Abstract

A new photonic approach of microwave waveform generator based on time-domain synthesis is proposed and experimentally demonstrated, in which two single-drive Mach-Zehnder modulators biased at quadrature point are severed as optical pulse carvers and various microwave waveforms can be generated by carving and overlapping optical field envelopes. The theoretical analysis and simulation are developed. In experiment, a square waveform with 50% duty cycle, triangular waveform with full duty cycle, and sawtooth (or reversed-sawtooth) waveform with 50% duty cycle are generated. Furthermore, a frequency doubling sawtooth (or reversed-sawtooth) waveform with full duty cycle is also obtained.

© 2015 Optical Society of America

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References

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  1. 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.
  2. A. I. Latkin, S. Boscolo, R. S. Bhamber, and S. K. Turitsyn, “Doubling of optical signals using triangularpulses,” J. Opt. Soc. Am. B 26(8), 1492–1496 (2009).
    [Crossref]
  3. R. S. Bhamber, A. I. Latkin, S. Boscolo, and S. K. Turitsyn, “All-optical TDM to WDM signal conversion and partial regeneration using XPM with triangular pulses,” in ECOC, Brussels, Belgium (2008), paper Th.1.B.2.
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    [Crossref]
  5. Z. Jiang, C.-B. Huang, D. E. Leaird, and A. M. Weiner, “Optical arbitrary waveform processing of more than 100 spectral comb lines,” Nat. Photonics 1(8), 463–467 (2007).
    [Crossref]
  6. 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] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
  11. W. Liu and J. Yao, “Photonic generation of microwave waveforms based on a polarization modulator in a Sagnac loop,” J. Lightwave Technol. 32(20), 3637–3644 (2014).
    [Crossref]
  12. J. Li, T. G. Ning, L. Pei, W. Jian, H. D. You, H. Y. Chen, and C. Zhang, “Photonic-assisted periodic triangular-shaped pulses generation with tunable repetition rate,” IEEE Photonics Technol. Lett. 25(10), 952–954 (2013).
    [Crossref]
  13. W. Li, W. T. Wang, W. H. Sun, W. Y. Wang, and N. H. Zhu, “Generation of triangular waveforms based on a microwave photonic filter with negative coefficient,” Opt. Express 22(12), 14993–15001 (2014).
    [Crossref] [PubMed]
  14. X. Liu, W. Pan, X. Zou, D. Zheng, L. Yan, B. Luo, and B. Lu, “Photonic generation of triangular-shaped Microwave pulses using SBS-based optical carrier processing,” J. Lightwave Technol. 32(20), 3797–3802 (2014).
    [Crossref]
  15. D. S. Wu, D. J. Richardson, and R. Slavik, “Optical Fourier synthesis of high-repetition-rate pulses,” Optica 2(1), 18–26 (2015).
    [Crossref]
  16. Y. Jiang, C. Ma, G. Bai, Z. Jia, Y. Zi, S. Cai, T. Wu, and F. Huang, “Photonic generation of triangular waveform by utilizing time-domain synthesis,” IEEE Photonics Technol. Lett. 27(16), 1725–1728 (2015).
    [Crossref]
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    [Crossref] [PubMed]

2015 (3)

D. S. Wu, D. J. Richardson, and R. Slavik, “Optical Fourier synthesis of high-repetition-rate pulses,” Optica 2(1), 18–26 (2015).
[Crossref]

Y. Jiang, C. Ma, G. Bai, Z. Jia, Y. Zi, S. Cai, T. Wu, and F. Huang, “Photonic generation of triangular waveform by utilizing time-domain synthesis,” IEEE Photonics Technol. Lett. 27(16), 1725–1728 (2015).
[Crossref]

C. Finot, “40-GHz photonic waveform generator by linear shaping of four spectral sidebands,” Opt. Lett. 40(7), 1422–1425 (2015).
[Crossref] [PubMed]

2014 (3)

2013 (4)

2012 (1)

2011 (2)

2009 (1)

2007 (1)

Z. Jiang, C.-B. Huang, D. E. Leaird, and A. M. Weiner, “Optical arbitrary waveform processing of more than 100 spectral comb lines,” Nat. Photonics 1(8), 463–467 (2007).
[Crossref]

Bai, G.

Y. Jiang, C. Ma, G. Bai, Z. Jia, Y. Zi, S. Cai, T. Wu, and F. Huang, “Photonic generation of triangular waveform by utilizing time-domain synthesis,” IEEE Photonics Technol. Lett. 27(16), 1725–1728 (2015).
[Crossref]

Bhamber, R. S.

Boscolo, S.

Cai, S.

Y. Jiang, C. Ma, G. Bai, Z. Jia, Y. Zi, S. Cai, T. Wu, and F. Huang, “Photonic generation of triangular waveform by utilizing time-domain synthesis,” IEEE Photonics Technol. Lett. 27(16), 1725–1728 (2015).
[Crossref]

Chen, H.

Chen, H. Y.

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

Dai, B.

Finot, C.

Gao, Z.

Ge, X.

Hraimel, B.

Huang, C.-B.

Z. Jiang, C.-B. Huang, D. E. Leaird, and A. M. Weiner, “Optical arbitrary waveform processing of more than 100 spectral comb lines,” Nat. Photonics 1(8), 463–467 (2007).
[Crossref]

Huang, F.

Y. Jiang, C. Ma, G. Bai, Z. Jia, Y. Zi, S. Cai, T. Wu, and F. Huang, “Photonic generation of triangular waveform by utilizing time-domain synthesis,” IEEE Photonics Technol. Lett. 27(16), 1725–1728 (2015).
[Crossref]

Jia, Z.

Y. Jiang, C. Ma, G. Bai, Z. Jia, Y. Zi, S. Cai, T. Wu, and F. Huang, “Photonic generation of triangular waveform by utilizing time-domain synthesis,” IEEE Photonics Technol. Lett. 27(16), 1725–1728 (2015).
[Crossref]

Jian, W.

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

Jiang, H.-Y.

Jiang, Y.

Y. Jiang, C. Ma, G. Bai, Z. Jia, Y. Zi, S. Cai, T. Wu, and F. Huang, “Photonic generation of triangular waveform by utilizing time-domain synthesis,” IEEE Photonics Technol. Lett. 27(16), 1725–1728 (2015).
[Crossref]

Jiang, Z.

Z. Jiang, C.-B. Huang, D. E. Leaird, and A. M. Weiner, “Optical arbitrary waveform processing of more than 100 spectral comb lines,” Nat. Photonics 1(8), 463–467 (2007).
[Crossref]

Kataoka, N.

Latkin, A. I.

Leaird, D. E.

Z. Jiang, C.-B. Huang, D. E. Leaird, and A. M. Weiner, “Optical arbitrary waveform processing of more than 100 spectral comb lines,” Nat. Photonics 1(8), 463–467 (2007).
[Crossref]

Li, J.

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

J. Li, X. Zhang, B. Hraimel, T. Ning, L. Pei, and K. Wu, “Performance analysis of a photonic-assisted periodic triangular-shaped pulses generator,” J. Lightwave Technol. 30(11), 1617–1624 (2012).
[Crossref]

Li, W.

Liu, W.

Liu, X.

Lu, B.

Luo, B.

Ma, C.

Y. Jiang, C. Ma, G. Bai, Z. Jia, Y. Zi, S. Cai, T. Wu, and F. Huang, “Photonic generation of triangular waveform by utilizing time-domain synthesis,” IEEE Photonics Technol. Lett. 27(16), 1725–1728 (2015).
[Crossref]

Ning, T.

Ning, T. G.

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

Pan, S.

Pan, W.

Pei, L.

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

J. Li, X. Zhang, B. Hraimel, T. Ning, L. Pei, and K. Wu, “Performance analysis of a photonic-assisted periodic triangular-shaped pulses generator,” J. Lightwave Technol. 30(11), 1617–1624 (2012).
[Crossref]

Richardson, D. J.

Slavik, R.

Sun, W. H.

Sun, Y.-F.

Turitsyn, S. K.

Wada, N.

Wang, W. T.

Wang, W. Y.

Wang, X.

Weiner, A. M.

Z. Jiang, C.-B. Huang, D. E. Leaird, and A. M. Weiner, “Optical arbitrary waveform processing of more than 100 spectral comb lines,” Nat. Photonics 1(8), 463–467 (2007).
[Crossref]

Wu, D. S.

Wu, K.

Wu, T.

Y. Jiang, C. Ma, G. Bai, Z. Jia, Y. Zi, S. Cai, T. Wu, and F. Huang, “Photonic generation of triangular waveform by utilizing time-domain synthesis,” IEEE Photonics Technol. Lett. 27(16), 1725–1728 (2015).
[Crossref]

Yan, L.

Yan, L.-S.

Yao, J.

Yao, J. P.

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

Yao, S.

Ye, J.

Yi, A.

You, H. D.

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

Zhang, C.

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

Zhang, F.

Zhang, X.

Zheng, D.

Zhu, N. H.

Zi, Y.

Y. Jiang, C. Ma, G. Bai, Z. Jia, Y. Zi, S. Cai, T. Wu, and F. Huang, “Photonic generation of triangular waveform by utilizing time-domain synthesis,” IEEE Photonics Technol. Lett. 27(16), 1725–1728 (2015).
[Crossref]

Zou, X.

Zou, X.-H.

IEEE Photonics Technol. Lett. (2)

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

Y. Jiang, C. Ma, G. Bai, Z. Jia, Y. Zi, S. Cai, T. Wu, and F. Huang, “Photonic generation of triangular waveform by utilizing time-domain synthesis,” IEEE Photonics Technol. Lett. 27(16), 1725–1728 (2015).
[Crossref]

J. Lightwave Technol. (4)

J. Opt. Soc. Am. B (1)

Nat. Photonics (1)

Z. Jiang, C.-B. Huang, D. E. Leaird, and A. M. Weiner, “Optical arbitrary waveform processing of more than 100 spectral comb lines,” Nat. Photonics 1(8), 463–467 (2007).
[Crossref]

Opt. Commun. (1)

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

Opt. Express (2)

Opt. Lett. (3)

Optica (1)

Other (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.

R. S. Bhamber, A. I. Latkin, S. Boscolo, and S. K. Turitsyn, “All-optical TDM to WDM signal conversion and partial regeneration using XPM with triangular pulses,” in ECOC, Brussels, Belgium (2008), paper Th.1.B.2.

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Figures (9)

Fig. 1
Fig. 1 Schematic diagrams of the proposed microwave waveform generator. LD: laser diode, WDM: wavelength division multiplexer, PC: polarization controller, MZM: Mach-Zehnder modulator, ODL: optical delay line, SMF: single mode fiber, ATT: attenuator.
Fig. 2
Fig. 2 The calculated values of, (a) the coefficients of first-, second- and third-order harmonics of photocurrent, (b) the coefficient ratio between the first-order harmonic and third-order tone versus the modulation index of the MZM, β.
Fig. 3
Fig. 3 (a) Sinusoidally driven MZM as pulse carver for square-shaped waveform generation. (b) The calculated waveforms with β of 0.752 (dot line), 0.965 (solid line) and 1.141 (dash line).
Fig. 4
Fig. 4 Simulation result of a triangular waveform generation by the superimposition of two square-shaped waveforms with π/2 phase shift. The modulation index of a MZM is 0.752.
Fig. 5
Fig. 5 The graphic illustration of a sawtooth (or reversed-sawtooth) waveform generation by carving a square pulse with a triangular time window. The frequency doubling sawtooth (or reversed-sawtooth) waveform can be further generated by multiplexing technique.
Fig. 6
Fig. 6 Measured (a), (c), (e) square-shaped waveform and (b), (d), (f) the corresponding electrical spectra when the MZM is biased at the quadrature point with modulation index of 0.752, 0.965 and 1.141, respectively.
Fig. 7
Fig. 7 Experiment results. (a) Generated triangular waveform with repetition frequency of 3 GHz. (b) The corresponding electrical spectrum.
Fig. 8
Fig. 8 Measured waveforms and electrical spectra. (a) 3-GHz sawtooth waveform with 50% duty cycle. (b) The corresponding electrical spectrum. (c) 3-GHz reversed-sawtooth waveform with 50% duty cycle. (d) The corresponding electrical spectrum.
Fig. 9
Fig. 9 Measured waveforms and electrical spectra. (a), (b) 6-GHz sawtooth waveform with full duty cycle. (c) The corresponding electrical spectrum. (d), (e) 6-GHz reversed-sawtooth waveform with full duty cycle. (f) The corresponding electrical spectrum.

Equations (14)

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E out (t)= E 0 cos[ φ 2 + πV(t) 2 V π ]cos( ω 0 t)
E out (t)= E 0 cos φ 2 cos( ω 0 t)cos(βcos ω m t) E 0 sin φ 2 cos( ω 0 t)sin(βcos ω m t)
E out = 2 2 E 0 cos ω 0 t[ J 0 (β)+2 n=1 (1) n J 2n (β)cos(2n ω m t) ] 2 2 E 0 cos ω 0 t[ 2 n=1 (1) n J 2n1 (β)cos[ (2n1) ω m t ] ]
E out 2 2 E 0 cos ω 0 t [ J 0 (β)2 J 1 (β)cos( ω m t) 2 J 2 (β)cos(2 ω m t)+2 J 3 (β)cos(3 ω m t) ]
i(t)DC+ A 2 cos( ω m t)+ B 2 cos(2 ω m t)+ C 2 cos(3 ω m t)
i(t)DC+ | A | 2 cos( ω m t+π)+ C 2 cos(3 ω m t) =DC+ | A | 2 sin( ω m t+ π 2 )+ C 2 sin(3 ω m t+ 3π 2 )
T sq (t)=DC+ n=1,3,5 1 n sin(n ω m t)
T tr (t)=DC+ n=1,3,5 1 n 2 cos(n ω m t)
T tr (t)=DC+cos( ω m t)+ 1 9 cos(3 ω m t)
i(t)= i 1 (t)+ i 2 (t)DC+ | A | 2 [ cos( ω m t+π)+ 1 9 cos(3 ω m t) ] + | A | 2 [ cos( ω m t+π+ π 2 )+ 1 9 cos(3 ω m t+ 3π 2 ) ] =DC+ 2 | A | 4 [ cos( ω m t+ 5π 4 )+ 1 9 cos(3 ω m t+ 15π 4 ) ]
T sa (t)=DC+ n=1 1 n sin(n ω m t)
T sq (t)={ 1,t[kT,kT+ T 2 ) 0,t[kT+ T 2 ,kT+T)
T tr (t)={ (2k+1)( 2 T )t,t[kT,kT+ T 2 ) ( 2 T )t(2k+1),t[kT+ T 2 ,kT+T)
T sq (t)× T tr (t)={ (2k+1)( 2 T )t,t[kT,kT+ T 2 ) 0,t[kT+ T 2 ,kT+T)

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