Abstract

Suppression of distortion induced by nonlinearity in a dynamical system (such as an analog optical link) is very challenging, particularly for a wide-bandwidth signal. Conventional compensation techniques are computationally intensive, significantly limiting their realization in real-time applications. Here, we propose and demonstrate an efficient digital postprocessing technique to suppress distortions added to a wideband signal by a nonlinear system with memory effect. Experimentally, digital broadband linearization of the photonic time-stretch analog-to-digital converter (TSADC) is demonstrated. In case of TSADC, a dynamic range improvement of >15dB compared to conventional memory-less correction method is achieved.

© 2011 Optical Society of America

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  1. A. Gelb and W. E. Vander Velde, Multiple-Input Describing Functions and Nonlinear System Design (McGraw-Hill, 1968).
  2. J. J. Bussgang, L. Ehrman, and J. W. Graham, Proc. IEEE 62, 1088 (1974).
    [CrossRef]
  3. W. J. Rugh, Nonlinear System Theory: the Volterra/Wiener Approach (The John Hopkins University, 1981).
  4. J. Capmany and D. Novak, Nat. Photon. 1, 319 (2007).
    [CrossRef]
  5. A. S. Bhushan, F. Coppinger, and B. Jalali, Electron. Lett. 34, 1081 (1998).
    [CrossRef]
  6. B. Jalali and F. Coppinger, “Data conversion using time manipulation,” U.S. patent number 6,288,659(September 11, 2001).
  7. Y. Han and B. Jalali, J. Lightwave Technol. 21, 3085 (2003).
    [CrossRef]
  8. G. C. Valley, Opt. Express 15, 1955 (2007).
    [CrossRef] [PubMed]
  9. S. Gupta and B. Jalali, Opt. Lett. 33, 2674 (2008).
    [CrossRef] [PubMed]
  10. S. Gupta, G. Valley, and B. Jalali, J. Lightwave Technol. 25, 3716 (2007).
    [CrossRef]
  11. J. Stigwall and S. Galt, J. Lightwave Technol. 25, 3017(2007).
    [CrossRef]
  12. S. Gupta, B. Jalali, J. Stigwall, and S. Galt, in International Topical Meeting on Microwave Photonics (IEEE, 2007), pp. 141–144.
  13. M. Birk, P. Gerard, R. Curto, L. Nelson, X. Zhou, P. Magill, T. J. Schmidt, C. Malouin, B. Zhang, E. Ibragimov, S. Khatana, M. Glavanovic, R. Lofland, R. Marcoccia, G. Nicholl, M. Nowell, and F. Forghieri, in National Fiber Optic Engineers Conference (Optical Society of America, 2010), paper PDPD1.
  14. L. E. Nelson, S. L. Woodward, S. Foo, X. Zhou, M. D. Feuer, D. Hanson, D. McGhan, H. Sun, M. Moyer, M. O. Sullivan, and P. D. Magill, J. Lightwave Technol. 27, 158 (2009)
    [CrossRef]
  15. T. J. Xia, G. Wellbrock, B. Basch, S. Kotrla, W. Lee, T. Tajima, K. Fukuchi, M. Cvijetic, J. Sugg, Y. Ma, B. Turner, C. Cole, and C. Urricariet, in National Fiber Optic Engineers Conference (Optical Society of America, 2010), paper PDPD4.

2009 (1)

2008 (1)

2007 (4)

2003 (1)

1998 (1)

A. S. Bhushan, F. Coppinger, and B. Jalali, Electron. Lett. 34, 1081 (1998).
[CrossRef]

1974 (1)

J. J. Bussgang, L. Ehrman, and J. W. Graham, Proc. IEEE 62, 1088 (1974).
[CrossRef]

Basch, B.

T. J. Xia, G. Wellbrock, B. Basch, S. Kotrla, W. Lee, T. Tajima, K. Fukuchi, M. Cvijetic, J. Sugg, Y. Ma, B. Turner, C. Cole, and C. Urricariet, in National Fiber Optic Engineers Conference (Optical Society of America, 2010), paper PDPD4.

Bhushan, A. S.

A. S. Bhushan, F. Coppinger, and B. Jalali, Electron. Lett. 34, 1081 (1998).
[CrossRef]

Birk, M.

M. Birk, P. Gerard, R. Curto, L. Nelson, X. Zhou, P. Magill, T. J. Schmidt, C. Malouin, B. Zhang, E. Ibragimov, S. Khatana, M. Glavanovic, R. Lofland, R. Marcoccia, G. Nicholl, M. Nowell, and F. Forghieri, in National Fiber Optic Engineers Conference (Optical Society of America, 2010), paper PDPD1.

Bussgang, J. J.

J. J. Bussgang, L. Ehrman, and J. W. Graham, Proc. IEEE 62, 1088 (1974).
[CrossRef]

Capmany, J.

J. Capmany and D. Novak, Nat. Photon. 1, 319 (2007).
[CrossRef]

Cole, C.

T. J. Xia, G. Wellbrock, B. Basch, S. Kotrla, W. Lee, T. Tajima, K. Fukuchi, M. Cvijetic, J. Sugg, Y. Ma, B. Turner, C. Cole, and C. Urricariet, in National Fiber Optic Engineers Conference (Optical Society of America, 2010), paper PDPD4.

Coppinger, F.

A. S. Bhushan, F. Coppinger, and B. Jalali, Electron. Lett. 34, 1081 (1998).
[CrossRef]

B. Jalali and F. Coppinger, “Data conversion using time manipulation,” U.S. patent number 6,288,659(September 11, 2001).

Curto, R.

M. Birk, P. Gerard, R. Curto, L. Nelson, X. Zhou, P. Magill, T. J. Schmidt, C. Malouin, B. Zhang, E. Ibragimov, S. Khatana, M. Glavanovic, R. Lofland, R. Marcoccia, G. Nicholl, M. Nowell, and F. Forghieri, in National Fiber Optic Engineers Conference (Optical Society of America, 2010), paper PDPD1.

Cvijetic, M.

T. J. Xia, G. Wellbrock, B. Basch, S. Kotrla, W. Lee, T. Tajima, K. Fukuchi, M. Cvijetic, J. Sugg, Y. Ma, B. Turner, C. Cole, and C. Urricariet, in National Fiber Optic Engineers Conference (Optical Society of America, 2010), paper PDPD4.

Ehrman, L.

J. J. Bussgang, L. Ehrman, and J. W. Graham, Proc. IEEE 62, 1088 (1974).
[CrossRef]

Feuer, M. D.

Foo, S.

Forghieri, F.

M. Birk, P. Gerard, R. Curto, L. Nelson, X. Zhou, P. Magill, T. J. Schmidt, C. Malouin, B. Zhang, E. Ibragimov, S. Khatana, M. Glavanovic, R. Lofland, R. Marcoccia, G. Nicholl, M. Nowell, and F. Forghieri, in National Fiber Optic Engineers Conference (Optical Society of America, 2010), paper PDPD1.

Fukuchi, K.

T. J. Xia, G. Wellbrock, B. Basch, S. Kotrla, W. Lee, T. Tajima, K. Fukuchi, M. Cvijetic, J. Sugg, Y. Ma, B. Turner, C. Cole, and C. Urricariet, in National Fiber Optic Engineers Conference (Optical Society of America, 2010), paper PDPD4.

Galt, S.

J. Stigwall and S. Galt, J. Lightwave Technol. 25, 3017(2007).
[CrossRef]

S. Gupta, B. Jalali, J. Stigwall, and S. Galt, in International Topical Meeting on Microwave Photonics (IEEE, 2007), pp. 141–144.

Gelb, A.

A. Gelb and W. E. Vander Velde, Multiple-Input Describing Functions and Nonlinear System Design (McGraw-Hill, 1968).

Gerard, P.

M. Birk, P. Gerard, R. Curto, L. Nelson, X. Zhou, P. Magill, T. J. Schmidt, C. Malouin, B. Zhang, E. Ibragimov, S. Khatana, M. Glavanovic, R. Lofland, R. Marcoccia, G. Nicholl, M. Nowell, and F. Forghieri, in National Fiber Optic Engineers Conference (Optical Society of America, 2010), paper PDPD1.

Glavanovic, M.

M. Birk, P. Gerard, R. Curto, L. Nelson, X. Zhou, P. Magill, T. J. Schmidt, C. Malouin, B. Zhang, E. Ibragimov, S. Khatana, M. Glavanovic, R. Lofland, R. Marcoccia, G. Nicholl, M. Nowell, and F. Forghieri, in National Fiber Optic Engineers Conference (Optical Society of America, 2010), paper PDPD1.

Graham, J. W.

J. J. Bussgang, L. Ehrman, and J. W. Graham, Proc. IEEE 62, 1088 (1974).
[CrossRef]

Gupta, S.

S. Gupta and B. Jalali, Opt. Lett. 33, 2674 (2008).
[CrossRef] [PubMed]

S. Gupta, G. Valley, and B. Jalali, J. Lightwave Technol. 25, 3716 (2007).
[CrossRef]

S. Gupta, B. Jalali, J. Stigwall, and S. Galt, in International Topical Meeting on Microwave Photonics (IEEE, 2007), pp. 141–144.

Han, Y.

Hanson, D.

Ibragimov, E.

M. Birk, P. Gerard, R. Curto, L. Nelson, X. Zhou, P. Magill, T. J. Schmidt, C. Malouin, B. Zhang, E. Ibragimov, S. Khatana, M. Glavanovic, R. Lofland, R. Marcoccia, G. Nicholl, M. Nowell, and F. Forghieri, in National Fiber Optic Engineers Conference (Optical Society of America, 2010), paper PDPD1.

Jalali, B.

S. Gupta and B. Jalali, Opt. Lett. 33, 2674 (2008).
[CrossRef] [PubMed]

S. Gupta, G. Valley, and B. Jalali, J. Lightwave Technol. 25, 3716 (2007).
[CrossRef]

Y. Han and B. Jalali, J. Lightwave Technol. 21, 3085 (2003).
[CrossRef]

A. S. Bhushan, F. Coppinger, and B. Jalali, Electron. Lett. 34, 1081 (1998).
[CrossRef]

S. Gupta, B. Jalali, J. Stigwall, and S. Galt, in International Topical Meeting on Microwave Photonics (IEEE, 2007), pp. 141–144.

B. Jalali and F. Coppinger, “Data conversion using time manipulation,” U.S. patent number 6,288,659(September 11, 2001).

Khatana, S.

M. Birk, P. Gerard, R. Curto, L. Nelson, X. Zhou, P. Magill, T. J. Schmidt, C. Malouin, B. Zhang, E. Ibragimov, S. Khatana, M. Glavanovic, R. Lofland, R. Marcoccia, G. Nicholl, M. Nowell, and F. Forghieri, in National Fiber Optic Engineers Conference (Optical Society of America, 2010), paper PDPD1.

Kotrla, S.

T. J. Xia, G. Wellbrock, B. Basch, S. Kotrla, W. Lee, T. Tajima, K. Fukuchi, M. Cvijetic, J. Sugg, Y. Ma, B. Turner, C. Cole, and C. Urricariet, in National Fiber Optic Engineers Conference (Optical Society of America, 2010), paper PDPD4.

Lee, W.

T. J. Xia, G. Wellbrock, B. Basch, S. Kotrla, W. Lee, T. Tajima, K. Fukuchi, M. Cvijetic, J. Sugg, Y. Ma, B. Turner, C. Cole, and C. Urricariet, in National Fiber Optic Engineers Conference (Optical Society of America, 2010), paper PDPD4.

Lofland, R.

M. Birk, P. Gerard, R. Curto, L. Nelson, X. Zhou, P. Magill, T. J. Schmidt, C. Malouin, B. Zhang, E. Ibragimov, S. Khatana, M. Glavanovic, R. Lofland, R. Marcoccia, G. Nicholl, M. Nowell, and F. Forghieri, in National Fiber Optic Engineers Conference (Optical Society of America, 2010), paper PDPD1.

Ma, Y.

T. J. Xia, G. Wellbrock, B. Basch, S. Kotrla, W. Lee, T. Tajima, K. Fukuchi, M. Cvijetic, J. Sugg, Y. Ma, B. Turner, C. Cole, and C. Urricariet, in National Fiber Optic Engineers Conference (Optical Society of America, 2010), paper PDPD4.

Magill, P.

M. Birk, P. Gerard, R. Curto, L. Nelson, X. Zhou, P. Magill, T. J. Schmidt, C. Malouin, B. Zhang, E. Ibragimov, S. Khatana, M. Glavanovic, R. Lofland, R. Marcoccia, G. Nicholl, M. Nowell, and F. Forghieri, in National Fiber Optic Engineers Conference (Optical Society of America, 2010), paper PDPD1.

Magill, P. D.

Malouin, C.

M. Birk, P. Gerard, R. Curto, L. Nelson, X. Zhou, P. Magill, T. J. Schmidt, C. Malouin, B. Zhang, E. Ibragimov, S. Khatana, M. Glavanovic, R. Lofland, R. Marcoccia, G. Nicholl, M. Nowell, and F. Forghieri, in National Fiber Optic Engineers Conference (Optical Society of America, 2010), paper PDPD1.

Marcoccia, R.

M. Birk, P. Gerard, R. Curto, L. Nelson, X. Zhou, P. Magill, T. J. Schmidt, C. Malouin, B. Zhang, E. Ibragimov, S. Khatana, M. Glavanovic, R. Lofland, R. Marcoccia, G. Nicholl, M. Nowell, and F. Forghieri, in National Fiber Optic Engineers Conference (Optical Society of America, 2010), paper PDPD1.

McGhan, D.

Moyer, M.

Nelson, L.

M. Birk, P. Gerard, R. Curto, L. Nelson, X. Zhou, P. Magill, T. J. Schmidt, C. Malouin, B. Zhang, E. Ibragimov, S. Khatana, M. Glavanovic, R. Lofland, R. Marcoccia, G. Nicholl, M. Nowell, and F. Forghieri, in National Fiber Optic Engineers Conference (Optical Society of America, 2010), paper PDPD1.

Nelson, L. E.

Nicholl, G.

M. Birk, P. Gerard, R. Curto, L. Nelson, X. Zhou, P. Magill, T. J. Schmidt, C. Malouin, B. Zhang, E. Ibragimov, S. Khatana, M. Glavanovic, R. Lofland, R. Marcoccia, G. Nicholl, M. Nowell, and F. Forghieri, in National Fiber Optic Engineers Conference (Optical Society of America, 2010), paper PDPD1.

Novak, D.

J. Capmany and D. Novak, Nat. Photon. 1, 319 (2007).
[CrossRef]

Nowell, M.

M. Birk, P. Gerard, R. Curto, L. Nelson, X. Zhou, P. Magill, T. J. Schmidt, C. Malouin, B. Zhang, E. Ibragimov, S. Khatana, M. Glavanovic, R. Lofland, R. Marcoccia, G. Nicholl, M. Nowell, and F. Forghieri, in National Fiber Optic Engineers Conference (Optical Society of America, 2010), paper PDPD1.

Rugh, W. J.

W. J. Rugh, Nonlinear System Theory: the Volterra/Wiener Approach (The John Hopkins University, 1981).

Schmidt, T. J.

M. Birk, P. Gerard, R. Curto, L. Nelson, X. Zhou, P. Magill, T. J. Schmidt, C. Malouin, B. Zhang, E. Ibragimov, S. Khatana, M. Glavanovic, R. Lofland, R. Marcoccia, G. Nicholl, M. Nowell, and F. Forghieri, in National Fiber Optic Engineers Conference (Optical Society of America, 2010), paper PDPD1.

Stigwall, J.

J. Stigwall and S. Galt, J. Lightwave Technol. 25, 3017(2007).
[CrossRef]

S. Gupta, B. Jalali, J. Stigwall, and S. Galt, in International Topical Meeting on Microwave Photonics (IEEE, 2007), pp. 141–144.

Sugg, J.

T. J. Xia, G. Wellbrock, B. Basch, S. Kotrla, W. Lee, T. Tajima, K. Fukuchi, M. Cvijetic, J. Sugg, Y. Ma, B. Turner, C. Cole, and C. Urricariet, in National Fiber Optic Engineers Conference (Optical Society of America, 2010), paper PDPD4.

Sullivan, M. O.

Sun, H.

Tajima, T.

T. J. Xia, G. Wellbrock, B. Basch, S. Kotrla, W. Lee, T. Tajima, K. Fukuchi, M. Cvijetic, J. Sugg, Y. Ma, B. Turner, C. Cole, and C. Urricariet, in National Fiber Optic Engineers Conference (Optical Society of America, 2010), paper PDPD4.

Turner, B.

T. J. Xia, G. Wellbrock, B. Basch, S. Kotrla, W. Lee, T. Tajima, K. Fukuchi, M. Cvijetic, J. Sugg, Y. Ma, B. Turner, C. Cole, and C. Urricariet, in National Fiber Optic Engineers Conference (Optical Society of America, 2010), paper PDPD4.

Urricariet, C.

T. J. Xia, G. Wellbrock, B. Basch, S. Kotrla, W. Lee, T. Tajima, K. Fukuchi, M. Cvijetic, J. Sugg, Y. Ma, B. Turner, C. Cole, and C. Urricariet, in National Fiber Optic Engineers Conference (Optical Society of America, 2010), paper PDPD4.

Valley, G.

Valley, G. C.

Vander Velde, W. E.

A. Gelb and W. E. Vander Velde, Multiple-Input Describing Functions and Nonlinear System Design (McGraw-Hill, 1968).

Wellbrock, G.

T. J. Xia, G. Wellbrock, B. Basch, S. Kotrla, W. Lee, T. Tajima, K. Fukuchi, M. Cvijetic, J. Sugg, Y. Ma, B. Turner, C. Cole, and C. Urricariet, in National Fiber Optic Engineers Conference (Optical Society of America, 2010), paper PDPD4.

Woodward, S. L.

Xia, T. J.

T. J. Xia, G. Wellbrock, B. Basch, S. Kotrla, W. Lee, T. Tajima, K. Fukuchi, M. Cvijetic, J. Sugg, Y. Ma, B. Turner, C. Cole, and C. Urricariet, in National Fiber Optic Engineers Conference (Optical Society of America, 2010), paper PDPD4.

Zhang, B.

M. Birk, P. Gerard, R. Curto, L. Nelson, X. Zhou, P. Magill, T. J. Schmidt, C. Malouin, B. Zhang, E. Ibragimov, S. Khatana, M. Glavanovic, R. Lofland, R. Marcoccia, G. Nicholl, M. Nowell, and F. Forghieri, in National Fiber Optic Engineers Conference (Optical Society of America, 2010), paper PDPD1.

Zhou, X.

L. E. Nelson, S. L. Woodward, S. Foo, X. Zhou, M. D. Feuer, D. Hanson, D. McGhan, H. Sun, M. Moyer, M. O. Sullivan, and P. D. Magill, J. Lightwave Technol. 27, 158 (2009)
[CrossRef]

M. Birk, P. Gerard, R. Curto, L. Nelson, X. Zhou, P. Magill, T. J. Schmidt, C. Malouin, B. Zhang, E. Ibragimov, S. Khatana, M. Glavanovic, R. Lofland, R. Marcoccia, G. Nicholl, M. Nowell, and F. Forghieri, in National Fiber Optic Engineers Conference (Optical Society of America, 2010), paper PDPD1.

Electron. Lett. (1)

A. S. Bhushan, F. Coppinger, and B. Jalali, Electron. Lett. 34, 1081 (1998).
[CrossRef]

J. Lightwave Technol. (4)

Nat. Photon. (1)

J. Capmany and D. Novak, Nat. Photon. 1, 319 (2007).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Proc. IEEE (1)

J. J. Bussgang, L. Ehrman, and J. W. Graham, Proc. IEEE 62, 1088 (1974).
[CrossRef]

Other (6)

W. J. Rugh, Nonlinear System Theory: the Volterra/Wiener Approach (The John Hopkins University, 1981).

A. Gelb and W. E. Vander Velde, Multiple-Input Describing Functions and Nonlinear System Design (McGraw-Hill, 1968).

B. Jalali and F. Coppinger, “Data conversion using time manipulation,” U.S. patent number 6,288,659(September 11, 2001).

S. Gupta, B. Jalali, J. Stigwall, and S. Galt, in International Topical Meeting on Microwave Photonics (IEEE, 2007), pp. 141–144.

M. Birk, P. Gerard, R. Curto, L. Nelson, X. Zhou, P. Magill, T. J. Schmidt, C. Malouin, B. Zhang, E. Ibragimov, S. Khatana, M. Glavanovic, R. Lofland, R. Marcoccia, G. Nicholl, M. Nowell, and F. Forghieri, in National Fiber Optic Engineers Conference (Optical Society of America, 2010), paper PDPD1.

T. J. Xia, G. Wellbrock, B. Basch, S. Kotrla, W. Lee, T. Tajima, K. Fukuchi, M. Cvijetic, J. Sugg, Y. Ma, B. Turner, C. Cole, and C. Urricariet, in National Fiber Optic Engineers Conference (Optical Society of America, 2010), paper PDPD4.

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Figures (3)

Fig. 1
Fig. 1

Block diagram of the demonstrated broadband linearization technique.

Fig. 2
Fig. 2

Experimental setup of the photonic TSADC to evaluate the broadband linearization technique. EDFA, Er-doped fiber amplifier; PD, photodetector; DCF, dispersion-compensating fiber; ADC, analog-to-digital converter.

Fig. 3
Fig. 3

Signal power for a two-tone test ( f 1 = 8.2 GHz , f 2 = 10.25 GHz ) (a) before any corrections for nonlinearity, (b) after conventional arcsine operation, showing incomplete cancellation of intermodulation distortion, (c) after broadband linearization, showing drastic improvement of in termodulation distortions ( 2 f 1 f 2 = 6.15 GHz and 2 f 2 f 1 = 12.3 GHz ) over conventional arcsine operation.

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