Abstract

We report a novel approach to generating full-duty-cycle triangular waveforms based on a microwave photonic filter (MPF) with negative coefficient. It is known that the Fourier series expansion of a triangular waveform has only odd-order harmonics. In this work, the undesired even-order harmonics are suppressed by the MPF that has a periodic transmission response. A triangular waveform at fundamental frequency can be generated by setting the bias of a Mach-Zehnder modulator (MZM) at quadrature point. However, it is found that a broadband 90° microwave phase shifter has to be used after photodetection to adjust the phases of odd-order harmonics. Alternatively, a frequency doubling triangular waveform can be generated by setting the bias of the MZM at maximum or minimum transmission point. This approach is more promising because the broadband microwave phase shifter is no longer required in this case but it is more power consuming. The proposed approach is theoretically analyzed and experimentally verified.

© 2014 Optical Society of America

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  1. J. Yao, “Photonic generation of microwave arbitrary waveforms,” Opt. Commun. 284(15), 3723–3736 (2011).
    [CrossRef]
  2. A. I. Latkin, S. Boscolo, R. S. Bhamber, and S. K. Turitsyn, “Optical frequency conversion, pulse compression and signal copying using triangular pulses,” in ECOC, Brussels, Belgium (2008), Paper Mo.3.F.4.
  3. A. I. Latkin, S. Boscolo, R. S. Bhamber, and S. K. Turitsyn, “Doubling of optical signals using triangular pulses,” J. Opt. Soc. Am. B 26(8), 1492–1496 (2009).
    [CrossRef]
  4. J. Chou, Y. Han, and B. Jalali, “Adaptive RF-photonic arbitrary waveform generator,” IEEE Photon. Technol. Lett. 15(4), 581–583 (2003).
    [CrossRef]
  5. J. Ye, L. Yan, W. Pan, B. Luo, X. Zou, A. Yi, and S. Yao, “Photonic generation of triangular-shaped pulses based on frequency-to-time conversion,” Opt. Lett. 36(8), 1458–1460 (2011).
    [CrossRef] [PubMed]
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    [CrossRef]
  7. J. Li, T. Ning, L. Pei, W. Peng, N. Jia, Q. Zhou, and X. Wen, “Photonic generation of triangular waveform signals by using a dual-parallel Mach-Zehnder modulator,” Opt. Lett. 36(19), 3828–3830 (2011).
    [CrossRef] [PubMed]
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    [CrossRef]
  9. J. Li, T. Ning, L. Pei, W. Jian, H. You, H. Chen, and C. Zhang, “Photonic-assisted periodic triangular-shaped pulses generation with tunable repetition rate,” IEEE Photon. Technol. Lett. 25(10), 952–954 (2013).
    [CrossRef]
  10. F. Zhang, X. Ge, and S. Pan, “Triangular pulse generation using a dual-parallel Mach-Zehnder modulator driven by a single-frequency radio frequency signal,” Opt. Lett. 38(21), 4491–4493 (2013).
    [CrossRef] [PubMed]
  11. W. Li, W. T. Wang, and N. H. Zhu, “Photonic generation of radio-frequency waveforms based on dual-parallel Mach-Zehnder modulator,” IEEE Photon. J. 6(3), 5500608 (2014).
  12. W. Liu and J. Yao, “Photonic generation of microwave waveforms based on a polarization modulator in a Sagnac loop,” J. Lightwave Technol. (to be published).
  13. X. Liu, W. Pan, X. Zou, D. Zheng, L. Yan, B. Luo, and B. Lu, “Photonic generation of triangular-shaped microwave pules using SBS-based optical carrier processing,” J. Lightwave Technol. (to be published).
  14. J. Capmany, B. Ortega, and D. Pastor, “A tutorial on microwave photonic filters,” J. Lightwave Technol. 24(1), 201–229 (2006).
    [CrossRef]

2014

W. Li, W. T. Wang, and N. H. Zhu, “Photonic generation of radio-frequency waveforms based on dual-parallel Mach-Zehnder modulator,” IEEE Photon. J. 6(3), 5500608 (2014).

Z. Wu, L. Lei, J. Dong, and X. Zhang, “Triangular-shaped pulse generation based on self-convolution of a rectangular-shaped pulse,” Opt. Lett. 39(8), 2258–2261 (2014).
[CrossRef]

2013

F. Zhang, X. Ge, and S. Pan, “Triangular pulse generation using a dual-parallel Mach-Zehnder modulator driven by a single-frequency radio frequency signal,” Opt. Lett. 38(21), 4491–4493 (2013).
[CrossRef] [PubMed]

J. Li, T. Ning, L. Pei, W. Jian, H. You, H. Chen, and C. Zhang, “Photonic-assisted periodic triangular-shaped pulses generation with tunable repetition rate,” IEEE Photon. Technol. Lett. 25(10), 952–954 (2013).
[CrossRef]

2012

2011

2009

2006

2003

J. Chou, Y. Han, and B. Jalali, “Adaptive RF-photonic arbitrary waveform generator,” IEEE Photon. Technol. Lett. 15(4), 581–583 (2003).
[CrossRef]

Bhamber, R. S.

Boscolo, S.

Capmany, J.

Chen, H.

J. Li, T. Ning, L. Pei, W. Jian, H. You, H. Chen, and C. Zhang, “Photonic-assisted periodic triangular-shaped pulses generation with tunable repetition rate,” IEEE Photon. Technol. Lett. 25(10), 952–954 (2013).
[CrossRef]

Chou, J.

J. Chou, Y. Han, and B. Jalali, “Adaptive RF-photonic arbitrary waveform generator,” IEEE Photon. Technol. Lett. 15(4), 581–583 (2003).
[CrossRef]

Dong, J.

Ge, X.

Han, Y.

J. Chou, Y. Han, and B. Jalali, “Adaptive RF-photonic arbitrary waveform generator,” IEEE Photon. Technol. Lett. 15(4), 581–583 (2003).
[CrossRef]

Hraimel, B.

Jalali, B.

J. Chou, Y. Han, and B. Jalali, “Adaptive RF-photonic arbitrary waveform generator,” IEEE Photon. Technol. Lett. 15(4), 581–583 (2003).
[CrossRef]

Jia, N.

Jian, W.

J. Li, T. Ning, L. Pei, W. Jian, H. You, H. Chen, and C. Zhang, “Photonic-assisted periodic triangular-shaped pulses generation with tunable repetition rate,” IEEE Photon. Technol. Lett. 25(10), 952–954 (2013).
[CrossRef]

Latkin, A. I.

Lei, L.

Li, J.

Li, W.

W. Li, W. T. Wang, and N. H. Zhu, “Photonic generation of radio-frequency waveforms based on dual-parallel Mach-Zehnder modulator,” IEEE Photon. J. 6(3), 5500608 (2014).

Liu, X.

X. Liu, W. Pan, X. Zou, D. Zheng, L. Yan, B. Luo, and B. Lu, “Photonic generation of triangular-shaped microwave pules using SBS-based optical carrier processing,” J. Lightwave Technol. (to be published).

Lu, B.

X. Liu, W. Pan, X. Zou, D. Zheng, L. Yan, B. Luo, and B. Lu, “Photonic generation of triangular-shaped microwave pules using SBS-based optical carrier processing,” J. Lightwave Technol. (to be published).

Luo, B.

J. Ye, L. Yan, W. Pan, B. Luo, X. Zou, A. Yi, and S. Yao, “Photonic generation of triangular-shaped pulses based on frequency-to-time conversion,” Opt. Lett. 36(8), 1458–1460 (2011).
[CrossRef] [PubMed]

X. Liu, W. Pan, X. Zou, D. Zheng, L. Yan, B. Luo, and B. Lu, “Photonic generation of triangular-shaped microwave pules using SBS-based optical carrier processing,” J. Lightwave Technol. (to be published).

Ning, T.

Ortega, B.

Pan, S.

Pan, W.

J. Ye, L. Yan, W. Pan, B. Luo, X. Zou, A. Yi, and S. Yao, “Photonic generation of triangular-shaped pulses based on frequency-to-time conversion,” Opt. Lett. 36(8), 1458–1460 (2011).
[CrossRef] [PubMed]

X. Liu, W. Pan, X. Zou, D. Zheng, L. Yan, B. Luo, and B. Lu, “Photonic generation of triangular-shaped microwave pules using SBS-based optical carrier processing,” J. Lightwave Technol. (to be published).

Pastor, D.

Pei, L.

Peng, W.

Turitsyn, S. K.

Wang, W. T.

W. Li, W. T. Wang, and N. H. Zhu, “Photonic generation of radio-frequency waveforms based on dual-parallel Mach-Zehnder modulator,” IEEE Photon. J. 6(3), 5500608 (2014).

Wen, X.

Wu, K.

Wu, Z.

Yan, L.

J. Ye, L. Yan, W. Pan, B. Luo, X. Zou, A. Yi, and S. Yao, “Photonic generation of triangular-shaped pulses based on frequency-to-time conversion,” Opt. Lett. 36(8), 1458–1460 (2011).
[CrossRef] [PubMed]

X. Liu, W. Pan, X. Zou, D. Zheng, L. Yan, B. Luo, and B. Lu, “Photonic generation of triangular-shaped microwave pules using SBS-based optical carrier processing,” J. Lightwave Technol. (to be published).

Yao, J.

J. Yao, “Photonic generation of microwave arbitrary waveforms,” Opt. Commun. 284(15), 3723–3736 (2011).
[CrossRef]

Yao, S.

Ye, J.

Yi, A.

You, H.

J. Li, T. Ning, L. Pei, W. Jian, H. You, H. Chen, and C. Zhang, “Photonic-assisted periodic triangular-shaped pulses generation with tunable repetition rate,” IEEE Photon. Technol. Lett. 25(10), 952–954 (2013).
[CrossRef]

Zhang, C.

J. Li, T. Ning, L. Pei, W. Jian, H. You, H. Chen, and C. Zhang, “Photonic-assisted periodic triangular-shaped pulses generation with tunable repetition rate,” IEEE Photon. Technol. Lett. 25(10), 952–954 (2013).
[CrossRef]

Zhang, F.

Zhang, X.

Zheng, D.

X. Liu, W. Pan, X. Zou, D. Zheng, L. Yan, B. Luo, and B. Lu, “Photonic generation of triangular-shaped microwave pules using SBS-based optical carrier processing,” J. Lightwave Technol. (to be published).

Zhou, Q.

Zhu, N. H.

W. Li, W. T. Wang, and N. H. Zhu, “Photonic generation of radio-frequency waveforms based on dual-parallel Mach-Zehnder modulator,” IEEE Photon. J. 6(3), 5500608 (2014).

Zou, X.

J. Ye, L. Yan, W. Pan, B. Luo, X. Zou, A. Yi, and S. Yao, “Photonic generation of triangular-shaped pulses based on frequency-to-time conversion,” Opt. Lett. 36(8), 1458–1460 (2011).
[CrossRef] [PubMed]

X. Liu, W. Pan, X. Zou, D. Zheng, L. Yan, B. Luo, and B. Lu, “Photonic generation of triangular-shaped microwave pules using SBS-based optical carrier processing,” J. Lightwave Technol. (to be published).

IEEE Photon. J.

W. Li, W. T. Wang, and N. H. Zhu, “Photonic generation of radio-frequency waveforms based on dual-parallel Mach-Zehnder modulator,” IEEE Photon. J. 6(3), 5500608 (2014).

IEEE Photon. Technol. Lett.

J. Chou, Y. Han, and B. Jalali, “Adaptive RF-photonic arbitrary waveform generator,” IEEE Photon. Technol. Lett. 15(4), 581–583 (2003).
[CrossRef]

J. Li, T. Ning, L. Pei, W. Jian, H. You, H. Chen, and C. Zhang, “Photonic-assisted periodic triangular-shaped pulses generation with tunable repetition rate,” IEEE Photon. Technol. Lett. 25(10), 952–954 (2013).
[CrossRef]

J. Lightwave Technol.

J. Opt. Soc. Am. B

Opt. Commun.

J. Yao, “Photonic generation of microwave arbitrary waveforms,” Opt. Commun. 284(15), 3723–3736 (2011).
[CrossRef]

Opt. Lett.

Other

W. Liu and J. Yao, “Photonic generation of microwave waveforms based on a polarization modulator in a Sagnac loop,” J. Lightwave Technol. (to be published).

X. Liu, W. Pan, X. Zou, D. Zheng, L. Yan, B. Luo, and B. Lu, “Photonic generation of triangular-shaped microwave pules using SBS-based optical carrier processing,” J. Lightwave Technol. (to be published).

A. I. Latkin, S. Boscolo, R. S. Bhamber, and S. K. Turitsyn, “Optical frequency conversion, pulse compression and signal copying using triangular pulses,” in ECOC, Brussels, Belgium (2008), Paper Mo.3.F.4.

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Figures (6)

Fig. 1
Fig. 1

Schematic diagrams of (a) the proposed triangular waveform generator, (b) and (c) the principle. LD: laser diode, MZM: Mach-Zehnder modulator, TODL: tunable optical delay line, BPD: balanced photodetector, VNA: vector network analyzer, ESA: electrical spectrum analyzer, OSC: oscilloscope.

Fig. 2
Fig. 2

Amplitude ratio between the third-order harmonic and the fundamental tone versus the modulation index of the MZM, β.

Fig. 3
Fig. 3

Measured transmission response of the MPF with a FSR of 10 GHz.

Fig. 4
Fig. 4

Measured (a), (c) electrical spectra and (b), (d) the waveforms when the MZM is biased at the quadrature point and a 90° broadband microwave phase shift was attached after the BPD (see Figs. 4(c) and 4(d)) or not (see Figs. 4(a) and 4(b)).

Fig. 5
Fig. 5

Measured (a), (c) electrical spectra and (b), (d) the corresponding waveforms when the MZM was biased at the maximum transmission point and the MPF was used to suppress the even-order harmonics (see Figs. 5(c) and 5(d)) or not (see Figs. 5(a) and 5(b)).

Fig. 6
Fig. 6

Measured (a) transmission response of the MPF with a FSR of 12 GHz, (b) electrical spectrum, and (c) triangular waveform at 6 GHz.

Equations (10)

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T ( t ) = D C + m = 1 , 3 , 5 1 m 2 cos ( m Ω t )
T ( t + t 0 ) = D C + m = 1 , 3 , 5 1 m 2 cos ( m Ω t + m Ω t 0 )
E(t)= 1 2 exp(j ω 0 t){exp[jβcos( ω m t)+j φ 2 ]+exp[jβcos( ω m t)j φ 2 ]}
E(t)= 1 2 exp(j ω 0 t){ n= j n J n exp(jn ω m t+j φ 2 )]+ n= (1) n j n J n exp(jn ω m tj φ 2 )}
i(t)= i pd1 (t) i pd2 (t) 1 2 E(t) E * (t) 1 2 E(t+ T 0 ) E * (t+ T 0 )
i(t)DC+ a 1 2 [cos( ω m t)cos( ω m t+ ω m T 0 )] + b 1 2 [cos(2 ω m t+π)cos(2 ω m t+π+2 ω m T 0 )] + c 1 2 [cos(3 ω m t+π)cos(3 ω m t+π+3 ω m T 0 )]
i(t)DC+ a 1 cos( ω m t)+ a 1 /9cos(3 ω m t+π)
i(t)DC+ a 1 cos( ω m t+π/2)+ a 1 /9cos(3 ω m t+3π/2)
i(t)DC+ a 2 2 [cos(2 ω m t+π)cos(2 ω m t+π+2 ω m T 0 )] + b 2 2 [cos(4 ω m t)cos(4 ω m t+4 ω m T 0 )] + c 2 2 [cos(6 ω m t+π)cos(6 ω m t+π+6 ω m T 0 )]
i(t)DC+ a 2 cos(2 ω m t+π)+ a 2 /9cos(6 ω m t+3π)

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