Abstract

Time stretch transformation of wideband waveforms boosts the performance of analog-to-digital converters and digital signal processors by slowing down analog electrical signals before digitization. The transform is based on dispersive Fourier transformation implemented in the optical domain. A coherent receiver would be ideal for capturing the time-stretched optical signal. Coherent receivers offer improved sensitivity, allow for digital cancellation of dispersion-induced impairments and optical nonlinearities, and enable decoding of phase-modulated optical data formats. Because time-stretch uses a chirped broadband (>1 THz) optical carrier, a new coherent detection technique is required. In this paper, we introduce and demonstrate coherent time stretch transformation; a technique that combines dispersive Fourier transform with optically broadband coherent detection.

© 2013 OSA

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2013 (2)

A. M. Fard, S. Gupta, and B. Jalali, “Photonic time-stretch digitizer and its extension to real-time spectroscopy and imaging,” Laser Photon. Rev.7(2), 207–263 (2013).
[CrossRef]

K. Goda and B. Jalali, “Dispersive Fourier transformation for fast continuous single-shot measurements,” Nat. Photonics7(2), 102–112 (2013).
[CrossRef]

2012 (1)

A. M. Fard, B. Buckley, S. Zlatanovic, C. S. Bres, S. Radic, and B. Jalali, “All-optical time-stretch digitizer,” Appl. Phys. Lett.101(5), 051113 (2012).
[CrossRef]

2011 (1)

A. Mahjoubfar, K. Goda, A. Ayazi, A. Fard, S. H. Kim, and B. Jalali, “High-speed nanometer-resolved imaging vibrometer and velocimeter,” Appl. Phys. Lett.98(10), 101107 (2011).
[CrossRef]

2009 (3)

K. Goda, D. R. Solli, K. K. Tsia, and B. Jalali, “Theory of amplified dispersive Fourier transformation,” Phys. Rev. A: At. Mol. Opt. Phys.80(4), 043821 (2009).
[CrossRef]

J. H. Sinsky and P. J. Winzer, “100-Gb/s optical communications: a microwave engineer's perspective,” IEEE Microw. Mag.10(2), 44–57 (2009).
[CrossRef]

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, “Performance of a 46-Gbps dual-polarization QPSK transceiver with real-time coherent equalization over high PMD fiber,” J. Lightwave Technol.27(3), 158–167 (2009).
[CrossRef]

2008 (4)

2007 (1)

J. Chou, O. Boyraz, D. Solli, and B. Jalali, “Femtosecond real-time single-shot digitizer,” Appl. Phys. Lett.91(16), 161105 (2007).
[CrossRef]

2006 (1)

2005 (1)

Y. Han, O. Boyraz, and B. Jalali, “Ultrawide-band photonic time-stretch A/D converter employing phase diversity,” IEEE Trans. Microw. Theory Tech.53(4), 1404–1408 (2005).
[CrossRef]

2004 (1)

M. G. Taylor, “Coherent detection method using DSP for demodulation of signal and subsequent equalization of propagation impairments,” IEEE Photon. Technol. Lett.16(2), 674–676 (2004).
[CrossRef]

2003 (1)

2001 (3)

J. M. Fuster, D. Novak, A. Nirmalathas, and J. Marti, “Single-sideband modulation in photonic time-stretch analogue-to-digital conversion,” Electron. Lett.37(1), 67–68 (2001).
[CrossRef]

T. Kawanishi, K. Kogo, S. Oikawa, and M. Izutsu, “Direct measurement of chirp parameters of high-speed Mach-Zehnder-type optical modulators,” Opt. Commun.195(5–6), 399–404 (2001).
[CrossRef]

N. Kurosawa, H. Kobayashi, K. Maruyama, H. Sugawara, and K. Kobayashi, “Explicit analysis of channel mismatch effects in time-interleaved ADC systems,” IEEE Trans. Circuits Syst. I, Fundam. Theory Appl48(3), 261–271 (2001).

1999 (2)

R. H. Walden, “Analog-to-digital converter survey and analysis,” IEEE J. Sel. Areas Comm.17(4), 539–550 (1999).
[CrossRef]

P. Kelkar, F. Coppinger, A. Bhushan, and B. Jalali, “Time-domain optical sensing,” Electron. Lett.35(19), 1661–1662 (1999).
[CrossRef]

1998 (1)

A. S. Bhushan, F. Coppinger, and B. Jalali, “Time-stretched analague-to-digital conversion,” Electron. Lett.34(11), 1081–1083 (1998).
[CrossRef]

1995 (1)

H. Schmuck, “Comparison of optical millimeter-wave system concepts with regard to chromatic dispersion,” Electron. Lett.31(21), 1848–1849 (1995).
[CrossRef]

1992 (1)

1987 (1)

T. Okoshi, “Recent advances in coherent optical fiber communication-systems,” J. Lightwave Technol.5(1), 44–52 (1987).
[CrossRef]

Adamiecki, A.

Ayazi, A.

A. Mahjoubfar, K. Goda, A. Ayazi, A. Fard, S. H. Kim, and B. Jalali, “High-speed nanometer-resolved imaging vibrometer and velocimeter,” Appl. Phys. Lett.98(10), 101107 (2011).
[CrossRef]

Barros, D. J. F.

Basch, B.

Bhushan, A.

P. Kelkar, F. Coppinger, A. Bhushan, and B. Jalali, “Time-domain optical sensing,” Electron. Lett.35(19), 1661–1662 (1999).
[CrossRef]

Bhushan, A. S.

A. S. Bhushan, F. Coppinger, and B. Jalali, “Time-stretched analague-to-digital conversion,” Electron. Lett.34(11), 1081–1083 (1998).
[CrossRef]

Boyraz, O.

J. Chou, O. Boyraz, D. Solli, and B. Jalali, “Femtosecond real-time single-shot digitizer,” Appl. Phys. Lett.91(16), 161105 (2007).
[CrossRef]

Y. Han, O. Boyraz, and B. Jalali, “Ultrawide-band photonic time-stretch A/D converter employing phase diversity,” IEEE Trans. Microw. Theory Tech.53(4), 1404–1408 (2005).
[CrossRef]

Bres, C. S.

A. M. Fard, B. Buckley, S. Zlatanovic, C. S. Bres, S. Radic, and B. Jalali, “All-optical time-stretch digitizer,” Appl. Phys. Lett.101(5), 051113 (2012).
[CrossRef]

Buckley, B.

A. M. Fard, B. Buckley, S. Zlatanovic, C. S. Bres, S. Radic, and B. Jalali, “All-optical time-stretch digitizer,” Appl. Phys. Lett.101(5), 051113 (2012).
[CrossRef]

Buhl, L. L.

Chandrasekhar, S.

Chou, J.

J. Chou, O. Boyraz, D. Solli, and B. Jalali, “Femtosecond real-time single-shot digitizer,” Appl. Phys. Lett.91(16), 161105 (2007).
[CrossRef]

Coppinger, F.

P. Kelkar, F. Coppinger, A. Bhushan, and B. Jalali, “Time-domain optical sensing,” Electron. Lett.35(19), 1661–1662 (1999).
[CrossRef]

A. S. Bhushan, F. Coppinger, and B. Jalali, “Time-stretched analague-to-digital conversion,” Electron. Lett.34(11), 1081–1083 (1998).
[CrossRef]

Corteselli, S.

Doerr, C. R.

Essiambre, R. J.

Fard, A.

A. Mahjoubfar, K. Goda, A. Ayazi, A. Fard, S. H. Kim, and B. Jalali, “High-speed nanometer-resolved imaging vibrometer and velocimeter,” Appl. Phys. Lett.98(10), 101107 (2011).
[CrossRef]

Fard, A. M.

A. M. Fard, S. Gupta, and B. Jalali, “Photonic time-stretch digitizer and its extension to real-time spectroscopy and imaging,” Laser Photon. Rev.7(2), 207–263 (2013).
[CrossRef]

A. M. Fard, B. Buckley, S. Zlatanovic, C. S. Bres, S. Radic, and B. Jalali, “All-optical time-stretch digitizer,” Appl. Phys. Lett.101(5), 051113 (2012).
[CrossRef]

Feuer, M. D.

Fishman, D. A.

Foo, S.

Fuster, J. M.

J. M. Fuster, D. Novak, A. Nirmalathas, and J. Marti, “Single-sideband modulation in photonic time-stretch analogue-to-digital conversion,” Electron. Lett.37(1), 67–68 (2001).
[CrossRef]

Gnauck, A. H.

Goda, K.

K. Goda and B. Jalali, “Dispersive Fourier transformation for fast continuous single-shot measurements,” Nat. Photonics7(2), 102–112 (2013).
[CrossRef]

A. Mahjoubfar, K. Goda, A. Ayazi, A. Fard, S. H. Kim, and B. Jalali, “High-speed nanometer-resolved imaging vibrometer and velocimeter,” Appl. Phys. Lett.98(10), 101107 (2011).
[CrossRef]

K. Goda, D. R. Solli, K. K. Tsia, and B. Jalali, “Theory of amplified dispersive Fourier transformation,” Phys. Rev. A: At. Mol. Opt. Phys.80(4), 043821 (2009).
[CrossRef]

Gupta, S.

A. M. Fard, S. Gupta, and B. Jalali, “Photonic time-stretch digitizer and its extension to real-time spectroscopy and imaging,” Laser Photon. Rev.7(2), 207–263 (2013).
[CrossRef]

S. Gupta and B. Jalali, “Time-warp correction and calibration in photonic time-stretch analog-to-digital converter,” Opt. Lett.33(22), 2674–2676 (2008).
[CrossRef] [PubMed]

Han, Y.

Y. Han, O. Boyraz, and B. Jalali, “Ultrawide-band photonic time-stretch A/D converter employing phase diversity,” IEEE Trans. Microw. Theory Tech.53(4), 1404–1408 (2005).
[CrossRef]

Y. Han and B. Jalali, “Photonic time-stretched analog-to-digital converter: Fundamental concepts and practical considerations,” J. Lightwave Technol.21(12), 3085–3103 (2003).
[CrossRef]

Y. Han and B. Jalali, “Differential photonic time-stretch analog-to-digital converter,” in Conference on Lasers and Electro-Optics (CLEO) (IEEE Cat. No.CH37419-TBR), (2003), p. CWH2.

Hanson, D.

Higuma, K.

Ip, E.

Izutsu, M.

T. Kawanishi, K. Kogo, S. Oikawa, and M. Izutsu, “Direct measurement of chirp parameters of high-speed Mach-Zehnder-type optical modulators,” Opt. Commun.195(5–6), 399–404 (2001).
[CrossRef]

Jalali, B.

A. M. Fard, S. Gupta, and B. Jalali, “Photonic time-stretch digitizer and its extension to real-time spectroscopy and imaging,” Laser Photon. Rev.7(2), 207–263 (2013).
[CrossRef]

K. Goda and B. Jalali, “Dispersive Fourier transformation for fast continuous single-shot measurements,” Nat. Photonics7(2), 102–112 (2013).
[CrossRef]

A. M. Fard, B. Buckley, S. Zlatanovic, C. S. Bres, S. Radic, and B. Jalali, “All-optical time-stretch digitizer,” Appl. Phys. Lett.101(5), 051113 (2012).
[CrossRef]

A. Mahjoubfar, K. Goda, A. Ayazi, A. Fard, S. H. Kim, and B. Jalali, “High-speed nanometer-resolved imaging vibrometer and velocimeter,” Appl. Phys. Lett.98(10), 101107 (2011).
[CrossRef]

K. Goda, D. R. Solli, K. K. Tsia, and B. Jalali, “Theory of amplified dispersive Fourier transformation,” Phys. Rev. A: At. Mol. Opt. Phys.80(4), 043821 (2009).
[CrossRef]

S. Gupta and B. Jalali, “Time-warp correction and calibration in photonic time-stretch analog-to-digital converter,” Opt. Lett.33(22), 2674–2676 (2008).
[CrossRef] [PubMed]

J. Chou, O. Boyraz, D. Solli, and B. Jalali, “Femtosecond real-time single-shot digitizer,” Appl. Phys. Lett.91(16), 161105 (2007).
[CrossRef]

Y. Han, O. Boyraz, and B. Jalali, “Ultrawide-band photonic time-stretch A/D converter employing phase diversity,” IEEE Trans. Microw. Theory Tech.53(4), 1404–1408 (2005).
[CrossRef]

Y. Han and B. Jalali, “Photonic time-stretched analog-to-digital converter: Fundamental concepts and practical considerations,” J. Lightwave Technol.21(12), 3085–3103 (2003).
[CrossRef]

P. Kelkar, F. Coppinger, A. Bhushan, and B. Jalali, “Time-domain optical sensing,” Electron. Lett.35(19), 1661–1662 (1999).
[CrossRef]

A. S. Bhushan, F. Coppinger, and B. Jalali, “Time-stretched analague-to-digital conversion,” Electron. Lett.34(11), 1081–1083 (1998).
[CrossRef]

Y. Han and B. Jalali, “Differential photonic time-stretch analog-to-digital converter,” in Conference on Lasers and Electro-Optics (CLEO) (IEEE Cat. No.CH37419-TBR), (2003), p. CWH2.

Kahn, J. M.

Kawanishi, T.

Kelkar, P.

P. Kelkar, F. Coppinger, A. Bhushan, and B. Jalali, “Time-domain optical sensing,” Electron. Lett.35(19), 1661–1662 (1999).
[CrossRef]

Kim, S. H.

A. Mahjoubfar, K. Goda, A. Ayazi, A. Fard, S. H. Kim, and B. Jalali, “High-speed nanometer-resolved imaging vibrometer and velocimeter,” Appl. Phys. Lett.98(10), 101107 (2011).
[CrossRef]

Kobayashi, H.

N. Kurosawa, H. Kobayashi, K. Maruyama, H. Sugawara, and K. Kobayashi, “Explicit analysis of channel mismatch effects in time-interleaved ADC systems,” IEEE Trans. Circuits Syst. I, Fundam. Theory Appl48(3), 261–271 (2001).

Kobayashi, K.

N. Kurosawa, H. Kobayashi, K. Maruyama, H. Sugawara, and K. Kobayashi, “Explicit analysis of channel mismatch effects in time-interleaved ADC systems,” IEEE Trans. Circuits Syst. I, Fundam. Theory Appl48(3), 261–271 (2001).

Kobayashi, T.

Kogo, K.

T. Kawanishi, K. Kogo, S. Oikawa, and M. Izutsu, “Direct measurement of chirp parameters of high-speed Mach-Zehnder-type optical modulators,” Opt. Commun.195(5–6), 399–404 (2001).
[CrossRef]

Kurosawa, N.

N. Kurosawa, H. Kobayashi, K. Maruyama, H. Sugawara, and K. Kobayashi, “Explicit analysis of channel mismatch effects in time-interleaved ADC systems,” IEEE Trans. Circuits Syst. I, Fundam. Theory Appl48(3), 261–271 (2001).

Lau, A. P. T.

Lee, W.

Magill, P. D.

Mahjoubfar, A.

A. Mahjoubfar, K. Goda, A. Ayazi, A. Fard, S. H. Kim, and B. Jalali, “High-speed nanometer-resolved imaging vibrometer and velocimeter,” Appl. Phys. Lett.98(10), 101107 (2011).
[CrossRef]

Marti, J.

J. M. Fuster, D. Novak, A. Nirmalathas, and J. Marti, “Single-sideband modulation in photonic time-stretch analogue-to-digital conversion,” Electron. Lett.37(1), 67–68 (2001).
[CrossRef]

Maruyama, K.

N. Kurosawa, H. Kobayashi, K. Maruyama, H. Sugawara, and K. Kobayashi, “Explicit analysis of channel mismatch effects in time-interleaved ADC systems,” IEEE Trans. Circuits Syst. I, Fundam. Theory Appl48(3), 261–271 (2001).

McGhan, D.

Moyer, M.

Nelson, L. E.

Nirmalathas, A.

J. M. Fuster, D. Novak, A. Nirmalathas, and J. Marti, “Single-sideband modulation in photonic time-stretch analogue-to-digital conversion,” Electron. Lett.37(1), 67–68 (2001).
[CrossRef]

Novak, D.

J. M. Fuster, D. Novak, A. Nirmalathas, and J. Marti, “Single-sideband modulation in photonic time-stretch analogue-to-digital conversion,” Electron. Lett.37(1), 67–68 (2001).
[CrossRef]

Oikawa, S.

T. Kawanishi, K. Kogo, S. Oikawa, and M. Izutsu, “Direct measurement of chirp parameters of high-speed Mach-Zehnder-type optical modulators,” Opt. Commun.195(5–6), 399–404 (2001).
[CrossRef]

Okoshi, T.

T. Okoshi, “Recent advances in coherent optical fiber communication-systems,” J. Lightwave Technol.5(1), 44–52 (1987).
[CrossRef]

Painchaud, Y.

Radic, S.

A. M. Fard, B. Buckley, S. Zlatanovic, C. S. Bres, S. Radic, and B. Jalali, “All-optical time-stretch digitizer,” Appl. Phys. Lett.101(5), 051113 (2012).
[CrossRef]

Raybon, G.

Schmuck, H.

H. Schmuck, “Comparison of optical millimeter-wave system concepts with regard to chromatic dispersion,” Electron. Lett.31(21), 1848–1849 (1995).
[CrossRef]

Sinsky, J. H.

J. H. Sinsky and P. J. Winzer, “100-Gb/s optical communications: a microwave engineer's perspective,” IEEE Microw. Mag.10(2), 44–57 (2009).
[CrossRef]

Solli, D.

J. Chou, O. Boyraz, D. Solli, and B. Jalali, “Femtosecond real-time single-shot digitizer,” Appl. Phys. Lett.91(16), 161105 (2007).
[CrossRef]

Solli, D. R.

K. Goda, D. R. Solli, K. K. Tsia, and B. Jalali, “Theory of amplified dispersive Fourier transformation,” Phys. Rev. A: At. Mol. Opt. Phys.80(4), 043821 (2009).
[CrossRef]

Song, H.

Sugawara, H.

N. Kurosawa, H. Kobayashi, K. Maruyama, H. Sugawara, and K. Kobayashi, “Explicit analysis of channel mismatch effects in time-interleaved ADC systems,” IEEE Trans. Circuits Syst. I, Fundam. Theory Appl48(3), 261–271 (2001).

Sullivan, M. O.

Sun, H.

Taylor, M. G.

M. G. Taylor, “Coherent detection method using DSP for demodulation of signal and subsequent equalization of propagation impairments,” IEEE Photon. Technol. Lett.16(2), 674–676 (2004).
[CrossRef]

Terasaki, A.

Tokunaga, E.

Tsia, K. K.

K. Goda, D. R. Solli, K. K. Tsia, and B. Jalali, “Theory of amplified dispersive Fourier transformation,” Phys. Rev. A: At. Mol. Opt. Phys.80(4), 043821 (2009).
[CrossRef]

Walden, R. H.

R. H. Walden, “Analog-to-digital converter survey and analysis,” IEEE J. Sel. Areas Comm.17(4), 539–550 (1999).
[CrossRef]

Wellbrock, G.

Winzer, P. J.

Woodward, S. L.

Xia, T. J.

Zhou, X.

Zlatanovic, S.

A. M. Fard, B. Buckley, S. Zlatanovic, C. S. Bres, S. Radic, and B. Jalali, “All-optical time-stretch digitizer,” Appl. Phys. Lett.101(5), 051113 (2012).
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Figures (6)

Fig. 1
Fig. 1

Schematic of TiSER. An analog RF input is modulated onto a pre-chirped broadband optical pulse train and stretched in a dispersive fiber resulting in a reduced bandwidth copy of the original signal. The optical signal is converted back to the electrical domain at the photodetector (PD). The signal is then digitized and processed by a real-time ADC and digital processor.

Fig. 2
Fig. 2

Mixing of relatively delayed chirped optical pulses results in a beat frequency in the time-domain. In (a) we illustrate the linear chirp of each pulse by a straight line on a frequency vs. time plot. The signal and LO pulses are delayed with respect to each other, resulting in interference of spectral components offset by a constant intermediate frequency, ωIF. (b) The interference results in a sinusoidal modulation along the optical pulse. If the signal pulse is modulated with an RF signal, the amplitude and phase information is encoded in the IF modulation, analogous to a coherent heterodyne signal.

Fig. 3
Fig. 3

Interference of two broadband, chirped optical pulses results in an intermediate beat frequency along the pulse. (a) In this example, a time delay of 36 ps between the two pulses results in an intermediate frequency of 4 GHz. (b) We characterized the intermediate frequency for a range of relative delays. The measured dispersion of 1090 ps/nm, calculated from the slope, agrees with the specifications of the dispersive fibers used.

Fig. 4
Fig. 4

Schematic of the optical portion of the cTiSER system. After photo-detection the time-stretched analog signal is digitized and processed digitally. In this demonstration, balanced detection was performed using a single PD, with the complementary pulses delayed in time to avoid overlap. Subtraction was performed digitally. D1: first dispersive fiber, D2: second dispersive fiber, OBPF: optical band-pass filter, VDL: variable delay line

Fig. 5
Fig. 5

When using direct detection, dispersion induced transfer function nulls arise, limiting the bandwidth of TiDER. Using coherent detection, we can recover the full complex field, which enables equalization of the dispersion penalty and a flat transfer function. The roll off at higher frequencies is due to limitations of the intensity modulator. Plotted along with the raw data is a sinusoidal model function fit to the un-equalized direct detection transfer function. The dispersion-induced phase was calculated from Eq. (6) and the additional chirp parameter was estimated from non-linear regression.

Fig. 6
Fig. 6

40 Gbit/s NRZ PRBS data was time-stretched and detected using optical direct detection (a) and broadband coherent detection (b). A dispersion penalty transfer function, characterized in Fig. 5, imparts a frequency limitation when using direct detection, which can be equalized digitally using coherent detection. Rise/fall times, measured at 10% and 90% levels, improved from 18.5/19.1 ps to 16.1/15.8 ps upon equalization.

Equations (6)

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I( t ) | E sig ( t ) | 2 + | E LO | 2 ±2Re{ E sig ( t ) E * LO exp( i ω IF t ) }
I( ω ) | E ˜ sig ( ω ) | 2 + | E ˜ LO ( ω ) | 2 ±2Re{ E ˜ sig ( ω ) E ˜ * LO ( ω )exp( iωτ ) }
exp( iωτ )exp( i t β 2 L τ )exp( i ω IF t )
E ˜ LO ( ω ) E env ( t ), E ˜ sig ( ω ) E env ( t ) E RF ( t )
I BD ( t ) | E env ( t ) | 2 Re{ E RF ( t )exp( i ω IF t ) }.
exp( i 1 2 β 2 L 2 S ω RF 2 ),

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