Abstract

We propose and experimentally demonstrate a novel and simple photonic microwave notch filter that uses a high-birefringent fiber that gives a fixed differential group delay (DGD), together with a DGD element that gives a tunable DGD. This configuration overcomes the problems of optical coherence interference and chromatic dispersion, which may occur in schemes that use fiber delay lines or fiber gratings. Also presented is a theoretical analysis for the performance of the microwave filter that uses the present configuration. The present scheme provides a continuous tuning capability for changing the notch frequency. Measured notch rejection is greater than 40dB. This scheme can operate over a wide wavelength range of the optical carrier. There is good agreement between experiment results and theoretical analysis.

© 2005 Optical Society of America

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References

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  1. W. Zhang, J. A. R. Williams, L. A. Everall, I. Bennion, “Fiber optical radio frequency notch filter with linear and continuous tuning by using a chirped grating,” Electron. Lett. 34, 1770–1772 (1998).
    [Crossref]
  2. D. B. Hunter, R. A. Minasian, “Reflectively tapped fiber optic transversal filter using in-fiber Bragg grating,” Electron. Lett. 31, 1010–1012 (1995).
    [Crossref]
  3. W. Zhang, J. A. R. Williams, I. Bennion, “Polarization synthesized optical transversal filter employing high birefringence fiber gratings,” IEEE Photonics Technol. Lett. 13, 523–525 (2001).
    [Crossref]
  4. X. Yi, C. Lu, X. Yang, W.-D. Zhong, F. Wei, L. Ding, Y. Wang, “Continuously tunable microwave-photonic filter design using high-birefringence linear chirped grating,” IEEE Photonics Technol. Lett. 15, 754–756 (2003).
    [Crossref]
  5. J. Capmany, D. Pastor, B. Ortega, “New and flexible fiber-optic delay-line filters using chirped Bragg gratings and laser arrays,” IEEE Trans. Microwave Theory Tech. 47, 1321–1326 (1999).
    [Crossref]
  6. W. Zhang, J. A. R. Williams, I. Bennion, “Optical fiber delay line filter free of limitation imposed by optical coherence,” Electron. Lett. 35, 2133–2134 (1999).
    [Crossref]
  7. F. Coppinger, S. Yegnanarayanan, P. D. Trinh, B. Jalali, I. L. Newberg, “Nonrecursive tunable photonic filter using wavelength-selective true time delay,” IEEE Photonics Technol. Lett. 8, 1214–1216 (1996).
    [Crossref]
  8. G. Keiser, Optical Fiber Communications (McGraw-Hill, New York, 2000).
  9. C. D. Poole, R. E. Wagner, “Phenomenological approach to polarization dispersion in long single mode fibers,” Electron. Lett. 22, 1029–1230 (1986).
    [Crossref]

2003 (1)

X. Yi, C. Lu, X. Yang, W.-D. Zhong, F. Wei, L. Ding, Y. Wang, “Continuously tunable microwave-photonic filter design using high-birefringence linear chirped grating,” IEEE Photonics Technol. Lett. 15, 754–756 (2003).
[Crossref]

2001 (1)

W. Zhang, J. A. R. Williams, I. Bennion, “Polarization synthesized optical transversal filter employing high birefringence fiber gratings,” IEEE Photonics Technol. Lett. 13, 523–525 (2001).
[Crossref]

1999 (2)

J. Capmany, D. Pastor, B. Ortega, “New and flexible fiber-optic delay-line filters using chirped Bragg gratings and laser arrays,” IEEE Trans. Microwave Theory Tech. 47, 1321–1326 (1999).
[Crossref]

W. Zhang, J. A. R. Williams, I. Bennion, “Optical fiber delay line filter free of limitation imposed by optical coherence,” Electron. Lett. 35, 2133–2134 (1999).
[Crossref]

1998 (1)

W. Zhang, J. A. R. Williams, L. A. Everall, I. Bennion, “Fiber optical radio frequency notch filter with linear and continuous tuning by using a chirped grating,” Electron. Lett. 34, 1770–1772 (1998).
[Crossref]

1996 (1)

F. Coppinger, S. Yegnanarayanan, P. D. Trinh, B. Jalali, I. L. Newberg, “Nonrecursive tunable photonic filter using wavelength-selective true time delay,” IEEE Photonics Technol. Lett. 8, 1214–1216 (1996).
[Crossref]

1995 (1)

D. B. Hunter, R. A. Minasian, “Reflectively tapped fiber optic transversal filter using in-fiber Bragg grating,” Electron. Lett. 31, 1010–1012 (1995).
[Crossref]

1986 (1)

C. D. Poole, R. E. Wagner, “Phenomenological approach to polarization dispersion in long single mode fibers,” Electron. Lett. 22, 1029–1230 (1986).
[Crossref]

Bennion, I.

W. Zhang, J. A. R. Williams, I. Bennion, “Polarization synthesized optical transversal filter employing high birefringence fiber gratings,” IEEE Photonics Technol. Lett. 13, 523–525 (2001).
[Crossref]

W. Zhang, J. A. R. Williams, I. Bennion, “Optical fiber delay line filter free of limitation imposed by optical coherence,” Electron. Lett. 35, 2133–2134 (1999).
[Crossref]

W. Zhang, J. A. R. Williams, L. A. Everall, I. Bennion, “Fiber optical radio frequency notch filter with linear and continuous tuning by using a chirped grating,” Electron. Lett. 34, 1770–1772 (1998).
[Crossref]

Capmany, J.

J. Capmany, D. Pastor, B. Ortega, “New and flexible fiber-optic delay-line filters using chirped Bragg gratings and laser arrays,” IEEE Trans. Microwave Theory Tech. 47, 1321–1326 (1999).
[Crossref]

Coppinger, F.

F. Coppinger, S. Yegnanarayanan, P. D. Trinh, B. Jalali, I. L. Newberg, “Nonrecursive tunable photonic filter using wavelength-selective true time delay,” IEEE Photonics Technol. Lett. 8, 1214–1216 (1996).
[Crossref]

Ding, L.

X. Yi, C. Lu, X. Yang, W.-D. Zhong, F. Wei, L. Ding, Y. Wang, “Continuously tunable microwave-photonic filter design using high-birefringence linear chirped grating,” IEEE Photonics Technol. Lett. 15, 754–756 (2003).
[Crossref]

Everall, L. A.

W. Zhang, J. A. R. Williams, L. A. Everall, I. Bennion, “Fiber optical radio frequency notch filter with linear and continuous tuning by using a chirped grating,” Electron. Lett. 34, 1770–1772 (1998).
[Crossref]

Hunter, D. B.

D. B. Hunter, R. A. Minasian, “Reflectively tapped fiber optic transversal filter using in-fiber Bragg grating,” Electron. Lett. 31, 1010–1012 (1995).
[Crossref]

Jalali, B.

F. Coppinger, S. Yegnanarayanan, P. D. Trinh, B. Jalali, I. L. Newberg, “Nonrecursive tunable photonic filter using wavelength-selective true time delay,” IEEE Photonics Technol. Lett. 8, 1214–1216 (1996).
[Crossref]

Keiser, G.

G. Keiser, Optical Fiber Communications (McGraw-Hill, New York, 2000).

Lu, C.

X. Yi, C. Lu, X. Yang, W.-D. Zhong, F. Wei, L. Ding, Y. Wang, “Continuously tunable microwave-photonic filter design using high-birefringence linear chirped grating,” IEEE Photonics Technol. Lett. 15, 754–756 (2003).
[Crossref]

Minasian, R. A.

D. B. Hunter, R. A. Minasian, “Reflectively tapped fiber optic transversal filter using in-fiber Bragg grating,” Electron. Lett. 31, 1010–1012 (1995).
[Crossref]

Newberg, I. L.

F. Coppinger, S. Yegnanarayanan, P. D. Trinh, B. Jalali, I. L. Newberg, “Nonrecursive tunable photonic filter using wavelength-selective true time delay,” IEEE Photonics Technol. Lett. 8, 1214–1216 (1996).
[Crossref]

Ortega, B.

J. Capmany, D. Pastor, B. Ortega, “New and flexible fiber-optic delay-line filters using chirped Bragg gratings and laser arrays,” IEEE Trans. Microwave Theory Tech. 47, 1321–1326 (1999).
[Crossref]

Pastor, D.

J. Capmany, D. Pastor, B. Ortega, “New and flexible fiber-optic delay-line filters using chirped Bragg gratings and laser arrays,” IEEE Trans. Microwave Theory Tech. 47, 1321–1326 (1999).
[Crossref]

Poole, C. D.

C. D. Poole, R. E. Wagner, “Phenomenological approach to polarization dispersion in long single mode fibers,” Electron. Lett. 22, 1029–1230 (1986).
[Crossref]

Trinh, P. D.

F. Coppinger, S. Yegnanarayanan, P. D. Trinh, B. Jalali, I. L. Newberg, “Nonrecursive tunable photonic filter using wavelength-selective true time delay,” IEEE Photonics Technol. Lett. 8, 1214–1216 (1996).
[Crossref]

Wagner, R. E.

C. D. Poole, R. E. Wagner, “Phenomenological approach to polarization dispersion in long single mode fibers,” Electron. Lett. 22, 1029–1230 (1986).
[Crossref]

Wang, Y.

X. Yi, C. Lu, X. Yang, W.-D. Zhong, F. Wei, L. Ding, Y. Wang, “Continuously tunable microwave-photonic filter design using high-birefringence linear chirped grating,” IEEE Photonics Technol. Lett. 15, 754–756 (2003).
[Crossref]

Wei, F.

X. Yi, C. Lu, X. Yang, W.-D. Zhong, F. Wei, L. Ding, Y. Wang, “Continuously tunable microwave-photonic filter design using high-birefringence linear chirped grating,” IEEE Photonics Technol. Lett. 15, 754–756 (2003).
[Crossref]

Williams, J. A. R.

W. Zhang, J. A. R. Williams, I. Bennion, “Polarization synthesized optical transversal filter employing high birefringence fiber gratings,” IEEE Photonics Technol. Lett. 13, 523–525 (2001).
[Crossref]

W. Zhang, J. A. R. Williams, I. Bennion, “Optical fiber delay line filter free of limitation imposed by optical coherence,” Electron. Lett. 35, 2133–2134 (1999).
[Crossref]

W. Zhang, J. A. R. Williams, L. A. Everall, I. Bennion, “Fiber optical radio frequency notch filter with linear and continuous tuning by using a chirped grating,” Electron. Lett. 34, 1770–1772 (1998).
[Crossref]

Yang, X.

X. Yi, C. Lu, X. Yang, W.-D. Zhong, F. Wei, L. Ding, Y. Wang, “Continuously tunable microwave-photonic filter design using high-birefringence linear chirped grating,” IEEE Photonics Technol. Lett. 15, 754–756 (2003).
[Crossref]

Yegnanarayanan, S.

F. Coppinger, S. Yegnanarayanan, P. D. Trinh, B. Jalali, I. L. Newberg, “Nonrecursive tunable photonic filter using wavelength-selective true time delay,” IEEE Photonics Technol. Lett. 8, 1214–1216 (1996).
[Crossref]

Yi, X.

X. Yi, C. Lu, X. Yang, W.-D. Zhong, F. Wei, L. Ding, Y. Wang, “Continuously tunable microwave-photonic filter design using high-birefringence linear chirped grating,” IEEE Photonics Technol. Lett. 15, 754–756 (2003).
[Crossref]

Zhang, W.

W. Zhang, J. A. R. Williams, I. Bennion, “Polarization synthesized optical transversal filter employing high birefringence fiber gratings,” IEEE Photonics Technol. Lett. 13, 523–525 (2001).
[Crossref]

W. Zhang, J. A. R. Williams, I. Bennion, “Optical fiber delay line filter free of limitation imposed by optical coherence,” Electron. Lett. 35, 2133–2134 (1999).
[Crossref]

W. Zhang, J. A. R. Williams, L. A. Everall, I. Bennion, “Fiber optical radio frequency notch filter with linear and continuous tuning by using a chirped grating,” Electron. Lett. 34, 1770–1772 (1998).
[Crossref]

Zhong, W.-D.

X. Yi, C. Lu, X. Yang, W.-D. Zhong, F. Wei, L. Ding, Y. Wang, “Continuously tunable microwave-photonic filter design using high-birefringence linear chirped grating,” IEEE Photonics Technol. Lett. 15, 754–756 (2003).
[Crossref]

Electron. Lett. (4)

W. Zhang, J. A. R. Williams, L. A. Everall, I. Bennion, “Fiber optical radio frequency notch filter with linear and continuous tuning by using a chirped grating,” Electron. Lett. 34, 1770–1772 (1998).
[Crossref]

D. B. Hunter, R. A. Minasian, “Reflectively tapped fiber optic transversal filter using in-fiber Bragg grating,” Electron. Lett. 31, 1010–1012 (1995).
[Crossref]

W. Zhang, J. A. R. Williams, I. Bennion, “Optical fiber delay line filter free of limitation imposed by optical coherence,” Electron. Lett. 35, 2133–2134 (1999).
[Crossref]

C. D. Poole, R. E. Wagner, “Phenomenological approach to polarization dispersion in long single mode fibers,” Electron. Lett. 22, 1029–1230 (1986).
[Crossref]

IEEE Photonics Technol. Lett. (3)

F. Coppinger, S. Yegnanarayanan, P. D. Trinh, B. Jalali, I. L. Newberg, “Nonrecursive tunable photonic filter using wavelength-selective true time delay,” IEEE Photonics Technol. Lett. 8, 1214–1216 (1996).
[Crossref]

W. Zhang, J. A. R. Williams, I. Bennion, “Polarization synthesized optical transversal filter employing high birefringence fiber gratings,” IEEE Photonics Technol. Lett. 13, 523–525 (2001).
[Crossref]

X. Yi, C. Lu, X. Yang, W.-D. Zhong, F. Wei, L. Ding, Y. Wang, “Continuously tunable microwave-photonic filter design using high-birefringence linear chirped grating,” IEEE Photonics Technol. Lett. 15, 754–756 (2003).
[Crossref]

IEEE Trans. Microwave Theory Tech. (1)

J. Capmany, D. Pastor, B. Ortega, “New and flexible fiber-optic delay-line filters using chirped Bragg gratings and laser arrays,” IEEE Trans. Microwave Theory Tech. 47, 1321–1326 (1999).
[Crossref]

Other (1)

G. Keiser, Optical Fiber Communications (McGraw-Hill, New York, 2000).

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Figures (4)

Fig. 1
Fig. 1

Filter configuration with the Hi - Bi fiber and tunable DGD element. EOM, electro-optic modulator.

Fig. 2
Fig. 2

Measured frequency response of the filter for the Hi - Bi fiber alone.

Fig. 3
Fig. 3

Measured frequency response of the filter with the Hi - Bi fiber and the DGD element.

Fig. 4
Fig. 4

Comparison between measured (triangles) and calculated (solid curve) FSR values, as a function of DGD values.

Equations (16)

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V ( t ) = 1 + m cos ω m t .
P i ( t ) = P i ( 1 + m cos ω m t ) ,
f ( t ) = P i [ 1 + m cos ( ω m t ) ] 1 2 cos ( ω 0 t ) ,
f ( t ) = P i ( 1 + 1 2 m cos ω m t ) cos ω 0 t = P i [ cos ω 0 t + m 4 cos ( ω 0 + ω m ) t + m 4 cos ( ω 0 ω m ) t ] .
F ( ω ω 0 ) = + f ( t ) exp [ j ( ω ω 0 ) t ] d t .
β ( ω ) = β 0 + β 1 ( ω ω 0 ) + 1 2 β 2 ( ω ω 0 ) 2 + ,
β m = ( m β ω m ) ω = ω 0 .
f Ω + ( t ) = M cos α 2 π { F ( ω ω 0 ) exp ( j Δ τ Δ ω 2 ) exp ( j β 1 L Δ ω j β 2 Δ ω 2 L 2 ) exp [ j ( ω ω 0 ) t ] d ω } ,
f Ω ( t ) = M sin α 2 π { F ( ω ω 0 ) exp ( j Δ τ Δ ω 2 ) exp ( j β 1 L Δ ω j β 2 Δ ω 2 L 2 ) exp [ j ( ω ω 0 ) t ] d ω } ,
f ( t ) = f Ω + ( t ) Ω + + f Ω ( t ) Ω .
f Ω + ( t ) = 2 2 M P i { cos ( ω 0 t ) + m 4 cos [ ω 0 t + ω m ( t + Δ τ 2 β 1 L ) ] + m 4 cos [ ω 0 t ω m ( t + Δ τ 2 β 1 L ) ] } ,
f Ω ( t ) = 2 2 M P i { cos ( ω 0 t ) + m 4 cos [ ω 0 t + ω m ( t Δ τ 2 β 1 L ) ] + m 4 cos [ ω 0 t ω m ( t Δ τ 2 β 1 L ) ] } .
P ( t ) = f ( t ) 2 = f ( t ) · f * ( t ) = f Ω + ( t ) 2 + f Ω ( t ) 2 .
I ( t ) = 1 2 R M 2 P i ( 1 2 + m 2 cos [ ω m ( t + Δ τ 2 β 1 L ) ] + m 2 8 { cos [ ω m ( t + Δ τ 2 β 1 L ) ] } 2 ) + 1 2 R M 2 P i ( 1 2 + m 2 cos [ ω m ( t Δ τ 2 β 1 L ) ] + m 2 8 { cos [ ω m ( t Δ τ 2 β 1 L ) ] } 2 ) .
H ( ω m ) = R 4 M 2 exp ( j Δ τ ω m 2 ) + exp ( j Δ τ ω m 2 ) = R 2 M 2 cos ( Δ τ ω m 2 ) .
f = ( k + 1 2 ) 1 Δ τ , k = 0 , 1 , 2 ,

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