## General second-harmonic pulse shaping in grating-engineered quasi-phase-matched nonlinear crystals

Optics Express, Vol. 13, Issue 9, pp. 3264-3276 (2005)

http://dx.doi.org/10.1364/OPEX.13.003264

Acrobat PDF (307 KB)

### Abstract

We describe a spectrogram-based simulated annealing algorithm for designing quasi-phase-matched crystals capable of producing second harmonic generation pulses of any chosen amplitude and phase profile. The approach applies a new and rapid analytic method for calculating the amplitude and phase of the second harmonic generation pulses generated by a quasi-phase-matched crystal containing an arbitrary grating design. The performance of the algorithm is illustrated by examples of femtosecond second harmonic pulses designed according to various target shapes including single, double and triple Gaussian pulses, positive and negative linear chirp and square, triangular and stepped profiles.

© 2005 Optical Society of America

## 1. Introduction

1. A. M. Weiner, D. E. Leaird, J.S. Patel, and J.R. Wullert, “Programmable shaping of femtosecond optical pulses by use of 128-element liquid crystal phase modulator,” IEEE J. Quantum Electron. **QE-28**908–920, (1992) [CrossRef]

2. E. Zeek, K. Maginnis, S. Backus, U. Russek, M. Murnane, G. Mourou, H. Kapteyn, and G. Vdovin, “Pulse compression by use of deformable mirrors,” Opt. Lett. **24**, 493–495 (1999) [CrossRef]

4. F. Verluise, V. Laude, Z. Cheng, Ch. Spielmann, and P. Tournois, “Amplitude and phase control of ultrashort pulses by use of an acousto-optic programmable dispersive filter pulse compression and shaping,” Opt. Lett. **25**575–577 (2000) [CrossRef]

*et al*. [5

5. M. A. Arbore, O. Marco, and M. M. Fejer, “Pulse compression during second-harmonic generation in aperiodic quasi-phase-matching gratings,” Opt. Lett. **22**, 865–867 (1997). [CrossRef] [PubMed]

6. M. A. Arbore, A. Galvanauskas, D. Harter, M. H. Chou, and M. M. Fejer, “Engineerable compressionof ultrashort pulses by use of second-harmonic generationin chirped-period-poled lithium niobate,” Opt. Lett. **22**, 1341–1343 (1997). [CrossRef]

7. P. Loza-Alvarez, D. T. Reid, P. Faller, M. Ebrahimzadeh, and W. Sibbett, “Simultaneous second-harmonic generation and femtosecond-pulse compression in aperiodically poled KTiOPO 4 with a RbTiOAsO 4 -based optical parametric oscillator,” J. Opt. Soc. Am. B **16**, 1553–1560 (1999). [CrossRef]

8. P. Loza-Alvarez, D. T. Reid, P. Faller, M. Ebrahimzadeh, W. Sibbett, H. Karlsson, and F. Laurell, “Simultaneous femtosecond-pulse compression and second-harmonic generation in aperiodically poled KTiOPO 4,” Opt. Lett. **24**, 1071–1073 (1999). [CrossRef]

9. T. Beddard, M. Ebrahimzadeh, D. T. Reid, and W. Sibbett, “Five-optical-cycle pulse generation in the mid infrared from an optical parametric oscillator based on aperiodically poled lithium niobate” Opt. Lett. **25**,1052–1054 (2000) [CrossRef]

10. D. Artigas and D.T. Reid, “Efficient femtosecond optical parametric oscillators based on aperiodically poled nonlinear crystals” Opt. Lett. **27**851–853 (2002). [CrossRef]

11. D. Artigas, D. T. Reid, M. M. Fejer, and L. Torner, “Pulse compression and gain enhancement in a degenerate optical parametric amplifier based on aperiodically poled crystals “Opt. Lett. **27**, 442–444 (2002) [CrossRef]

12. L. Gallmann, G. Steinmeyer, U. Keller, G. Imeshev, M. M. Fejer, and J. P. Meyn, “Generation of sub-6-fs blue pulses by frequency doubling with quasi-phase-matching gratings” Opt. Lett. **26**, 614–616 (2001). [CrossRef]

13. L. Gallmann, G. Steinmeyer, G. Imeshev, J. P. Meyn, U. Keller, and M. M. Fejer. “Sub-6-fs blue pulses generated by quas-phase-matcheing second harmonic generation pulse compression” Appl. Phys. B **74**S237–S243 (2002). [CrossRef]

14. G. Imeshev, M. A. Arbore, M. M. Fejer, A. Galvanauskas, M. Fermann, and D. Harter “Ultrashort-pulse second-harmonic generation with longitudinally nonuniform quasi-phase-matching gratings: pulse compression and shaping “J. Opt. Soc. Am. B **17**, 304–318 (2000). [CrossRef]

15. G. Imeshev, M. A. Arbore, S. Kasriel, and M. M. Fejer “Pulse shaping and compression by second-harmonic generation with quasi-phase-matching gratings in the presence of arbitrary dispersion” J. Opt. Soc. Am. B **17**, 1420–1437 (2000). [CrossRef]

16. G. Imeshev, M. M. Fejer, A. Galvanauskas, and D. Harter “Pulse shaping by difference-frequency mixing with quasi-phase-matching gratings” J. Opt. Soc. Am. B **18**, 534–539 (2001) [CrossRef]

## 2. Transfer function description of SHG pulse shaping in QPM crystals

*κ*=-

*ω*

_{SHG}/

*cn*

_{SHG},

*d*

_{ijk}is the absolute value of the nonlinear coefficient,

*ω*

_{SHG}and

*n*

_{SHG}are, respectively, the carrier frequency and refractive index of the SHG pulse and

**Q**=[

*q*

_{1},

*q*

_{1}+

*q*

_{2},

*q*

_{1}+

*q*

_{2}+

*q*

_{3},…,

*q*

_{1}+…+

*q*

_{n}] is a vector containing the end position of every domain as shown in Fig. 1.

*k*(Ω) where Ω is the difference between the carrier frequency of the pulse and the frequency of any given spectral component of the pulse. Arbore

*et al*[5

5. M. A. Arbore, O. Marco, and M. M. Fejer, “Pulse compression during second-harmonic generation in aperiodic quasi-phase-matching gratings,” Opt. Lett. **22**, 865–867 (1997). [CrossRef] [PubMed]

*F*is the Fourier-transform operator and

*E*

_{1}(

*t*) is the complex amplitude of the fundamental input pulse. By combining Eq. (1) and (2) it is therefore possible to accurately predict the exact amplitude and phase of the SHG pulse generated by combining any input pulse with any quasi-phasematched crystal simply by taking the inverse Fourier transform of Eq. (2):

*k*

_{o}=Δ

*k*

_{Ω=0}and the coefficient σ(

*z*) is the spatially changing polarity of the domain orientation. The group velocity of wave

*i*is

*ν*

_{i}=1/

*k′*

_{i}, where

*k′*

_{i}=

*dk*

_{i}/

*dω*

_{i}and the group velocity dispersion is

*k″*

_{i}=

*d*

^{2}

*k*

_{i}/

*i*=1 represents the fundamental wave and

*i*=2 represents the SHG wave). This approach is able to take account of the depletion of the fundamental pulse and the effect of GVM between the fundamental and second-harmonic pulses but is computationally intensive, typically taking several minutes to run on a fast personal computer if a reasonable resolution is required. By contrast, we note that the frequency-dependent wave-vector mismatch, Δ

*k*(Ω), present in the analytic model (Eq. (1)–(3)) implicitly ensures that GVM is included because

*∂*(Δ

*k*(Ω))/

*∂ω*

_{SHG}=1/

*v*

_{SHG}-1/

*v*

_{FP}where

*v*

_{FP}and

*v*

_{SHG}are the group velocities of the fundamental and second-harmonic pulses respectively. In our numerical implementation of Eq. (4) we used a step size of typically 1/15th of the domain width used in the QPM grating design and this allowed us to exactly calculate change of the amplitude and phase of the SHG process during propagation through crystal under arbitrary QPM conditions. Numerical pulse propagation is necessarily computationally intensive but, by contrast, the new analytic method we describe here is highly efficient, running in a fraction of the time taken by the conventional calculation and consisting of no more than a summation followed by two fast Fourier transforms.

*q*

_{m}, between the domain width at any position and the domain size for exact QPM, 9.11

*µ*m. Fig. 2 shows the full results obtained and is organised according to rows and columns. Each row represents a separate combination of crystal grating design and input pump chirp while the columns (from left to right) depict: (a) the SHG pulse temporal intensity and phase profile; (b) the intensity and phase of the crystal transfer function

*E*

_{crys}(Ω) expressed in terms of the SHG wavelength; (c) the percentage converted power with propagation distance in the crystal, and; (d) the variation from the exact QPM period of the domain size distribution in the crystal. The cases studied (in row order of Fig. 2, beginning with the top row) were: (i) an unchirped grating and an unchirped fundamental pulse; (ii) a linearly positively chirped grating and an unchirped fundamental pulse; (iii) a randomly perturbed grating and an unchirped fundamental pulse; (iv) a linearly positively chirped grating and a positively chirped fundamental pulse, and; (v) a linearly positively chirped grating and a negatively chirped fundamental pulse. In all of the results, solid lines denote the new model and the symbols (‘*’) represent the results of a conventional pulse propagation model. In all cases the agreement between the two models is very close, demonstrating that the simple model is more than adequate for predicting the pulse shapes produced by QPM SHG. From these results, it is clear that the proposed analytic method can exactly describe the SHG process even in the case of a randomly structured grating design. It is also evident that the SHG pulse is compressed (Fig. 2(iv)) and stretched (Fig. 2(v)) by a chirped grating exactly as is expected. The results also show that the new method can exactly describe the SHG nonlinear frequency conversion process when the efficiency of conversion is less than a few percent.

## 3. Designing aperiodic QPM gratings to create target pulse profiles

25. R. Buffa. “Transient second-harmonic generation with spatially non-uniform nonlinear coefficients”, Opt. Lett. **27**, 1058–1060 (2002) [CrossRef]

**Q**) to be simultaneously optimised. In our earlier work [18

18. D. T. Reid, “Engineered quasi-phase-matching for second-garmonic generation” J. Opt. A: Pure Appl. Opt. **5**S97–S102 (2003) [CrossRef]

*E*

_{crys}(Ω), and we now extend this approach to the general case of finding the crystal design needed to yield a SHG pulse with any chosen intensity and phase profile.

27. D. J. Kane and R. Trebino, “Single-short measurement of the intensity and phase of an arbitrary ultrashort pulses by using frequency-resolved optical gating” Opt. Lett. **18**, 823–825 (1993) [CrossRef] [PubMed]

27. D. J. Kane and R. Trebino, “Single-short measurement of the intensity and phase of an arbitrary ultrashort pulses by using frequency-resolved optical gating” Opt. Lett. **18**, 823–825 (1993) [CrossRef] [PubMed]

*k*th) iteration of the algorithm, every crystal domain was randomly perturbed by up to 1% and the modified design accepted or rejected on the basis of the implied change to the error,

*e*

_{k}. Fig. 3 illustrates the algorithm. The procedure was run iteratively until (typically)

*e*

_{k}<0.005, at which point the QPM grating design obtained was assumed to represent the best possible for generating the target pulse. The domain sizes throughout the crystal are represented by the vector

**P**=[

*q*

_{1},

*q*

_{2},

*q*

_{3},…,

*q*

_{n}] and

**P**

_{o}is the optimum QPM design for each case.

*ϕ′*~7000 fs

^{2}); (f) a negatively chirped 300fs Gaussian pulse (

*ϕ′*~-7000 fs

^{2}); (g) a 400fs square pulse; (h) a 200fs triangular pulse, and; (i) a 400fs stepped square pulse. For each target case we have plotted in Fig. 5–8 the results of the simulated annealing algorithm. Each figure follows a similar format with the columns representing (from left to right): the PG-FROG spectrogram of the target pulse; the calculated PG-FROG spectrogram of the best SHG pulse; the SHG power evolution through the crystal calculated by numerical code (symbols) and the new analytic method (solid curve), and; the distribution of domain sizes throughout the crystal. The typical iteration time required for each design was around 25–45 minutes, depending which target was chosen.

## 4. Conclusions

28. M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, IEEE J. Quantum. Electron. 28, 2631 (1992) [CrossRef]

## Acknowledgments

## References and links

1. | A. M. Weiner, D. E. Leaird, J.S. Patel, and J.R. Wullert, “Programmable shaping of femtosecond optical pulses by use of 128-element liquid crystal phase modulator,” IEEE J. Quantum Electron. |

2. | E. Zeek, K. Maginnis, S. Backus, U. Russek, M. Murnane, G. Mourou, H. Kapteyn, and G. Vdovin, “Pulse compression by use of deformable mirrors,” Opt. Lett. |

3. | A.M. Weiner and A.M. Kanan, “Femtosecond Pulse Shaping for Synthesis, Processing, and Time-to-Space Conversion of Ultrafast Optical Waveforms,” IEEE J. Quantum Electron. |

4. | F. Verluise, V. Laude, Z. Cheng, Ch. Spielmann, and P. Tournois, “Amplitude and phase control of ultrashort pulses by use of an acousto-optic programmable dispersive filter pulse compression and shaping,” Opt. Lett. |

5. | M. A. Arbore, O. Marco, and M. M. Fejer, “Pulse compression during second-harmonic generation in aperiodic quasi-phase-matching gratings,” Opt. Lett. |

6. | M. A. Arbore, A. Galvanauskas, D. Harter, M. H. Chou, and M. M. Fejer, “Engineerable compressionof ultrashort pulses by use of second-harmonic generationin chirped-period-poled lithium niobate,” Opt. Lett. |

7. | P. Loza-Alvarez, D. T. Reid, P. Faller, M. Ebrahimzadeh, and W. Sibbett, “Simultaneous second-harmonic generation and femtosecond-pulse compression in aperiodically poled KTiOPO 4 with a RbTiOAsO 4 -based optical parametric oscillator,” J. Opt. Soc. Am. B |

8. | P. Loza-Alvarez, D. T. Reid, P. Faller, M. Ebrahimzadeh, W. Sibbett, H. Karlsson, and F. Laurell, “Simultaneous femtosecond-pulse compression and second-harmonic generation in aperiodically poled KTiOPO 4,” Opt. Lett. |

9. | T. Beddard, M. Ebrahimzadeh, D. T. Reid, and W. Sibbett, “Five-optical-cycle pulse generation in the mid infrared from an optical parametric oscillator based on aperiodically poled lithium niobate” Opt. Lett. |

10. | D. Artigas and D.T. Reid, “Efficient femtosecond optical parametric oscillators based on aperiodically poled nonlinear crystals” Opt. Lett. |

11. | D. Artigas, D. T. Reid, M. M. Fejer, and L. Torner, “Pulse compression and gain enhancement in a degenerate optical parametric amplifier based on aperiodically poled crystals “Opt. Lett. |

12. | L. Gallmann, G. Steinmeyer, U. Keller, G. Imeshev, M. M. Fejer, and J. P. Meyn, “Generation of sub-6-fs blue pulses by frequency doubling with quasi-phase-matching gratings” Opt. Lett. |

13. | L. Gallmann, G. Steinmeyer, G. Imeshev, J. P. Meyn, U. Keller, and M. M. Fejer. “Sub-6-fs blue pulses generated by quas-phase-matcheing second harmonic generation pulse compression” Appl. Phys. B |

14. | G. Imeshev, M. A. Arbore, M. M. Fejer, A. Galvanauskas, M. Fermann, and D. Harter “Ultrashort-pulse second-harmonic generation with longitudinally nonuniform quasi-phase-matching gratings: pulse compression and shaping “J. Opt. Soc. Am. B |

15. | G. Imeshev, M. A. Arbore, S. Kasriel, and M. M. Fejer “Pulse shaping and compression by second-harmonic generation with quasi-phase-matching gratings in the presence of arbitrary dispersion” J. Opt. Soc. Am. B |

16. | G. Imeshev, M. M. Fejer, A. Galvanauskas, and D. Harter “Pulse shaping by difference-frequency mixing with quasi-phase-matching gratings” J. Opt. Soc. Am. B |

17. | S. Helmfrid and G. Arvidsson “Influence of randomly varying domain lengths and nonuniform effective index on second-harmonic generation in quasi-phase-matching waveguides” J. Opt. Soc. Am. B |

18. | D. T. Reid, “Engineered quasi-phase-matching for second-garmonic generation” J. Opt. A: Pure Appl. Opt. |

19. | Y. Zang and B-Y Gu “Optimal design of aperiodically poled lithium niobate crystals for multiple wavelengths parametric amplification” Opt. Comm. |

20. | W.H. Glenn, “Second harmonic generation by picosecond optical pulses” IEEE J. Quantum Electronics , |

21. | E. Sidick, A. Knoesen, and A. Dienes. “Ultrashort-pulse second-harmonic generation. I. Transform-limited fundamental pulses” J. Opt. Soc. Am. B |

22. | E. Sidick, A. Knoesen, and A. Dienes “Ultra-short pulse second harmonic generation in quasi-phase matched structures” Pure Appl. Opt. |

23. | G. P. Agrawal, “ |

24. | A. Yariv “ |

25. | R. Buffa. “Transient second-harmonic generation with spatially non-uniform nonlinear coefficients”, Opt. Lett. |

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

27. | D. J. Kane and R. Trebino, “Single-short measurement of the intensity and phase of an arbitrary ultrashort pulses by using frequency-resolved optical gating” Opt. Lett. |

28. | M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, IEEE J. Quantum. Electron. 28, 2631 (1992) [CrossRef] |

**OCIS Codes**

(190.2620) Nonlinear optics : Harmonic generation and mixing

(190.4400) Nonlinear optics : Nonlinear optics, materials

(320.5540) Ultrafast optics : Pulse shaping

**ToC Category:**

Research Papers

**History**

Original Manuscript: March 10, 2005

Revised Manuscript: April 13, 2005

Published: May 2, 2005

**Citation**

Usman Sapaev and Derryck Reid, "General second-harmonic pulse shaping in grating-engineered quasi-phase-matched nonlinear crystals," Opt. Express **13**, 3264-3276 (2005)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-9-3264

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### References

- A. M. Weiner, D. E. Leaird, J.S. Patel, J.R. Wullert, �??Programmable shaping of femtosecond optical pulses by use of 128-element liquid crystal phase modulator,�?? IEEE J. Quantum Electron. QE-28 908-920, (1992). [CrossRef]
- E. Zeek, K. Maginnis, S. Backus, U. Russek, M. Murnane, G. Mourou, H. Kapteyn, G. Vdovin, �??Pulse compression by use of deformable mirrors,�?? Opt. Lett. 24, 493-495 (1999). [CrossRef]
- A.M. Weiner and A.M. Kanan, "Femtosecond Pulse Shaping for Synthesis, Processing, and Time-to-Space Conversion of Ultrafast Optical Waveforms," IEEE J. Quantum Electron. QE-4, 317-331 (1998).
- F. Verluise, V. Laude, Z. Cheng, Ch. Spielmann, P. Tournois, �??Amplitude and phase control of ultrashort pulses by use of an acousto-optic programmable dispersive filter pulse compression and shaping,�?? Opt. Lett. 25, 575-577 (2000). [CrossRef]
- M. A. Arbore, O. Marco and M. M. Fejer, �??Pulse compression during second-harmonic generation in aperiodic quasi-phase-matching gratings,�?? Opt. Lett. 22, 865-867 (1997). [CrossRef] [PubMed]
- M. A. Arbore, A. Galvanauskas, D. Harter, M. H. Chou and M. M. Fejer, �??Engineerable compression of ultrashort pulses by use of second-harmonic generation in chirped-period-poled lithium niobate,�?? Opt. Lett. 22, 1341-1343 (1997). [CrossRef]
- P. Loza-Alvarez, D. T. Reid, P. Faller, M. Ebrahimzadeh, W. Sibbett, �??Simultaneous second-harmonic generation and femtosecond-pulse compression in aperiodically poled KTiOPO 4 with a RbTiOAsO 4 -based optical parametric oscillator," J. Opt. Soc. Am. B 16, 1553-1560 (1999). [CrossRef]
- P. Loza-Alvarez, D. T. Reid, P. Faller, M. Ebrahimzadeh, W. Sibbett, H. Karlsson, F. Laurell, �??Simultaneous femtosecond-pulse compression and second-harmonic generation in aperiodically poled KTiOPO 4," Opt. Lett. 24, 1071-1073 (1999). [CrossRef]
- T.Beddard, M.Ebrahimzadeh, D. T. Reid and W. Sibbett, �??Five-optical-cycle pulse generation in the mid infrared from an optical parametric oscillator based on aperiodically poled lithium niobate," Opt. Lett. 25, 1052- 1054 (2000). [CrossRef]
- D. Artigas and D.T.Reid, �??Efficient femtosecond optical parametric oscillators based on aperiodically poled nonlinear crystals,�?? Opt. Lett. 27, 851-853 (2002). [CrossRef]
- D. Artigas, D. T. Reid, M. M. Fejer and L. Torner, �??Pulse compression and gain enhancement in a degenerate optical parametric amplifier based on aperiodically poled crystals," Opt. Lett. 27, 442-444 (2002). [CrossRef]
- L. Gallmann, G. Steinmeyer, U. Keller, G. Imeshev, M. M. Fejer and J. P. Meyn, �??Generation of sub-6-fs blue pulses by frequency doubling with quasi-phase-matching gratings,�?? Opt. Lett. 26, 614-616 (2001). [CrossRef]
- L. Gallmann, G. Steinmeyer, G. Imeshev, J. P. Meyn, U. Keller, M. M. Fejer, �??Sub-6-fs blue pulses generated by quas-phase-matcheing second harmonic generation pulse compression," Appl. Phys. B 74, S237-S243 (2002). [CrossRef]
- G. Imeshev, M. A. Arbore, M. M. Fejer, A. Galvanauskas, M. Fermann, D. Harter �??Ultrashort-pulse second-harmonic generation with longitudinally nonuniform quasi-phase-matching gratings: pulse compression and shaping," J. Opt. Soc. Am. B 17, 304-318 (2000). [CrossRef]
- G. Imeshev, M. A. Arbore, S. Kasriel, M. M. Fejer, �??Pulse shaping and compression by second-harmonic generation with quasi-phase-matching gratings in the presence of arbitrary dispersion,�?? J. Opt. Soc. Am. B 17, 1420-1437 (2000). [CrossRef]
- G. Imeshev, M. M. Fejer, A. Galvanauskas, D. Harter, �??Pulse shaping by difference-frequency mixing with quasi-phase-matching gratings,�?? J. Opt. Soc. Am. B 18, 534-539 (2001). [CrossRef]
- S. Helmfrid, G. Arvidsson, �??Influence of randomly varying domain lengths and nonuniform effective index on second-harmonic generation in quasi-phase-matching waveguides,�?? J. Opt. Soc. Am. B 8, 797-805 (1991). [CrossRef]
- D. T. Reid, �??Engineered quasi-phase-matching for second-garmonic generation,�?? J. Opt. A: Pure Appl. Opt. 5, S97-S102 (2003). [CrossRef]
- Y. Zang, B-Y Gu, �??Optimal design of aperiodically poled lithium niobate crystals for multiple wavelengths parametric amplification,�?? Opt. Comm. 192, 417-425 (2001). [CrossRef]
- W. H. Glenn, �??Second harmonic generation by picosecond optical pulses,�?? IEEE J. Quantum Electronics QE-5, 284-290 (1969). [CrossRef]
- E. Sidick, A. Knoesen, A. Dienes, �??Ultrashort-pulse second-harmonic generation. I. Transform-limited fundamental pulses,�?? J. Opt. Soc. Am. B 12, 1704-1078 (1995). [CrossRef]
- E. Sidick, A. Knoesen, A. Dienes, �??Ultra-short pulse second harmonic generation in quasi-phase matched structures,�?? Pure Appl. Opt. 5, 709-722 (1996). [CrossRef]
- G. P. Agrawal, Nonlinear Fiber Optics, 2nd Edn, (Academic Press).
- A. Yariv, Quantum Electronics 3rd ed. (New York: Wiley).
- R. Buffa, �??Transient second-harmonic generation with spatially non-uniform nonlinear coefficients�??, Opt. Lett. 27, 1058-1060 (2002). [CrossRef]
- W. H. Press, S. A Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes, 2nd ed. (Cambridge: Cambridge University Press).
- D. J. Kane, R. Trebino, �??Single-short measurement of the intensity and phase of an arbitrary ultrashort pulses by using frequency-resolved optical gating,�?? Opt. Lett. 18, 823-825 (1993). [CrossRef] [PubMed]
- M. M. Fejer, G. A. Magel, D. H. Jundt and R. L. Byer, IEEE J. Quantum. Electron. 28, 2631 (1992). [CrossRef]

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