Abstract

We propose and experimentally demonstrate a reconfigurable microwave signal processor, with a bandwidth up to tens of gigahertz. In this technique, any microwave signal processing function with a phase shift of π could be performed by shaping the input optical intensity spectrum. The phase shift of π is implemented by using a differential detection. Thanks to the broad bandwidth provided by the incoherent optical source and the high resolution of the user-defined optical filter, the frequency response of our approach could be in a great agreement with that of an ideal signal processing function. In the experiment, temporal intensity Hilbert transformations and temporal intensity differentiations of Gaussian-like pulses with widths of 125ps, 85ps and 68ps are accurately achieved.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2017 (3)

D. Pérez, I. Gasulla, L. Crudgington, D. J. Thomson, A. Z. Khokhar, K. Li, W. Cao, G. Z. Mashanovich, and J. Capmany, “Multipurpose silicon photonics signal processor core,” Nat. Commun. 8(1), 636 (2017).
[Crossref] [PubMed]

M. Li, S. Sun, A. Malacarne, S. LaRochelle, J. Yao, N. Zhu, and J. Azana, “Reconfigurable single-shot incoherent optical signal processing system for chirped microwave signal compression,” Sci. Bull. 62(4), 242–248 (2017).
[Crossref]

J. Capmany, “Single-shot incoherent optical processing of microwave signals: opening the path to low cost high performance analog photonics,” Sci. Bull. 62(9), 652–653 (2017).
[Crossref]

2016 (2)

W. Liu, M. Li, R. S. Guzzon, E. J. Norberg, J. S. Parker, M. Lu, L. A. Coldren, and J. Yao, “A fully reconfigurable photonic integrated signal processor,” Nat. Photonics 10(3), 190–195 (2016).
[Crossref]

M. Li, Y. Deng, J. Tang, S. Sun, J. Yao, J. Azaña, and N. Zhu, “Reconfigurable optical signal processing based on a distributed feedback semiconductor optical amplifier,” Sci. Rep. 6(1), 19985 (2016).
[Crossref] [PubMed]

2015 (1)

S. Sun, Y. Deng, N. Zhu, and M. Li, “Tunable fractional-order photonic differentiator using a distributed feedback semiconductor optical amplifier,” Opt. Eng. 55(3), 031105 (2015).
[Crossref]

2014 (1)

2013 (3)

2012 (5)

2011 (4)

M. Li, L. Y. Shao, J. Albert, and J. Yao, “Continuously Tunable Photonic Fractional Temporal Differentiator Based on a Tilted Fiber Bragg Grating,” IEEE Photonics Technol. Lett. 23(4), 251–253 (2011).
[Crossref]

Z. Li, H. Chi, X. Zhang, and J. Yao, “A continuously tunable microwave fractional Hilbert transformer based on a photonic microwave delay-line filter using a polarization modulator,” IEEE Photonics Technol. Lett. 23(22), 1694–1696 (2011).
[Crossref]

T. X. H. Huang, X. Yi, and R. A. Minasian, “Microwave photonic quadrature filter based on an all-optical programmable Hilbert transformer,” Opt. Lett. 36(22), 4440–4442 (2011).
[Crossref] [PubMed]

Z. Li, H. Chi, X. Zhang, and J. Yao, “Optical single-sideband modulation using a fiber-Bragg-grating-based optical Hilbert transformer,” IEEE Photonics Technol. Lett. 23(9), 558–560 (2011).
[Crossref]

2010 (4)

2009 (5)

2008 (1)

1999 (1)

Albert, J.

M. Li, L. Y. Shao, J. Albert, and J. Yao, “Continuously Tunable Photonic Fractional Temporal Differentiator Based on a Tilted Fiber Bragg Grating,” IEEE Photonics Technol. Lett. 23(4), 251–253 (2011).
[Crossref]

Asghari, M. H.

Ashrafi, R.

Azana, J.

M. Li, S. Sun, A. Malacarne, S. LaRochelle, J. Yao, N. Zhu, and J. Azana, “Reconfigurable single-shot incoherent optical signal processing system for chirped microwave signal compression,” Sci. Bull. 62(4), 242–248 (2017).
[Crossref]

Azaña, J.

M. Li, Y. Deng, J. Tang, S. Sun, J. Yao, J. Azaña, and N. Zhu, “Reconfigurable optical signal processing based on a distributed feedback semiconductor optical amplifier,” Sci. Rep. 6(1), 19985 (2016).
[Crossref] [PubMed]

M. Burla, L. R. Cortés, M. Li, X. Wang, L. Chrostowski, and J. Azaña, “Integrated waveguide Bragg gratings for microwave photonics signal processing,” Opt. Express 21(21), 25120–25147 (2013).
[Crossref] [PubMed]

R. Ashrafi and J. Azaña, “Terahertz bandwidth all-optical Hilbert transformers based on long-period gratings,” Opt. Lett. 37(13), 2604–2606 (2012).
[Crossref] [PubMed]

A. Malacarne, R. Ashrafi, M. Li, S. LaRochelle, J. Yao, and J. Azaña, “Single-shot photonic time-intensity integration based on a time-spectrum convolution system,” Opt. Lett. 37(8), 1355–1357 (2012).
[Crossref] [PubMed]

R. Ashrafi and J. Azaña, “Figure of merit for photonic differentiators,” Opt. Express 20(3), 2626–2639 (2012).
[Crossref] [PubMed]

Y. Park and J. Azaña, “Ultrahigh dispersion of broadband microwave signals by incoherent photonic processing,” Opt. Express 18(14), 14752–14761 (2010).
[Crossref] [PubMed]

Y. Park and J. Azaña, “Optical signal processors based on a time-spectrum convolution,” Opt. Lett. 35(6), 796–798 (2010).
[Crossref] [PubMed]

Y. Park and J. Azaña, “Ultrafast photonic intensity integrator,” Opt. Lett. 34(8), 1156–1158 (2009).
[Crossref] [PubMed]

M. H. Asghari and J. Azaña, “All-optical Hilbert transformer based on a single phase-shifted fiber Bragg grating: design and analysis,” Opt. Lett. 34(3), 334–336 (2009).
[Crossref] [PubMed]

R. Slavik, Y. Park, D. Krcmarik, and J. Azaña, “Stable all-fiber photonic temporal differentiator using a long-period fiber grating interferometer,” Opt. Commun. 282(12), 2339–2342 (2009).
[Crossref]

Beeker, W.

Bui, L. A.

Burla, M.

Cao, W.

D. Pérez, I. Gasulla, L. Crudgington, D. J. Thomson, A. Z. Khokhar, K. Li, W. Cao, G. Z. Mashanovich, and J. Capmany, “Multipurpose silicon photonics signal processor core,” Nat. Commun. 8(1), 636 (2017).
[Crossref] [PubMed]

Capmany, J.

D. Pérez, I. Gasulla, L. Crudgington, D. J. Thomson, A. Z. Khokhar, K. Li, W. Cao, G. Z. Mashanovich, and J. Capmany, “Multipurpose silicon photonics signal processor core,” Nat. Commun. 8(1), 636 (2017).
[Crossref] [PubMed]

J. Capmany, “Single-shot incoherent optical processing of microwave signals: opening the path to low cost high performance analog photonics,” Sci. Bull. 62(9), 652–653 (2017).
[Crossref]

Chi, H.

Z. Li, Y. Han, H. Chi, X. Zhang, and J. Yao, “A Continuously Tunable Microwave Fractional Hilbert Transformer Based on a Nonuniformly Spaced Photonic Microwave Delay-Line Filter,” J. Lightwave Technol. 30(12), 1948–1953 (2012).

Z. Li, H. Chi, X. Zhang, and J. Yao, “Optical single-sideband modulation using a fiber-Bragg-grating-based optical Hilbert transformer,” IEEE Photonics Technol. Lett. 23(9), 558–560 (2011).
[Crossref]

Z. Li, H. Chi, X. Zhang, and J. Yao, “A continuously tunable microwave fractional Hilbert transformer based on a photonic microwave delay-line filter using a polarization modulator,” IEEE Photonics Technol. Lett. 23(22), 1694–1696 (2011).
[Crossref]

Chrostowski, L.

Coldren, L. A.

W. Liu, M. Li, R. S. Guzzon, E. J. Norberg, J. S. Parker, M. Lu, L. A. Coldren, and J. Yao, “A fully reconfigurable photonic integrated signal processor,” Nat. Photonics 10(3), 190–195 (2016).
[Crossref]

Cortés, L. R.

Crudgington, L.

D. Pérez, I. Gasulla, L. Crudgington, D. J. Thomson, A. Z. Khokhar, K. Li, W. Cao, G. Z. Mashanovich, and J. Capmany, “Multipurpose silicon photonics signal processor core,” Nat. Commun. 8(1), 636 (2017).
[Crossref] [PubMed]

Deng, Y.

M. Li, Y. Deng, J. Tang, S. Sun, J. Yao, J. Azaña, and N. Zhu, “Reconfigurable optical signal processing based on a distributed feedback semiconductor optical amplifier,” Sci. Rep. 6(1), 19985 (2016).
[Crossref] [PubMed]

S. Sun, Y. Deng, N. Zhu, and M. Li, “Tunable fractional-order photonic differentiator using a distributed feedback semiconductor optical amplifier,” Opt. Eng. 55(3), 031105 (2015).
[Crossref]

Dezfooliyan, A.

Dorrer, C.

Dumais, P.

Dyer, S. D.

Emami, H.

Gasulla, I.

D. Pérez, I. Gasulla, L. Crudgington, D. J. Thomson, A. Z. Khokhar, K. Li, W. Cao, G. Z. Mashanovich, and J. Capmany, “Multipurpose silicon photonics signal processor core,” Nat. Commun. 8(1), 636 (2017).
[Crossref] [PubMed]

Gates, J. C.

Guzzon, R. S.

W. Liu, M. Li, R. S. Guzzon, E. J. Norberg, J. S. Parker, M. Lu, L. A. Coldren, and J. Yao, “A fully reconfigurable photonic integrated signal processor,” Nat. Photonics 10(3), 190–195 (2016).
[Crossref]

Han, Y.

Heideman, R.

Holmes, C.

Huang, T. X. H.

Khan, M. R.

Khokhar, A. Z.

D. Pérez, I. Gasulla, L. Crudgington, D. J. Thomson, A. Z. Khokhar, K. Li, W. Cao, G. Z. Mashanovich, and J. Capmany, “Multipurpose silicon photonics signal processor core,” Nat. Commun. 8(1), 636 (2017).
[Crossref] [PubMed]

Krcmarik, D.

R. Slavik, Y. Park, D. Krcmarik, and J. Azaña, “Stable all-fiber photonic temporal differentiator using a long-period fiber grating interferometer,” Opt. Commun. 282(12), 2339–2342 (2009).
[Crossref]

LaRochelle, S.

M. Li, S. Sun, A. Malacarne, S. LaRochelle, J. Yao, N. Zhu, and J. Azana, “Reconfigurable single-shot incoherent optical signal processing system for chirped microwave signal compression,” Sci. Bull. 62(4), 242–248 (2017).
[Crossref]

A. Malacarne, R. Ashrafi, M. Li, S. LaRochelle, J. Yao, and J. Azaña, “Single-shot photonic time-intensity integration based on a time-spectrum convolution system,” Opt. Lett. 37(8), 1355–1357 (2012).
[Crossref] [PubMed]

Leinse, A.

Li, K.

D. Pérez, I. Gasulla, L. Crudgington, D. J. Thomson, A. Z. Khokhar, K. Li, W. Cao, G. Z. Mashanovich, and J. Capmany, “Multipurpose silicon photonics signal processor core,” Nat. Commun. 8(1), 636 (2017).
[Crossref] [PubMed]

Li, M.

M. Li, S. Sun, A. Malacarne, S. LaRochelle, J. Yao, N. Zhu, and J. Azana, “Reconfigurable single-shot incoherent optical signal processing system for chirped microwave signal compression,” Sci. Bull. 62(4), 242–248 (2017).
[Crossref]

M. Li, Y. Deng, J. Tang, S. Sun, J. Yao, J. Azaña, and N. Zhu, “Reconfigurable optical signal processing based on a distributed feedback semiconductor optical amplifier,” Sci. Rep. 6(1), 19985 (2016).
[Crossref] [PubMed]

W. Liu, M. Li, R. S. Guzzon, E. J. Norberg, J. S. Parker, M. Lu, L. A. Coldren, and J. Yao, “A fully reconfigurable photonic integrated signal processor,” Nat. Photonics 10(3), 190–195 (2016).
[Crossref]

S. Sun, Y. Deng, N. Zhu, and M. Li, “Tunable fractional-order photonic differentiator using a distributed feedback semiconductor optical amplifier,” Opt. Eng. 55(3), 031105 (2015).
[Crossref]

M. Burla, L. R. Cortés, M. Li, X. Wang, L. Chrostowski, and J. Azaña, “Integrated waveguide Bragg gratings for microwave photonics signal processing,” Opt. Express 21(21), 25120–25147 (2013).
[Crossref] [PubMed]

A. Malacarne, R. Ashrafi, M. Li, S. LaRochelle, J. Yao, and J. Azaña, “Single-shot photonic time-intensity integration based on a time-spectrum convolution system,” Opt. Lett. 37(8), 1355–1357 (2012).
[Crossref] [PubMed]

M. Li, L. Y. Shao, J. Albert, and J. Yao, “Continuously Tunable Photonic Fractional Temporal Differentiator Based on a Tilted Fiber Bragg Grating,” IEEE Photonics Technol. Lett. 23(4), 251–253 (2011).
[Crossref]

M. Li and J. Yao, “Experimental demonstration of a wideband photonic temporal Hilbert transformer based on a single fiber Bragg grating,” IEEE Photonics Technol. Lett. 22(21), 1559–1561 (2010).
[Crossref]

M. Li and J. Yao, “All-fiber temporal photonic fractional Hilbert transformer based on a directly designed fiber Bragg grating,” Opt. Lett. 35(2), 223–225 (2010).
[Crossref] [PubMed]

Li, Z.

Z. Li, Y. Han, H. Chi, X. Zhang, and J. Yao, “A Continuously Tunable Microwave Fractional Hilbert Transformer Based on a Nonuniformly Spaced Photonic Microwave Delay-Line Filter,” J. Lightwave Technol. 30(12), 1948–1953 (2012).

Z. Li, H. Chi, X. Zhang, and J. Yao, “Optical single-sideband modulation using a fiber-Bragg-grating-based optical Hilbert transformer,” IEEE Photonics Technol. Lett. 23(9), 558–560 (2011).
[Crossref]

Z. Li, H. Chi, X. Zhang, and J. Yao, “A continuously tunable microwave fractional Hilbert transformer based on a photonic microwave delay-line filter using a polarization modulator,” IEEE Photonics Technol. Lett. 23(22), 1694–1696 (2011).
[Crossref]

Liu, W.

W. Liu, M. Li, R. S. Guzzon, E. J. Norberg, J. S. Parker, M. Lu, L. A. Coldren, and J. Yao, “A fully reconfigurable photonic integrated signal processor,” Nat. Photonics 10(3), 190–195 (2016).
[Crossref]

Lu, M.

W. Liu, M. Li, R. S. Guzzon, E. J. Norberg, J. S. Parker, M. Lu, L. A. Coldren, and J. Yao, “A fully reconfigurable photonic integrated signal processor,” Nat. Photonics 10(3), 190–195 (2016).
[Crossref]

Malacarne, A.

M. Li, S. Sun, A. Malacarne, S. LaRochelle, J. Yao, N. Zhu, and J. Azana, “Reconfigurable single-shot incoherent optical signal processing system for chirped microwave signal compression,” Sci. Bull. 62(4), 242–248 (2017).
[Crossref]

A. Malacarne, R. Ashrafi, M. Li, S. LaRochelle, J. Yao, and J. Azaña, “Single-shot photonic time-intensity integration based on a time-spectrum convolution system,” Opt. Lett. 37(8), 1355–1357 (2012).
[Crossref] [PubMed]

Mashanovich, G. Z.

D. Pérez, I. Gasulla, L. Crudgington, D. J. Thomson, A. Z. Khokhar, K. Li, W. Cao, G. Z. Mashanovich, and J. Capmany, “Multipurpose silicon photonics signal processor core,” Nat. Commun. 8(1), 636 (2017).
[Crossref] [PubMed]

Mennea, P. L.

Minasian, R. A.

Mitchell, A.

Norberg, E. J.

W. Liu, M. Li, R. S. Guzzon, E. J. Norberg, J. S. Parker, M. Lu, L. A. Coldren, and J. Yao, “A fully reconfigurable photonic integrated signal processor,” Nat. Photonics 10(3), 190–195 (2016).
[Crossref]

Park, Y.

Parker, J. S.

W. Liu, M. Li, R. S. Guzzon, E. J. Norberg, J. S. Parker, M. Lu, L. A. Coldren, and J. Yao, “A fully reconfigurable photonic integrated signal processor,” Nat. Photonics 10(3), 190–195 (2016).
[Crossref]

Pérez, D.

D. Pérez, I. Gasulla, L. Crudgington, D. J. Thomson, A. Z. Khokhar, K. Li, W. Cao, G. Z. Mashanovich, and J. Capmany, “Multipurpose silicon photonics signal processor core,” Nat. Commun. 8(1), 636 (2017).
[Crossref] [PubMed]

Rochford, K. B.

Roeloffzen, C.

Sarkhosh, N.

Shahoei, H.

Shao, L. Y.

M. Li, L. Y. Shao, J. Albert, and J. Yao, “Continuously Tunable Photonic Fractional Temporal Differentiator Based on a Tilted Fiber Bragg Grating,” IEEE Photonics Technol. Lett. 23(4), 251–253 (2011).
[Crossref]

Sima, C.

Slavik, R.

R. Slavik, Y. Park, D. Krcmarik, and J. Azaña, “Stable all-fiber photonic temporal differentiator using a long-period fiber grating interferometer,” Opt. Commun. 282(12), 2339–2342 (2009).
[Crossref]

Smith, P. G. R.

Sun, S.

M. Li, S. Sun, A. Malacarne, S. LaRochelle, J. Yao, N. Zhu, and J. Azana, “Reconfigurable single-shot incoherent optical signal processing system for chirped microwave signal compression,” Sci. Bull. 62(4), 242–248 (2017).
[Crossref]

M. Li, Y. Deng, J. Tang, S. Sun, J. Yao, J. Azaña, and N. Zhu, “Reconfigurable optical signal processing based on a distributed feedback semiconductor optical amplifier,” Sci. Rep. 6(1), 19985 (2016).
[Crossref] [PubMed]

S. Sun, Y. Deng, N. Zhu, and M. Li, “Tunable fractional-order photonic differentiator using a distributed feedback semiconductor optical amplifier,” Opt. Eng. 55(3), 031105 (2015).
[Crossref]

Tang, J.

M. Li, Y. Deng, J. Tang, S. Sun, J. Yao, J. Azaña, and N. Zhu, “Reconfigurable optical signal processing based on a distributed feedback semiconductor optical amplifier,” Sci. Rep. 6(1), 19985 (2016).
[Crossref] [PubMed]

Thomson, D. J.

D. Pérez, I. Gasulla, L. Crudgington, D. J. Thomson, A. Z. Khokhar, K. Li, W. Cao, G. Z. Mashanovich, and J. Capmany, “Multipurpose silicon photonics signal processor core,” Nat. Commun. 8(1), 636 (2017).
[Crossref] [PubMed]

Wang, X.

Weiner, A. M.

Yao, J.

M. Li, S. Sun, A. Malacarne, S. LaRochelle, J. Yao, N. Zhu, and J. Azana, “Reconfigurable single-shot incoherent optical signal processing system for chirped microwave signal compression,” Sci. Bull. 62(4), 242–248 (2017).
[Crossref]

M. Li, Y. Deng, J. Tang, S. Sun, J. Yao, J. Azaña, and N. Zhu, “Reconfigurable optical signal processing based on a distributed feedback semiconductor optical amplifier,” Sci. Rep. 6(1), 19985 (2016).
[Crossref] [PubMed]

W. Liu, M. Li, R. S. Guzzon, E. J. Norberg, J. S. Parker, M. Lu, L. A. Coldren, and J. Yao, “A fully reconfigurable photonic integrated signal processor,” Nat. Photonics 10(3), 190–195 (2016).
[Crossref]

H. Shahoei, P. Dumais, and J. Yao, “Continuously tunable photonic fractional Hilbert transformer using a high-contrast germanium-doped silica-on-silicon microring resonator,” Opt. Lett. 39(9), 2778–2781 (2014).
[Crossref] [PubMed]

Z. Li, Y. Han, H. Chi, X. Zhang, and J. Yao, “A Continuously Tunable Microwave Fractional Hilbert Transformer Based on a Nonuniformly Spaced Photonic Microwave Delay-Line Filter,” J. Lightwave Technol. 30(12), 1948–1953 (2012).

A. Malacarne, R. Ashrafi, M. Li, S. LaRochelle, J. Yao, and J. Azaña, “Single-shot photonic time-intensity integration based on a time-spectrum convolution system,” Opt. Lett. 37(8), 1355–1357 (2012).
[Crossref] [PubMed]

M. Li, L. Y. Shao, J. Albert, and J. Yao, “Continuously Tunable Photonic Fractional Temporal Differentiator Based on a Tilted Fiber Bragg Grating,” IEEE Photonics Technol. Lett. 23(4), 251–253 (2011).
[Crossref]

Z. Li, H. Chi, X. Zhang, and J. Yao, “A continuously tunable microwave fractional Hilbert transformer based on a photonic microwave delay-line filter using a polarization modulator,” IEEE Photonics Technol. Lett. 23(22), 1694–1696 (2011).
[Crossref]

Z. Li, H. Chi, X. Zhang, and J. Yao, “Optical single-sideband modulation using a fiber-Bragg-grating-based optical Hilbert transformer,” IEEE Photonics Technol. Lett. 23(9), 558–560 (2011).
[Crossref]

M. Li and J. Yao, “Experimental demonstration of a wideband photonic temporal Hilbert transformer based on a single fiber Bragg grating,” IEEE Photonics Technol. Lett. 22(21), 1559–1561 (2010).
[Crossref]

M. Li and J. Yao, “All-fiber temporal photonic fractional Hilbert transformer based on a directly designed fiber Bragg grating,” Opt. Lett. 35(2), 223–225 (2010).
[Crossref] [PubMed]

J. Yao, “Microwave Photonics,” J. Lightwave Technol. 27(3), 314–335 (2009).
[Crossref]

Yi, X.

Zervas, M. N.

Zhang, X.

Z. Li, Y. Han, H. Chi, X. Zhang, and J. Yao, “A Continuously Tunable Microwave Fractional Hilbert Transformer Based on a Nonuniformly Spaced Photonic Microwave Delay-Line Filter,” J. Lightwave Technol. 30(12), 1948–1953 (2012).

Z. Li, H. Chi, X. Zhang, and J. Yao, “A continuously tunable microwave fractional Hilbert transformer based on a photonic microwave delay-line filter using a polarization modulator,” IEEE Photonics Technol. Lett. 23(22), 1694–1696 (2011).
[Crossref]

Z. Li, H. Chi, X. Zhang, and J. Yao, “Optical single-sideband modulation using a fiber-Bragg-grating-based optical Hilbert transformer,” IEEE Photonics Technol. Lett. 23(9), 558–560 (2011).
[Crossref]

Zhu, N.

M. Li, S. Sun, A. Malacarne, S. LaRochelle, J. Yao, N. Zhu, and J. Azana, “Reconfigurable single-shot incoherent optical signal processing system for chirped microwave signal compression,” Sci. Bull. 62(4), 242–248 (2017).
[Crossref]

M. Li, Y. Deng, J. Tang, S. Sun, J. Yao, J. Azaña, and N. Zhu, “Reconfigurable optical signal processing based on a distributed feedback semiconductor optical amplifier,” Sci. Rep. 6(1), 19985 (2016).
[Crossref] [PubMed]

S. Sun, Y. Deng, N. Zhu, and M. Li, “Tunable fractional-order photonic differentiator using a distributed feedback semiconductor optical amplifier,” Opt. Eng. 55(3), 031105 (2015).
[Crossref]

Zhuang, L.

IEEE Photonics Technol. Lett. (4)

Z. Li, H. Chi, X. Zhang, and J. Yao, “Optical single-sideband modulation using a fiber-Bragg-grating-based optical Hilbert transformer,” IEEE Photonics Technol. Lett. 23(9), 558–560 (2011).
[Crossref]

M. Li and J. Yao, “Experimental demonstration of a wideband photonic temporal Hilbert transformer based on a single fiber Bragg grating,” IEEE Photonics Technol. Lett. 22(21), 1559–1561 (2010).
[Crossref]

Z. Li, H. Chi, X. Zhang, and J. Yao, “A continuously tunable microwave fractional Hilbert transformer based on a photonic microwave delay-line filter using a polarization modulator,” IEEE Photonics Technol. Lett. 23(22), 1694–1696 (2011).
[Crossref]

M. Li, L. Y. Shao, J. Albert, and J. Yao, “Continuously Tunable Photonic Fractional Temporal Differentiator Based on a Tilted Fiber Bragg Grating,” IEEE Photonics Technol. Lett. 23(4), 251–253 (2011).
[Crossref]

J. Lightwave Technol. (3)

Nat. Commun. (1)

D. Pérez, I. Gasulla, L. Crudgington, D. J. Thomson, A. Z. Khokhar, K. Li, W. Cao, G. Z. Mashanovich, and J. Capmany, “Multipurpose silicon photonics signal processor core,” Nat. Commun. 8(1), 636 (2017).
[Crossref] [PubMed]

Nat. Photonics (1)

W. Liu, M. Li, R. S. Guzzon, E. J. Norberg, J. S. Parker, M. Lu, L. A. Coldren, and J. Yao, “A fully reconfigurable photonic integrated signal processor,” Nat. Photonics 10(3), 190–195 (2016).
[Crossref]

Opt. Commun. (1)

R. Slavik, Y. Park, D. Krcmarik, and J. Azaña, “Stable all-fiber photonic temporal differentiator using a long-period fiber grating interferometer,” Opt. Commun. 282(12), 2339–2342 (2009).
[Crossref]

Opt. Eng. (1)

S. Sun, Y. Deng, N. Zhu, and M. Li, “Tunable fractional-order photonic differentiator using a distributed feedback semiconductor optical amplifier,” Opt. Eng. 55(3), 031105 (2015).
[Crossref]

Opt. Express (7)

Opt. Lett. (9)

M. Li and J. Yao, “All-fiber temporal photonic fractional Hilbert transformer based on a directly designed fiber Bragg grating,” Opt. Lett. 35(2), 223–225 (2010).
[Crossref] [PubMed]

M. H. Asghari and J. Azaña, “All-optical Hilbert transformer based on a single phase-shifted fiber Bragg grating: design and analysis,” Opt. Lett. 34(3), 334–336 (2009).
[Crossref] [PubMed]

C. Sima, J. C. Gates, C. Holmes, P. L. Mennea, M. N. Zervas, and P. G. R. Smith, “Terahertz bandwidth photonic Hilbert transformers based on synthesized planar Bragg grating fabrication,” Opt. Lett. 38(17), 3448–3451 (2013).
[Crossref] [PubMed]

R. Ashrafi and J. Azaña, “Terahertz bandwidth all-optical Hilbert transformers based on long-period gratings,” Opt. Lett. 37(13), 2604–2606 (2012).
[Crossref] [PubMed]

H. Shahoei, P. Dumais, and J. Yao, “Continuously tunable photonic fractional Hilbert transformer using a high-contrast germanium-doped silica-on-silicon microring resonator,” Opt. Lett. 39(9), 2778–2781 (2014).
[Crossref] [PubMed]

T. X. H. Huang, X. Yi, and R. A. Minasian, “Microwave photonic quadrature filter based on an all-optical programmable Hilbert transformer,” Opt. Lett. 36(22), 4440–4442 (2011).
[Crossref] [PubMed]

Y. Park and J. Azaña, “Ultrafast photonic intensity integrator,” Opt. Lett. 34(8), 1156–1158 (2009).
[Crossref] [PubMed]

A. Malacarne, R. Ashrafi, M. Li, S. LaRochelle, J. Yao, and J. Azaña, “Single-shot photonic time-intensity integration based on a time-spectrum convolution system,” Opt. Lett. 37(8), 1355–1357 (2012).
[Crossref] [PubMed]

Y. Park and J. Azaña, “Optical signal processors based on a time-spectrum convolution,” Opt. Lett. 35(6), 796–798 (2010).
[Crossref] [PubMed]

Sci. Bull. (2)

M. Li, S. Sun, A. Malacarne, S. LaRochelle, J. Yao, N. Zhu, and J. Azana, “Reconfigurable single-shot incoherent optical signal processing system for chirped microwave signal compression,” Sci. Bull. 62(4), 242–248 (2017).
[Crossref]

J. Capmany, “Single-shot incoherent optical processing of microwave signals: opening the path to low cost high performance analog photonics,” Sci. Bull. 62(9), 652–653 (2017).
[Crossref]

Sci. Rep. (1)

M. Li, Y. Deng, J. Tang, S. Sun, J. Yao, J. Azaña, and N. Zhu, “Reconfigurable optical signal processing based on a distributed feedback semiconductor optical amplifier,” Sci. Rep. 6(1), 19985 (2016).
[Crossref] [PubMed]

Other (1)

S. L. Hahn, Transforms and Applications Handbook (Chemical Rubber Company, 2010), Chap. 7.

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Figures (11)

Fig. 1
Fig. 1 Principle of the conventional TSC system. PD: Photodetector. The symbol represents the convolution process. The intensity profile of an output signal is a convolution between the time-mapped optical energy spectrum profile and the temporal intensity modulation waveform. Note that the orange line denotes the optical path and the green line represents the electrical path.
Fig. 2
Fig. 2 Basic principle of the reconfigurable microwave signal processor. (a) Schematic diagram of our proposal; (b) Principle of the proposed HT; (c) Principle of the proposed differentiator. (d) Principle of a signal processor with two phase jumps. The orange and green lines represent the optical and electrical paths, respectively.
Fig. 3
Fig. 3 Simulated intensity responses and phase responses of our proposal. (a) and (b) represent the intensity response and the phase response of the proposed Hilbert transform, respectively; (c) and (d) represent the intensity response and the phase response of the proposed differentiator. The blue, red and yellow lines are simulation results while the violet dash line denotes frequency responses of ideal signal processing functions. Note that k 1 = 4 π p s , k 2 = 1.4 π p s , ψ 2 1 = ( 544 / 2 π ) p s 2 / r a d , ψ 2 2 = ( 3888 / 2 π ) p s 2 / r a d and the bandwidth of the optical spectrum is around 2.5THz.
Fig. 4
Fig. 4 Simulated frequency response of a signal processor with two phase jumps. (a) represents the designed impulse response. The impulse response is a sinc-like function while the part of the main lobe is negative. Note that k = 1.4 π p s , ψ 2 2 = ( 3888 / 2 π ) p s 2 / r a d and the temporal duration of the negative part is around 0.7ns. (b) shows the intensity response of the designed impulse response. (c) is the comparison between profiles of the input microwave signal and the output microwave signal. The RF bandwidth of the input Gaussian pulse is around 1GHz. (d) The phase response of the designed impulse response.
Fig. 5
Fig. 5 Experimental setup. Link 1: measurement of the frequency response. Link 2: measurement of output signals. Link 3: measurement of the shaped optical spectrum. SLD: Super luminescent diode, IM: Intensity modulator, AWG: Arbitrary waveform generator, SMF: Single mode fiber, VNA: Vector network analyzer, EDFA: Erbium-doped optical fiber amplifier, OSA: Optical spectrum analyzer, WS: WaveShaper, BPD: Balanced photodetector, OSC: Oscilloscope, TDL: Tunable delay line. The orange line represents the optical path while the green line shows the electrical path.
Fig. 6
Fig. 6 Measured frequency responses of our proposal and shaped optical energy spectrums. (a-c) shaped optical spectrums, RF intensity responses and phase responses of the HT; (d-f) Corresponding results of the differentiator. Comparisons between the simulation and measured results are also shown in these figures. Note that Port2 connects with the negative branch of the BPD while Port1 links the positive branch. The bandwidth of the optical spectrum is around 2.5THz and these experimental results are measured without averaging.
Fig. 7
Fig. 7 Measured outputs of the proposed HT and differentiator. The blue, red dash and yellow lines represent the measured input signals, outputs of the ideal signal processing functions and the measured output signals, respectively. (a), (b) and (c) Experimental and simulated results of temporal intensity Hilbert transformation. (d), (e) and (f) Experimental and simulated results of temporal intensity differentiation. The input signals in each row are the same and these experimental results are measured with averaging.
Fig. 8
Fig. 8 Experimental setup for measuring frequency responses of the EA, IM and BPD. TLS: Tunable laser source; IM: Intensity modulator; EA: Electrical amplifier; VNA: Vector network analyzer; BPD: Balanced photodetector; TDL: Tunable delay line. An optical coupler (50/50) is used before the TDLs.
Fig. 9
Fig. 9 Comparison between RF intensity responses of the proposed HT, the negative microwave photonics filter and the EA. Note that the negative microwave photonics filter is measured with three different time delays, Delay1, Delay2 and Delay3.
Fig. 10
Fig. 10 Simulation of the proposed HT with different time-delayed difference. (a), (b) and (c) represent frequency responses of the proposed HTs with different time-delayed differences (the red line) and the HT with no time-delayed difference (the blue line). (d), (e) and (f) represent the corresponding output signals (the red line), which are compared with the ideal outputs (the yellow line). The RF bandwidth of the input Gaussian pulse (the blue line) is around 20GHz. Note that k =4 π p s , ψ 2 = ( 544 / 2 π ) p s 2 / r a d and the bandwidth of the optical signal is 2.5THz. Based on our calculation, Δ t =0 .004 n s is the maximum value to make the frequency response invariant.
Fig. 11
Fig. 11 Details about the intensity responses of the proposed HTs with different time-delayed differences. The blue lines represent the frequency response of the HT with no time-delayed difference while the red lines give the results with different time-delayed differences. Note that all the parameters are same with the simulation in Fig. 10.

Equations (8)

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I o u t p u t ( t ) S ( f o ) I m w ( t ) 2 π f o = t / ψ 2 ,
h ( t ) H i l b e r t I ( t ) = 1 / ( π t ) I ( t ) ,
H ( f ) H i l b e r t = { j f 0 j f < 0 .
h ( f ) H i l b e r t S ( f o ) 2 π f o = t / ψ 2 = { | sin c ( k / ψ 2 ( t - t c ) ) | Δ t / 2 > t t c > 0 0 t t c = 0 | sin c ( k / ψ 2 ( t - t c ) ) | Δ t / 2 < t t c < 0 ,
H ( f ) = { 2 π j f f 0 2 π j f f < 0 .
h ( t ) d i f f S ( f o ) f o = t / ψ 2 = { | sin c ( k / ψ 2 ( t - t c ) ) | 2 Δ t / 2 > t t c > 0 0 t t c = 0 | sin c ( k / ψ 2 ( t - t c ) ) | 2 Δ t / 2 < t t c < 0 .
h ( t ) = h 1 ( t ) δ ( t + Δ t /2 ) h 2 ( t ) δ ( t Δ t /2 ) t = 2 π f o ψ 2 ,
H ( ω ) = H 1 2 ( ω ) + H 2 2 ( ω ) 2 H 1 ( ω ) H 2 ( ω ) cos ( ω Δ t ) ,

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