Abstract

We present a theoretical and experimental analysis of nonlinear microwave photonic filters. Far from the conventional condition of low modulation index commonly used to neglect high-order terms, we have analyzed the harmonic distortion involved in microwave photonic structures with periodic and non-periodic frequency responses. We show that it is possible to design microwave photonic filters with reduced harmonic distortion and high linearity even under large signal operation.

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References

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  1. J. Capmany and D. Novak, “Microwave photonics combines two worlds,” Nat. Photonics 1(6), 319–330 (2007).
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  2. J. Yao, “Microwave photonics,” J. Lightwave Technol. 27(3), 314–335 (2009).
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    [CrossRef]
  4. R. A. Minasian, K. E. Alameb, and E. H. W. Chan, “Photonics-based interference mitigation,” IEEE Trans. Microw. Theory Tech. 49(10), 1894–1899 (2001).
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  5. M. Bolea, J. Mora, B. Ortega, and J. Capmany, “Photonic arbitrary waveform generation applicable to multiband UWB communications,” Opt. Express 18(25), 26259–26267 (2010).
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  6. J. Dai, K. Xu, X. Sun, Y. Li, J. Niu, Q. Lv, J. Wu, X. Hong, and J. Lin, “Instantaneous frequency measurement system with tunable measurements range utilizing fiber-based incoherent microwave photonic filters,” in Proc. Microwave Photonics 2010 MWP ’10. Int. Topical Meeting on, Montreal, 1–4 (2010).
  7. J. Capmany, D. Pastor, and B. Ortega, “New and flexible fiber-optic delay line filters using chirped Bragg gratings and laser arrays,” IEEE Trans. Microw. Theory Tech. 47(7), 1321–1326 (1999).
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  8. J. Mora, B. Ortega, J. Capmany, J. Cruz, M. Andres, D. Pastor, and S. Sales, “Automatic tunable and reconfigurable fiberoptic microwave filters based on a broadband optical source sliced by uniform fiber Bragg gratings,” Opt. Express 10(22), 1291–1298 (2002).
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  11. Y. Dai and J. Yao, “Nonuniformly-spaced photonic microwave delayline filter,” Opt. Express 16(7), 4713–4718 (2008).
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  12. J. Mora, B. Ortega, A. Díez, J. L. Cruz, M. V. Andrés, J. Capmany, and D. Pastor, “Photonic microwave tunable single-bandpass filter based on a Mach-Zehnder Interferometer,” J. Lightwave Technol. 24(7), 2500–2509 (2006).
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2011 (1)

2010 (1)

2009 (1)

2008 (1)

2007 (1)

J. Capmany and D. Novak, “Microwave photonics combines two worlds,” Nat. Photonics 1(6), 319–330 (2007).
[CrossRef]

2006 (2)

2005 (1)

2002 (1)

2001 (1)

R. A. Minasian, K. E. Alameb, and E. H. W. Chan, “Photonics-based interference mitigation,” IEEE Trans. Microw. Theory Tech. 49(10), 1894–1899 (2001).
[CrossRef]

1999 (1)

J. Capmany, D. Pastor, and B. Ortega, “New and flexible fiber-optic delay line filters using chirped Bragg gratings and laser arrays,” IEEE Trans. Microw. Theory Tech. 47(7), 1321–1326 (1999).
[CrossRef]

1980 (1)

Alameb, K. E.

R. A. Minasian, K. E. Alameb, and E. H. W. Chan, “Photonics-based interference mitigation,” IEEE Trans. Microw. Theory Tech. 49(10), 1894–1899 (2001).
[CrossRef]

Andres, M.

Andrés, M. V.

Bolea, M.

Capmany, J.

Chan, E. H. W.

R. A. Minasian, K. E. Alameb, and E. H. W. Chan, “Photonics-based interference mitigation,” IEEE Trans. Microw. Theory Tech. 49(10), 1894–1899 (2001).
[CrossRef]

Cruz, J.

Cruz, J. L.

Dai, Y.

Díez, A.

Huang, T. X. H.

Marcuse, D.

Minasian, R. A.

T. X. H. Huang, X. Yi, and R. A. Minasian, “Single passband microwave photonic filter using continuous-time impulse response,” Opt. Express 19(7), 6231–6242 (2011).
[CrossRef] [PubMed]

R. A. Minasian, K. E. Alameb, and E. H. W. Chan, “Photonics-based interference mitigation,” IEEE Trans. Microw. Theory Tech. 49(10), 1894–1899 (2001).
[CrossRef]

Mora, J.

Novak, D.

J. Capmany and D. Novak, “Microwave photonics combines two worlds,” Nat. Photonics 1(6), 319–330 (2007).
[CrossRef]

Ortega, B.

Pastor, D.

Sales, S.

Yao, J.

Yi, X.

Appl. Opt. (1)

IEEE Trans. Microw. Theory Tech. (2)

R. A. Minasian, K. E. Alameb, and E. H. W. Chan, “Photonics-based interference mitigation,” IEEE Trans. Microw. Theory Tech. 49(10), 1894–1899 (2001).
[CrossRef]

J. Capmany, D. Pastor, and B. Ortega, “New and flexible fiber-optic delay line filters using chirped Bragg gratings and laser arrays,” IEEE Trans. Microw. Theory Tech. 47(7), 1321–1326 (1999).
[CrossRef]

J. Lightwave Technol. (3)

Nat. Photonics (1)

J. Capmany and D. Novak, “Microwave photonics combines two worlds,” Nat. Photonics 1(6), 319–330 (2007).
[CrossRef]

Opt. Express (5)

Other (1)

J. Dai, K. Xu, X. Sun, Y. Li, J. Niu, Q. Lv, J. Wu, X. Hong, and J. Lin, “Instantaneous frequency measurement system with tunable measurements range utilizing fiber-based incoherent microwave photonic filters,” in Proc. Microwave Photonics 2010 MWP ’10. Int. Topical Meeting on, Montreal, 1–4 (2010).

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Figures (4)

Fig. 1
Fig. 1

Scheme of a microwave photonic filter when harmonic distortion is considered.

Fig. 2
Fig. 2

Experimental setup for measurements of the electrical transfer function in microwave photonic filters with harmonic distorsion. Inset (a) corresponds to uniform profile sliced combining AWGs and inset (b) to gaussian profile sliced by MZI.

Fig. 3
Fig. 3

Experimental (solid line) and theoretical (dashed line) RF power of (a) fundamental tone, (b) second harmonic and (c) third harmonic for (left column) AWGs slicing and (right column) MZI slicing. Dotted line represents theoretical CSE for (a) fundamental tone, (b) second harmonic and (c) third harmonic.

Fig. 4
Fig. 4

Experimental (dotted line) and theoretical (solid line) RF power of (■) fundamental tone, (●) second and (▲) third harmonic for (a) AWGs and (b) MZI slicing as a function of RF input power.

Equations (6)

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e IN (t)= 1 2π n= + { + s n ( V o ) E s ( ω ) e j( ω+nΩ )t dω }
e OUT (t)= 1 2π n= + { + s n E s ( ω ) H opt ( ω+nΩ ) e j( ω+nΩ )t dω }
V RF OUT (t)= | e OUT (t) | 2 Z o
V RF OUT (t)= V o 2 k= + H k RF ( Ω ) e jkΩt +c.c.
H opt ( ω )= e jβ( ω )L with β( ω )= β o ( ω o )+ β 1 ( ω ω o )+ 1 2 β 2 ( ω ω o ) 2 .
H k RF (Ω)= P o Z o π V o e j β 1 L( kΩ ) n= + s n s nk * e j 1 2 β 2 L( k2n ) Ω 2 CSE + | E( ω ) | 2 e j β 2 L( ω ω o )( kΩ ) dω + | E( ω ) | 2 dω

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