Abstract

We present a theoretical model that describes with great precision the effect of fiber chromatic dispersion over the transfer function of an analog fiber system driven by a Fabry–Perot (FP) semiconductor laser. Experimental results confirm the validity of the developed model. In essence the impact of chromatic dispersion manifests in three ways. First, there is a carrier suppression (or fading) effect that is also present when a single-mode laser is employed. Second, there is a transversal filtering effect owing to the fact that the FP laser modes experience different propagation delays. Third, there is a low-pass effect owing to the linewidth of the longitudinal modes.

© 2005 Optical Society of America

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References

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  1. A. Seeds, "Microwave photonics," IEEE Trans. Microwave Theory Tech. 50, 877-887 (2002), and references therein.
    [Crossref]
  2. C. Cox, E. Ackerman, R. Helky, and G. R. Betts, "Techniques and performance of intensity-modulation, direct-detection analog links," IEEE Trans. Microwave Theory Tech. 45, 1375-1383 (1997).
    [Crossref]
  3. H. Ogawa, "Microwave and millimeter-wave fiber optic technologies for subcarrier transmission systems," IEICE Trans. Commun. E76-B, 1078-1090 (1993).
  4. J. C. Fan, C. L. Lu, and L. G. Kazovsky, "Dynamic range requirements for microcellular personal communication systems using analog fiber-optic links," IEEE Trans. Microwave Theory Tech. 45, 1390-1397 (1997).
    [Crossref]
  5. K. I. Kitayama, "Ultimate performance of optical DSB signal-based millimetre-wave fiber-radio systems: effect of laser phase noise," J. Lightwave Technol. 17, 1774-1781 (1999).
    [Crossref]
  6. S. Hunziker and W. Baechtold, "Fiber dispersion induced nonlinearities in fiber-optic links with multimode laser diodes," IEEE Photonics Technol. Lett. 9, 371-373 (1997).
    [Crossref]
  7. D. Marcuse, "Pulse distortion in single mode fibers: part 2," Appl. Opt. 20, 2969-2974 (1981).
    [Crossref] [PubMed]
  8. G. Meslener, "Chromatic dispersion induced distortion of modulated monochromatic light employing direct detection," IEEE J. Quantum Electron. 20, 1208-1216 (1984).
    [Crossref]
  9. A. Yariv, Optical Electronics, 2nd ed. (Holt Rinehart & Winston, 1985).
  10. F. Devaux, Y. Sorel, and J. F. Kerdiles, "Simple measurement of fiber dispersion and of chirp parameter of intensity modulated light emitter," J. Lightwave Technol. 11, 1937-1940 (1993).
    [Crossref]
  11. A. V. Oppenheim and R. W. Schaffer, Discrete Time Signal Processing (Prentice-Hall, 1998).
  12. D. Pastor, B. Ortega, J. Capmany, S. Sales, A. Martínez, and P. Muñoz, "Flexible and tunable microwave filters based on arrayed waveguide gratings," in Proceedings of the International Topical Meeting on Microwave Photonics (IEEE, 2002), pp. 189-192.

2002 (1)

A. Seeds, "Microwave photonics," IEEE Trans. Microwave Theory Tech. 50, 877-887 (2002), and references therein.
[Crossref]

1999 (1)

1997 (3)

C. Cox, E. Ackerman, R. Helky, and G. R. Betts, "Techniques and performance of intensity-modulation, direct-detection analog links," IEEE Trans. Microwave Theory Tech. 45, 1375-1383 (1997).
[Crossref]

J. C. Fan, C. L. Lu, and L. G. Kazovsky, "Dynamic range requirements for microcellular personal communication systems using analog fiber-optic links," IEEE Trans. Microwave Theory Tech. 45, 1390-1397 (1997).
[Crossref]

S. Hunziker and W. Baechtold, "Fiber dispersion induced nonlinearities in fiber-optic links with multimode laser diodes," IEEE Photonics Technol. Lett. 9, 371-373 (1997).
[Crossref]

1993 (2)

H. Ogawa, "Microwave and millimeter-wave fiber optic technologies for subcarrier transmission systems," IEICE Trans. Commun. E76-B, 1078-1090 (1993).

F. Devaux, Y. Sorel, and J. F. Kerdiles, "Simple measurement of fiber dispersion and of chirp parameter of intensity modulated light emitter," J. Lightwave Technol. 11, 1937-1940 (1993).
[Crossref]

1984 (1)

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

1981 (1)

Ackerman, E.

C. Cox, E. Ackerman, R. Helky, and G. R. Betts, "Techniques and performance of intensity-modulation, direct-detection analog links," IEEE Trans. Microwave Theory Tech. 45, 1375-1383 (1997).
[Crossref]

Baechtold, W.

S. Hunziker and W. Baechtold, "Fiber dispersion induced nonlinearities in fiber-optic links with multimode laser diodes," IEEE Photonics Technol. Lett. 9, 371-373 (1997).
[Crossref]

Betts, G. R.

C. Cox, E. Ackerman, R. Helky, and G. R. Betts, "Techniques and performance of intensity-modulation, direct-detection analog links," IEEE Trans. Microwave Theory Tech. 45, 1375-1383 (1997).
[Crossref]

Capmany, J.

D. Pastor, B. Ortega, J. Capmany, S. Sales, A. Martínez, and P. Muñoz, "Flexible and tunable microwave filters based on arrayed waveguide gratings," in Proceedings of the International Topical Meeting on Microwave Photonics (IEEE, 2002), pp. 189-192.

Cox, C.

C. Cox, E. Ackerman, R. Helky, and G. R. Betts, "Techniques and performance of intensity-modulation, direct-detection analog links," IEEE Trans. Microwave Theory Tech. 45, 1375-1383 (1997).
[Crossref]

Devaux, F.

F. Devaux, Y. Sorel, and J. F. Kerdiles, "Simple measurement of fiber dispersion and of chirp parameter of intensity modulated light emitter," J. Lightwave Technol. 11, 1937-1940 (1993).
[Crossref]

Fan, J. C.

J. C. Fan, C. L. Lu, and L. G. Kazovsky, "Dynamic range requirements for microcellular personal communication systems using analog fiber-optic links," IEEE Trans. Microwave Theory Tech. 45, 1390-1397 (1997).
[Crossref]

Helky, R.

C. Cox, E. Ackerman, R. Helky, and G. R. Betts, "Techniques and performance of intensity-modulation, direct-detection analog links," IEEE Trans. Microwave Theory Tech. 45, 1375-1383 (1997).
[Crossref]

Hunziker, S.

S. Hunziker and W. Baechtold, "Fiber dispersion induced nonlinearities in fiber-optic links with multimode laser diodes," IEEE Photonics Technol. Lett. 9, 371-373 (1997).
[Crossref]

Kazovsky, L. G.

J. C. Fan, C. L. Lu, and L. G. Kazovsky, "Dynamic range requirements for microcellular personal communication systems using analog fiber-optic links," IEEE Trans. Microwave Theory Tech. 45, 1390-1397 (1997).
[Crossref]

Kerdiles, J. F.

F. Devaux, Y. Sorel, and J. F. Kerdiles, "Simple measurement of fiber dispersion and of chirp parameter of intensity modulated light emitter," J. Lightwave Technol. 11, 1937-1940 (1993).
[Crossref]

Kitayama, K. I.

Lu, C. L.

J. C. Fan, C. L. Lu, and L. G. Kazovsky, "Dynamic range requirements for microcellular personal communication systems using analog fiber-optic links," IEEE Trans. Microwave Theory Tech. 45, 1390-1397 (1997).
[Crossref]

Marcuse, D.

Martínez, A.

D. Pastor, B. Ortega, J. Capmany, S. Sales, A. Martínez, and P. Muñoz, "Flexible and tunable microwave filters based on arrayed waveguide gratings," in Proceedings of the International Topical Meeting on Microwave Photonics (IEEE, 2002), pp. 189-192.

Meslener, G.

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

Muñoz, P.

D. Pastor, B. Ortega, J. Capmany, S. Sales, A. Martínez, and P. Muñoz, "Flexible and tunable microwave filters based on arrayed waveguide gratings," in Proceedings of the International Topical Meeting on Microwave Photonics (IEEE, 2002), pp. 189-192.

Ogawa, H.

H. Ogawa, "Microwave and millimeter-wave fiber optic technologies for subcarrier transmission systems," IEICE Trans. Commun. E76-B, 1078-1090 (1993).

Oppenheim, A. V.

A. V. Oppenheim and R. W. Schaffer, Discrete Time Signal Processing (Prentice-Hall, 1998).

Ortega, B.

D. Pastor, B. Ortega, J. Capmany, S. Sales, A. Martínez, and P. Muñoz, "Flexible and tunable microwave filters based on arrayed waveguide gratings," in Proceedings of the International Topical Meeting on Microwave Photonics (IEEE, 2002), pp. 189-192.

Pastor, D.

D. Pastor, B. Ortega, J. Capmany, S. Sales, A. Martínez, and P. Muñoz, "Flexible and tunable microwave filters based on arrayed waveguide gratings," in Proceedings of the International Topical Meeting on Microwave Photonics (IEEE, 2002), pp. 189-192.

Sales, S.

D. Pastor, B. Ortega, J. Capmany, S. Sales, A. Martínez, and P. Muñoz, "Flexible and tunable microwave filters based on arrayed waveguide gratings," in Proceedings of the International Topical Meeting on Microwave Photonics (IEEE, 2002), pp. 189-192.

Schaffer, R. W.

A. V. Oppenheim and R. W. Schaffer, Discrete Time Signal Processing (Prentice-Hall, 1998).

Seeds, A.

A. Seeds, "Microwave photonics," IEEE Trans. Microwave Theory Tech. 50, 877-887 (2002), and references therein.
[Crossref]

Sorel, Y.

F. Devaux, Y. Sorel, and J. F. Kerdiles, "Simple measurement of fiber dispersion and of chirp parameter of intensity modulated light emitter," J. Lightwave Technol. 11, 1937-1940 (1993).
[Crossref]

Yariv, A.

A. Yariv, Optical Electronics, 2nd ed. (Holt Rinehart & Winston, 1985).

Appl. Opt. (1)

IEEE J. Quantum Electron. (1)

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

IEEE Photonics Technol. Lett. (1)

S. Hunziker and W. Baechtold, "Fiber dispersion induced nonlinearities in fiber-optic links with multimode laser diodes," IEEE Photonics Technol. Lett. 9, 371-373 (1997).
[Crossref]

IEEE Trans. Microwave Theory Tech. (3)

A. Seeds, "Microwave photonics," IEEE Trans. Microwave Theory Tech. 50, 877-887 (2002), and references therein.
[Crossref]

C. Cox, E. Ackerman, R. Helky, and G. R. Betts, "Techniques and performance of intensity-modulation, direct-detection analog links," IEEE Trans. Microwave Theory Tech. 45, 1375-1383 (1997).
[Crossref]

J. C. Fan, C. L. Lu, and L. G. Kazovsky, "Dynamic range requirements for microcellular personal communication systems using analog fiber-optic links," IEEE Trans. Microwave Theory Tech. 45, 1390-1397 (1997).
[Crossref]

IEICE Trans. Commun. (1)

H. Ogawa, "Microwave and millimeter-wave fiber optic technologies for subcarrier transmission systems," IEICE Trans. Commun. E76-B, 1078-1090 (1993).

J. Lightwave Technol. (2)

K. I. Kitayama, "Ultimate performance of optical DSB signal-based millimetre-wave fiber-radio systems: effect of laser phase noise," J. Lightwave Technol. 17, 1774-1781 (1999).
[Crossref]

F. Devaux, Y. Sorel, and J. F. Kerdiles, "Simple measurement of fiber dispersion and of chirp parameter of intensity modulated light emitter," J. Lightwave Technol. 11, 1937-1940 (1993).
[Crossref]

Other (3)

A. V. Oppenheim and R. W. Schaffer, Discrete Time Signal Processing (Prentice-Hall, 1998).

D. Pastor, B. Ortega, J. Capmany, S. Sales, A. Martínez, and P. Muñoz, "Flexible and tunable microwave filters based on arrayed waveguide gratings," in Proceedings of the International Topical Meeting on Microwave Photonics (IEEE, 2002), pp. 189-192.

A. Yariv, Optical Electronics, 2nd ed. (Holt Rinehart & Winston, 1985).

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Figures (7)

Fig. 1
Fig. 1

System layout of a radio-over-fiber (RoF) system driven by a Fabry–Perot laser.

Fig. 2
Fig. 2

Diagram showing the impact of a nonconstant group delay on the propagation of each Fabry–Perot laser longitudinal mode and on the phase shift experienced by their modulation sidebands.

Fig. 3
Fig. 3

Logarithmic curve for the position of the first notch due to CSE in gigahertz as a function of the link length in kilometers in the case of a link with a standard dispersion parameter in the third window ( β 2 = 21 ps 2 km ) . The curves are shown for different values of the chirp parameter ( α = 3 , 0, and 3). Also depicted is the FSR value of the undesired transversal filter due to the effect of chromatic dispersion.

Fig. 4
Fig. 4

Transfer functions of a 16 uniform and Lorentzian windowed-coefficient transversal filter as a function of the normalized (by the filter incremental delay τ) frequency Ω.

Fig. 5
Fig. 5

Equation (26) as a function of the link length in kilometers using as a parameter typical values of Δ ν .

Fig. 6
Fig. 6

Experimental setup to test the validity of Eq. (21).

Fig. 7
Fig. 7

Experimental results. (a)–(d) show the transfer functions [measured in solid trace and simulated using Eq. (21) in broken trace] for different link lengths [ z = 1.4 km in (a), z = 2.8 km for (b), z = 7 km for (c), and z = 22.4 km for (d)] in all the figures we include as well the measured transfer function (thick broken curve) obtained when the fiber link is driven by a single-mode external-cavity laser.

Equations (30)

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E s ( t ) = k = N 2 N 2 A k ( t ) exp ( j w k t ) .
A k ( t ) A r * ( t ) = A k ( t ) A k * ( t ) δ k r ,
E ̃ s ( w ) = 1 2 π k = N 2 N 2 A k ( t ) exp [ j ( w w k ) t ] d w .
E ̃ s ( w ) E ̃ s * ( w ) = k = N 2 N 2 S s k ( w w k ) δ ( w w ) ,
S s k ( w ) = 1 2 π R k ( u ) exp [ j ( w w k ) u ] d u ,
R k ( t t ) = A k ( t ) A k * ( t ) .
E ( t ) = s ( t ) E s ( t ) ,
E ̃ ( w ) = 1 2 π E ̃ s ( w ) F ( w w ) d w ,
H f ( w , z ) = exp [ j β ( w ) z ] .
E ̃ 0 ( w ) = E ̃ ( w ) H f ( w ) .
i ( t ) = R E 0 ( t ) 2 = R k = N 2 N 2 S s k ( w w k ) F ( w w ) exp ( j { ( w w ) t [ β ( w ) β ( w ) ] z } ) d w 2 d w = R k = N 2 N 2 S s k ( w w k ) U k ( w , z , t ) d w ,
s ( t ) = A ( 1 + m cos Ω t ) = A + A m 2 exp ( j Ω t ) + A m 2 exp ( j Ω t ) .
s ( t ) = [ A ( 1 + m cos Ω t ) ] 1 2 .
s ( t ) = A r = 0 C r cos ( r Ω t ) .
F ( u ) = A { C 0 δ ( u ) + 1 2 r = 1 C r [ δ ( u r Ω ) + δ ( u + r Ω ) ] } .
β ( w ) = β 0 k + β 1 k ( w w k ) + 1 2 β 2 k ( w w k ) 2 .
β ( w ) β ( w ) = + β 1 k ( w w ) + 1 2 β 2 k { ( w w ) [ w w + 2 ( w w k ) ] } .
U k ( w , t , z ) = F ( w w ) exp j ( { ( w w ) t [ β ( w ) β ( w ) ] z } ) d w 2 = { 2 A C 0 C 1 cos ( β 2 k z Ω 2 2 ) + A r = 1 C r C r + 1 cos [ ( 2 r + 1 ) β 2 k z Ω 2 2 ] } exp j { [ Ω ( t β 1 k z ) β 2 k Ω ( w w k ) ] } .
S s k ( w w k ) = P k W k ( w w k ) 2 + ( W k 2 ) 2 .
i ( t ) exp ( j Ω t ) = π R exp ( j Ω t ) k = N 2 N 2 P k { 2 A C 0 C 1 cos ( β 2 k z Ω 2 2 ) + A r = 1 C r C r + 1 cos [ ( 2 r + 1 ) β 2 k z Ω 2 2 ] } × exp ( W k β 2 k z Ω 2 ) exp ( j β 1 k z Ω ) .
H ( Ω ) = 2 π R m k = N 2 N 2 { 2 C 0 C 1 cos ( β 2 k z Ω 2 2 ) + r = 1 C r C r + 1 cos [ ( 2 r + 1 ) β 2 k z Ω 2 2 ] } × [ exp ( W k β 2 k z Ω 2 ) ] [ P k exp ( j β 1 k z Ω ) ] .
H ( Ω ) = 4 π R C 0 C 1 m cos ( β 2 z Ω 2 2 ) exp ( W β 2 z Ω 2 ) k = N 2 N 2 P k exp ( j τ 1 k Ω ) ,
C 0 = 1 ,
C 1 = m ( 1 + j α ) 4 ,
H ( Ω ) = π R 1 + α 2 cos [ β 2 z Ω 2 2 + arctan ( α ) ] exp ( W β 2 z Ω 2 ) k = N 2 N 2 P k exp ( j τ 1 k Ω ) .
H ( Ω ) = π R 1 + α 2 cos [ β 2 z Ω 2 2 + arctan ( α ) ] .
H ( Ω ) = 4 π R C 0 C 1 m cos ( β 2 z Ω 2 2 ) exp ( W β 2 z Ω 2 ) k = N 2 N 2 P k exp [ j ( k + N 2 ) τ Ω ] = 4 π R C 0 C 1 m H CSE ( Ω ) H coh ( Ω ) H trans ( Ω ) .
H trans ( Ω ) = k = N 2 N 2 P k exp [ j ( k + N 2 ) τ Ω ] ,
P k = P 0 K 2 k 2 + K 2 ,
f 3 dB = ln 2 2 π 2 Δ ν β 2 z ,

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