## Coherent time-stretch transformation for real-time capture of wideband signals |

Optics Express, Vol. 21, Issue 18, pp. 21618-21627 (2013)

http://dx.doi.org/10.1364/OE.21.021618

Acrobat PDF (1297 KB)

### 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

## 1. Introduction

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

13. 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]

15. 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]

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

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

7. P. J. Winzer and R. J. Essiambre, “Advanced modulation formats for high-capacity optical transport networks,” J. Lightwave Technol. **24**(12), 4711–4728 (2006). [CrossRef]

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

20. K. Goda and B. Jalali, “Dispersive Fourier transformation for fast continuous single-shot measurements,” Nat. Photonics **7**(2), 102–112 (2013). [CrossRef]

21. 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]

22. B. W. Buckley, A. Fard, and B. Jalali, “Time-stretch analog-to-digital conversion using phase modulation and broadband coherent detection for improving resolution,” in *Optical Fiber Communication Conference/National Fiber Optic Engineers Conference 2011, OSA Technical Digest Series (Optical Society of America**,**2011**), **paper OThW4**.* [CrossRef]

23. 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]

## 2. Coherent detection

_{sig}(t)exp(iω

_{sig}t) and E

_{LO}exp(iω

_{LO}t) respectively, where E

_{sig}(t) carries the information, E

_{LO}is the approximately time independent electric field amplitude of the LO source, and ω

_{sig}and ω

_{LO}are the optical carrier frequencies. The physical fields are the real portions of the complex fields written here. The optical intensity, converted to a current signal at the PD, is proportional to the amplitude squared of the sum of the electric fieldswhere ω

_{IF}= ω

_{sig}-ω

_{LO}is the intermediate frequency (IF), and the asterisk signifies complex conjugation. The last term on the right of Eq. (1) is the cross term of interest, which scales linearly with the signal and LO electric fields, and which is upshifted to the IF. In homodyne detection, the signal and LO operate at the same frequency so the IF cancels to zero, leaving only phase offsets. In heterodyne detection the signal and LO operate at different optical frequencies, and the IF is some finite RF frequency given by the difference of the two. The plus and minus signs in front of the cross term represent the complementary outputs of a 2 × 2 interferometric mixer. Balanced detection is achieved by subtracting the two complementary outputs, leaving only the cross term.

_{sig}(t) can be determined in DSP. This capability has spurred the recent advances in coherent lightwave technology, in which phase and amplitude modulated signal formats are employed for improved spectral efficiency and robustness to impairments [7

7. P. J. Winzer and R. J. Essiambre, “Advanced modulation formats for high-capacity optical transport networks,” J. Lightwave Technol. **24**(12), 4711–4728 (2006). [CrossRef]

24. E. Ip, A. P. T. Lau, D. J. F. Barros, and J. M. Kahn, “Coherent detection in optical fiber systems,” Opt. Express **16**(2), 753–791 (2008). [CrossRef] [PubMed]

26. 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]

## 3. Coherent dispersive Fourier transformation

27. E. Tokunaga, A. Terasaki, and T. Kobayashi, “Frequency-domain interferometer for femtosecond time-resolved phase spectroscopy,” Opt. Lett. **17**(16), 1131–1133 (1992). [CrossRef] [PubMed]

_{2}L), where β

_{2}is the dispersion parameter and L is the length of the fiber [28

28. 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]

_{IF}= τ/(β

_{2}L), the IF frequency of the now time domain signal. The optical spectra of the signal and LO pulses are also transformed into time-domain traces. Advantageously, the IF can be adjusted, even for a fixed dispersion, simply by controlling the relative time-delay τ. An example of a time-stretch pulse exhibiting an IF of 4 GHz, corresponding to a τ of 35 ps, is shown in Fig. 3(a), and the IFs for various time delays are plotted in Fig. 3(b). A linear fit is well matched to the data, with a slope indicating a dispersion of 1090 ps/nm, in good agreement with the dispersion used.

_{RF}(t) is the time-stretched RF signal, and E

_{env}(t) is the optical spectrum of the original broadband pulse mapped to the time-domain. To be precise, we should add the time delay τ into the argument for the LO pulse, i.e. E

_{env}(t + τ). However, relative to the total pulse width after dispersion (~10 ns), the time delay τ (<50 ps) is negligible. Additionally, the resolution of the ODFT [28

28. 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]

_{env}(t). After balanced detection, the signal is proportional to the cross term of Eq. (2), with the substitutions of Eq. (3) and Eq. (4),The task, finally, is to characterize the envelope trace and to employ coherent lightwave communication processing techniques to recover the full phase and amplitude information of the linear time-stretched RF signal.

## 4. Experimental setup

## 5. Digital signal processing

## 6. Dispersion compensation

_{2}Lω

^{2}/2) [32]. In an optical communication link using double sideband modulation and direct detection, this dispersion induced phase leads to an intensity transfer function proportional to cos

^{2}(β

_{2}Lω

_{RF}

^{2}/2), limiting the bandwidth of the system [33

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

_{2}is the length of the second dispersive fiber, and ω

_{RF}is the pre-stretched frequency of the RF signal [12

12. 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]

12. 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]

34. 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]

35. 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]

^{2}. The z-cut MZM imparted an additional chirp-induced phase to the sinusoidal transfer function, shifting the first dispersion null to a lower frequency and further limiting the RF bandwidth. A non-linear regression estimated the chirp parameter to be 0.61, and this effect was accounted for in the dispersion compensation [36

36. 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]

## 7. Conclusion

## Acknowledgments

## References and links

1. | R. H. Walden, “Analog-to-digital converter survey and analysis,” IEEE J. Sel. Areas Comm. |

2. | A. Yen, |

3. | J. M. d. Silva and H. Mendonça, |

4. | J. Murphy, “Development of high performance analog-to-digital converters for defense applications,” in |

5. | 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, “Field trial of a real-time, single wavelength, coherent 100 Gbit/s PM-QPSK channel upgrade of an installed 1800 km link,” in |

6. | 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. |

7. | P. J. Winzer and R. J. Essiambre, “Advanced modulation formats for high-capacity optical transport networks,” J. Lightwave Technol. |

8. | P. J. Winzer, G. Raybon, H. Song, A. Adamiecki, S. Corteselli, A. H. Gnauck, D. A. Fishman, C. R. Doerr, S. Chandrasekhar, L. L. Buhl, T. J. Xia, G. Wellbrock, W. Lee, B. Basch, T. Kawanishi, K. Higuma, and Y. Painchaud, “100-Gb/s DQPSK transmission: From laboratory experiments to field trials,” J. Lightwave Technol. |

9. | J. H. Sinsky and P. J. Winzer, “100-Gb/s optical communications: a microwave engineer's perspective,” IEEE Microw. Mag. |

10. | A. S. Bhushan, F. Coppinger, and B. Jalali, “Time-stretched analague-to-digital conversion,” Electron. Lett. |

11. | B. Jalali and F. M. A. Coppinger, “Data conversion using time manipulation,” US Patent 6,288,659 (2001). |

12. | Y. Han and B. Jalali, “Photonic time-stretched analog-to-digital converter: Fundamental concepts and practical considerations,” J. Lightwave Technol. |

13. | A. M. Fard, S. Gupta, and B. Jalali, “Photonic time-stretch digitizer and its extension to real-time spectroscopy and imaging,” Laser Photon. Rev. |

14. | 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 Appl |

15. | S. Gupta and B. Jalali, “Time-warp correction and calibration in photonic time-stretch analog-to-digital converter,” Opt. Lett. |

16. | J. Chou, O. Boyraz, D. Solli, and B. Jalali, “Femtosecond real-time single-shot digitizer,” Appl. Phys. Lett. |

17. | G. P. Agrawal, |

18. | T. Okoshi, “Recent advances in coherent optical fiber communication-systems,” J. Lightwave Technol. |

19. | P. Kelkar, F. Coppinger, A. Bhushan, and B. Jalali, “Time-domain optical sensing,” Electron. Lett. |

20. | K. Goda and B. Jalali, “Dispersive Fourier transformation for fast continuous single-shot measurements,” Nat. Photonics |

21. | A. M. Fard, B. Buckley, S. Zlatanovic, C. S. Bres, S. Radic, and B. Jalali, “All-optical time-stretch digitizer,” Appl. Phys. Lett. |

22. | B. W. Buckley, A. Fard, and B. Jalali, “Time-stretch analog-to-digital conversion using phase modulation and broadband coherent detection for improving resolution,” in |

23. | 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. |

24. | E. Ip, A. P. T. Lau, D. J. F. Barros, and J. M. Kahn, “Coherent detection in optical fiber systems,” Opt. Express |

25. | E. Ip and J. M. Kahn, “Compensation of dispersion and nonlinear impairments using digital backpropagation,” J. Lightwave Technol. |

26. | M. G. Taylor, “Coherent detection method using DSP for demodulation of signal and subsequent equalization of propagation impairments,” IEEE Photon. Technol. Lett. |

27. | E. Tokunaga, A. Terasaki, and T. Kobayashi, “Frequency-domain interferometer for femtosecond time-resolved phase spectroscopy,” Opt. Lett. |

28. | K. Goda, D. R. Solli, K. K. Tsia, and B. Jalali, “Theory of amplified dispersive Fourier transformation,” Phys. Rev. A: At. Mol. Opt. Phys. |

29. | M. A. T. L. A. B. Release, 2012a, The MathWorks, Inc., Natick, Massachusetts, United States. |

30. | L. Cohen, |

31. | 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) |

32. | G. P. Agrawal, |

33. | H. Schmuck, “Comparison of optical millimeter-wave system concepts with regard to chromatic dispersion,” Electron. Lett. |

34. | J. M. Fuster, D. Novak, A. Nirmalathas, and J. Marti, “Single-sideband modulation in photonic time-stretch analogue-to-digital conversion,” Electron. Lett. |

35. | Y. Han, O. Boyraz, and B. Jalali, “Ultrawide-band photonic time-stretch A/D converter employing phase diversity,” IEEE Trans. Microw. Theory Tech. |

36. | T. Kawanishi, K. Kogo, S. Oikawa, and M. Izutsu, “Direct measurement of chirp parameters of high-speed Mach-Zehnder-type optical modulators,” Opt. Commun. |

**OCIS Codes**

(030.1670) Coherence and statistical optics : Coherent optical effects

(060.1660) Fiber optics and optical communications : Coherent communications

(060.2310) Fiber optics and optical communications : Fiber optics

(070.1170) Fourier optics and signal processing : Analog optical signal processing

(140.4050) Lasers and laser optics : Mode-locked lasers

(260.2030) Physical optics : Dispersion

(320.1590) Ultrafast optics : Chirping

**ToC Category:**

Fiber Optics and Optical Communications

**History**

Original Manuscript: June 17, 2013

Revised Manuscript: August 28, 2013

Manuscript Accepted: August 29, 2013

Published: September 6, 2013

**Citation**

Brandon W. Buckley, Asad M. Madni, and Bahram Jalali, "Coherent time-stretch transformation for real-time capture of wideband signals," Opt. Express **21**, 21618-21627 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-18-21618

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### References

- R. H. Walden, “Analog-to-digital converter survey and analysis,” IEEE J. Sel. Areas Comm.17(4), 539–550 (1999). [CrossRef]
- A. Yen, Flow Cytometry: Advanced Research and Clinical Applications (CRC Press, Inc., 1989), Vol. 1.
- J. M. d. Silva and H. Mendonça, ADC Applications, Architectures and Terminology, Dynamic Characterisation of Analogue-to Digital Converters (Kluwer Academic Publishers, 2005), Vol. 860, pp. 3–45.
- J. Murphy, “Development of high performance analog-to-digital converters for defense applications,” in GaAs IC Symposium. IEEE Gallium Arsenide Integrated Circuit Symposium. 19th Annual Technical Digest 1997 (Cat. No.97CH36098), (1997), pp. 83–86.
- 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, “Field trial of a real-time, single wavelength, coherent 100 Gbit/s PM-QPSK channel upgrade of an installed 1800 km link,” in Optical Fiber Communication (OFC), collocated National Fiber Optic Engineers Conference,2010Conference on (OFC/NFOEC), paper PDPD1.
- 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]
- P. J. Winzer and R. J. Essiambre, “Advanced modulation formats for high-capacity optical transport networks,” J. Lightwave Technol.24(12), 4711–4728 (2006). [CrossRef]
- P. J. Winzer, G. Raybon, H. Song, A. Adamiecki, S. Corteselli, A. H. Gnauck, D. A. Fishman, C. R. Doerr, S. Chandrasekhar, L. L. Buhl, T. J. Xia, G. Wellbrock, W. Lee, B. Basch, T. Kawanishi, K. Higuma, and Y. Painchaud, “100-Gb/s DQPSK transmission: From laboratory experiments to field trials,” J. Lightwave Technol.26(20), 3388–3402 (2008). [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]
- A. S. Bhushan, F. Coppinger, and B. Jalali, “Time-stretched analague-to-digital conversion,” Electron. Lett.34(11), 1081–1083 (1998). [CrossRef]
- B. Jalali and F. M. A. Coppinger, “Data conversion using time manipulation,” US Patent 6,288,659 (2001).
- 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]
- 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]
- 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).
- 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]
- G. P. Agrawal, Fiber-Optic Communication Systems, 3rd Ed. (John Wiley & Sons, Inc., 2002), pp. 478–517.
- T. Okoshi, “Recent advances in coherent optical fiber communication-systems,” J. Lightwave Technol.5(1), 44–52 (1987). [CrossRef]
- P. Kelkar, F. Coppinger, A. Bhushan, and B. Jalali, “Time-domain optical sensing,” Electron. Lett.35(19), 1661–1662 (1999). [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]
- B. W. Buckley, A. Fard, and B. Jalali, “Time-stretch analog-to-digital conversion using phase modulation and broadband coherent detection for improving resolution,” in Optical Fiber Communication Conference/National Fiber Optic Engineers Conference 2011, OSA Technical Digest Series (Optical Society of America,2011), paper OThW4. [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]
- E. Ip, A. P. T. Lau, D. J. F. Barros, and J. M. Kahn, “Coherent detection in optical fiber systems,” Opt. Express16(2), 753–791 (2008). [CrossRef] [PubMed]
- E. Ip and J. M. Kahn, “Compensation of dispersion and nonlinear impairments using digital backpropagation,” J. Lightwave Technol.26(20), 3416–3425 (2008). [CrossRef]
- 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]
- E. Tokunaga, A. Terasaki, and T. Kobayashi, “Frequency-domain interferometer for femtosecond time-resolved phase spectroscopy,” Opt. Lett.17(16), 1131–1133 (1992). [CrossRef] [PubMed]
- 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]
- M. A. T. L. A. B. Release, 2012a, The MathWorks, Inc., Natick, Massachusetts, United States.
- L. Cohen, Time-frequency analysis (Prentice Hall PTR, 1995), pp. 30–31.
- 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.
- G. P. Agrawal, Nonlinear Fiber Optics, 4th Ed. (Academic Press, 2007), pp. 51–78.
- H. Schmuck, “Comparison of optical millimeter-wave system concepts with regard to chromatic dispersion,” Electron. Lett.31(21), 1848–1849 (1995). [CrossRef]
- 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]
- 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]
- 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]

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