Abstract

In this paper, a novel microwave photonic filter (MPF) with multiple independently tunable passbands is proposed. A broadband optical source (BOS) is employed and split by a 1:N coupler into several branches. One branch is directed to a phase modulator which is modulated by a radio frequency signal and the other branches are delayed by optical delay lines (ODLs), respectively. All of these branches are combined by another 1:N coupler and sent to a dispersion compensation fiber which is used to introduce group delay dispersion to the optical signal. At a photodetector, each time-delayed broadband lightwave beating with the sidebands produced by the phase modulator forms a passband of the MPF. By tuning the delay of each broadband lightwave, the center frequency of the passband can be independently tuned. An MPF with two independently tunable passbands is experimentally demonstrated. The two passbands can be tuned from DC to 30 GHz with a 3-dB bandwidth of about 250 MHz. The stability and dynamic range of the MPF are also evaluated. By employing more branches delayed by ODLs, more passbands can be generated.

© 2015 Optical Society of America

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References

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    [Crossref]
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    [Crossref] [PubMed]
  5. J. Palaci, G. E. Villanueva, J. V. Galan, J. Marti, and B. Vidal, “Single bandpass photonic microwave filter based on a notch ring resonator,” IEEE Photonics Technol. Lett. 22(17), 1276–1278 (2010).
    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
  12. L. Gao, X. Y. Zhang, B.-J. Hu, and Q. Xue, “Novel multi-stub loaded resonators and their applications to various bandpass filters,” IEEE Trans. Microw. Theory Tech. 62(5), 1162–1172 (2014).
    [Crossref]
  13. J.-C. Liu, J.-W. Wang, B.-H. Zeng, and D.-C. Chang, “CPW-fed dual-mode double-square-ring resonators for quad-band filters,” IEEE Microw. Wirel. Compon. Lett. 20(3), 142–144 (2010).
    [Crossref]
  14. Y. Jiang, P. P. Shum, P. Zu, J. Zhou, G. Bai, J. Xu, Z. Zhou, H. Li, and S. Wang, “A selectable multiband bandpass microwave photonic filter,” IEEE Photonics J. 5(3), 5500509 (2013).
    [Crossref]
  15. H. Chen, Z. Xu, H. Fu, S. Zhang, C. Wu, H. Wu, H. Xu, and Z. Cai, “Switchable and tunable microwave frequency multiplication based on a dual-passband microwave photonic filter,” Opt. Express 23(8), 9835–9843 (2015).
    [Crossref] [PubMed]
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    [Crossref]
  17. X. Han, E. Xu, W. Liu, and J. Yao, “Tunable dual-passband microwave photonic filter using orthogonal polarization modulation,” IEEE Photon. Technol. Lett.to be published.
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
  21. F. Zeng and J. Yao, “All-optical bandpass microwave filter based on an electro-optic phase modulator,” Opt. Express 12(16), 3814–3819 (2004).
    [Crossref] [PubMed]
  22. Y. Zhang and S. Pan, “Complex coefficient microwave photonic filter using a polarization-modulator-based phase shifter,” IEEE Photonics Technol. Lett. 25(2), 187–189 (2013).
    [Crossref]
  23. A. Loayssa, J. Capmany, M. Sagues, and J. Mora, “Demonstration of incoherent microwave photonic filters with all-optical complex coefficients,” IEEE Photonics Technol. Lett. 18(16), 1744–1746 (2006).
    [Crossref]
  24. X. Xue, X. Zheng, H. Zhang, and B. Zhou, “Analysis and compensation of third-order dispersion induced RF distortions in highly reconfigurable microwave photonic filters,” J. Lightwave Technol. 31(13), 2263–2270 (2013).
    [Crossref]
  25. G. Peraita, A. J. Torregrosa, H. Maestre, and C. R. Fernandez-Pousa, “Broadband linearization of dispersive delay line using a chirped fiber bragg grating,” IEEE Photonics Technol. Lett. 27(10), 1044–1135 (2015).
    [Crossref]
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    [Crossref] [PubMed]
  27. X. Xue, X. Zheng, H. Zhang, and B. Zhou, “Highly reconfigurable microwave photonic single-bandpass filter with complex continuous-time impulse responses,” Opt. Express 20(24), 26929–26934 (2012).
    [Crossref] [PubMed]

2015 (3)

R. Gomez-Garcia and A. C. Guyette, “Reconfigurable multi-band microwave filters,” IEEE Trans. Microw. Theory Tech. 63(4), 1294–1307 (2015).
[Crossref]

H. Chen, Z. Xu, H. Fu, S. Zhang, C. Wu, H. Wu, H. Xu, and Z. Cai, “Switchable and tunable microwave frequency multiplication based on a dual-passband microwave photonic filter,” Opt. Express 23(8), 9835–9843 (2015).
[Crossref] [PubMed]

G. Peraita, A. J. Torregrosa, H. Maestre, and C. R. Fernandez-Pousa, “Broadband linearization of dispersive delay line using a chirped fiber bragg grating,” IEEE Photonics Technol. Lett. 27(10), 1044–1135 (2015).
[Crossref]

2014 (3)

D. W. Grund, S. Shi, G. J. Schneider, J. Murakowski, and D. W. Prather, “Improved configuration and reduction of phase noise in a narrow linewidth ultrawideband optical RF source,” Opt. Lett. 39(16), 4667–4670 (2014).
[Crossref] [PubMed]

L. Gao, J. Zhang, X. Chen, and J. Yao, “Microwave photonic filter with two independently tunable passbands using a phase modulator and an equivalent phase-shifted fiber bragg grating,” IEEE Trans. Microw. Theory Tech. 62(2), 380–387 (2014).
[Crossref]

L. Gao, X. Y. Zhang, B.-J. Hu, and Q. Xue, “Novel multi-stub loaded resonators and their applications to various bandpass filters,” IEEE Trans. Microw. Theory Tech. 62(5), 1162–1172 (2014).
[Crossref]

2013 (5)

G. Chaudhary, Y. Jeong, and J. Lim, “Dual-band bandpass filter with independently tunable center frequencies and bandwidths,” IEEE Trans. Microw. Theory Tech. 61(1), 107–116 (2013).
[Crossref]

Y. Jiang, P. P. Shum, P. Zu, J. Zhou, G. Bai, J. Xu, Z. Zhou, H. Li, and S. Wang, “A selectable multiband bandpass microwave photonic filter,” IEEE Photonics J. 5(3), 5500509 (2013).
[Crossref]

L. Li, X. Yi, T. X. H. Huang, and R. A. Minasian, “Shifted dispersion-induced radio-frequency fading in microwave photonic filters using a dual-input Mach-Zehnder electro-optic modulator,” Opt. Lett. 38(7), 1164–1166 (2013).
[Crossref] [PubMed]

X. Xue, X. Zheng, H. Zhang, and B. Zhou, “Analysis and compensation of third-order dispersion induced RF distortions in highly reconfigurable microwave photonic filters,” J. Lightwave Technol. 31(13), 2263–2270 (2013).
[Crossref]

Y. Zhang and S. Pan, “Complex coefficient microwave photonic filter using a polarization-modulator-based phase shifter,” IEEE Photonics Technol. Lett. 25(2), 187–189 (2013).
[Crossref]

2012 (3)

X. Xue, X. Zheng, H. Zhang, and B. Zhou, “Highly reconfigurable microwave photonic single-bandpass filter with complex continuous-time impulse responses,” Opt. Express 20(24), 26929–26934 (2012).
[Crossref] [PubMed]

W. Li, M. Li, and J. P. Yao, “A narrow-passband and frequency-tunable micro-wave photonic filter based on phase-modulation to intensity-modulation conversion using a phase-shifted fiber Bragg grating,” IEEE Trans. Microw. Theory Tech. 60(5), 1287–1296 (2012).
[Crossref]

W. Li and J. Yao, “A wideband frequency tunable optoelectronic oscillator incorporating a tunable microwave photonic filter based on phase-modulation to intensity-modulation conversion using a phase-shifted fiber Bragg grating,” IEEE Trans. Microw. Theory Tech. 60(6), 1735–1742 (2012).
[Crossref]

2011 (1)

2010 (2)

J. Palaci, G. E. Villanueva, J. V. Galan, J. Marti, and B. Vidal, “Single bandpass photonic microwave filter based on a notch ring resonator,” IEEE Photonics Technol. Lett. 22(17), 1276–1278 (2010).
[Crossref]

J.-C. Liu, J.-W. Wang, B.-H. Zeng, and D.-C. Chang, “CPW-fed dual-mode double-square-ring resonators for quad-band filters,” IEEE Microw. Wirel. Compon. Lett. 20(3), 142–144 (2010).
[Crossref]

2007 (1)

2006 (4)

J. Yao, “Microwave photonics,” J. Lightwave Technol. 54(2), 832–846 (2006).

J. Capmany, B. Ortega, and D. Pastor, “A tutorial on microwave photonic filters,” J. Lightwave Technol. 24(1), 201–229 (2006).
[Crossref]

J. Mora, B. Ortega, A. Diez, J. L. Cruz, M. V. Andres, J. Capmany, and D. Pastor, “Photonic microwave tunable single-bandpass filter based on Mach-Zehnder interferometer,” J. Lightwave Technol. 24(7), 2500–2509 (2006).
[Crossref]

A. Loayssa, J. Capmany, M. Sagues, and J. Mora, “Demonstration of incoherent microwave photonic filters with all-optical complex coefficients,” IEEE Photonics Technol. Lett. 18(16), 1744–1746 (2006).
[Crossref]

2005 (1)

M. Popov, P.-Y. Fonjallaz, and O. Gunnarsson, “Compact microwave photonic transversal filter with 40-dB sidelobe suppression,” IEEE Photon. Technol. Lett. 17(3), 663–665 (2005).
[Crossref]

2004 (1)

2003 (1)

2001 (1)

G.-H. Duan and E. Georgiev, “Non-white photodetection noise at the output of an optical amplifier: theory and experiment,” IEEE J. Quantum Electron. 37(8), 1008–1014 (2001).
[Crossref]

Andres, M. V.

Bai, G.

Y. Jiang, P. P. Shum, P. Zu, J. Zhou, G. Bai, J. Xu, Z. Zhou, H. Li, and S. Wang, “A selectable multiband bandpass microwave photonic filter,” IEEE Photonics J. 5(3), 5500509 (2013).
[Crossref]

Cai, Z.

Capmany, J.

Chang, D.-C.

J.-C. Liu, J.-W. Wang, B.-H. Zeng, and D.-C. Chang, “CPW-fed dual-mode double-square-ring resonators for quad-band filters,” IEEE Microw. Wirel. Compon. Lett. 20(3), 142–144 (2010).
[Crossref]

Chaudhary, G.

G. Chaudhary, Y. Jeong, and J. Lim, “Dual-band bandpass filter with independently tunable center frequencies and bandwidths,” IEEE Trans. Microw. Theory Tech. 61(1), 107–116 (2013).
[Crossref]

Chen, H.

Chen, X.

L. Gao, J. Zhang, X. Chen, and J. Yao, “Microwave photonic filter with two independently tunable passbands using a phase modulator and an equivalent phase-shifted fiber bragg grating,” IEEE Trans. Microw. Theory Tech. 62(2), 380–387 (2014).
[Crossref]

Cruz, J. L.

Diez, A.

Duan, G.-H.

G.-H. Duan and E. Georgiev, “Non-white photodetection noise at the output of an optical amplifier: theory and experiment,” IEEE J. Quantum Electron. 37(8), 1008–1014 (2001).
[Crossref]

Fernandez-Pousa, C. R.

G. Peraita, A. J. Torregrosa, H. Maestre, and C. R. Fernandez-Pousa, “Broadband linearization of dispersive delay line using a chirped fiber bragg grating,” IEEE Photonics Technol. Lett. 27(10), 1044–1135 (2015).
[Crossref]

Fonjallaz, P.-Y.

M. Popov, P.-Y. Fonjallaz, and O. Gunnarsson, “Compact microwave photonic transversal filter with 40-dB sidelobe suppression,” IEEE Photon. Technol. Lett. 17(3), 663–665 (2005).
[Crossref]

Fu, H.

Galan, J. V.

J. Palaci, G. E. Villanueva, J. V. Galan, J. Marti, and B. Vidal, “Single bandpass photonic microwave filter based on a notch ring resonator,” IEEE Photonics Technol. Lett. 22(17), 1276–1278 (2010).
[Crossref]

Gao, L.

L. Gao, X. Y. Zhang, B.-J. Hu, and Q. Xue, “Novel multi-stub loaded resonators and their applications to various bandpass filters,” IEEE Trans. Microw. Theory Tech. 62(5), 1162–1172 (2014).
[Crossref]

L. Gao, J. Zhang, X. Chen, and J. Yao, “Microwave photonic filter with two independently tunable passbands using a phase modulator and an equivalent phase-shifted fiber bragg grating,” IEEE Trans. Microw. Theory Tech. 62(2), 380–387 (2014).
[Crossref]

Georgiev, E.

G.-H. Duan and E. Georgiev, “Non-white photodetection noise at the output of an optical amplifier: theory and experiment,” IEEE J. Quantum Electron. 37(8), 1008–1014 (2001).
[Crossref]

Gomez-Garcia, R.

R. Gomez-Garcia and A. C. Guyette, “Reconfigurable multi-band microwave filters,” IEEE Trans. Microw. Theory Tech. 63(4), 1294–1307 (2015).
[Crossref]

Grund, D. W.

Gunnarsson, O.

M. Popov, P.-Y. Fonjallaz, and O. Gunnarsson, “Compact microwave photonic transversal filter with 40-dB sidelobe suppression,” IEEE Photon. Technol. Lett. 17(3), 663–665 (2005).
[Crossref]

Guyette, A. C.

R. Gomez-Garcia and A. C. Guyette, “Reconfigurable multi-band microwave filters,” IEEE Trans. Microw. Theory Tech. 63(4), 1294–1307 (2015).
[Crossref]

Han, X.

X. Han, E. Xu, W. Liu, and J. Yao, “Tunable dual-passband microwave photonic filter using orthogonal polarization modulation,” IEEE Photon. Technol. Lett.to be published.

Hu, B.-J.

L. Gao, X. Y. Zhang, B.-J. Hu, and Q. Xue, “Novel multi-stub loaded resonators and their applications to various bandpass filters,” IEEE Trans. Microw. Theory Tech. 62(5), 1162–1172 (2014).
[Crossref]

Huang, T. X. H.

Jeong, Y.

G. Chaudhary, Y. Jeong, and J. Lim, “Dual-band bandpass filter with independently tunable center frequencies and bandwidths,” IEEE Trans. Microw. Theory Tech. 61(1), 107–116 (2013).
[Crossref]

Jiang, Y.

Y. Jiang, P. P. Shum, P. Zu, J. Zhou, G. Bai, J. Xu, Z. Zhou, H. Li, and S. Wang, “A selectable multiband bandpass microwave photonic filter,” IEEE Photonics J. 5(3), 5500509 (2013).
[Crossref]

Li, H.

Y. Jiang, P. P. Shum, P. Zu, J. Zhou, G. Bai, J. Xu, Z. Zhou, H. Li, and S. Wang, “A selectable multiband bandpass microwave photonic filter,” IEEE Photonics J. 5(3), 5500509 (2013).
[Crossref]

Li, L.

Li, M.

W. Li, M. Li, and J. P. Yao, “A narrow-passband and frequency-tunable micro-wave photonic filter based on phase-modulation to intensity-modulation conversion using a phase-shifted fiber Bragg grating,” IEEE Trans. Microw. Theory Tech. 60(5), 1287–1296 (2012).
[Crossref]

Li, W.

W. Li and J. Yao, “A wideband frequency tunable optoelectronic oscillator incorporating a tunable microwave photonic filter based on phase-modulation to intensity-modulation conversion using a phase-shifted fiber Bragg grating,” IEEE Trans. Microw. Theory Tech. 60(6), 1735–1742 (2012).
[Crossref]

W. Li, M. Li, and J. P. Yao, “A narrow-passband and frequency-tunable micro-wave photonic filter based on phase-modulation to intensity-modulation conversion using a phase-shifted fiber Bragg grating,” IEEE Trans. Microw. Theory Tech. 60(5), 1287–1296 (2012).
[Crossref]

Lim, J.

G. Chaudhary, Y. Jeong, and J. Lim, “Dual-band bandpass filter with independently tunable center frequencies and bandwidths,” IEEE Trans. Microw. Theory Tech. 61(1), 107–116 (2013).
[Crossref]

Liu, J.-C.

J.-C. Liu, J.-W. Wang, B.-H. Zeng, and D.-C. Chang, “CPW-fed dual-mode double-square-ring resonators for quad-band filters,” IEEE Microw. Wirel. Compon. Lett. 20(3), 142–144 (2010).
[Crossref]

Liu, W.

X. Han, E. Xu, W. Liu, and J. Yao, “Tunable dual-passband microwave photonic filter using orthogonal polarization modulation,” IEEE Photon. Technol. Lett.to be published.

Loayssa, A.

A. Loayssa, J. Capmany, M. Sagues, and J. Mora, “Demonstration of incoherent microwave photonic filters with all-optical complex coefficients,” IEEE Photonics Technol. Lett. 18(16), 1744–1746 (2006).
[Crossref]

Maestre, H.

G. Peraita, A. J. Torregrosa, H. Maestre, and C. R. Fernandez-Pousa, “Broadband linearization of dispersive delay line using a chirped fiber bragg grating,” IEEE Photonics Technol. Lett. 27(10), 1044–1135 (2015).
[Crossref]

Marti, J.

J. Palaci, G. E. Villanueva, J. V. Galan, J. Marti, and B. Vidal, “Single bandpass photonic microwave filter based on a notch ring resonator,” IEEE Photonics Technol. Lett. 22(17), 1276–1278 (2010).
[Crossref]

Martí, J.

Martinez, A.

Minasian, R. A.

Mora, J.

J. Mora, B. Ortega, A. Diez, J. L. Cruz, M. V. Andres, J. Capmany, and D. Pastor, “Photonic microwave tunable single-bandpass filter based on Mach-Zehnder interferometer,” J. Lightwave Technol. 24(7), 2500–2509 (2006).
[Crossref]

A. Loayssa, J. Capmany, M. Sagues, and J. Mora, “Demonstration of incoherent microwave photonic filters with all-optical complex coefficients,” IEEE Photonics Technol. Lett. 18(16), 1744–1746 (2006).
[Crossref]

Muñoz, P.

Murakowski, J.

Ortega, B.

Palaci, J.

J. Palaci, G. E. Villanueva, J. V. Galan, J. Marti, and B. Vidal, “Single bandpass photonic microwave filter based on a notch ring resonator,” IEEE Photonics Technol. Lett. 22(17), 1276–1278 (2010).
[Crossref]

Pan, S.

Y. Zhang and S. Pan, “Complex coefficient microwave photonic filter using a polarization-modulator-based phase shifter,” IEEE Photonics Technol. Lett. 25(2), 187–189 (2013).
[Crossref]

Pastor, D.

Peraita, G.

G. Peraita, A. J. Torregrosa, H. Maestre, and C. R. Fernandez-Pousa, “Broadband linearization of dispersive delay line using a chirped fiber bragg grating,” IEEE Photonics Technol. Lett. 27(10), 1044–1135 (2015).
[Crossref]

Piqueras, M. A.

Popov, M.

M. Popov, P.-Y. Fonjallaz, and O. Gunnarsson, “Compact microwave photonic transversal filter with 40-dB sidelobe suppression,” IEEE Photon. Technol. Lett. 17(3), 663–665 (2005).
[Crossref]

Prather, D. W.

Sagues, M.

A. Loayssa, J. Capmany, M. Sagues, and J. Mora, “Demonstration of incoherent microwave photonic filters with all-optical complex coefficients,” IEEE Photonics Technol. Lett. 18(16), 1744–1746 (2006).
[Crossref]

Sales, S.

Schneider, G. J.

Shi, S.

Shum, P. P.

Y. Jiang, P. P. Shum, P. Zu, J. Zhou, G. Bai, J. Xu, Z. Zhou, H. Li, and S. Wang, “A selectable multiband bandpass microwave photonic filter,” IEEE Photonics J. 5(3), 5500509 (2013).
[Crossref]

Torregrosa, A. J.

G. Peraita, A. J. Torregrosa, H. Maestre, and C. R. Fernandez-Pousa, “Broadband linearization of dispersive delay line using a chirped fiber bragg grating,” IEEE Photonics Technol. Lett. 27(10), 1044–1135 (2015).
[Crossref]

Vidal, B.

J. Palaci, G. E. Villanueva, J. V. Galan, J. Marti, and B. Vidal, “Single bandpass photonic microwave filter based on a notch ring resonator,” IEEE Photonics Technol. Lett. 22(17), 1276–1278 (2010).
[Crossref]

B. Vidal, M. A. Piqueras, and J. Martí, “Tunable and reconfigurable photonic microwave filter based on stimulated Brillouin scattering,” Opt. Lett. 32(1), 23–25 (2007).
[Crossref] [PubMed]

Villanueva, G. E.

J. Palaci, G. E. Villanueva, J. V. Galan, J. Marti, and B. Vidal, “Single bandpass photonic microwave filter based on a notch ring resonator,” IEEE Photonics Technol. Lett. 22(17), 1276–1278 (2010).
[Crossref]

Wang, J.-W.

J.-C. Liu, J.-W. Wang, B.-H. Zeng, and D.-C. Chang, “CPW-fed dual-mode double-square-ring resonators for quad-band filters,” IEEE Microw. Wirel. Compon. Lett. 20(3), 142–144 (2010).
[Crossref]

Wang, S.

Y. Jiang, P. P. Shum, P. Zu, J. Zhou, G. Bai, J. Xu, Z. Zhou, H. Li, and S. Wang, “A selectable multiband bandpass microwave photonic filter,” IEEE Photonics J. 5(3), 5500509 (2013).
[Crossref]

Wu, C.

Wu, H.

Xu, E.

X. Han, E. Xu, W. Liu, and J. Yao, “Tunable dual-passband microwave photonic filter using orthogonal polarization modulation,” IEEE Photon. Technol. Lett.to be published.

Xu, H.

Xu, J.

Y. Jiang, P. P. Shum, P. Zu, J. Zhou, G. Bai, J. Xu, Z. Zhou, H. Li, and S. Wang, “A selectable multiband bandpass microwave photonic filter,” IEEE Photonics J. 5(3), 5500509 (2013).
[Crossref]

Xu, Z.

Xue, Q.

L. Gao, X. Y. Zhang, B.-J. Hu, and Q. Xue, “Novel multi-stub loaded resonators and their applications to various bandpass filters,” IEEE Trans. Microw. Theory Tech. 62(5), 1162–1172 (2014).
[Crossref]

Xue, X.

Yao, J.

L. Gao, J. Zhang, X. Chen, and J. Yao, “Microwave photonic filter with two independently tunable passbands using a phase modulator and an equivalent phase-shifted fiber bragg grating,” IEEE Trans. Microw. Theory Tech. 62(2), 380–387 (2014).
[Crossref]

W. Li and J. Yao, “A wideband frequency tunable optoelectronic oscillator incorporating a tunable microwave photonic filter based on phase-modulation to intensity-modulation conversion using a phase-shifted fiber Bragg grating,” IEEE Trans. Microw. Theory Tech. 60(6), 1735–1742 (2012).
[Crossref]

J. Yao, “Microwave photonics,” J. Lightwave Technol. 54(2), 832–846 (2006).

F. Zeng and J. Yao, “All-optical bandpass microwave filter based on an electro-optic phase modulator,” Opt. Express 12(16), 3814–3819 (2004).
[Crossref] [PubMed]

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J. Lightwave Technol. (4)

Opt. Express (4)

Opt. Lett. (4)

Other (1)

X. Han, E. Xu, W. Liu, and J. Yao, “Tunable dual-passband microwave photonic filter using orthogonal polarization modulation,” IEEE Photon. Technol. Lett.to be published.

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Figures (11)

Fig. 1
Fig. 1 Schematic diagram of the proposed MPF with multiple independently tunable passbands. Broadband optical source: BOS, optical filter: OF, optical delay line: ODL, variable optical attenuator: VOA, phase modulator: PM, polarization controller: PC, dispersion compensation fiber: DCF, erbium-doped fiber amplifier: EDFA, photodetector: PD, vector network analyzer: VNA.
Fig. 2
Fig. 2 Illustration of the optical signal before and after the DCF. Blue lines: the optical signal after phase modulating. Red lines: the optical signal delayed by ODL1. Yellow lines: the optical signal delayed by ODL2.
Fig. 3
Fig. 3 The optical spectrum of the BOS after OF.
Fig. 4
Fig. 4 The frequency response with two passbands.
Fig. 5
Fig. 5 The measured (black line) and simulated (red line) bandpass responses centered at 8 GHz and 14 GHz, respectively. The magnitude is normalized.
Fig. 6
Fig. 6 (a) The 1st passband is fixed while the 2nd passband is tuned. (b) The 2nd passband is fixed while the 1st passband is tuned.
Fig. 7
Fig. 7 The stability of the center frequency and magnitude of (a) 1st passband and (b) 2nd passband in 1.5 h with 5 min interval.
Fig. 8
Fig. 8 The measured fundamental power and the third order intermodulation power for the (a) 1st passband and (b) 2nd passband of the MPF.
Fig. 9
Fig. 9 An alternative configuration of MPF with multiple passbands based on a BOS.
Fig. 10
Fig. 10 Illustration of the optical signal before and after the DCF. Blue lines: the optical signal after phase modulating. Red lines: the optical signal delayed by ODL1. Yellow lines: the optical signal delayed by ODL2.
Fig. 11
Fig. 11 Measured frequency response (blue line) and the simulation CSE curve (red line). The magnitude is normalized.

Equations (35)

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e(t)= 1 2π E(Ω)exp(jΩt)dΩ ,
E(Ω)= N(Ω) expjθ(Ω),
<expjθ(Ω)>=0 <expj[θ(Ω)θ( Ω )]>=2πδ(Ω Ω ),
e (t) P = k P e(t)exp[ jγcos( ω e t) ]= k P e(t) n= j n J n (γ)exp(jn ω e t) k P e(t)[ J 0 (γ)+j J 1 (γ)exp(j ω e t)+j J 1 (γ)exp(j ω e t)],
E P (Ω)= k P J 0 (γ)E(Ω)+j k P J 1 (γ)E(Ω ω e )+j k P J 1 (γ)E(Ω+ ω e ).
E 1 (Ω)= k 1 exp(jΩ t 1 )E(Ω).
E 2 (Ω)= k 2 exp(jΩ t 2 )E(Ω).
E C (Ω)= E P (Ω)+ E 1 (Ω)+ E 2 (Ω).
T(Ω)=| T(Ω) |exp[jΦ(Ω)].
Φ(Ω)=Φ( Ω 0 )+ τ 0 (Ω Ω 0 )+ 1 2 D Ω (Ω Ω 0 ) 2 ,
E PD (Ω)= E C (Ω)T(Ω).
I(t)= e PD (t) e PD * (t) .
I(ω)= 1 2π E PD (ω) E PD * (ω) = 2π E C (Ω) E C * (Ωω) T(Ω) T * (Ωω)dΩ ,
H RF (ω)=I(ω)/{ π V e [ δ(ω ω e )+δ(ω+ ω e ) ] }= H 0 (ω)+ H 1 (ω)+ H 2 (ω)
H 0 (ω)= 2 k P 2 J 0 (γ) J 1 (γ) π V e exp(jω τ 0 )sin( D Ω ω 2 /2) H b (ω),
H 1 (ω)= 2 k 1 k P J 1 (γ) π V e exp(ω τ 0 ) N(Ω)exp[j D Ω (Ω Ω 0 )ω]sin(Ω t 1 D Ω ω 2 /2)dΩ = k 1 k P J 1 (γ) π V e expj(π/2ω τ 0 D Ω ω 2 /2+ t 1 Ω 0 ) H b (ω t 1 D Ω ) + k 1 k P J 1 (γ) π V e expj(π/2ω τ 0 + D Ω ω 2 /2 t 1 Ω 0 ) H b (ω+ t 1 D Ω )
H 2 (ω)= 2 k 1 k P J 1 (γ) π V e exp(ω τ 0 ) N(Ω)exp[j D Ω (Ω Ω 0 )ω]sin(Ω t 2 D Ω ω 2 /2)dΩ = k 2 k P J 1 (γ) π V e expj(π/2ω τ 0 D Ω ω 2 /2+ t 2 Ω 0 ) H b (ω t 2 D Ω ) + k 2 k P J 1 (γ) π V e expj(π/2ω τ 0 + D Ω ω 2 /2 t 2 Ω 0 ) H b (ω+ t 2 D Ω ),
H n (ω)N( Ω n )ΔΩsin( Ω n t D Ω ω 2 /2)exp[ jω τ d ( Ω n ) ]
H RF (ω) n= [ N( Ω n )ΔΩsin( Ω n t D Ω ω 2 /2) ] exp[ jω τ d ( Ω n ) ] = N(Ω)sin(Ω t D Ω ω 2 /2) exp[ jω τ d (Ω) ]dΩ =exp(jω τ 0 ) N(Ω)sin(Ω t D Ω ω 2 /2) exp[ jω D Ω (Ω Ω 0 ) ]dΩ.
H RF (ω) j 2 n= [ N( Ω n )Δ Ω n expj( Ω n t D Ω ω 2 /2) ] exp[ jω τ d ( Ω n ) ] + j 2 n= [ N( Ω n )Δ Ω n expj( Ω n t + D Ω ω 2 /2) ] exp[ jω τ d ( Ω n ) ]
N(Ω)={ N| Ω Ω 0 |<ΔΩ/2 0other ,
H b (ω)=NΔΩsinc(ω D Ω ΔΩ/2).
E C (Ω)=E(Ω)+exp(j t 1 Ω)E(Ω)+exp(j t 2 Ω)E(Ω).
E P (Ω)= J 0 (γ) E C (Ω)+j J 1 (γ) E C (Ω ω e )+j J 1 (γ) E C (Ω+ ω e ) = J 0 (γ)E(Ω)+j J 1 (γ)E(Ω ω e )+j J 1 (γ)E(Ω+ ω e ) + J 0 (γ)exp(j t 1 Ω)E(Ω)+j J 1 (γ)exp[j t 1 (Ω ω e )]E(Ω ω e )+j J 1 (γ)exp[j t 1 (Ω+ ω e )]E(Ω+ ω e ) + J 0 (γ)exp(j t 2 Ω)E(Ω)+j J 1 (γ)exp[j t 2 (Ω ω e )]E(Ω ω e )+j J 1 (γ)exp[j t 2 (Ω+ ω e )]E(Ω+ ω e ).
H RF (ω)= H 0 (ω)+ H 1 (ω)+ H 2 (ω)+ H 3 (ω),
H 0 (ω)=3j J 0 (γ) J 1 (γ) π V e N(Ω) [ T(Ω+ω) T * (Ω)T(Ω) T * (Ωω) ]dΩ = 6 J 0 (γ) J 1 (γ) π V e exp(j τ d ω)sin( D Ω ω 2 /2) H b (ω),
H 1 + (ω)=j J 0 (γ) J 1 (γ) π V e exp(j τ 1 Ω)N(Ω)[ T(Ω+ω) T * (Ω)T(Ω) T * (Ωω) ] dΩ = 2 J 0 (γ) J 1 (γ) π V e expj( t 1 Ω 0 τ 0 ω)sin( D Ω ω 2 /2) H b (ω t 1 D Ω ),
H 2 + (ω)=j J 0 (γ) J 1 (γ) π V e exp(j τ 2 Ω)N(Ω)[ T(Ω+ω) T * (Ω)T(Ω) T * (Ωω) ] dΩ = 2 J 0 (γ) J 1 (γ) π V e expj( t 2 Ω 0 τ 0 ω)sin( D Ω ω 2 /2) H b (ω t 2 D Ω ),
H 3 + (ω)=j J 0 (γ) J 1 (γ) π V e exp[j( t 2 t 1 )Ω]N(Ω)[ T(Ω+ω) T * (Ω)T(Ω) T * (Ωω) ] dΩ = 2 J 0 (γ) J 1 (γ) π V e expj[( t 2 t 1 ) Ω 0 τ 0 ω]sin( D Ω ω 2 /2) H b (ω t 2 t 1 D Ω ).
I(ω)= 2π E C (Ω) E C * (Ωω) T(Ω) T * (Ωω)dΩ = 2π [ k P J 0 (γ)E(Ω)+j k P J 1 (γ)E(Ω ω e )+j k P J 1 (γ)E(Ω+ ω e )+ E 1 (Ω)+ E 2 (Ω) ] [ k P J 0 (γ) E * (Ωω)j k P J 1 (γ) E * (Ωω ω e )j k P J 1 (γ) E * (Ωω+ ω e )+ E 1 * (Ωω)+ E 2 * (Ωω) ] T(Ω) T * (Ωω)dΩ
I 0 (ω)= 2π j k p 2 J 0 (γ) J 1 (γ)E(Ω) E * (Ωω ω e ) j k p 2 J 0 (γ) J 1 (γ)E(Ω) E * (Ωω+ω ) e +j k p 2 J 0 (γ) J 1 (γ)E(Ω ω e ) E * (Ωω)+j k p 2 J 0 (γ) J 1 (γ)E(Ω+ ω e ) E * (Ωω) T(Ω) T * (Ωω)dΩ = 2π j k p 2 J 0 (γ) J 1 (γ) [ N(Ω) N(Ωω ω e ) 2πδ(ω+ ω e ) N(Ω) N(Ωω+ ω e ) 2πδ(ω ω e ) + N(Ω ω e ) N(Ωω) 2πδ(ω ω e )+ N(Ω+ ω e ) N(Ωω) 2πδ(ω+ ω e ) ]T(Ω) T * (Ωω)dΩ =j k P 2 J 0 (γ) J 1 (γ) N(Ω) [ H(Ω+ω) H * (Ω)H(Ω) H * (Ωω) ]dΩ[ δ(ω+ ω e )+δ(ω ω e ) ]
H 0 (ω)= I 0 (ω) π V e [ δ(ω ω e )+δ(ω+ ω e ) ] = 2 k P 2 J 0 (γ) J 1 (γ) π V e exp(jω τ 0 )sin( D Ω ω 2 /2) H b (ω)
I 1 (ω)= 2π E 1 * (Ωω)j k p J 1 (γ)E(Ω ω e )+ E 1 * (Ωω)j k p J 1 (γ)E(Ω+ ω e ) + E 1 (Ω)(j k p J(γ)) E * (Ωω ω e )+ E 1 (Ω)(j k p J(γ)) E * (Ωω+ ω e ) T(Ω) T * (Ωω)dΩ = 2π j k 1 k p J 1 (γ){ exp[j(Ωω) τ 1 ] N(Ωω) N(Ω ω e ) 2πδ(ω ω e )T(Ω) T * (Ωω)dΩ + exp[j(Ωω) τ 1 ] N(Ωω) N(Ω+ ω e ) 2πδ(ω+ ω e )T(Ω) T * (Ωω)dΩ exp(jΩ τ 1 ) N(Ω) N(Ωω ω e ) 2πδ(ω+ ω e )T(Ω) T * (Ωω)dΩ exp(jΩ τ 1 ) N(Ω) N(Ωω+ ω e ) 2πδ(ω ω e )T(Ω) T * (Ωω)dΩ } =j k 1 k p J 1 (γ){ [ δ(ω ω e )+δ(ω+ ω e ) ] exp[j(Ωω) τ 1 ]N(Ωω)T(Ω) T * (Ωω)dΩ [ δ(ω ω e )+δ(ω+ ω e ) ] exp(jΩ τ 1 )N(Ω)T(Ω) T * (Ωω)dΩ } =j k 1 k p J 1 (γ){ N(Ω)[ exp(jΩ τ 1 )T(Ω+ω) T * (Ω)exp(jΩ τ 1 )T(Ω) T * (Ωω) ]dΩ } [ δ(ω ω e )+δ(ω+ ω e ) ]
H 1 (ω)= I 1 (ω) π V e [ δ(ω ω e )+δ(ω+ ω e ) ] = 2 k 1 k P J 1 (γ) π V e exp(ω τ 0 ) N(Ω)exp[j D Ω (Ω Ω 0 )ω]sin(Ω t 1 D Ω ω 2 /2)dΩ
I int (ω)= 2π E 1 (Ω) E 2 * (Ωω)+ E 1 * (Ωω) E 2 (Ω) T(Ω) T * (Ωω)dΩ = 2π [ k 1 k 2 exp(jΩ τ 1 )exp[j(Ωω) τ 2 ] E(Ω) E * (Ωω) + k 1 k 2 exp[j(Ωω) τ 1 ]exp(jΩ τ 2 ) E(Ω) E * (Ωω) ]T(Ω) T * (Ωω)dΩ = 2π k 1 k 2 { exp[jΩ τ 1 +j(Ωω) τ 2 ]+exp[j(Ωω) τ 1 jΩ τ 2 ] } N(Ω) N(Ωω) 2π δ(ω) T(Ω) T * (Ωω)dΩ = k 1 k 2 2cos[Ω( τ 2 τ 1 )] N(Ω)T(Ω) T * (Ω)dΩδ(ω)

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