Optical Review

, Volume 25, Issue 5, pp 598–607 | Cite as

Chirp-coefficient bisection iteration method for phase-intensity reconstruction of chirped pulses

  • Gan Gao
  • Yijie Shen
  • Decai Deng
  • Yuan Meng
  • Linlu He
  • Mali Gong
  • Haitao ZhangEmail author
Regular Paper


A new method is proposed to systematically measure the phase-intensity information of chirped pulses that is based on the chirp-coefficient bisection iteration (CBI) concept. Through the CBI procedure with measured spectrum and temporal intensity profiles (or intensity autocorrelations), spectral and temporal amplitude–phase information can be rapidly retrieved. We experimentally verified that our method has high precision for nanosecond- and picosecond-level pulses and low precision for femtosecond-level pulses. Our proposed method does not require a sophisticated setup and has the advantage of accurate determination of temporal and spectral chirp coefficients with various orders. It also has lower cost, simple operation, in particular covers a wider measurement range than the main current methods. Moreover, the retrieved waveforms can reveal both the pulse shape and the actual intensity with spectral and temporal chirped coefficients of various orders, which can be directly used in various pulse propagation analyses such as chirped pulse amplification.


Ultrafast lasers Fiber optics Ultrafast measurements Nonlinear optics Chirped pulses 



This research was supported by the National Natural Science Foundation of China No. 61475081.

Compliance with ethical standards

Conflict of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.


  1. 1.
    Trebino, R., Kane, D.J.: Using phase retrieval to measure the intensity and phase of ultrashort pulses: frequency-resolved optical gating. J. Opt. Soc. Am. A. 10(5), 1101–1111 (1993). ADSCrossRefGoogle Scholar
  2. 2.
    Iaconis, C., Walmsley, I.A.: Spectral phase interferometry for direct electric-field reconstruction of ultrashort optical pulses. Opt. Lett. 23(10), 792–794 (1998). ADSCrossRefGoogle Scholar
  3. 3.
    Su, J., Shaw, E.D.: Phase and amplitude reconstruction from 2D frequency domain interferogram for mid-infrared short optical pulse. In: Optoelectronics ‘99—integrated optoelectronic devices, p. 8. SPIE, ‎Bellingham (1999)Google Scholar
  4. 4.
    Nicholson, J.W., Jasapara, J., Rudolph, W., Omenetto, F.G., Taylor, A.J.: Full-field characterization of femtosecond pulses by spectrum and cross-correlation measurements. Opt. Lett. 24(23), 1774–1776 (1999). ADSCrossRefGoogle Scholar
  5. 5.
    Baltuska, A., Pugzlys, A., Pshenichnikov, M.S., Wiersma, D.A.: Rapid amplitude–phase reconstruction of femtosecond pulses from intensity autocorrelation and spectrum. In: Lasers and Electro-Optics, 1999. CLEO ‘99. Summaries of Papers Presented at the Conference on May 1999, pp. 264–265Google Scholar
  6. 6.
    Jung-Ho, C., Weiner, A.M.: Ambiguity of ultrashort pulse shapes retrieved from the intensity autocorrelation and the power spectrum. IEEE J. Sel. Top. Quantum Electron. 7(4), 656–666 (2001). ADSCrossRefGoogle Scholar
  7. 7.
    Radzewicz, C., Wasylczyk, P., Krasinski, J.S.: A poor man’s FROG. Opt. Commun. 186(4), 329–333 (2000). ADSCrossRefGoogle Scholar
  8. 8.
    O’Shea, P., Kimmel, M., Gu, X., Trebino, R.: Highly simplified device for ultrashort-pulse measurement. Opt. Lett. 26(12), 932–934 (2001). ADSCrossRefGoogle Scholar
  9. 9.
    Cohen, J., Lee, D., Chauhan, V., Vaughan, P., Trebino, R.: Highly simplified device for measuring the intensity and phase of picosecond pulses. Opt. Express. 18(16), 17484–17497 (2010). ADSCrossRefGoogle Scholar
  10. 10.
    Konishi, T., Tanimura, K., Oshita, Y., Ichioka, Y.: Optical spectrogram scope (OSS) for measurement of ultrashort pulses. In: International Symposium on Optical Science and Technology, p. 6. SPIE, (2002)Google Scholar
  11. 11.
    Liu, C., Ruan, S., Liu, C., Long, J.: A novel measuring implementation of femtosecond pulse amplitude and phase based on frequency-resolved optical gating. In: Asia-Pacific optical communications, p. 6. SPIE, Bellingham (2005)Google Scholar
  12. 12.
    Shen, X., Wang, P., Liu, J., Kobayashi, T., Li, R.: Self-referenced spectral interferometry for femtosecond pulse characterization. Appl. Sci. 7(4), 407 (2017)CrossRefGoogle Scholar
  13. 13.
    Tajalli, A., Chanteau, B., Kretschmar, M., Kurz, H.G., Zuber, D., Kovačev, M., Morgner, U., Nagy, T.: Few-cycle optical pulse characterization via cross-polarized wave generation dispersion scan technique. Opt. Lett. 41(22), 5246–5249 (2016). ADSCrossRefGoogle Scholar
  14. 14.
    Fan, W., Du, S., Zhang, B., Liu, D., Yan, Y., Zhu, B., Shui, M., Zhang, X., Wang, Y., Gu, Y.: Study of the frequency domain interference method for chirp measurement. Optik Int. J. Light Electron Opt. 127(1), 1–4 (2016). CrossRefGoogle Scholar
  15. 15.
    Zheng, S., Cai, Y., Pan, X., Zeng, X., Li, J., Li, Y., Zhu, T., Lin, Q., Xu, S.: Two-step phase-shifting SPIDER. Sci. Rep. 6, 33837 (2016). ADSCrossRefGoogle Scholar
  16. 16.
    Runge, A.F.J., Aguergaray, C., Provo, R., Erkintalo, M., Broderick, N.G.R.: All-normal dispersion fiber lasers mode-locked with a nonlinear amplifying loop mirror. Opt. Fiber Technol. 20(6), 657–665 (2014). ADSCrossRefGoogle Scholar
  17. 17.
    Gan, G., Haitao, Z., Yuhe, L., Decai, D.: All-normal-dispersion fiber laser with NALM: power scalability of the single-pulse regime. Laser Phys. Lett. 15(3), 035106 (2018)ADSCrossRefGoogle Scholar
  18. 18.
    Agrawal, G.: Chap. 2 - Pulse Propagation in Fibers. In: Nonlinear fiber optics. 5th Edn, pp. 27–56. Academic Press, Boston (2013)CrossRefGoogle Scholar
  19. 19.
    Boscolo, S., Finot, C., Karakuzu, H., Petropoulos, P.: Pulse shaping in mode-locked fiber lasers by in-cavity spectral filter. Opt. Lett. 39(3), 438–441 (2014). ADSCrossRefGoogle Scholar
  20. 20.
    Theodoros, P.H., İlkay, B., Nalan, A.: Pulse shaping mechanism in mode-locked lasers. J. Opt. 18(6), 06LT01 (2016)CrossRefGoogle Scholar
  21. 21.
    Paschotta, R., Häring, R., Garnache, A., Hoogland, S., Tropper, A.C., Keller, U.: Soliton-like pulse-shaping mechanism in passively mode-locked surface-emitting semiconductor lasers. Appl. Phys. B. 75(4), 445–451 (2002). ADSCrossRefGoogle Scholar
  22. 22.
    Limpert, J., Schreiber, T., Clausnitzer, T., Zöllner, K., Fuchs, H.J., Kley, E.B., Zellmer, H., Tünnermann, A.: High-power femtosecond Yb-doped fiber amplifier. Opt. Express. 10(14), 628–638 (2002). ADSCrossRefGoogle Scholar
  23. 23.
    Deng, Y., Chien, C.-Y., Fidric, B.G., Kafka, J.D.: Generation of sub-50 fs pulses from a high-power Yb-doped fiber amplifier. Opt. Lett. 34(22), 3469–3471 (2009). ADSCrossRefGoogle Scholar
  24. 24.
    Oktem, B., Ülgüdür, C., Ilday, F.: Soliton–similariton fibre laser. Nat. Photonics. 4, 307 (2010). CrossRefGoogle Scholar

Copyright information

© The Optical Society of Japan 2018

Authors and Affiliations

  • Gan Gao
    • 1
  • Yijie Shen
    • 1
  • Decai Deng
    • 1
  • Yuan Meng
    • 1
  • Linlu He
    • 1
  • Mali Gong
    • 1
  • Haitao Zhang
    • 1
    Email author
  1. 1.State Key Laboratory of Precision Measurement Technology and Instruments, Center for Photonics and Electronics, Department of Precision InstrumentsTsinghua UniversityBeijingChina

Personalised recommendations