## Simultaneous amplitude and phase measurement for periodic optical signals using time-resolved optical filtering

Optics Express, Vol. 14, Issue 1, pp. 103-113 (2006)

http://dx.doi.org/10.1364/OPEX.14.000103

Acrobat PDF (852 KB)

### Abstract

Time-resolved optical filtering (TROF) measures the spectrogram or sonogram by a fast photodiode followed a tunable narrowband optical filter. For periodic signal and to match the spectrogram, numerical TROF algorithm is used to find the original complex electric field or equivalently both the amplitude and phase. For phase-modulated optical signals, the TROF algorithm is initiated using the craters and ridges of the spectrogram.

© 2006 Optical Society of America

## 1. Introduction

1. A. H. Gnauck, G. Raybon, S. Chandrasekhar, J. Leuthold, C. Doerr, L. Stulz, A. Agrawal, S. Banerjee, D. Grosz, S. Hunsche, A. Kung, A. Marhelyuk, D. Maymar, M. Movassaghi, X. Liu, C. Xu, X. Wei, and D. M. Gill , “2.5 Tb/s (64 × 42.7 Gb/s) transmission over 40 × 100 km NZDSF using RZ-DPSK format and all-Raman-amplified spans,” in *Optical Fiber Commun. Conf*. (Optical Society of America, Washington, D.C., 2002). Postdeadline paper FC2.

6. C. Xu, X. Liu, and X. Wei, “Differential phase-shift keying for high spectral efficiency optical transmissions,” IEEE J. Sel. Top. Quantum Electron. **10**(2), 281–293 (2004). [CrossRef]

10. N. G. Walker and J. E. Carroll, “Simultaneous phase and amplitude measurements on optical signals using a multiport junction,” Electron. Lett. **20**(23), 981–983 (1984). [CrossRef]

11. T. G. Hodgkinson, R. A. Harmon, and D. W. Smith, “Demodulation of optical DPSK using in-phase and quadrature detection,” Electron. Lett. **21**(21), 867–868 (1985). [CrossRef]

12. C. Dorrer, C. R. Doerr, I. Kang, R. Ryf, J. Leuthold, and P. J. Winzer, “Measurement of eye diagrams and constellation diagrams of optical sources using linear optics and waveguide technology,” J. Lightwave Technol. **23**(1), 178–186 (2005). [CrossRef]

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

14. D.-S. Ly-Gagnon, K. Katoh, and K. Kikuchi, “Unrepeatered optical transmission of 20 Gbit/s quadrature phase-shift keying signals over 210 km using homodyne phase-diversity receiver and digital signal processing,” Electron. Lett. **41**(4), 59–60 (2005). [CrossRef]

15. R. Trebino and J. D. Kane, “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). [CrossRef]

*E*(

*t*) is the complex electric field,

*G*(

*t*) is the waveform of the gating pulse, and τ is the time-delay of the gating pulse. Numerically, the FROG trace is the calculation of the spectrogram using short-time Fourier transform [18

18. L. Cohen, “Time-frequency distributions-a review,” Proc. IEEE **77**(7), 941–981 (1989). [CrossRef]

*E*(ω) is the spectrum of the optical signal,

*H*(ω) is the frequency response of the tunable optical filter, and

*v*is the center frequency of

*H*(ω). In FROG, the spectrogram is used to retrieve the phase of

*E*(

*t*). In TROF, the sonogram is used to retrieve the phase of

*E*(ω) and equivalently, via inverse Fourier transform, the phase of

*E*(

*t*).

15. R. Trebino and J. D. Kane, “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). [CrossRef]

20. A. Baltuska, M. S. Pshenichnikov, and D. A. Wiersma, “Amplitude and phase characterization of 4.5-fs pulses by frequency-resolved optical gating,” Opt. Lett. **23**(18), 1474–1476 (1998). [CrossRef]

16. R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbügel, B. A. Richman, and D. J. Kane, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. **68**(9), 3277–3295 (1997). [CrossRef]

23. R. Trebino, *Frequency-Resolved Optical Gating: The Measurement of Ultrashort Laser Pulses* (Kluwer Academic, Boston, 2002). [CrossRef]

^{7}-1 pseudo-random binary sequence (PRBS) as a periodic signal.

24. J. L. A. Chilla and O. E. Martinez, “Analysis of a method of phase measurement of ultrashort pulses in the frequency domain,” IEEE J. Quantum Electron. **27**(5), 1228–1235 (1991). [CrossRef]

26. D. T. Reid, “Algorithm for complete and rapid retrieval of ultrashort pulse amplitude and phase from a sonogram,” IEEE J. Quantum Electron. **35**(11), 1584–1589 (1999). [CrossRef]

25. K. Taira and K. Kikuchi, “Optical sampling system at 1.55μm for the measurement of pulse waveform and phase employing sonogram characterization,” IEEE Photonics Technol. Lett. **13**(5), 505–507 (2001). [CrossRef]

28. R. G. M. P. Koumans and A. Yariv, “Pulse characterization at 1.5 μm using time-resolved optical gating based on dispersive propagation,” IEEE Photonics Technol. Lett. **12**(6),666–668 (2000). [CrossRef]

25. K. Taira and K. Kikuchi, “Optical sampling system at 1.55μm for the measurement of pulse waveform and phase employing sonogram characterization,” IEEE Photonics Technol. Lett. **13**(5), 505–507 (2001). [CrossRef]

26. D. T. Reid, “Algorithm for complete and rapid retrieval of ultrashort pulse amplitude and phase from a sonogram,” IEEE J. Quantum Electron. **35**(11), 1584–1589 (1999). [CrossRef]

28. R. G. M. P. Koumans and A. Yariv, “Pulse characterization at 1.5 μm using time-resolved optical gating based on dispersive propagation,” IEEE Photonics Technol. Lett. **12**(6),666–668 (2000). [CrossRef]

29. “Spectrogram,” Wikipedia Encyclopedia. URL http://en.wikipedia.org/wiki/Spectrogram.

30. R. A. Linke, “Modulation induced transient chirping in single frequency lasers,” IEEE J. Quantum Electron. **QE–21**(6), 593–597 (1985). [CrossRef]

## 2. TROF Trace of DPSK Signals

*T*and expressed as a Fourier series of

*c*are the Fourier coefficients of

_{k}*E*(

*t*),

*H*(ω) is the frequency response of the tunable narrowband optical filter, and

*v*are the centered frequencies in the measurement of the TROF trace.

*E*(

*t*) using the TROF trace of Eq. (4). For illustration purpose and to understand the problem, the “direct” problem is simulated. The “direct” problem finds the TROF trace of a known signal, in here, a phase-modulated optical signal.

*H*(ω) has a Gaussian response and a full-width-half-maximum (FWHM) bandwidth of half the data rate of 0.5/

*T*, where

_{b}*T*is the bit period of the data stream. Figure 1 uses a 7-bit data pattern of +1,-1,-1, +1,-1,+1,+1 as an example for illustration purpose. The center frequencies of the tunable filter [

_{b}*v*in Eq. (4)] tune between ±2/

*T*, i.e., twice the data rate. The important properties of a TROF trace are all shown in Fig. 1 for periodic phase-modulated signals.

_{b}*V*

_{π}[6

6. C. Xu, X. Liu, and X. Wei, “Differential phase-shift keying for high spectral efficiency optical transmissions,” IEEE J. Sel. Top. Quantum Electron. **10**(2), 281–293 (2004). [CrossRef]

7. A. H. Gnauck and P. J. Winzer, “Optical phase-shift-keyed transmission,” J. Lightwave Technol. **23**(1), 115–130 (2005). [CrossRef]

1. A. H. Gnauck, G. Raybon, S. Chandrasekhar, J. Leuthold, C. Doerr, L. Stulz, A. Agrawal, S. Banerjee, D. Grosz, S. Hunsche, A. Kung, A. Marhelyuk, D. Maymar, M. Movassaghi, X. Liu, C. Xu, X. Wei, and D. M. Gill , “2.5 Tb/s (64 × 42.7 Gb/s) transmission over 40 × 100 km NZDSF using RZ-DPSK format and all-Raman-amplified spans,” in *Optical Fiber Commun. Conf*. (Optical Society of America, Washington, D.C., 2002). Postdeadline paper FC2.

6. C. Xu, X. Liu, and X. Wei, “Differential phase-shift keying for high spectral efficiency optical transmissions,” IEEE J. Sel. Top. Quantum Electron. **10**(2), 281–293 (2004). [CrossRef]

7. A. H. Gnauck and P. J. Winzer, “Optical phase-shift-keyed transmission,” J. Lightwave Technol. **23**(1), 115–130 (2005). [CrossRef]

32. I. Lyubomirsky and C.-C. Chien, “DPSK demodulator based on optical discriminator filter,” IEEE Photonics Technol. Lett. **17**(2), 492–494 (2005). [CrossRef]

*D*= 17 ps/km/nm. The lower curves of Fig. 1(b) include the non-zero imaginary part of the electric field. The real part of Fig. 1(b) is not as smooth as that for Fig. 1(a). Similar to Fig. 1(a), even with fiber dispersion, the TROF trace of Fig. 1(b) has both craters and ridges. Those craters and ridges can use to initiate the TROF algorithm. Due to fiber dispersion, each crater and ridge in the TROF trace is rotated. Later parts of this paper measure the TROF traces of NRZ-DPSK signals with and without chromatic dispersion and find the corresponding electric field of

*E*(

*t*).

1. A. H. Gnauck, G. Raybon, S. Chandrasekhar, J. Leuthold, C. Doerr, L. Stulz, A. Agrawal, S. Banerjee, D. Grosz, S. Hunsche, A. Kung, A. Marhelyuk, D. Maymar, M. Movassaghi, X. Liu, C. Xu, X. Wei, and D. M. Gill , “2.5 Tb/s (64 × 42.7 Gb/s) transmission over 40 × 100 km NZDSF using RZ-DPSK format and all-Raman-amplified spans,” in *Optical Fiber Commun. Conf*. (Optical Society of America, Washington, D.C., 2002). Postdeadline paper FC2.

**10**(2), 281–293 (2004). [CrossRef]

7. A. H. Gnauck and P. J. Winzer, “Optical phase-shift-keyed transmission,” J. Lightwave Technol. **23**(1), 115–130 (2005). [CrossRef]

## 3. TROF Measurement and TROF Algorithm

^{7}-1 PRBS with a period of

*T*= 12.7 ns. The PRBS includes all permutations of 7-bit length pattern except the all zero pattern. The NRZ-DPSK signal is passed to the TROF measurement equipment with or without passing through optical fiber. The fiber has a dispersion coefficient of

*D*= 17 ps/km/nm. An Erbium-doped fiber amplifier (EDFA) is used to compensate for the loss at the tunable optical filter.

*H*(ω -

*v*) with center frequencies of

_{l}*v*, and a high-speed optical-to-electric converter. Similar to [31], Figure 2 uses the monochromator in Agilent 86146B with a FWHM bandwidth of 0.04 nm as the tunable optical filter. Operated around the wavelength of 1553 nm, the FWHM bandwidth is about 5 GHz. The optical-to-electrical converter is the sampling module of Agilent 86116A together with the 86100B digital communication analyzer mainframe. The sampling module has a bandwidth of 53 GHz for optical signal, more than sufficient for 10-Gb/s signal. From the physical properties of the monochromator [33], the frequency response of

_{l}*H*(ω) is linear phase without chirp. The transfer function of

*H*(ω) is also shown in Fig. 2. Figure 3 shows the measured TROF traces for a NRZ-DPSK signal after the propagation of 0, 20, 40, and 60 km of standard single-mode optical fiber.

*N*= 2048 evenly sample points. With 64 centered frequency of

*v*scanned within ±0.14 nm of the signal wavelength, each TROF trace is a 64 × 2048 array of data. In the wavelength of 1553 nm, ±0.14 nm corresponds to ±17.5 GHz. Unlike FROG or similar technique with a square data array and a fast algorithm [17

_{l}17. D. J. Kane, “Recent progress toward real-time measurement of ultrashort laser pulses,” IEEE J. Quantum Electron. **35**(4), 421–431 (1999). [CrossRef]

26. D. T. Reid, “Algorithm for complete and rapid retrieval of ultrashort pulse amplitude and phase from a sonogram,” IEEE J. Quantum Electron. **35**(11), 1584–1589 (1999). [CrossRef]

^{7}-1 bits, the TROF traces of Fig. 3 are very similar to Figs. 1(a) and (b) without and with chromatic dispersion, respectively. Without chromatic dispersion, similar craters and ridges appear in Fig. 3 symmetrical with respect to the signal wavelength. With the increases of chromatic dispersion, the TROF trace becomes more asymmetric with respect to the center wavelength and clockwise rotated. The rotation angle increases with the amount of chromatic dispersion. The TROF trace of Fig. 1(b) is the vertical flip of those in Fig. 3 as the

*y*-axis is frequency in Fig. 1(b) and the

*y*-axis is wavelength in Fig. 3. Because the increase of wavelength decreases the frequency, the TROF trace with wavelength shift as

*y*-axis is the vertical flip of the TROF trace with frequency shift as

*y*-axis.

*E*(

*t*) is uniquely determined by its TROF trace up to a complex constant factor. However, the method from the Appendix cannot convert to a practical numerical method because noise in the TROF trace leads to divergent electric field of

*E*(

*t*).

*I*

_{meas}(

*t*,

_{m}*v*) at each time sample of

_{l}*t*of Fig. 3, numerical optimization is used to find the complex electric field of

_{m}*E*(

*t*) from Eq. (3). The TROF algorithm minimizes the mean-square error (MSE) of

*I*

_{TROF}(

*t*,

_{m}*v*) is calculated numerically using Eq. (4), similar to the traces of Fig. 1.

_{l}*E*=

_{m}*E*(

*t*) to minimize the MSE of Eq. (5) [34]. Conjugate gradient method is especially suitable for this optimization problem. The gradient of the MSE, ∇ℰ , composites the differentiation of

_{m}*N*evenly samples in time domain, based on discrete Fourier transform, the Fourier coefficients of

*c*are

_{k}*E*(

*t*,

_{m}*v*), the term of Eq. (7) depends solely on the difference of

_{l}*m*-

*k*. Numerically, the values of Eq. (7) and the electric field of Eq. (8) can be evaluated by fast Fourier transform.

*I*

_{meas}(t,

*v*) in early and later parts of the measurement. The TROF trace measurement of Fig. 3 already shortens the measurement time to minimize this effect. With chromatic dispersion, there is also bigger difference between the initial guess and the optimized electric field than the case without chromatic dispersion. With longer distance, the amplifier noise for 60-km measurement is also larger than that without optical fiber.

_{l}## 4. Discussion

35. K. Kikuchi and K. Taira, “Theory of sonogram characterization of optical pulses,” IEEE J. Quantum Electron. **37**(4), 533–537 (2001). [CrossRef]

24. J. L. A. Chilla and O. E. Martinez, “Analysis of a method of phase measurement of ultrashort pulses in the frequency domain,” IEEE J. Quantum Electron. **27**(5), 1228–1235 (1991). [CrossRef]

*I*

_{meas}(

*t*,

*v*) =

_{l}*I*

_{Trof}(

*t*,

*v*)⊗

*h*(

_{s}*t*), where ⊗ denotes convolution and

*h*(

_{s}*t*) is the impulse response of the optical sampling head. To include the contribution of

*h*(

_{s}*t*) to the theory of the Appendix,

*i*(

_{m}*v*) defined by Eq. (13) becomes

*i*(

_{m}*v*)

*H*(2

_{s}*πm*/

*T*), where

*H*(ω) is the frequency response of the optical sampling head. For 10-Gb/s signal, only the parts of

_{s}*H*(ω) with frequencies less than 20 GHz are important. With a 53-GHz sampling head,

_{s}*h*(

_{s}*t*) is a very short impulse response and

*H*(ω) has a very wide bandwidth. Without chromatic dispersion, the ripples of Fig. 4 may be from the electrical sampling head. Measured using the same sampling head, the intensity of an optical signal has similar ripples. In the measurement of optical signal for communication purpose, the ripples from the sampling head are usually tolerated as measurement artifacts.

_{s}*E*is a real signal. For practical complex signal of

_{m}*E*, the number of unknown variables is doubled. Only minor modifications are required for both Eq. (6) and Eq. (7) for complex signal.

_{m}16. R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbügel, B. A. Richman, and D. J. Kane, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. **68**(9), 3277–3295 (1997). [CrossRef]

17. D. J. Kane, “Recent progress toward real-time measurement of ultrashort laser pulses,” IEEE J. Quantum Electron. **35**(4), 421–431 (1999). [CrossRef]

23. R. Trebino, *Frequency-Resolved Optical Gating: The Measurement of Ultrashort Laser Pulses* (Kluwer Academic, Boston, 2002). [CrossRef]

27. R. G. M. P. Koumans and A. Yariv, “Time-resolved optical gating based on dispersive propagation: a new method to characterize optical pulses,” IEEE J. Quantum Electron. **36**(2),137–44 (2000). [CrossRef]

28. R. G. M. P. Koumans and A. Yariv, “Pulse characterization at 1.5 μm using time-resolved optical gating based on dispersive propagation,” IEEE Photonics Technol. Lett. **12**(6),666–668 (2000). [CrossRef]

## 5. Conclusion

## Appendix: Theory of TROF for Periodic Signals

*h*(τ) and

_{m}*r*(τ) as

_{m}18. L. Cohen, “Time-frequency distributions-a review,” Proc. IEEE **77**(7), 941–981 (1989). [CrossRef]

35. K. Kikuchi and K. Taira, “Theory of sonogram characterization of optical pulses,” IEEE J. Quantum Electron. **37**(4), 533–537 (2001). [CrossRef]

*h*(τ). Although similar theory is not discussed in both [18

_{m}18. L. Cohen, “Time-frequency distributions-a review,” Proc. IEEE **77**(7), 941–981 (1989). [CrossRef]

35. K. Kikuchi and K. Taira, “Theory of sonogram characterization of optical pulses,” IEEE J. Quantum Electron. **37**(4), 533–537 (2001). [CrossRef]

*E*(

*t*) from the sonogram of

*I*

_{TROF}(

*t*,

*v*) up to a constant factor of

*c*

_{0}or

*c*

_{1}. However, the kernel of

*h*(τ) is very small for large τ. For example, if

_{m}*H*(ω) = exp(-ω

^{2}/2ω

^{2}

_{0}) as a Gaussian filter, the kernel of

_{0}. In theory, ∫

*i*(

_{m}*v*)

*e*

^{-jvτ}is either comparable or smaller than

*h*(τ). In practical calculation, a small

_{m}*h*(τ) is numerically difficult to handle. If the measurement of the TROF trace of

_{m}*I*

_{TROF}(

*t*,

*v*) has noise or the calculation of

*i*(

_{m}*v*) has small numerical error, the electric field of

*E*(

*t*) has enormous error. Nevertheless, the technique is applicable for short pulse with finite support [25

25. K. Taira and K. Kikuchi, “Optical sampling system at 1.55μm for the measurement of pulse waveform and phase employing sonogram characterization,” IEEE Photonics Technol. Lett. **13**(5), 505–507 (2001). [CrossRef]

## Acknowledgments

## References and links

1. | A. H. Gnauck, G. Raybon, S. Chandrasekhar, J. Leuthold, C. Doerr, L. Stulz, A. Agrawal, S. Banerjee, D. Grosz, S. Hunsche, A. Kung, A. Marhelyuk, D. Maymar, M. Movassaghi, X. Liu, C. Xu, X. Wei, and D. M. Gill , “2.5 Tb/s (64 × 42.7 Gb/s) transmission over 40 × 100 km NZDSF using RZ-DPSK format and all-Raman-amplified spans,” in |

2. | B. Zhu, L. E. Nelson, S. Stulz, A. H. Gnauck, C. Doerr, J. Leuthold, L. Grüner-Nielsen, M. O. Pederson, J. Kim, R. Lingle, Y. Emori, Y. Ohki, N. Tsukiji, A. Oguri, and S. Namiki, “6.4-Tb/s (160 × 42.7 Gb/s) transmission with 0.8 bit/s/Hz spectral efficiency over 32 × 100 km of fiber using CSRZ-DPSK format,” in |

3. | C. Rasmussen, T. Fjelde, J. Bennike, F. Liu, S. Dey, B. Mikkelsen, P. Mamyshev, P. Serbe, P. van de Wagt, Y. Akasaka, D. Harris, D. Gapontsev, V. Ivshin, and P. Reeves-Hall, “DWDM 40G transmission over trans-Pacific distance (10,000 km) using CSRZ-DPSK, enhanced FEC and all-Raman amplified 100 km Ultra-WaveTM fiber spans,” in |

4. | J.-X. Cai, D. G. Foursa, L. Liu, C. R. Davidson, Y. Cai, W. W. Patterson, A. J. Lucero, B. Bakhshi, G. Mohs, P. C. Corbett, V. Gupta, W. Anderson, M. Vaa, G. Domagala, M. Mazurczyk, H. Li, S. Jiang, M. Nissov, A. N. Pilipetskii, and N. S. Bergano, “RZ-DPSK field trial over 13,100 km of installed non slope-matched submarine fibers,” in |

5. | G. Charlet, R. Dischler, A. Klekamp, P. Tran, H. Mardoyan, L. Pierre, W. Idler, and S. Bigo, “WDM bit-to-bit alternate-polarisation RZ-DPSK transmission at 40 × 42.7 Gbit/s over transpacific distance with large Q-factor margin,” in |

6. | C. Xu, X. Liu, and X. Wei, “Differential phase-shift keying for high spectral efficiency optical transmissions,” IEEE J. Sel. Top. Quantum Electron. |

7. | A. H. Gnauck and P. J. Winzer, “Optical phase-shift-keyed transmission,” J. Lightwave Technol. |

8. | K.-P. Ho, |

9. | T. Mizuochi, K. Ishida, T. Kobayashi, J. Abe, K. Kinjo, K. Motoshima, and K. Kasahara, “A comparative study of DPSK and OOK WDM transmission over transoceanic distances and their performance degradations due to nonlinear phase noise,” J. Lightwave Technol. |

10. | N. G. Walker and J. E. Carroll, “Simultaneous phase and amplitude measurements on optical signals using a multiport junction,” Electron. Lett. |

11. | T. G. Hodgkinson, R. A. Harmon, and D. W. Smith, “Demodulation of optical DPSK using in-phase and quadrature detection,” Electron. Lett. |

12. | C. Dorrer, C. R. Doerr, I. Kang, R. Ryf, J. Leuthold, and P. J. Winzer, “Measurement of eye diagrams and constellation diagrams of optical sources using linear optics and waveguide technology,” J. Lightwave Technol. |

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

14. | D.-S. Ly-Gagnon, K. Katoh, and K. Kikuchi, “Unrepeatered optical transmission of 20 Gbit/s quadrature phase-shift keying signals over 210 km using homodyne phase-diversity receiver and digital signal processing,” Electron. Lett. |

15. | R. Trebino and J. D. Kane, “Using phase retrieval to measure the intensity and phase of ultrashort pulses: frequency-resolved optical gating,” J. Opt. Soc. Am. A |

16. | R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbügel, B. A. Richman, and D. J. Kane, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. |

17. | D. J. Kane, “Recent progress toward real-time measurement of ultrashort laser pulses,” IEEE J. Quantum Electron. |

18. | L. Cohen, “Time-frequency distributions-a review,” Proc. IEEE |

19. | S. Qian, |

20. | A. Baltuska, M. S. Pshenichnikov, and D. A. Wiersma, “Amplitude and phase characterization of 4.5-fs pulses by frequency-resolved optical gating,” Opt. Lett. |

21. | N. Nishizawa and T. Goto, “Experimental analysis of ultrashort pulse propagation in optical fibers around zero-dispersion region using cross-correlation frequency resolved optical gating,” Opt. Express |

22. | L. Gallmann, D. Sutter, N. Matuschek, G. Steinmeyer, and U. Keller, “Techniques for the characterization of sub-10-fs optical pulses: a comparison,” Appl. Phys. B |

23. | R. Trebino, |

24. | J. L. A. Chilla and O. E. Martinez, “Analysis of a method of phase measurement of ultrashort pulses in the frequency domain,” IEEE J. Quantum Electron. |

25. | K. Taira and K. Kikuchi, “Optical sampling system at 1.55μm for the measurement of pulse waveform and phase employing sonogram characterization,” IEEE Photonics Technol. Lett. |

26. | D. T. Reid, “Algorithm for complete and rapid retrieval of ultrashort pulse amplitude and phase from a sonogram,” IEEE J. Quantum Electron. |

27. | R. G. M. P. Koumans and A. Yariv, “Time-resolved optical gating based on dispersive propagation: a new method to characterize optical pulses,” IEEE J. Quantum Electron. |

28. | R. G. M. P. Koumans and A. Yariv, “Pulse characterization at 1.5 μm using time-resolved optical gating based on dispersive propagation,” IEEE Photonics Technol. Lett. |

29. | “Spectrogram,” Wikipedia Encyclopedia. URL http://en.wikipedia.org/wiki/Spectrogram. |

30. | R. A. Linke, “Modulation induced transient chirping in single frequency lasers,” IEEE J. Quantum Electron. |

31. | Agilent App. Note 1550-7, Making Time-Resolved Chirp Measurements Using the Optical Spectrum Analyzer and Digital Communications Analyzer, (2002). |

32. | I. Lyubomirsky and C.-C. Chien, “DPSK demodulator based on optical discriminator filter,” IEEE Photonics Technol. Lett. |

33. | K. R. Wildnauer and Z. Azary, “A double-pass monochromator for wavelength selection in an optical spectrum analyzer,” Hewlett-Packard J. |

34. | W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, |

35. | K. Kikuchi and K. Taira, “Theory of sonogram characterization of optical pulses,” IEEE J. Quantum Electron. |

**OCIS Codes**

(060.5060) Fiber optics and optical communications : Phase modulation

(120.5050) Instrumentation, measurement, and metrology : Phase measurement

(320.7100) Ultrafast optics : Ultrafast measurements

**ToC Category:**

Instrumentation, Measurement, and Metrology

**Citation**

Keang-Po Ho, Hsi-Cheng Wang, and Hau-Kai Chen, "Simultaneous amplitude and phase measurement for periodic optical signals using time-resolved optical filtering," Opt. Express **14**, 103-113 (2006)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-1-103

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### References

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