Abstract

The impact of group delay ripples of chirped fiber gratings (CFG) on the performance of optical beamforming networks (OBFN) is investigated. The paper theoretically analyzes the quantified relations among the amplitude and period of CFG, the optical angle frequency interval at the inter-element arrays and the beampointing shift. The wavelength instability of the optical source is also investigated. This instability-induced phase jitter of RF signal has been verified experimentally. The theoretical models are proposed to analyze the performance of CFG-based OBFN systems.

© 2008 Optical Society of America

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References

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  1. A. J. Seeds, "Microwave Photonics," IEEE Transactions on Microwave Theory and Techniques 50, 877-887 (2002).
    [CrossRef]
  2. G. Grosskopf, "Maximum directivity beam-former at 60 GHz with optical feeder," IEEE Trans. Antennas Propag. 51, 3040-3046 (2003).
    [CrossRef]
  3. B. Kuhlow, G. Przyrembel, H. Ehlers, G. Großkopf, R. Eggemann, D. Rohde, and S. Zinal, "Optical beam forming of MM-wave array antennas in a 60 GHz radio over fiber system," in Optical Fiber Communication Conference, Technical Digest (Optical Society of America, 2003), paper FM4. http://www.opticsinfobase.org/abstract.cfm?URI=OFC-2003-FM4
  4. N. A. Riza, M. A. Arain, and S. A. Khan, "Hybrid analog-digital variable fiber-optic delay line," J. Lightwave Technol. 22, 619-624 (2004).
    [CrossRef]
  5. Y. Jiang, "Dispersion-enhanced photonic crystal fiber array for a true time-delay structured X-band phased array antenna," IEEE Photonic Technol. Lett. 17, 187 -189 (2005).
    [CrossRef]
  6. J. E. Román, M. Y. Frankel, P. J. Mattews, and R. D. Esman, "Time steered array with a chirped grating beamformer," Electron. Lett. 33, 652-653 (1997).
    [CrossRef]
  7. J. L. Corral, J. Mart?, S. Regidor, J. M. Foster, R. Laming, and J. M. Cole, "Continuously variable true time-delay optical feeder for phased-array antenna employing chirped fiber gratings," IEEE Trans. Microwave Theory Tech. 45, 1531-1536 (1997).
    [CrossRef]
  8. Y. Liu, J. Yao, X. Dong, and J. Yang, "Tunable chirping of a fiber Bragg grating without center wavelength shift using a simply supported beam," Opt. Eng. 41, 740-751 (2002).
    [CrossRef]
  9. S.-S. Lee, H.-D. Chae, D.-H. Kim, H.-J. Kim and K.-T. Kim, "Continuous photonic microwave true-time delay using a side-polished fiber Bragg grating with heating electrode," Microwave Opt. Technol. Lett. 44, 35-37 (2005).
    [CrossRef]
  10. K. Ennser, M. Ibsen, M. Durkin, M. N. Zervas, and R. I. Laming, "Influence of nonideal chirped fiber grating characteristics on dispersion cancellation," IEEE Photon. Technol. Lett. 10, 1476-1478 (1998).
    [CrossRef]
  11. M. R. Matthews, J. Porque, C. D. Hoyle, M. J. Vos, and T. L. Smith, "Simple model of errors in chirped fiber gratings," Opt. Express 12, 189-197 (2004).
    [CrossRef] [PubMed]
  12. L. R. Chen, "Influence of grating group delay ripple on the reduction of dispersion induced intensity noise in subcarrier multiplexed systems," Opt. Commun. 187, 125-128 (2001).
    [CrossRef]

2005 (2)

Y. Jiang, "Dispersion-enhanced photonic crystal fiber array for a true time-delay structured X-band phased array antenna," IEEE Photonic Technol. Lett. 17, 187 -189 (2005).
[CrossRef]

S.-S. Lee, H.-D. Chae, D.-H. Kim, H.-J. Kim and K.-T. Kim, "Continuous photonic microwave true-time delay using a side-polished fiber Bragg grating with heating electrode," Microwave Opt. Technol. Lett. 44, 35-37 (2005).
[CrossRef]

2004 (2)

2003 (1)

G. Grosskopf, "Maximum directivity beam-former at 60 GHz with optical feeder," IEEE Trans. Antennas Propag. 51, 3040-3046 (2003).
[CrossRef]

2002 (2)

A. J. Seeds, "Microwave Photonics," IEEE Transactions on Microwave Theory and Techniques 50, 877-887 (2002).
[CrossRef]

Y. Liu, J. Yao, X. Dong, and J. Yang, "Tunable chirping of a fiber Bragg grating without center wavelength shift using a simply supported beam," Opt. Eng. 41, 740-751 (2002).
[CrossRef]

2001 (1)

L. R. Chen, "Influence of grating group delay ripple on the reduction of dispersion induced intensity noise in subcarrier multiplexed systems," Opt. Commun. 187, 125-128 (2001).
[CrossRef]

1998 (1)

K. Ennser, M. Ibsen, M. Durkin, M. N. Zervas, and R. I. Laming, "Influence of nonideal chirped fiber grating characteristics on dispersion cancellation," IEEE Photon. Technol. Lett. 10, 1476-1478 (1998).
[CrossRef]

1997 (2)

J. E. Román, M. Y. Frankel, P. J. Mattews, and R. D. Esman, "Time steered array with a chirped grating beamformer," Electron. Lett. 33, 652-653 (1997).
[CrossRef]

J. L. Corral, J. Mart?, S. Regidor, J. M. Foster, R. Laming, and J. M. Cole, "Continuously variable true time-delay optical feeder for phased-array antenna employing chirped fiber gratings," IEEE Trans. Microwave Theory Tech. 45, 1531-1536 (1997).
[CrossRef]

Arain, A.

Chae, H.-D.

S.-S. Lee, H.-D. Chae, D.-H. Kim, H.-J. Kim and K.-T. Kim, "Continuous photonic microwave true-time delay using a side-polished fiber Bragg grating with heating electrode," Microwave Opt. Technol. Lett. 44, 35-37 (2005).
[CrossRef]

Chen, L. R.

L. R. Chen, "Influence of grating group delay ripple on the reduction of dispersion induced intensity noise in subcarrier multiplexed systems," Opt. Commun. 187, 125-128 (2001).
[CrossRef]

Corral, J. L.

J. L. Corral, J. Mart?, S. Regidor, J. M. Foster, R. Laming, and J. M. Cole, "Continuously variable true time-delay optical feeder for phased-array antenna employing chirped fiber gratings," IEEE Trans. Microwave Theory Tech. 45, 1531-1536 (1997).
[CrossRef]

Dong, X.

Y. Liu, J. Yao, X. Dong, and J. Yang, "Tunable chirping of a fiber Bragg grating without center wavelength shift using a simply supported beam," Opt. Eng. 41, 740-751 (2002).
[CrossRef]

Durkin, M.

K. Ennser, M. Ibsen, M. Durkin, M. N. Zervas, and R. I. Laming, "Influence of nonideal chirped fiber grating characteristics on dispersion cancellation," IEEE Photon. Technol. Lett. 10, 1476-1478 (1998).
[CrossRef]

Ennser, K.

K. Ennser, M. Ibsen, M. Durkin, M. N. Zervas, and R. I. Laming, "Influence of nonideal chirped fiber grating characteristics on dispersion cancellation," IEEE Photon. Technol. Lett. 10, 1476-1478 (1998).
[CrossRef]

Esman, R. D.

J. E. Román, M. Y. Frankel, P. J. Mattews, and R. D. Esman, "Time steered array with a chirped grating beamformer," Electron. Lett. 33, 652-653 (1997).
[CrossRef]

Frankel, M. Y.

J. E. Román, M. Y. Frankel, P. J. Mattews, and R. D. Esman, "Time steered array with a chirped grating beamformer," Electron. Lett. 33, 652-653 (1997).
[CrossRef]

Grosskopf, G.

G. Grosskopf, "Maximum directivity beam-former at 60 GHz with optical feeder," IEEE Trans. Antennas Propag. 51, 3040-3046 (2003).
[CrossRef]

Hoyle, C. D.

Ibsen, M.

K. Ennser, M. Ibsen, M. Durkin, M. N. Zervas, and R. I. Laming, "Influence of nonideal chirped fiber grating characteristics on dispersion cancellation," IEEE Photon. Technol. Lett. 10, 1476-1478 (1998).
[CrossRef]

Jiang, Y.

Y. Jiang, "Dispersion-enhanced photonic crystal fiber array for a true time-delay structured X-band phased array antenna," IEEE Photonic Technol. Lett. 17, 187 -189 (2005).
[CrossRef]

Khan, S. A.

Kim, D.-H.

S.-S. Lee, H.-D. Chae, D.-H. Kim, H.-J. Kim and K.-T. Kim, "Continuous photonic microwave true-time delay using a side-polished fiber Bragg grating with heating electrode," Microwave Opt. Technol. Lett. 44, 35-37 (2005).
[CrossRef]

Kim, H.-J.

S.-S. Lee, H.-D. Chae, D.-H. Kim, H.-J. Kim and K.-T. Kim, "Continuous photonic microwave true-time delay using a side-polished fiber Bragg grating with heating electrode," Microwave Opt. Technol. Lett. 44, 35-37 (2005).
[CrossRef]

Kim, K.-T.

S.-S. Lee, H.-D. Chae, D.-H. Kim, H.-J. Kim and K.-T. Kim, "Continuous photonic microwave true-time delay using a side-polished fiber Bragg grating with heating electrode," Microwave Opt. Technol. Lett. 44, 35-37 (2005).
[CrossRef]

Laming, R. I.

K. Ennser, M. Ibsen, M. Durkin, M. N. Zervas, and R. I. Laming, "Influence of nonideal chirped fiber grating characteristics on dispersion cancellation," IEEE Photon. Technol. Lett. 10, 1476-1478 (1998).
[CrossRef]

Lee, S.-S.

S.-S. Lee, H.-D. Chae, D.-H. Kim, H.-J. Kim and K.-T. Kim, "Continuous photonic microwave true-time delay using a side-polished fiber Bragg grating with heating electrode," Microwave Opt. Technol. Lett. 44, 35-37 (2005).
[CrossRef]

Liu, Y.

Y. Liu, J. Yao, X. Dong, and J. Yang, "Tunable chirping of a fiber Bragg grating without center wavelength shift using a simply supported beam," Opt. Eng. 41, 740-751 (2002).
[CrossRef]

Mattews, P. J.

J. E. Román, M. Y. Frankel, P. J. Mattews, and R. D. Esman, "Time steered array with a chirped grating beamformer," Electron. Lett. 33, 652-653 (1997).
[CrossRef]

Matthews, M. R.

Muzammil, N. A.

Porque, J.

Riza, N. A.

Román, J. E.

J. E. Román, M. Y. Frankel, P. J. Mattews, and R. D. Esman, "Time steered array with a chirped grating beamformer," Electron. Lett. 33, 652-653 (1997).
[CrossRef]

Seeds, A. J.

A. J. Seeds, "Microwave Photonics," IEEE Transactions on Microwave Theory and Techniques 50, 877-887 (2002).
[CrossRef]

Smith, T. L.

Vos, M. J.

Yang, J.

Y. Liu, J. Yao, X. Dong, and J. Yang, "Tunable chirping of a fiber Bragg grating without center wavelength shift using a simply supported beam," Opt. Eng. 41, 740-751 (2002).
[CrossRef]

Yao, J.

Y. Liu, J. Yao, X. Dong, and J. Yang, "Tunable chirping of a fiber Bragg grating without center wavelength shift using a simply supported beam," Opt. Eng. 41, 740-751 (2002).
[CrossRef]

Zervas, M. N.

K. Ennser, M. Ibsen, M. Durkin, M. N. Zervas, and R. I. Laming, "Influence of nonideal chirped fiber grating characteristics on dispersion cancellation," IEEE Photon. Technol. Lett. 10, 1476-1478 (1998).
[CrossRef]

Electron. Lett. (1)

J. E. Román, M. Y. Frankel, P. J. Mattews, and R. D. Esman, "Time steered array with a chirped grating beamformer," Electron. Lett. 33, 652-653 (1997).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

K. Ennser, M. Ibsen, M. Durkin, M. N. Zervas, and R. I. Laming, "Influence of nonideal chirped fiber grating characteristics on dispersion cancellation," IEEE Photon. Technol. Lett. 10, 1476-1478 (1998).
[CrossRef]

IEEE Photonic Technol. Lett. (1)

Y. Jiang, "Dispersion-enhanced photonic crystal fiber array for a true time-delay structured X-band phased array antenna," IEEE Photonic Technol. Lett. 17, 187 -189 (2005).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

J. L. Corral, J. Mart?, S. Regidor, J. M. Foster, R. Laming, and J. M. Cole, "Continuously variable true time-delay optical feeder for phased-array antenna employing chirped fiber gratings," IEEE Trans. Microwave Theory Tech. 45, 1531-1536 (1997).
[CrossRef]

IEEE Transactions on Antenna and Propagation (1)

G. Grosskopf, "Maximum directivity beam-former at 60 GHz with optical feeder," IEEE Trans. Antennas Propag. 51, 3040-3046 (2003).
[CrossRef]

IEEE Transactions on Microwave Theory and Techniches (1)

A. J. Seeds, "Microwave Photonics," IEEE Transactions on Microwave Theory and Techniques 50, 877-887 (2002).
[CrossRef]

J. Lightwave Technol. (1)

Microwave and Optical Technol. Lett. (1)

S.-S. Lee, H.-D. Chae, D.-H. Kim, H.-J. Kim and K.-T. Kim, "Continuous photonic microwave true-time delay using a side-polished fiber Bragg grating with heating electrode," Microwave Opt. Technol. Lett. 44, 35-37 (2005).
[CrossRef]

Opt. Commun. (1)

L. R. Chen, "Influence of grating group delay ripple on the reduction of dispersion induced intensity noise in subcarrier multiplexed systems," Opt. Commun. 187, 125-128 (2001).
[CrossRef]

Opt. Eng. (1)

Y. Liu, J. Yao, X. Dong, and J. Yang, "Tunable chirping of a fiber Bragg grating without center wavelength shift using a simply supported beam," Opt. Eng. 41, 740-751 (2002).
[CrossRef]

Opt. Express (1)

Other (1)

B. Kuhlow, G. Przyrembel, H. Ehlers, G. Großkopf, R. Eggemann, D. Rohde, and S. Zinal, "Optical beam forming of MM-wave array antennas in a 60 GHz radio over fiber system," in Optical Fiber Communication Conference, Technical Digest (Optical Society of America, 2003), paper FM4. http://www.opticsinfobase.org/abstract.cfm?URI=OFC-2003-FM4

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Figures (6)

Fig. 1.
Fig. 1.

Schematic diagram of wideband CFG based optical beamforming networks. PC: polarization controller, PD: photodiode and DEMUX: demultiplexer

Fig. 2.
Fig. 2.

Zoom of simulated and measured GDR of CFG. Insertion: the measured GDR over 3dB reflection bandwidth by optical vector analyzer

Fig. 3.
Fig. 3.

The measured standard deviation of RF phase jittering versus frequency for different RF frequency signal (scatter symbol) and the corresponding theoretical curves (solid line)

Fig. 4.
Fig. 4.

The Calculated mean square sidelobe levels versus RF frequency for different parameters of CFG

Fig. 5.
Fig. 5.

The calculated eight-element antenna radiation pattern (a) and beampointing shift (b) over different optical wavelength step at inter-element arrays(left: 0, 504, 864pm and right:0~864pm)

Fig. 6.
Fig. 6.

Calculated beampointing shift over different the period of GDR and the peak-to-peak amplitude of GDR

Equations (12)

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τ ( ω ) = τ 0 + D λ 0 2 2 π c ( ω 0 ω ) + τ G D R ( ω ) = τ l i n e ( ω ) + τ G D R ( ω )
τ G D R ( ω ) = k = 1 n A g , k * sin ( ω T g , k + θ g , k )
Ψ ( ω , ω RF ) = [ τ l i n e ( ω ) k = 1 n A g , k sin ( ω R F T g , k ) ω R F T g , k sin ( ω T g , k + θ g , k ) ] ω R F
Δ Φ R F ( t ) = Ψ ( ω + Δ ω c ( t ) , ω R F ) Ψ ( ω , ω R F )
~ [ τ 1 ( ω 0 ) + D λ 0 2 ω 2 π c k = 1 n A g , k sin ( ω + Δ ω c ( t ) T g , k + θ g , k ) cos ( ω R F T g , k ) ] Δ ω c ( t )
+ [ D λ 0 2 ω R F 2 π c k = 1 n A g , k sin ( ω R F T g , k ) ω R F T g , k sin ( ω + 1 2 Δ ω c ( t ) T g , k + θ g , k ) ] Δ ω c ( t )
d ϕ R F = { [ τ 1 ( ω 0 ) + D λ 0 2 ω 2 π c k = 1 n A g , k sin ( ω + Δ ω c ( t ) T g , k + θ g , k ) cos ( ω R F T g , k ) ] 2 σ ω R F 2
+ [ D λ 0 2 ω R F 2 π c k = 1 n A g , k sin ( ω R F T g , k ) ω R F T g , k sin ( ω + 1 2 Δ ω c ( t ) T g , k + θ g , k ) ] 2 σ ω c 2 } 1 2
< { [ τ 1 ( ω 0 ) + D λ 0 2 ω 2 π c A p p 2 ] 2 σ ω R F 2 + [ D λ 0 2 ω R F 2 π c A pp 2 ] 2 σ ω c 2 } 1 2
σ ω R F ~ 2 π ( 8 ( N C ) f c f c 3 I n 2 ) 1 2
σ 2 ¯ 1 0 log ( d ϕ RF 2 NG 0 )
d θ B ~ c d cos θ B * { k = 1 n A g , k sin ( ω R F T g , k ) ω R F T g , k sin ( ω 0 + Δω 2 T g , k + θ g , k ) sin ( Δω 2 T g , k ) + d ϕ R F ( N 1 ) ω R F }

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