microwave Theory Technol. 54, 2181–2187 (2006).
[CrossRef]

G. H. Smith and D. Novak, “Broad-band millimeter-wave fiber-wireless transmission system using electrical and optical SSB modulation,” IEEE Photon. Technol. Lett. 10, 141–143 (1998).

Qi, X.

X. Qi, J. Liu, X. Zhang, and L. Xie, “Fiber dispersion and nonlinearity influences on transmissions of AM and FM data modulation signals in radio-over-fiber system,” IEEE J. Quantum Electron. 46, 1170–1177 (2010).
[CrossRef]

Ramos, F.

F. Ramos and J. Marti, “Frequency transfer function of dispersive and nonlinear single-mode optical fibers in microwave optical systems,” IEEE Photon. Technol. Lett. 12, 549–551 (2000).

Sakamoto, N.

K. Takano, N. Sakamoto, and K. Nakagawa, “SPM effect on carrier-suppressed optical SSB transmission with NRZ and RZ formats,” Electron. Lett. 40, 1150–1151 (2004).

Smith, G. H.

G. H. Smith and D. Novak, “Broad-band millimeter-wave fiber-wireless transmission system using electrical and optical SSB modulation,” IEEE Photon. Technol. Lett. 10, 141–143 (1998).

Takano, K.

K. Takano, N. Sakamoto, and K. Nakagawa, “SPM effect on carrier-suppressed optical SSB transmission with NRZ and RZ formats,” Electron. Lett. 40, 1150–1151 (2004).

Waterhouse, R.

C. Lim, A. Nirmalathas, M. Bakaul, K. Lee, D. Novak, and R. Waterhouse, “Mitigation strategy for transmission impairments in millimeterwave radio-over-fiber networks,” J. Opt. Netw. 8, 201–214 (2009).

C. Lim, M. Attygalle, A. Nirmalathas, D. Novak, and R. Waterhouse, “Analysis of optical carrier-to-sideband ratio for improving transmission performance in fiber-radio links,” IEEE Trans. Microwave Theory Technol. 54, 2181–2187 (2006).
[CrossRef]

Williams, J. A. R.

P. C. Won, W. Zhang, J. A. R. Williams, and I. Bennion, “Imperfect mitigation of dispersion induced power penalty in high power single-sideband modulated radio-on-fiber links,” in Technical Digest of Quantum Electronics and Laser Science Conference (OSA, 2005), Vol. 3, pp. 1741–1743.

Won, P. C.

P. C. Won, W. Zhang, J. A. R. Williams, and I. Bennion, “Imperfect mitigation of dispersion induced power penalty in high power single-sideband modulated radio-on-fiber links,” in Technical Digest of Quantum Electronics and Laser Science Conference (OSA, 2005), Vol. 3, pp. 1741–1743.

Xie, L.

X. Qi, J. Liu, X. Zhang, and L. Xie, “Fiber dispersion and nonlinearity influences on transmissions of AM and FM data modulation signals in radio-over-fiber system,” IEEE J. Quantum Electron. 46, 1170–1177 (2010).
[CrossRef]

Zhang, W.

P. C. Won, W. Zhang, J. A. R. Williams, and I. Bennion, “Imperfect mitigation of dispersion induced power penalty in high power single-sideband modulated radio-on-fiber links,” in Technical Digest of Quantum Electronics and Laser Science Conference (OSA, 2005), Vol. 3, pp. 1741–1743.

Zhang, X.

X. Qi, J. Liu, X. Zhang, and L. Xie, “Fiber dispersion and nonlinearity influences on transmissions of AM and FM data modulation signals in radio-over-fiber system,” IEEE J. Quantum Electron. 46, 1170–1177 (2010).
[CrossRef]

Electron. Lett. (1)

K. Takano, N. Sakamoto, and K. Nakagawa, “SPM effect on carrier-suppressed optical SSB transmission with NRZ and RZ formats,” Electron. Lett. 40, 1150–1151 (2004).

IEEE J. Quantum Electron. (2)

X. Qi, J. Liu, X. Zhang, and L. Xie, “Fiber dispersion and nonlinearity influences on transmissions of AM and FM data modulation signals in radio-over-fiber system,” IEEE J. Quantum Electron. 46, 1170–1177 (2010).
[CrossRef]

G. J. Meslener, “Chromatic dispersion induced distortion of modulated monochromatic light employing direct detection,” IEEE J. Quantum Electron. QE-20, 1208–1216 (1984).
[CrossRef]

IEEE Photon. Technol. Lett. (2)

G. H. Smith and D. Novak, “Broad-band millimeter-wave fiber-wireless transmission system using electrical and optical SSB modulation,” IEEE Photon. Technol. Lett. 10, 141–143 (1998).

F. Ramos and J. Marti, “Frequency transfer function of dispersive and nonlinear single-mode optical fibers in microwave optical systems,” IEEE Photon. Technol. Lett. 12, 549–551 (2000).

IEEE Trans. Microwave Theory Technol. (1)

C. Lim, M. Attygalle, A. Nirmalathas, D. Novak, and R. Waterhouse, “Analysis of optical carrier-to-sideband ratio for improving transmission performance in fiber-radio links,” IEEE Trans. Microwave Theory Technol. 54, 2181–2187 (2006).
[CrossRef]

J. Lightwave Technol. (1)

J. Opt. Netw. (1)

Other (5)

P. C. Won, W. Zhang, J. A. R. Williams, and I. Bennion, “Imperfect mitigation of dispersion induced power penalty in high power single-sideband modulated radio-on-fiber links,” in Technical Digest of Quantum Electronics and Laser Science Conference (OSA, 2005), Vol. 3, pp. 1741–1743.

J. Maeda, K. Kusama, and S. Ebisawa, “Effects of fiber nonlinearity on radio-over-fiber transmission of DSB-BPSK signal,” (IEEE, 2010), pp. 716–717.

G. P. Agrawal, Nonlinear Fiber Optics, 4th ed. (Academic, 2007).

“Cisco visual networking index: Global mobile data traffic forecast update, 2012–2017,” http://www.cisco.com/en/US/solutions/collateral/ns341/ns525/ns537/ns705/ns827/white_paper_c11-520862.html (2013).

H. Al-Raweshidy and S. Komaki, Radio Over Fiber Technologies for Mobile Communications Networks (Artech House, 2002).

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Figures (11)

Fig. 1.
Fig. 1.

Evolution of RF complex amplitude in the MI regime, following Eq. (26). γ=1.4W1km1, β2=20ps/km, Ω=2π×22GHz, P0=100mW, z=010km. Initial RF amplitude is at (1,0).

Fig. 2.
Fig. 2.

Evolution of RF complex amplitude in the dispersive regime, following Eq. (30). γ=1.4W1km1, β2=20ps/km, Ω=2π×60GHz, P0=100mW, Z=010km. Initial RF amplitude is at (1,0).

Fig. 3.
Fig. 3.

QAM symbols in normalized coordinates.

Fig. 4.
Fig. 4.

Temporal change in optical power at 0 km (dashed line) and 10 km (solid line). Carrier frequency 22 GHz, modulation index 0.9.

Fig. 5.
Fig. 5.

Optical spectrum at 0 km (gray) and 10 km (black). Carrier frequency 22 GHz, modulation index 0.9, average optical power 100 mW.

Fig. 6.
Fig. 6.

Constellation map of the RF signal at 0 km (open circles) and 10 km (filled circles). Carrier frequency, 22 GHz; modulation index, 0.9; average optical power 100 mW. Scales correspond to Fig. 3.

Fig. 7.
Fig. 7.

Evolution of three symbols, (1,1), (3,1), and (3,3), in complex phase space. (a) modulation index m=0.3; (b) m=0.9. Carrier frequency, 22 GHz; average optical power, 100 mW. Scales correspond to Fig. 3.

Fig. 8.
Fig. 8.

Temporal change in optical power at 0 km (dashed line) and 10 km (solid line). Carrier frequency 60 GHz, modulation index 0.9.

Fig. 9.
Fig. 9.

Optical spectrum at 0 km (gray) and 10 km (black). Carrier frequency, 60 GHz; modulation index, 0.9; average optical power, 100 mW.

Fig. 10.
Fig. 10.

Constellation map of RF signal at 0 km (open circles) and at 10 km (filled circles). Carrier frequency, 60 GHz; modulation index, 0.9; average optical power, 100 mW. Scales correspond to Fig. 3. The phase is adjusted so that the inner most signal points coincide.

Fig. 11.
Fig. 11.

Evolution of symbols, (1,1), (3,1), and (3,3), in complex phase space. Modulation index is m=0.3 in (a) and (a′) and m=0.9 in (b) and (b′). In (a′) and (b′), the initial phase of (3,1) is rotated to coincide with that of (1,1) and (3,3). Carrier frequency, 60 GHz; average optical power, 100 mW. Scales correspond to Fig. 3.

Tables (1)

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Table 1. Calculation Parameters

Equations (45)

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u(Z,T)Z=jβ222u(Z,T)T2jγ|u(Z,T)|2u(Z,T),
u(Z,T)=aC(Z)+aU(Z)exp(jΩT)+aL(Z)exp(jΩT),
daC(Z)dZ=jγ[{|aC(Z)|2+2|aU(Z)|2+2|aL(Z)|2}aC(Z)+2aC*(Z)aL(Z)aU(Z)],
daU(Z)dZ=jγ[{2|aC(Z)|2+|aU(Z)|2+|aL(Z)|2}aU(Z)+aC2(Z)aL*(Z)]jβ22Ω2aU(Z),
daL(Z)dZ=jγ[{2|aC(Z)|2+|aU(Z)|2+|aL(Z)|2}aL(Z)+aC2(Z)aU*(Z)]jβ22Ω2aL(Z),
aC(0)=P0exp(jθ0),aU(0)0,aL(0)=0,
|aL(Z)|2<|aU(Z)|2|aC(Z)|2.
daC(Z)dZjγ|aC(Z)|2aC(Z),
aC(Z)=P0exp(jθ0jγP0Z).
daU(Z)dZ=j(2γP0+β22Ω2)aU(Z)jγP0exp(2jθ0)exp(2jγP0Z)aL*(Z),
daL(Z)dZ=j(2γP0+β22Ω2)aL(Z)jγP0exp(2jθ0)exp(2jγP0Z)aU*(Z).
aU(Z)=a˜U(Z)exp(jγP0Z),
aL(Z)=a˜L(Z)exp(jγP0Z),
da˜U(Z)dZ=j(γP0+β22Ω2)a˜U(Z)jγP0exp(2jθ0)a˜L*(Z),
da˜L(Z)dZ=j(γP0+β22Ω2)a˜L(Z)jγP0exp(2jθ0)a˜U*(Z).
ddZ[a˜U(Z)a˜L*(Z)]=M[a˜U(Z)a˜L*(Z)],
M=[j(γP0+β22Ω2)jγP0exp(2jθ0)jγP0exp(2jθ0)j(γP0+β22Ω2)].
s2+β22Ω2(2γP0+β22Ω2)=0,
s=±λ,λ=β22Ω2(2γP0+β22Ω2).
β2<0and2γP0>|β2|Ω2/2
λ=|β2|2Ω2(2γP0|β2|2Ω2),
a˜U(Z)=aU(0)×[cosh(λZ)jγP0|β2|Ω2/2λsinh(λZ)],
a˜L*(Z)=jaU(0)γP0exp(2jθ0)λsinh(λZ).
|u(Z,T)|2=|aC(Z)|2+|aU(Z)|2+|aL(Z)|2+aC(Z)aU*(Z)exp(jΩt)+aC*(Z)aU(Z)exp(jΩt)+aC(Z)aL*(Z)exp(jΩt)+aC*(Z)aL(Z)exp(jΩt)+aU(Z)aL*(Z)exp(2jΩt)+aU*(Z)aL(Z)exp(2jΩt).
B(Z)=aC*(Z)aU(Z)+aC(Z)aL*(Z).
B(Z)=P0exp(jθ0)aU(0)×[cosh(λZ)+j|β2|Ω22λsinh(λZ)].
λ=jΛ,Λ=|β2|2Ω2(|β2|2Ω22γP0)
B(Z)=P0exp(jθ0)aU(0)[cos(ΛZ)+j|β2|Ω22Λsin(ΛZ)].
Blinear(Z)=P0exp(jθ0)aU(0)exp(j|β2|Ω22Z).
η(Z)B(Z)Blinear(Z)=[cos(ΛZ)+j|β2|Ω22Λsin(ΛZ)]exp(j|β2|Ω22Z).
η(Z)=r(k+1)cosθrcos[(k+1)θ]+j{r(k+1)sinθrsin[(k+1)θ]},
k+1=(1+1κ)/(11κ),
θ=(11κ)|β2|Ω2Z/2,
r=(11κ)/(21κ),
κ=4γP0/|(β2|Ω2).
uDSB=P0[1+mv(t)],
|aL(Z)|2|aL(0)|2=0,
|aC(Z)|2|aC(0)|2=(1α)P0,
|aU(Z)|2|aU(0)|2=αP0.
daC(Z)dZ=jγ[(1α)P0+2αP0]aC(Z),
daU(Z)dZ=jγ[2(1α)P0+αP0]aU(Z),
aC(Z)=aC(Z)exp[jγ(1+α)P0Z],
aU(Z)=aU(Z)exp[jγ(2α)P0Z],
B(Z)aC*(Z)aU(Z)P0(1α)αexp[jγ(12α)P0Z],
|β2|Ω24γ=π2|β2|γf02,

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