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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 11 — Jun. 3, 2013
  • pp: 13062–13067
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Measurement of the chirp characteristics of linearly chirped pulses by a frequency domain interference method

Wei Fan, Bin Zhu, Yinzhong Wu, Feng Qian, Min Shui, Sai Du, Bo Zhang, Yuchi Wu, Jianting Xin, Zongqing Zhao, Leifeng Cao, Yuxiao Wang, and Yuqiu Gu  »View Author Affiliations


Optics Express, Vol. 21, Issue 11, pp. 13062-13067 (2013)
http://dx.doi.org/10.1364/OE.21.013062


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Abstract

A linear optical technique for chirp characteristics measurement based on frequency domain interference is developed. This technique can be applied to measure the temporal structure of linearly chirped pulses which have become increasingly important in ultrafast optics. To confirm this technique, an experiment is carried out to measure the chirp rate and duration of a picosecond chirped pulse with an imaging spectrometer.

© 2013 OSA

1. Introduction

Linearly chirped pulse is widely used as probe light today because the ultrafast information in time domain could be mapped to frequency domain linearly with a chirped probe pulse and recorded by a spectrometer without fast response detectors [1

1. C. Y. Chien, B. La Fontaine, A. Desparois, Z. Jiang, T. W. Johnston, J. C. Kieffer, H. Pépin, F. Vidal, and H. P. Mercure, “Single-shot chirped-pulse spectral interferometry used to measure the femtosecond ionization dynamics of air,” Opt. Lett. 25(8), 578–580 (2000). [CrossRef] [PubMed]

,2

2. J.-P. Geindre, P. Audebert, S. Rebibo, and J.-C. Gauthier, “Single-shot spectral interferometry with chirped pulses,” Opt. Lett. 26(20), 1612–1614 (2001). [CrossRef] [PubMed]

]. So far, the chirped pulses have played an important role in terahertz detection [3

3. B. Yellampalle, K. Y. Kim, G. Rodriguez, J. H. Glownia, and A. J. Taylor, “Algorithm for high-resolution single-shot THz measurement using in-line spectral interferometry with chirped pulses,” Appl. Phys. Lett. 87(21), 211109 (2005). [CrossRef]

5

5. K. Y. Kim, B. Yellampalle, G. Rodriguez, R. D. Averitt, A. J. Taylor, and J. H. Glownia, “Single-shot, interferometric, high-resolution, terahertz field diagnostic,” Appl. Phys. Lett. 88(4), 041123 (2006). [CrossRef]

], laser driven shock waves [6

6. C. A. Bolme, S. D. McGrane, D. S. Moore, and D. J. Funk, “Single shot measurements of laser driven shock waves using ultrafast dynamic ellipsometry,” J. Appl. Phys. 102(3), 033513 (2007). [CrossRef]

9

9. J. C. Crowhurst, M. R. Armstrong, K. B. Knight, J. M. Zaug, and E. M. Behymer, “Invariance of the dissipative action at ultrahigh strain rates above the strong shock threshold,” Phys. Rev. Lett. 107(14), 144302 (2011). [CrossRef] [PubMed]

], laser-induced plasmas [10

10. S. Rebibo, J.-P. Geindre, P. Audebert, G. Grillon, J.-P. Chambaret, and J.-C. Gauthier, “Single-shot spectral interferometry of femtosecond laser-produced plasmas,” Laser Part. Beams 19(1), 67–73 (2001). [CrossRef]

14

14. Y. B. S. R. Prasad, S. Barnwal, P. A. Naik, J. A. Chakera, and P. D. Gupta, “Chirped pulse interferometry for time resolved density and velocity measurements of laser produced plasmas,” J. Appl. Phys. 110(2), 023305 (2011). [CrossRef]

], et al. Typically, a linearly chirped pulse is obtained by travelling a femtosecond pulse through a grating pair or highly dispersive material, its chirp characteristics can be measured by streak camera coupled to a spectrometer [13

13. Y. B. S. R. Prasad, S. Barnwal, P. A. Naik, J. A. Chakera, R. A. Khan, and P. D. Gupta, “Chirped pulse shadowgraphy for single shot time resolved plasma expansion measurements,” Appl. Phys. Lett. 96(22), 221503 (2010). [CrossRef]

], cross correlation method [15

15. S. Yamaguchi and H. Hamaguchi, “Convenient method of measuring the chirp structure of femtosecond white-light continuum pulses,” Appl. Spectrosc. 49(10), 1513–1515 (1995). [CrossRef]

], optical Kerr gate technique (OKG) [16

16. C. Nagura, A. Suda, H. Kawano, M. Obara, and K. Midorikawa, “Generation and characterization of ultrafast white-light continuum in condensed media,” Appl. Opt. 41(18), 3735–3742 (2002). [CrossRef] [PubMed]

18

18. W. J. Tan, H. Liu, J. H. Si, and X. Hou, “Control of the gated spectra with narrow bandwidth from a supercontinuum using ultrafast optical Kerr gate of bismuth glass,” Appl. Phys. Lett. 93(5), 051109 (2008). [CrossRef]

], two-photon absorption [19

19. T. F. Albrecht, K. Seibert, and H. Kurz, “Chirp measurement of large-bandwidth femtosecond optical pulses using two-photon absorption,” Opt. Commun. 84(5-6), 223–227 (1991). [CrossRef]

], or cross phase modulation (XPM) [20

20. K. Y. Kim, I. Alexeev, and H. M. Milchberg, “Single-shot supercontinuum spectral interferometry,” Appl. Phys. Lett. 81(22), 4124–4126 (2002). [CrossRef]

]. However, streak camera is limited by picosecond time resolution which is unsatisfactory for short-duration pulse measurement. For the other methods, nonlinear optical materials with large nonlinearities and fast response time, and relatively high intensity laser pulses are essential [18

18. W. J. Tan, H. Liu, J. H. Si, and X. Hou, “Control of the gated spectra with narrow bandwidth from a supercontinuum using ultrafast optical Kerr gate of bismuth glass,” Appl. Phys. Lett. 93(5), 051109 (2008). [CrossRef]

]. Consequently, the application of these techniques is limited.

In this paper, we developed a linear optical technique to measure the chirp characteristics of linearly chirped pulses without intensity restrictions and nonlinear optical materials. Using this method, we performed a demonstrative experiment to measure the chirp rate and duration of a picosecond chirped pulse.

2. Measurement principle

Consider a Fourier transform-limited Gaussian pulse whose electric field is
El(t)=E0exp(a0t2)exp(iω0t),
(1)
Where a0=2ln2/τ02,τ0is the full width at half maximum (FWHM) of the pulse intensity, andω0is the center frequency. When the pulse propagates through a pulse stretcher (e.g., a pair of gratings, a piece of dispersion glass), a linearly chirped pulse is obtained and the corresponding electric field is
Ec(t)=Ec0exp(at2)exp[i(ω0+bt)t],
(2)
Where a=2ln2/τc2,τc is the duration of the chirped pulse (FWHM), bis half of the chirp rate which is an important parameter for chirped pulse, its absolute value |b|Δω/(2τc) whileb2a2is satisfied. Here, Δωis the pulse spectral bandwidth (FWHM), and the time-bandwidth product of a chirp-free pulse is a constant Δωτ0=C0. It is clear that the linear chirp rate2bis determined by the bandwidth and duration of the chirped pulse, the former can be easily measured with a spectrometer while the latter is difficult to acquire accurately without adopting nonlinear techniques and an optical streak camera. Therefore, we propose a linear optical measurement of the chirped pulse durations (or chirp rate) with a spectrometer.

According to the principle of frequency domain interference, after the two pulses above enter into the spectrometer with a time delayT, a spectral interferogram would be acquired, and the intensity distribution of the spectral interference fringes is
I(ω)=|{El(t)}+{Ec(tT)}|2=|{El(t)}|2+|{Ec(tT)}|2+2|{El(t)}||{Ec(tT)}|cos(ϕcϕl),=I0(ω)+I1(ω)cos(Δϕ)
(3)
wherestands for Fourier transform, I0(ω)=|{El(t)}|2+|{Ec(tT)}|2 is the sum of the two pulse spectra, which is considered as a DC background. The second term of Eq. (3) is an AC term, where I1(ω)=2|{El(t)}||{Ec(tT)}| is the modulation amplitude and Δϕ is the phase difference between the two pulses
Δϕ=b(ωω0)24(a2+b2)ωT+arg(a+ib)=b4(a2+b2){ω[ω02(a2+b2)bT]}2b4(a2+b2){ω02[ω02(a2+b2)bT]2}+arg(a+ib).
(4)
Since the DC term and the modulation amplitude of the AC term both vary much slower than cos(Δϕ), the fringe distribution is mainly determined by Δϕ. From Eq. (4), we can see that there is an extremum ofΔϕwhen
ω=ωs=ω02(a2+b2)T/bω02bT,b2a2
(5)
which is
1λs=1λ02bT2πc
(6)
in the wavelength domain (cis the speed of light). It is obvious that ωs locates the widest fringe for the slowest variation of Δϕ. As shown in Eq. (5), there is a linear relationship between ωs and the time delayT, the linearly dependent coefficient is the chirp rate2b. Therefore, measuring ωs at different time delays gives the chirp rate, and knowing the spectral bandwidth further gives the duration. For the measurement of chirped pulse duration, the accuracy of conventional methods such as OKG is limited by the response time of nonlinear material, the duration of gate pulse, and the frequency-time mapping uncertainty. In contrast, our accuracy is limited by the last factor only because ωs can be determined accurately by taking the average of symmetric order fringe positions (see later discussions). Consequently, the frequency-time mapping uncertainty τ0τc determines the measurement accuracy which decreases as τc approaches τ0. In the deduction above, although the chirped pulse has the same spectrum as the Fourier transform-limited pulse, the technique is also feasible when their spectra only partially overlap.

To show this technique more specifically, the frequency domain interference between a femtosecond pulse and the corresponding picosecond chirped pulse is simulated. In this simulation, the pulse duration is 30fs and 40ps respectively, the chirp rate is2b=2.2100×106rad/fs2, the time delay isT=5ps, and the center wavelength is λ0=800nm. Figure 1
Fig. 1 The spectral interference fringes between a femtosecond pulse and the corresponding picosecond chirped pulse in the wavelength domain.
shows the simulated 1D spectral interference fringes in the wavelength domain. We can see that there is a very wide fringe on the pattern as predicted. However, the extremum of the widest fringe does not locate exactly on the central position λs because cos(Δϕ) in Eq. (3) is modulated by the DC background and the modulation amplitude. Fortunately, the modulation becomes weaker and weaker when the fringe width is decreasing. Therefore, compared to determine it by the minimum of the widest fringe, taking the average of symmetric order fringe positions gives λs much more precisely, here we adopted λs=1/2(λ1st+λ1st)=803.78nm. Putλsand T in Eq. (6), we recovered a chirp rate 2b=2.2100×106rad/fs2 which matches very well with the input. Therefore, the central position λs can be determined quite precisely although the extremum position of the widest fringe deviates from it.

3. Experiment

To confirm our proposal, an experiment was carried out. It was performed on a Ti: sapphire laser oscillator which delivers 30fs, 790nm pulses at a repetition rate of 84MHz, the energy is ~9nJ per pulse. Figure 2
Fig. 2 Experimental setup to measure the chirp characteristics of linearly chirped pulses, BS-beam splitter, M-planar mirror, G-grating.
shows the experimental setup for measuring the chirp characteristics of linearly chirped pulses. The incident pulse is split into two by a beam splitter BS1, a portion of the laser pulse travels through a pair of gratings which stretch the pulse temporally, after reflected by BS2 and going on through another beam splitter BS3, the stretched pulse is perpendicularly reflected by a planar mirror M5 which is mounted on a translation stage. The other portion of the laser pulse is used as a reference pulse. These two beams are recombined at BS3, and an imaging spectrometer is used to record the spectral interferogram. The chirp rate and duration of the stretched pulse are then measured by the frequency domain interference technique as described above.

In this experiment, a sequence of time delays between the chirped pulse and the reference pulse are achieved by moving M5 with a certain step length which has been accurately calibrated by frequency domain interferometry. In the calibration, M6 is inserted into the optical path, and then a Michelson interferometer is formed. The spectral interferogram of two chirped pulses is recorded by the spectrometer. Finally, we get the step length by reading out the fringe width variation between adjacent interferogram, and calibration results show that the step length is 93.02±2.69μm.

Figure 3(a)
Fig. 3 (a) Spectral interferogram at time delays of 7441.2fs, 11781.9fs, 16122.6fs and 20463.3fs. (b) 1D spectral interferogram at the time delay of 7441.2fs.
shows spectral interferogram of a femtosecond laser pulse and the corresponding chirped pulse at four different time delays. One can see that there is a very wide fringe in each interferogram, and the widest fringe shifts in the same direction as the time delay increases. What is more, fringe widths on both sides are approximately symmetric and decrease gradually when departing from the widest fringes, as theoretically predicted. Integrating in the vertical direction gives an 1D distribution of Fig. 3(a) at 7441.2fs time delay, as shown in Fig. 3(b), revealing a similar fringe distribution to Fig. 1. Figure 4
Fig. 4 The central position ωs versus time delay T, and the spectrum of the chirped pulse. The inset is a zoom-in to show an error bar.
shows our measurement of the widest fringe central positionωsversus time delay. Each central position was measured for ten times, and the inset in Fig. 4 is a zoom-in to show an error bar. There is an approximately linear relationship between the central position and the time delay, which matches well with the effect of grating stretcher, and our fit gives the chirp rate 2b=4.13×106±1.58×108rad/fs2 (negative chirp for grating-based pulse stretcher). Figure 4 also shows the chirped pulse spectrum whose width is Δω=0.0982rad/fs (FWHM)). Put them in τc=Δω/|2b| leads to the duration τc23.8ps, the relative uncertainty is 3.44%.

Additionally, the reference pulse is not strictly Fourier transform-limited but slightly chirped by inserted optical elements dispersion. One might worry if this would affect the measurement of the chirp characteristics. Actually, the technique is safe as long as τ0τc is satisfied no matter the reference pulse is chirped or not.

4. Conclusion

A diagnostic technique was proposed for measuring the chirp characteristics of linearly chirped pulses that widely used in single shot, ultrafast measurements. Compared to conventional nonlinear techniques, this technique can be carried out without nonlinear optical materials and pulse intensity restrictions. Using this method, we performed the chirp measurement of a picosecond chirped pulse, the experimental results shows that the frequency of the chirped pulse is mapped to time linearly as we expected.

Acknowledgments

This research was supported by the National Natural Science Foundation of China (Grant No. 11174259, 10902101).

References and links

1.

C. Y. Chien, B. La Fontaine, A. Desparois, Z. Jiang, T. W. Johnston, J. C. Kieffer, H. Pépin, F. Vidal, and H. P. Mercure, “Single-shot chirped-pulse spectral interferometry used to measure the femtosecond ionization dynamics of air,” Opt. Lett. 25(8), 578–580 (2000). [CrossRef] [PubMed]

2.

J.-P. Geindre, P. Audebert, S. Rebibo, and J.-C. Gauthier, “Single-shot spectral interferometry with chirped pulses,” Opt. Lett. 26(20), 1612–1614 (2001). [CrossRef] [PubMed]

3.

B. Yellampalle, K. Y. Kim, G. Rodriguez, J. H. Glownia, and A. J. Taylor, “Algorithm for high-resolution single-shot THz measurement using in-line spectral interferometry with chirped pulses,” Appl. Phys. Lett. 87(21), 211109 (2005). [CrossRef]

4.

B. Yellampalle, K. Y. Kim, G. Rodriguez, J. H. Glownia, and A. J. Taylor, “Details of electro-optic terahertz detection with a chirped probe pulse,” Opt. Express 15(3), 1376–1383 (2007). [CrossRef] [PubMed]

5.

K. Y. Kim, B. Yellampalle, G. Rodriguez, R. D. Averitt, A. J. Taylor, and J. H. Glownia, “Single-shot, interferometric, high-resolution, terahertz field diagnostic,” Appl. Phys. Lett. 88(4), 041123 (2006). [CrossRef]

6.

C. A. Bolme, S. D. McGrane, D. S. Moore, and D. J. Funk, “Single shot measurements of laser driven shock waves using ultrafast dynamic ellipsometry,” J. Appl. Phys. 102(3), 033513 (2007). [CrossRef]

7.

C. A. Bolme, S. D. McGrane, D. S. Moore, V. H. Whitley, and D. J. Funk, “Single shot Hugoniot of cyclohexane using a spatially resolved laser driven shock wave,” Appl. Phys. Lett. 93(19), 191903 (2008). [CrossRef]

8.

M. R. Armstrong, J. C. Crowhurst, S. Bastea, and J. M. Zaug, “Ultrafast observation of shocked states in a precompressed material,” J. Appl. Phys. 108(2), 023511 (2010). [CrossRef]

9.

J. C. Crowhurst, M. R. Armstrong, K. B. Knight, J. M. Zaug, and E. M. Behymer, “Invariance of the dissipative action at ultrahigh strain rates above the strong shock threshold,” Phys. Rev. Lett. 107(14), 144302 (2011). [CrossRef] [PubMed]

10.

S. Rebibo, J.-P. Geindre, P. Audebert, G. Grillon, J.-P. Chambaret, and J.-C. Gauthier, “Single-shot spectral interferometry of femtosecond laser-produced plasmas,” Laser Part. Beams 19(1), 67–73 (2001). [CrossRef]

11.

K. Y. Kim, I. Alexeev, and H. M. Milchberg, “Single-shot measurement of laser-induced double step ionization of helium,” Opt. Express 10(26), 1563–1572 (2002). [CrossRef] [PubMed]

12.

Y.-H. Chen, S. Varma, I. Alexeev, and H. M. Milchberg, “Measurement of transient nonlinear refractive index in gases using xenon supercontinuum single-shot spectral interferometry,” Opt. Express 15(12), 7458–7467 (2007). [CrossRef] [PubMed]

13.

Y. B. S. R. Prasad, S. Barnwal, P. A. Naik, J. A. Chakera, R. A. Khan, and P. D. Gupta, “Chirped pulse shadowgraphy for single shot time resolved plasma expansion measurements,” Appl. Phys. Lett. 96(22), 221503 (2010). [CrossRef]

14.

Y. B. S. R. Prasad, S. Barnwal, P. A. Naik, J. A. Chakera, and P. D. Gupta, “Chirped pulse interferometry for time resolved density and velocity measurements of laser produced plasmas,” J. Appl. Phys. 110(2), 023305 (2011). [CrossRef]

15.

S. Yamaguchi and H. Hamaguchi, “Convenient method of measuring the chirp structure of femtosecond white-light continuum pulses,” Appl. Spectrosc. 49(10), 1513–1515 (1995). [CrossRef]

16.

C. Nagura, A. Suda, H. Kawano, M. Obara, and K. Midorikawa, “Generation and characterization of ultrafast white-light continuum in condensed media,” Appl. Opt. 41(18), 3735–3742 (2002). [CrossRef] [PubMed]

17.

H. Liu, W. J. Tan, J. H. Si, X. Hou, and X. Hou, “Acquisition of gated spectra from a supercontinuum using ultrafast optical Kerr gate of lead phthalocyanine-doped hybrid glasses,” Opt. Express 16(17), 13486–13491 (2008). [CrossRef] [PubMed]

18.

W. J. Tan, H. Liu, J. H. Si, and X. Hou, “Control of the gated spectra with narrow bandwidth from a supercontinuum using ultrafast optical Kerr gate of bismuth glass,” Appl. Phys. Lett. 93(5), 051109 (2008). [CrossRef]

19.

T. F. Albrecht, K. Seibert, and H. Kurz, “Chirp measurement of large-bandwidth femtosecond optical pulses using two-photon absorption,” Opt. Commun. 84(5-6), 223–227 (1991). [CrossRef]

20.

K. Y. Kim, I. Alexeev, and H. M. Milchberg, “Single-shot supercontinuum spectral interferometry,” Appl. Phys. Lett. 81(22), 4124–4126 (2002). [CrossRef]

OCIS Codes
(120.4820) Instrumentation, measurement, and metrology : Optical systems
(320.1590) Ultrafast optics : Chirping

ToC Category:
Ultrafast Optics

History
Original Manuscript: April 2, 2013
Revised Manuscript: May 10, 2013
Manuscript Accepted: May 13, 2013
Published: May 20, 2013

Citation
Wei Fan, Bin Zhu, Yinzhong Wu, Feng Qian, Min Shui, Sai Du, Bo Zhang, Yuchi Wu, Jianting Xin, Zongqing Zhao, Leifeng Cao, Yuxiao Wang, and Yuqiu Gu, "Measurement of the chirp characteristics of linearly chirped pulses by a frequency domain interference method," Opt. Express 21, 13062-13067 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-11-13062


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References

  1. C. Y. Chien, B. La Fontaine, A. Desparois, Z. Jiang, T. W. Johnston, J. C. Kieffer, H. Pépin, F. Vidal, and H. P. Mercure, “Single-shot chirped-pulse spectral interferometry used to measure the femtosecond ionization dynamics of air,” Opt. Lett.25(8), 578–580 (2000). [CrossRef] [PubMed]
  2. J.-P. Geindre, P. Audebert, S. Rebibo, and J.-C. Gauthier, “Single-shot spectral interferometry with chirped pulses,” Opt. Lett.26(20), 1612–1614 (2001). [CrossRef] [PubMed]
  3. B. Yellampalle, K. Y. Kim, G. Rodriguez, J. H. Glownia, and A. J. Taylor, “Algorithm for high-resolution single-shot THz measurement using in-line spectral interferometry with chirped pulses,” Appl. Phys. Lett.87(21), 211109 (2005). [CrossRef]
  4. B. Yellampalle, K. Y. Kim, G. Rodriguez, J. H. Glownia, and A. J. Taylor, “Details of electro-optic terahertz detection with a chirped probe pulse,” Opt. Express15(3), 1376–1383 (2007). [CrossRef] [PubMed]
  5. K. Y. Kim, B. Yellampalle, G. Rodriguez, R. D. Averitt, A. J. Taylor, and J. H. Glownia, “Single-shot, interferometric, high-resolution, terahertz field diagnostic,” Appl. Phys. Lett.88(4), 041123 (2006). [CrossRef]
  6. C. A. Bolme, S. D. McGrane, D. S. Moore, and D. J. Funk, “Single shot measurements of laser driven shock waves using ultrafast dynamic ellipsometry,” J. Appl. Phys.102(3), 033513 (2007). [CrossRef]
  7. C. A. Bolme, S. D. McGrane, D. S. Moore, V. H. Whitley, and D. J. Funk, “Single shot Hugoniot of cyclohexane using a spatially resolved laser driven shock wave,” Appl. Phys. Lett.93(19), 191903 (2008). [CrossRef]
  8. M. R. Armstrong, J. C. Crowhurst, S. Bastea, and J. M. Zaug, “Ultrafast observation of shocked states in a precompressed material,” J. Appl. Phys.108(2), 023511 (2010). [CrossRef]
  9. J. C. Crowhurst, M. R. Armstrong, K. B. Knight, J. M. Zaug, and E. M. Behymer, “Invariance of the dissipative action at ultrahigh strain rates above the strong shock threshold,” Phys. Rev. Lett.107(14), 144302 (2011). [CrossRef] [PubMed]
  10. S. Rebibo, J.-P. Geindre, P. Audebert, G. Grillon, J.-P. Chambaret, and J.-C. Gauthier, “Single-shot spectral interferometry of femtosecond laser-produced plasmas,” Laser Part. Beams19(1), 67–73 (2001). [CrossRef]
  11. K. Y. Kim, I. Alexeev, and H. M. Milchberg, “Single-shot measurement of laser-induced double step ionization of helium,” Opt. Express10(26), 1563–1572 (2002). [CrossRef] [PubMed]
  12. Y.-H. Chen, S. Varma, I. Alexeev, and H. M. Milchberg, “Measurement of transient nonlinear refractive index in gases using xenon supercontinuum single-shot spectral interferometry,” Opt. Express15(12), 7458–7467 (2007). [CrossRef] [PubMed]
  13. Y. B. S. R. Prasad, S. Barnwal, P. A. Naik, J. A. Chakera, R. A. Khan, and P. D. Gupta, “Chirped pulse shadowgraphy for single shot time resolved plasma expansion measurements,” Appl. Phys. Lett.96(22), 221503 (2010). [CrossRef]
  14. Y. B. S. R. Prasad, S. Barnwal, P. A. Naik, J. A. Chakera, and P. D. Gupta, “Chirped pulse interferometry for time resolved density and velocity measurements of laser produced plasmas,” J. Appl. Phys.110(2), 023305 (2011). [CrossRef]
  15. S. Yamaguchi and H. Hamaguchi, “Convenient method of measuring the chirp structure of femtosecond white-light continuum pulses,” Appl. Spectrosc.49(10), 1513–1515 (1995). [CrossRef]
  16. C. Nagura, A. Suda, H. Kawano, M. Obara, and K. Midorikawa, “Generation and characterization of ultrafast white-light continuum in condensed media,” Appl. Opt.41(18), 3735–3742 (2002). [CrossRef] [PubMed]
  17. H. Liu, W. J. Tan, J. H. Si, X. Hou, and X. Hou, “Acquisition of gated spectra from a supercontinuum using ultrafast optical Kerr gate of lead phthalocyanine-doped hybrid glasses,” Opt. Express16(17), 13486–13491 (2008). [CrossRef] [PubMed]
  18. W. J. Tan, H. Liu, J. H. Si, and X. Hou, “Control of the gated spectra with narrow bandwidth from a supercontinuum using ultrafast optical Kerr gate of bismuth glass,” Appl. Phys. Lett.93(5), 051109 (2008). [CrossRef]
  19. T. F. Albrecht, K. Seibert, and H. Kurz, “Chirp measurement of large-bandwidth femtosecond optical pulses using two-photon absorption,” Opt. Commun.84(5-6), 223–227 (1991). [CrossRef]
  20. K. Y. Kim, I. Alexeev, and H. M. Milchberg, “Single-shot supercontinuum spectral interferometry,” Appl. Phys. Lett.81(22), 4124–4126 (2002). [CrossRef]

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