Abstract

We propose and experimentally demonstrate a tunable fractional order photonic differentiator using an on-chip electrically tuned Mach-Zehnder interferometer (MZI) structure. The phase shift at the resonant frequency of the MZI varies when applying different voltages, which can implement the fractional differentiation. Due to the large 3-dB bandwidth of the MZI, the differentiator is expected to have an operation bandwidth of several hundred GHz. The proposed fractional order differentiator is demonstrated experimentally. A Gaussian-like pulse with a bandwidth of about 200 GHz is temporally differentiated with a tunable order range from 0.83 to 1.03.

© 2014 Optical Society of America

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  1. J. Azaña and M. Kulishov, “All-fibre ultrafast optical differentiator based on π phase-shifted long-period grating,” Electron. Lett. 41(25), 1368–1369 (2005).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  5. N. K. Berger, B. Levit, B. Fischer, M. Kulishov, D. V. Plant, and J. Azaña, “Temporal differentiation of optical signals using a phase-shifted fiber Bragg grating,” Opt. Express 15(2), 371–381 (2007).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  13. M. Li, H.-S. Jeong, J. Azaña, and T.-J. Ahn, “25-terahertz-bandwidth all-optical temporal differentiator,” Opt. Express 20(27), 28273–28280 (2012).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
  18. M. Li, L.-Y. Shao, J. Albert, and J. Yao, “Continuously tunable photonic fractional temporal differentiator based on a tilted fiber Bragg grating,” IEEE Photon. Technol. Lett. 23(4), 251–253 (2011).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  21. G. T. Reed and A. P. Knights, Silicon Photonics (John Wiley, 2004).
  22. H. Xu, Z. Li, Y. Zhu, Y. Li, Y. Yu, and J. Yu, “Silicon optical modulator with integrated grating couplers based on 0.18-μm complementary metal oxide semiconductor technology,” Opt. Eng. 50(4), 044001 (2011).
    [CrossRef]
  23. T. Yang, J. Dong, L. Liu, S. Liao, S. Tan, L. Shi, D. Gao, and X. Zhang, “Experimental observation of optical differentiation and optical Hilbert transformation using a single SOI microdisk chip,” Sci. Rep. 4, 3960 (2014).

2014 (1)

T. Yang, J. Dong, L. Liu, S. Liao, S. Tan, L. Shi, D. Gao, and X. Zhang, “Experimental observation of optical differentiation and optical Hilbert transformation using a single SOI microdisk chip,” Sci. Rep. 4, 3960 (2014).

2013 (4)

H. Shahoei, D.-X. Xu, J. H. Schmid, and J. Yao, “Photonic fractional-order differentiator using an SOI microring resonator with an MMI coupler,” IEEE Photon. Technol. Lett. 25(15), 1408–1411 (2013).
[CrossRef]

J. Dong, A. Zheng, D. Gao, L. Lei, D. Huang, and X. Zhang, “Compact, flexible and versatile photonic differentiator using silicon Mach-Zehnder interferometers,” Opt. Express 21(6), 7014–7024 (2013).
[CrossRef] [PubMed]

J. Dong, A. Zheng, D. Gao, S. Liao, L. Lei, D. Huang, and X. Zhang, “High-order photonic differentiator employing on-chip cascaded microring resonators,” Opt. Lett. 38(5), 628–630 (2013).
[CrossRef] [PubMed]

H. You, T. Ning, W. Jian, L. Pei, X. Wen, J. Li, and H. Chen, “Optical temporal differentiator using a twin-core fiber,” Opt. Eng. 52(1), 015005 (2013).
[CrossRef]

2012 (2)

M. Li, H.-S. Jeong, J. Azaña, and T.-J. Ahn, “25-terahertz-bandwidth all-optical temporal differentiator,” Opt. Express 20(27), 28273–28280 (2012).
[CrossRef] [PubMed]

H. Shahoei, J. Albert, and J. Yao, “Tunable fractional order temporal differentiator by optically pumping a tilted fiber Bragg grating,” IEEE Photon. Technol. Lett. 24(9), 730–732 (2012).
[CrossRef]

2011 (3)

H. Xu, Z. Li, Y. Zhu, Y. Li, Y. Yu, and J. Yu, “Silicon optical modulator with integrated grating couplers based on 0.18-μm complementary metal oxide semiconductor technology,” Opt. Eng. 50(4), 044001 (2011).
[CrossRef]

T.-J. Ahn and J. Azaña, “Wavelength-selective directional couplers as ultrafast optical differentiators,” Opt. Express 19(8), 7625–7632 (2011).
[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 Photon. Technol. Lett. 23(4), 251–253 (2011).
[CrossRef]

2009 (2)

2008 (2)

2007 (5)

2006 (1)

2005 (2)

J. Azaña and M. Kulishov, “All-fibre ultrafast optical differentiator based on π phase-shifted long-period grating,” Electron. Lett. 41(25), 1368–1369 (2005).
[CrossRef]

M. Kulishov and J. Azaña, “Long-period fiber gratings as ultrafast optical differentiators,” Opt. Lett. 30(20), 2700–2702 (2005).
[CrossRef] [PubMed]

Ahn, T.-J.

Albert, J.

H. Shahoei, J. Albert, and J. Yao, “Tunable fractional order temporal differentiator by optically pumping a tilted fiber Bragg grating,” IEEE Photon. Technol. Lett. 24(9), 730–732 (2012).
[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 Photon. Technol. Lett. 23(4), 251–253 (2011).
[CrossRef]

Andrés, M. V.

Azaña, J.

M. Li, H.-S. Jeong, J. Azaña, and T.-J. Ahn, “25-terahertz-bandwidth all-optical temporal differentiator,” Opt. Express 20(27), 28273–28280 (2012).
[CrossRef] [PubMed]

T.-J. Ahn and J. Azaña, “Wavelength-selective directional couplers as ultrafast optical differentiators,” Opt. Express 19(8), 7625–7632 (2011).
[CrossRef] [PubMed]

R. Slavík, Y. Park, M. Kulishov, and J. Azaña, “Terahertz-bandwidth high-order temporal differentiators based on phase-shifted long-period fiber gratings,” Opt. Lett. 34(20), 3116–3118 (2009).
[CrossRef] [PubMed]

M. Kulishov and J. Azaña, “Design of high-order all-optical temporal differentiators based on multiple-phase-shifted fiber Bragg gratings,” Opt. Express 15(10), 6152–6166 (2007).
[CrossRef] [PubMed]

N. K. Berger, B. Levit, B. Fischer, M. Kulishov, D. V. Plant, and J. Azaña, “Temporal differentiation of optical signals using a phase-shifted fiber Bragg grating,” Opt. Express 15(2), 371–381 (2007).
[CrossRef] [PubMed]

Y. Park, J. Azaña, and R. Slavík, “Ultrafast all-optical first- and higher-order differentiators based on interferometers,” Opt. Lett. 32(6), 710–712 (2007).
[CrossRef] [PubMed]

R. Slavík, Y. Park, M. Kulishov, R. Morandotti, and J. Azaña, “Ultrafast all-optical differentiators,” Opt. Express 14(22), 10699–10707 (2006).
[CrossRef] [PubMed]

M. Kulishov and J. Azaña, “Long-period fiber gratings as ultrafast optical differentiators,” Opt. Lett. 30(20), 2700–2702 (2005).
[CrossRef] [PubMed]

J. Azaña and M. Kulishov, “All-fibre ultrafast optical differentiator based on π phase-shifted long-period grating,” Electron. Lett. 41(25), 1368–1369 (2005).
[CrossRef]

Berger, N. K.

Chen, H.

H. You, T. Ning, W. Jian, L. Pei, X. Wen, J. Li, and H. Chen, “Optical temporal differentiator using a twin-core fiber,” Opt. Eng. 52(1), 015005 (2013).
[CrossRef]

Cuadrado-Laborde, C.

C. Cuadrado-Laborde and M. V. Andrés, “In-fiber all-optical fractional differentiator,” Opt. Lett. 34(6), 833–835 (2009).
[CrossRef] [PubMed]

C. Cuadrado-Laborde, “All-optical ultrafast fractional differentiator,” Opt. Quantum Electron. 40(13), 983–990 (2008).
[CrossRef]

Dong, J.

Fischer, B.

Gao, D.

Huang, D.

Jeong, H.-S.

Jian, W.

H. You, T. Ning, W. Jian, L. Pei, X. Wen, J. Li, and H. Chen, “Optical temporal differentiator using a twin-core fiber,” Opt. Eng. 52(1), 015005 (2013).
[CrossRef]

Kulishov, M.

Lei, L.

Levit, B.

Li, J.

H. You, T. Ning, W. Jian, L. Pei, X. Wen, J. Li, and H. Chen, “Optical temporal differentiator using a twin-core fiber,” Opt. Eng. 52(1), 015005 (2013).
[CrossRef]

Li, M.

M. Li, H.-S. Jeong, J. Azaña, and T.-J. Ahn, “25-terahertz-bandwidth all-optical temporal differentiator,” Opt. Express 20(27), 28273–28280 (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 Photon. Technol. Lett. 23(4), 251–253 (2011).
[CrossRef]

Li, Y.

H. Xu, Z. Li, Y. Zhu, Y. Li, Y. Yu, and J. Yu, “Silicon optical modulator with integrated grating couplers based on 0.18-μm complementary metal oxide semiconductor technology,” Opt. Eng. 50(4), 044001 (2011).
[CrossRef]

Li, Z.

H. Xu, Z. Li, Y. Zhu, Y. Li, Y. Yu, and J. Yu, “Silicon optical modulator with integrated grating couplers based on 0.18-μm complementary metal oxide semiconductor technology,” Opt. Eng. 50(4), 044001 (2011).
[CrossRef]

Liao, S.

T. Yang, J. Dong, L. Liu, S. Liao, S. Tan, L. Shi, D. Gao, and X. Zhang, “Experimental observation of optical differentiation and optical Hilbert transformation using a single SOI microdisk chip,” Sci. Rep. 4, 3960 (2014).

J. Dong, A. Zheng, D. Gao, S. Liao, L. Lei, D. Huang, and X. Zhang, “High-order photonic differentiator employing on-chip cascaded microring resonators,” Opt. Lett. 38(5), 628–630 (2013).
[CrossRef] [PubMed]

Liu, D.

Liu, F.

Liu, L.

T. Yang, J. Dong, L. Liu, S. Liao, S. Tan, L. Shi, D. Gao, and X. Zhang, “Experimental observation of optical differentiation and optical Hilbert transformation using a single SOI microdisk chip,” Sci. Rep. 4, 3960 (2014).

Morandotti, R.

Ning, T.

H. You, T. Ning, W. Jian, L. Pei, X. Wen, J. Li, and H. Chen, “Optical temporal differentiator using a twin-core fiber,” Opt. Eng. 52(1), 015005 (2013).
[CrossRef]

Park, Y.

Pei, L.

H. You, T. Ning, W. Jian, L. Pei, X. Wen, J. Li, and H. Chen, “Optical temporal differentiator using a twin-core fiber,” Opt. Eng. 52(1), 015005 (2013).
[CrossRef]

Plant, D. V.

Qiang, L.

Qiu, M.

Schmid, J. H.

H. Shahoei, D.-X. Xu, J. H. Schmid, and J. Yao, “Photonic fractional-order differentiator using an SOI microring resonator with an MMI coupler,” IEEE Photon. Technol. Lett. 25(15), 1408–1411 (2013).
[CrossRef]

Shahoei, H.

H. Shahoei, D.-X. Xu, J. H. Schmid, and J. Yao, “Photonic fractional-order differentiator using an SOI microring resonator with an MMI coupler,” IEEE Photon. Technol. Lett. 25(15), 1408–1411 (2013).
[CrossRef]

H. Shahoei, J. Albert, and J. Yao, “Tunable fractional order temporal differentiator by optically pumping a tilted fiber Bragg grating,” IEEE Photon. Technol. Lett. 24(9), 730–732 (2012).
[CrossRef]

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 Photon. Technol. Lett. 23(4), 251–253 (2011).
[CrossRef]

Shi, L.

T. Yang, J. Dong, L. Liu, S. Liao, S. Tan, L. Shi, D. Gao, and X. Zhang, “Experimental observation of optical differentiation and optical Hilbert transformation using a single SOI microdisk chip,” Sci. Rep. 4, 3960 (2014).

Slavík, R.

Su, Y.

Tan, S.

T. Yang, J. Dong, L. Liu, S. Liao, S. Tan, L. Shi, D. Gao, and X. Zhang, “Experimental observation of optical differentiation and optical Hilbert transformation using a single SOI microdisk chip,” Sci. Rep. 4, 3960 (2014).

Wang, T.

Wen, X.

H. You, T. Ning, W. Jian, L. Pei, X. Wen, J. Li, and H. Chen, “Optical temporal differentiator using a twin-core fiber,” Opt. Eng. 52(1), 015005 (2013).
[CrossRef]

Xu, D.-X.

H. Shahoei, D.-X. Xu, J. H. Schmid, and J. Yao, “Photonic fractional-order differentiator using an SOI microring resonator with an MMI coupler,” IEEE Photon. Technol. Lett. 25(15), 1408–1411 (2013).
[CrossRef]

Xu, H.

H. Xu, Z. Li, Y. Zhu, Y. Li, Y. Yu, and J. Yu, “Silicon optical modulator with integrated grating couplers based on 0.18-μm complementary metal oxide semiconductor technology,” Opt. Eng. 50(4), 044001 (2011).
[CrossRef]

Xu, J.

Yang, T.

T. Yang, J. Dong, L. Liu, S. Liao, S. Tan, L. Shi, D. Gao, and X. Zhang, “Experimental observation of optical differentiation and optical Hilbert transformation using a single SOI microdisk chip,” Sci. Rep. 4, 3960 (2014).

Yao, J.

H. Shahoei, D.-X. Xu, J. H. Schmid, and J. Yao, “Photonic fractional-order differentiator using an SOI microring resonator with an MMI coupler,” IEEE Photon. Technol. Lett. 25(15), 1408–1411 (2013).
[CrossRef]

H. Shahoei, J. Albert, and J. Yao, “Tunable fractional order temporal differentiator by optically pumping a tilted fiber Bragg grating,” IEEE Photon. Technol. Lett. 24(9), 730–732 (2012).
[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 Photon. Technol. Lett. 23(4), 251–253 (2011).
[CrossRef]

Ye, T.

You, H.

H. You, T. Ning, W. Jian, L. Pei, X. Wen, J. Li, and H. Chen, “Optical temporal differentiator using a twin-core fiber,” Opt. Eng. 52(1), 015005 (2013).
[CrossRef]

Yu, J.

H. Xu, Z. Li, Y. Zhu, Y. Li, Y. Yu, and J. Yu, “Silicon optical modulator with integrated grating couplers based on 0.18-μm complementary metal oxide semiconductor technology,” Opt. Eng. 50(4), 044001 (2011).
[CrossRef]

Yu, Y.

H. Xu, Z. Li, Y. Zhu, Y. Li, Y. Yu, and J. Yu, “Silicon optical modulator with integrated grating couplers based on 0.18-μm complementary metal oxide semiconductor technology,” Opt. Eng. 50(4), 044001 (2011).
[CrossRef]

Zhang, X.

Zhang, Z.

Zheng, A.

Zhu, Y.

H. Xu, Z. Li, Y. Zhu, Y. Li, Y. Yu, and J. Yu, “Silicon optical modulator with integrated grating couplers based on 0.18-μm complementary metal oxide semiconductor technology,” Opt. Eng. 50(4), 044001 (2011).
[CrossRef]

Electron. Lett. (1)

J. Azaña and M. Kulishov, “All-fibre ultrafast optical differentiator based on π phase-shifted long-period grating,” Electron. Lett. 41(25), 1368–1369 (2005).
[CrossRef]

IEEE Photon. Technol. Lett. (3)

M. Li, L.-Y. Shao, J. Albert, and J. Yao, “Continuously tunable photonic fractional temporal differentiator based on a tilted fiber Bragg grating,” IEEE Photon. Technol. Lett. 23(4), 251–253 (2011).
[CrossRef]

H. Shahoei, J. Albert, and J. Yao, “Tunable fractional order temporal differentiator by optically pumping a tilted fiber Bragg grating,” IEEE Photon. Technol. Lett. 24(9), 730–732 (2012).
[CrossRef]

H. Shahoei, D.-X. Xu, J. H. Schmid, and J. Yao, “Photonic fractional-order differentiator using an SOI microring resonator with an MMI coupler,” IEEE Photon. Technol. Lett. 25(15), 1408–1411 (2013).
[CrossRef]

Opt. Eng. (2)

H. You, T. Ning, W. Jian, L. Pei, X. Wen, J. Li, and H. Chen, “Optical temporal differentiator using a twin-core fiber,” Opt. Eng. 52(1), 015005 (2013).
[CrossRef]

H. Xu, Z. Li, Y. Zhu, Y. Li, Y. Yu, and J. Yu, “Silicon optical modulator with integrated grating couplers based on 0.18-μm complementary metal oxide semiconductor technology,” Opt. Eng. 50(4), 044001 (2011).
[CrossRef]

Opt. Express (7)

Opt. Lett. (7)

Opt. Quantum Electron. (1)

C. Cuadrado-Laborde, “All-optical ultrafast fractional differentiator,” Opt. Quantum Electron. 40(13), 983–990 (2008).
[CrossRef]

Sci. Rep. (1)

T. Yang, J. Dong, L. Liu, S. Liao, S. Tan, L. Shi, D. Gao, and X. Zhang, “Experimental observation of optical differentiation and optical Hilbert transformation using a single SOI microdisk chip,” Sci. Rep. 4, 3960 (2014).

Other (1)

G. T. Reed and A. P. Knights, Silicon Photonics (John Wiley, 2004).

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Figures (7)

Fig. 1
Fig. 1

The magnitude (a) and phase response (b) of the MZI operating at 1550 nm for different value of β .

Fig. 2
Fig. 2

(a) The amplitude response and (b) the phase response of the transmission spectrum of the MZI with β = 1.03. The solid lines shows the magnitude and phase response of an ideal differentiator. (c) Simulated output pulse from the MZI. The solid line shows the output pulse from an ideal differentiator. The fractional order is 0.83.

Fig. 3
Fig. 3

Micrographs of (a) MZI, (b) coupling grating, (c) MMI, (d) integrated p-i-n diode.

Fig. 4
Fig. 4

Measured transfer functions of the MZI at different voltages, zigzag line (positive voltages): voltages applied on Arm A, solid line: without voltage, dash and dot line: voltages applied on Arm B.

Fig. 5
Fig. 5

Experimental setup for the fractional order differentiator with on chip MZI structure.

Fig. 6
Fig. 6

(a) An input Gaussian-like pulse with an FWHM of 5.4 ps, and the differentiated pulses at the different voltages corresponding to differentiation orders of (b) N = 0.83, (c) N = 0.85, (d) N = 0.88, (e) N = 0.93, (f) N = 0.96, (g) N = 0.98, (h) N = 1.00, (i) N = 1.03.

Fig. 7
Fig. 7

Measured spectra of input Gaussian-like pulse and the output pulse.

Equations (2)

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E out ( ω )= [ j( ω ω 0 ) ] N E in ( ω )
H( ω )=1+βexp[j( ωτ+ φ 0 )]

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