Abstract

A coherence-free microwave photonic filter configuration is presented. The configuration is based on a Sagnac loop interferometer containing a single-drive intensity modulator without a nonreciprocal bias unit. A notch response is obtained by modulating the clockwise and counterclockwise propagating waves inside the Sagnac loop at different times. A general theoretical analysis for both the reflected signal and the transmitted signal is obtained. Measured results verify the theoretical expressions and demonstrate a robust notch filter response.

© 2007 Optical Society of America

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References

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  2. R. A. Minasian, "Photonic signal processing of microwave signals," IEEE Trans. Microwave Theory Technol. 54, 832-846 (2006).
    [CrossRef]
  3. D. Pastor and J. Capmany, "Fibre optic tunable transversal filter using laser array and linearly chirped fibre grating," Electron. Lett. 34, 1684-1685 (1998).
    [CrossRef]
  4. E. H. W. Chan, K. E. Alameh, and J. A. R. Minasian, "Photonics bandpass filters with high skirt selectivity and stopband attenuation," J. Lightwave Technol. 20, 1962-1967 (2002).
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  5. W. Zhang, J. A. R. Williams, and I. Bennion, "Optical fiber delay line filter free of limitation imposed by optical coherence," Electron. Lett. 35, 2133-2134 (1999).
    [CrossRef]
  6. W. Zhang, J. A. R. Williams, and I. Bennion, "Polarization synthesized optical transversal filter employing high birefringence fiber Gratings," IEEE Photon. Technol. Lett. 13, 523-525 (2001).
    [CrossRef]
  7. E. H. W. Chan and R. A. Minasian, "Coherent-free photonic notch filter," Electron. Lett. 40, 1375-1377 (2004).
    [CrossRef]
  8. M. L. Dennis, I. N. Dualing III, and W. K. Burns, "Inherently bias free amplitude modulator," Electron. Lett. 32, 547-548 (1996).
    [CrossRef]
  9. M. Y. Frankel and R. D. Esman, "Optical single-sideband suppressed-carrier modulator for wide-band signal processing," J. Lightwave Technol. 16, 859-863 (1998).
    [CrossRef]

2006 (1)

R. A. Minasian, "Photonic signal processing of microwave signals," IEEE Trans. Microwave Theory Technol. 54, 832-846 (2006).
[CrossRef]

2005 (1)

2004 (1)

E. H. W. Chan and R. A. Minasian, "Coherent-free photonic notch filter," Electron. Lett. 40, 1375-1377 (2004).
[CrossRef]

2002 (1)

2001 (1)

W. Zhang, J. A. R. Williams, and I. Bennion, "Polarization synthesized optical transversal filter employing high birefringence fiber Gratings," IEEE Photon. Technol. Lett. 13, 523-525 (2001).
[CrossRef]

1999 (1)

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

1998 (2)

D. Pastor and J. Capmany, "Fibre optic tunable transversal filter using laser array and linearly chirped fibre grating," Electron. Lett. 34, 1684-1685 (1998).
[CrossRef]

M. Y. Frankel and R. D. Esman, "Optical single-sideband suppressed-carrier modulator for wide-band signal processing," J. Lightwave Technol. 16, 859-863 (1998).
[CrossRef]

1996 (1)

M. L. Dennis, I. N. Dualing III, and W. K. Burns, "Inherently bias free amplitude modulator," Electron. Lett. 32, 547-548 (1996).
[CrossRef]

Electron. Lett. (4)

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

E. H. W. Chan and R. A. Minasian, "Coherent-free photonic notch filter," Electron. Lett. 40, 1375-1377 (2004).
[CrossRef]

M. L. Dennis, I. N. Dualing III, and W. K. Burns, "Inherently bias free amplitude modulator," Electron. Lett. 32, 547-548 (1996).
[CrossRef]

D. Pastor and J. Capmany, "Fibre optic tunable transversal filter using laser array and linearly chirped fibre grating," Electron. Lett. 34, 1684-1685 (1998).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

W. Zhang, J. A. R. Williams, and I. Bennion, "Polarization synthesized optical transversal filter employing high birefringence fiber Gratings," IEEE Photon. Technol. Lett. 13, 523-525 (2001).
[CrossRef]

IEEE Trans. Microwave Theory Technol. (1)

R. A. Minasian, "Photonic signal processing of microwave signals," IEEE Trans. Microwave Theory Technol. 54, 832-846 (2006).
[CrossRef]

J. Lightwave Technol. (3)

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Figures (4)

Fig. 1
Fig. 1

(Color online) Experimental setup.

Fig. 2
Fig. 2

(Color online) Measured and calculated response of the low-pass filter when the length difference is 2.42   m .

Fig. 3
Fig. 3

(Color online) Measured and calculated response of the low-pass filter when the length difference is 0.914   m .

Fig. 4
Fig. 4

(Color online) Comparison of measured reflected and transmitted signal responses when the length difference is 0.914   m .

Equations (16)

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E ( t ) = cos [ m cos ( ω m t ) + θ 2 ] cos ( ω 0 t ) ,
E ( t ) = J 0 ( m / 2 ) cos ( θ / 2 ) cos ( ω 0 t ) J 1 ( m / 2 ) sin ( θ / 2 ) × { cos [ ( ω 0 ω m ) t ] + cos [ ( ω 0 + ω m ) t ] } J 2 ( m / 2 ) cos ( θ / 2 ) { cos [ ( ω 0 2 ω m ) t ] + cos [ ( ω 0 + 2 ω m ) t ] } J 3 ( m / 2 ) sin ( θ / 2 ) × { cos [ ( ω 0 3 ω m ) t ] + cos [ ( ω 0 + 3 ω m ) t ] } +   .
E ( t ) = J 0 ( m / 2 ) cos ( θ / 2 ) cos ( ω 0 t ) J 1 ( m / 2 ) sin ( θ / 2 ) × { cos [ ( ω 0 ω m ) t ] + cos [ ( ω 0 + ω m ) t ] } .
E ( t ) = cos ( θ / 2 ) cos ω 0 t + sin ( θ / 2 )
× [ m 1 + ε 2 4 cos [ ( ω 0 + ω m ) t arctan ( ε ) ] + m 1 + ε 2 4 cos [ ( ω 0 ω m ) t arctan ( ε ) ] ] ,
E CW ( t ) = 2 2 M P i exp { j [ ω 0 ( t T 1 T 2 ) ] } [ cos ( θ 1 / 2 ) + m 1 1 + ε 2 4 sin ( θ 1 / 2 ) cos [ ω m ( t T 2 ) ( β 2 L 2 ω m 2 / 2 ) arctan ( ε ) ] ] ,
E CCW ( t ) = 2 2 M P i exp { j [ ω 0 ( t T 1 T 2 ) + π / 2 + ϕ ] } × [ cos ( θ 2 / 2 ) + m 2 1 + ε 2 4 sin ( θ 2 / 2 ) × cos [ ω m ( t T 1 ) ( β 2 L 1 ω m 2 / 2 ) arctan ( ε ) ] ] ,
V π ,rev = V π ,for ω m τ x sin ( ω m τ x ) .
E R ( t ) = { 2 2 P i M exp { j [ ω 0 ( t T 1 T 2 ) ] } { cos ( θ / 2 ) + m 1 + ε 2 4 sin ( θ / 2 ) cos { ω m ( t T 2 ) [ β 2 ( L 2 + L 3 ) ω m 2 / 2 ] arctan ( ε ) } } } + { 2 2 P i M exp { j [ ω 0 ( t T 1 T 2 ) + ϕ ] } × { cos ( θ / 2 ) + m 1 + ε 2 4 sin ( θ / 2 ) cos { ω m ( t T 1 ) [ β 2 ( L 1 + L 3 ) ω m 2 / 2 ] arctan ( ε ) } } } ,
E T ( t ) = { 2 2 P i M exp { j [ ω 0 ( t T 1 T 2 ) ] } { cos ( θ / 2 ) + m 1 + ε 2 4 sin ( θ / 2 ) cos { ω m ( t T 2 ) [ β 2 ( L 2 + L 4 ) ω m 2 / 2 ] arctan ( ε ) } } } + { 2 2 P i M exp { j [ ω 0 ( t T 1 T 2 ) + π + ϕ ] } × { cos ( θ / 2 ) + m 1 + ε 2 4 sin ( θ / 2 ) cos { ω m ( t T 1 ) [ β 2 ( L 1 + L 4 ) ω m 2 / 2 ] arctan ( ε ) } } } ,
I R ( t ) = E R ( t ) E R * ( t ) = [ 1 + cos ( ϕ ) ] M 2 R P i 1 + ε 2 2 × { cos { [ β 2 ( L 2 + L 3 ) ω m 2 / 2 ] + arctan ( ε ) } × { cos 2 ( θ / 2 ) + m 4 sin ( θ ) cos [ ω m ( t T 2 ) ] } + cos { [ β 2 ( L 1 + L 3 ) ω m 2 / 2 ] + arctan ( ε ) } × { cos 2 ( θ / 2 ) + m 4 sin ( θ ) cos [ ω m ( t T 1 ) ] } } ,
I T ( t ) = E T ( t ) E T * ( t ) = [ 1 cos ( ϕ ) ] M 2 R P i 1 + ε 2 2 × { cos { [ β 2 ( L 2 + L 4 ) ω m 2 / 2 ] + arctan ( ε ) } × { cos 2 ( θ / 2 ) + m 4 sin ( θ ) cos [ ω m ( t T 2 ) ] } + cos { [ β 2 ( L 1 + L 4 ) ω m 2 / 2 ] + arctan ( ε ) } × { cos 2 ( θ / 2 ) + m 4 sin ( θ ) cos [ ω m ( t T 1 ) ] } } .
I R ( t ) = [ 1 + cos ( ϕ ) ] M 2 R P i 2 { cos 2 ( θ / 2 ) + m 2 sin ( θ ) × cos [ ω m ( T 2 T 1 2 ) ] cos [ ω m ( t T 2 + T 1 2 ) ] } ,
I T ( t ) = [ 1 cos ( ϕ ) ] M 2 R P i 2 { cos 2 ( θ / 2 ) + m 2 sin ( θ ) × cos [ ω m ( T 2 T 1 2 ) ] cos [ ω m ( t T 2 + T 1 2 ) ] } .
P ( ω m ) { cos [ ω m ( T 2 T 1 2 ) ] } 2 = 1 + cos [ ω m ( T 2 T 1 ) ] 2 .
Δ T = T 2 T 1 = n ( L 2 L 1 ) c .

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