Abstract

A simple and general technique for recovering the phase profile of a given optical waveform from temporal intensity measurements is introduced and experimentally demonstrated. The proposed method involves the measurement of the temporal intensity profiles at the input and output of a linear optical time differentiator. The signal phase profile can be unambiguously recovered from these intensity measurements using a direct and noniterative algorithm. Given that ultrafast optical differentiators can be readily implemented in all-fiber or free-space platforms, the proposed technique could be applied over time waveforms with durations ranging from the subpicosecond to the nanosecond regime.

© 2007 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |

  1. C. Dorrer, IEEE J. Quantum Electron. 12, 843 (2006).
    [CrossRef]
  2. R. Slavík, Y. Park, M. Kulishov, R. Morandotti, and J. Azaña, Opt. Express 14, 10699 (2006).
    [CrossRef] [PubMed]
  3. Y. Park, J. Azaña, and R. Slavík, Opt. Lett. 32, 710 (2007).
    [CrossRef] [PubMed]
  4. J. C. Bortz, J. Opt. Soc. Am. A 1, 35 (1984).
    [CrossRef]
  5. C. Dorrer, Opt. Lett. 30, 3237 (2005).
    [CrossRef] [PubMed]
  6. C. Dorrer, Electron. Lett. 42, 649 (2006).
    [CrossRef]

2007 (1)

2006 (3)

C. Dorrer, IEEE J. Quantum Electron. 12, 843 (2006).
[CrossRef]

C. Dorrer, Electron. Lett. 42, 649 (2006).
[CrossRef]

R. Slavík, Y. Park, M. Kulishov, R. Morandotti, and J. Azaña, Opt. Express 14, 10699 (2006).
[CrossRef] [PubMed]

2005 (1)

1984 (1)

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1
Fig. 1

Experimental setup used for our proof-of-concept demonstrations. FFL, femtosecond fiber laser; Diff (LPFG), long-period fiber grating differentiator; BPF, bandpass filter; EDFA, amplifier; PC, polarization controller.

Fig. 2
Fig. 2

(a) Measured temporal intensity profiles u ( t ) 2 of the pulses after linear dispersive propagation through 5 and 10 km of SMF-28. (b) Pulse instantaneous frequency profiles retrieved by PROUD (solid curves) together with the corresponding linear fitting curves (dashed curves). Inset: measured temporal intensity profiles u ( t ) 2 (solid curve) and v ( t ) 2 (dashed curve) for the case of 5 km dispersive propagation. a.u., arbitrary units.

Fig. 3
Fig. 3

Measured optical spectra (a) and temporal intensity profiles (b) of the pulse under test (solid curve) and of the waveform at the differentiator output (dashed curve).

Fig. 4
Fig. 4

Experimentally recovered (solid curve) and numerically simulated (dashed curve) amplitude (a) and phase (b) temporal profiles of the optical waveform under test.

Equations (2)

Equations on this page are rendered with MathJax. Learn more.

v ( t ) = A ( u ( t ) t + j u ( t ) ϕ ( t ) t + j Δ ω u ( t ) ) e j ϕ ( t ) ,
ϕ ( t ) t = [ ( v ( t ) A ) 2 ( u ( t ) t ) 2 ] u ( t ) 2 Δ ω .

Metrics