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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 22, Iss. 4 — Feb. 24, 2014
  • pp: 4075–4082
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Generation of octave-spanning supercontinuum by Raman-assisted four-wave mixing in single-crystal diamond

Chih-Hsuan Lu, Li-Fan Yang, Miaochan Zhi, Alexei V. Sokolov, Shang-Da Yang, Chia-Chen Hsu, and A. H. Kung  »View Author Affiliations


Optics Express, Vol. 22, Issue 4, pp. 4075-4082 (2014)
http://dx.doi.org/10.1364/OE.22.004075


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Abstract

An octave-spanning coherent supercontinuum is generated by non-collinear Raman-assisted four-wave mixing in single-crystal diamond using 7.7 fs laser pulses that have been chirped to about 420 fs in duration. The use of ultrabroad bandwidth pulses as input results in substantial overlap of the generated spectrum of the anti-Stokes sidebands, creating a phase-locked supercontinuum when all the sidebands are combined to overlap in time and space. The overall bandwidth of the generated supercontinuum is sufficient to support its compression to isolated few-to-single cycle attosecond transients. The significant spectral overlap of adjacent anti-Stokes sidebands allows the utilization of straight-forward spectral interferometry to test the relative phase coherence of the anti-Stokes outputs and is demonstrated here for two adjacent pairs of sidebands. The method can subsequently be employed to set the relative phase of the sidebands for pulse compression and for the synthesis of arbitrary field transients.

© 2014 Optical Society of America

1. Introduction

Optical transients in the single-cycle to sub-cycle regime are femtosecond to attosecond fields that are invaluable in elucidating ultrafast electronic processes in atoms, molecules and condensed matter and for realizing nonlinear optics in the sub-cycle regime. One prerequisite to the successful synthesis of these transient fields is to have a coherent light source that possesses an octave-spanning spectrum. Such a light source can be generated by focusing intense millijoule level femtosecond laser pulses into a gas or a solid medium to make use of laser-induced Kerr nonlinearity to broaden the pulse’s spectrum [1

1. E. E. Serebryannikov, E. Goulielmakis, and A. M. Zheltikov, “Generation of supercontinuum compressible to single-cycle pulse widths in an ionizing gas,” New J. Phys. 10(9), 093001 (2008). [CrossRef]

]. Indeed with this approach attosecond transients have recently been synthesized successfully [2

2. A. Wirth, M. Th. Hassan, I. Grguraš, J. Gagnon, A. Moulet, T. T. Luu, S. Pabst, R. Santra, Z. A. Alahmed, A. M. Azzeer, V. S. Yakovlev, V. Pervak, F. Krausz, and E. Goulielmakis, “Synthesized light transients,” Science 334(6053), 195–200 (2011). [CrossRef] [PubMed]

,3

3. M. Th. Hassan, A. Wirth, I. Grguraš, A. Moulet, T. T. Luu, J. Gagnon, V. Pervak, and E. Goulielmakis, “Invited Article: Attosecond photonics: Synthesis and control of light transients,” Rev. Sci. Instrum. 83(11), 111301 (2012). [CrossRef] [PubMed]

]. An alternative approach for generating a broad spectrum is the molecular modulation technique [4

4. S. E. Harris and A. V. Sokolov, “Subfemtosecond pulse generation by molecular modulation,” Phys. Rev. Lett. 81(14), 2894–2897 (1998). [CrossRef]

]. Using molecular gases driven in the steady state regime by narrowband nanosecond lasers, this technique has successfully produced frequency combs that consist of up to a couple hundred Stokes and anti-Stokes sidebands [5

5. A. V. Sokolov, D. R. Walker, D. D. Yavuz, G. Y. Yin, and S. E. Harris, “Raman generation by phased and antiphased molecular states,” Phys. Rev. Lett. 85(3), 562–565 (2000). [CrossRef] [PubMed]

] and has been used to demonstrate the synthesis of a periodic train of ultrashort optical fields of arbitrary shape in the visible-UV spectral region, where such pulses inevitably express single-cycle nature, and allow non-sinusoidal field synthesis [6

6. H. S. Chan, Z. M. Hsieh, W. H. Liang, A. H. Kung, C. K. Lee, C. J. Lai, R. P. Pan, and L. H. Peng, “Synthesis and measurement of ultrafast waveforms from five discrete optical harmonics,” Science 331(6021), 1165–1168 (2011). [CrossRef] [PubMed]

].

2. Experimental

We begin with 23 fs long pulses centered at λ = 790 nm from a commercial 1 kHz chirp-pulse amplified mode-locked Ti:sapphire laser (Femtopower HE PRO CEP). We expand the spectrum of these pulses by self-phase modulation in helium inside a hollow waveguide (inner core diameter 250 µm) to obtain wavelength coverage from 690 nm to 870 nm at the 50% intensity level (a width of 3000 cm−1). A spectrum of this pulse is shown in Fig. 1
Fig. 1 Schematic of the experimental setup. BS1: 2% beamsplitter; BS2: 50/50 beam-splitter; CP: compensation plate; Stretcher: 4 mm thick SF56A glass. The focusing mirror has a radius of curvature of 40 cm. About 2% of the compressed output from the hollow fiber is stretched and split into two and then recombined at the diamond crystal with a relative time delay between the two pulses provided by the delay stage. A spectrum of the pulse incident onto the crystal is shown in the upper left quadrant.
. The broadened pulse is first compressed with negatively-chirped mirrors to a near-transform-limited duration of 7.7 fs. The main portion of this pulse is used for a high harmonic generation experiment. We used about 2% of the compressed laser power for the purpose of the experiments described here. The 2% value was chosen because we found that this value is sufficient for demonstrating the idea being put forward in this paper while leaving sufficient laser power for other experiments. The 2% pulse was chirped to about 420 fs FWHM (chirp rate 7400 fs2) by passing the pulse through a 4 mm thick SF56A glass. For CFWM in condensed phase it is prudent to lengthen the pulse to avoid self-phase modulation and opticaldamage in the medium [18

18. Z. Cui, M. Chaturvedi, B. Tian, J. Ackert, F. C. Turner, and D. Strickland, “Spectral red-shifting of multi-frequency Raman orders,” Opt. Commun. 288, 118–121 (2013). [CrossRef]

]. We determined experimentally that the present chirp rate is optimal for the pulse power used in this experiment. A smaller chirp would cause optical damage in our set-up and with a larger chirp the generated bandwidth and overall efficiency would have suffered.

Each chirped pulse was then split into two pulses by a broadband ~50% beamsplitter coated for minimal second-order dispersion. One of the split pulses served as the pump pulse and traveled on a path that can be delayed (see Fig. 1). The other pulse (signal) passed through a chirp compensator to equalize the chirp acquired by each split pulse after their separation. The split pulses were then focused and recombined to cross each other at an angle over a spot of diameter 40 μm in a 0.5 mm thick CVD-grown single-crystal diamond. The polarization of the pulses is parallel to the [110] direction of the crystal. After attenuation and accounting for losses in the beam paths, the average power of the chirped beams incident onto the diamond crystal was 3.3 mW (pump) and 3.0 mW (signal) respectively. The corresponding incident intensities were 6.25 × 1011 W/cm2 and 5.7 × 1011 W/cm2.

A time delay between the two chirped pulses creates an instantaneous frequency difference between them when they cross each other in the crystal [13

13. M. Zhi and A. V. Sokolov, “Broadband generation in a Raman crystal driven by a pair of time-delayed linearly chirped pulses,” New J. Phys. 10(2), 025032 (2008). [CrossRef]

]. The pulses interact by CFWM to produce sidebands that exited from the diamond crystal in a range of angles away from the two crossing incident pulses as depicted in Fig. 1. The intensity and spectrum of each generated sideband were recorded and analysed with an optical spectrometer equipped with a calibrated diode array detector (Ocean Optics HR4000).

3. Results and discussion

We did experiments at several external crossing angles between the two input pulses from ~2° to ~5°, recording the anti-Stokes sidebands as we scanned the relative delay time between the two pulses. We found that, for all incident angles, intense CFWM output consisting of several Stokes and anti-Stokes sidebands occurs only for a span of time delay that is short compared to the chirped pulse duration of 420 fs (see Fig. 2
Fig. 2 Anti-Stokes output generated as a function of the relative delay between the two input pulses for a 3° crossing angle between the two input pulses. ASn stands for nth anti-Stokes sideband. From top to bottom: AS1, AS2, AS3, AS4 and AS5.
). In CFWM the generation of each sideband is determined by off-angle phase-matching of the frequencies involved [8

8. H. Crespo, J. T. Mendonça, and A. Dos Santos, “Cascaded highly nondegenerate four-wave-mixing phenomenon in transparent isotropic condensed media,” Opt. Lett. 25(11), 829–831 (2000). [CrossRef] [PubMed]

,15

15. J. Liu and T. Kobayashi, “Cascaded four-wave mixing in transparent bulk media,” Opt. Commun. 283, 1114–1123 (2010). [CrossRef] [PubMed]

]. This result means that for chirped pulses there is only a limited span of time delay for which the instantaneous frequencies of the pulses can satisfy the phase-matching condition.

We further found that the 3° crossing angle produces the largest number of Stokes and anti-Stokes sidebands. At this angle, more than three Stokes and ten anti-Stokes sidebands were generated. Due to a smaller dispersion on the red side, the first two Stokes beams exiting the diamond crystal spatially overlapped in part with the pump. Recording the spectrum of the Stokes spectra inevitably included a portion of the more intense pump spectrum. Analysis of the Stokes sidebands becomes quite ambiguous. Therefore, only the anti-Stokes sidebands have been studied in greater detail and reported below.

In our experiment the largest number of anti-Stokes sidebands produced occurred at a relative time delay of 220 ± 10 fs. A mirror image of the angular distribution of the sidebands appeared at negative time delay of the same value due to symmetry of the set up. This provided an excellent way to determine the zero time with an accuracy of a few fs for the experiment. Figure 2 shows the intensity of the first 5 anti-Stokes sidebands generated as a function of relative time delay between the two incident pulses at the 3° crossing angle. As can be seen, the third and higher anti-Stokes orders appear only within a relative time delay window of 60 fs (FWHM) centered at about 220 fs. The instantaneous frequency difference corresponding to the time delay of 220 fs is 1221 ± 200 cm−1. This value is within experimental uncertainty equal to the 1332 cm−1 Raman frequency of diamond. The proximity of the two values is not accidental. Evidently successful generation of many sidebands needs good conversion efficiency so that it is a prerequisite that both the phase-matching condition and near-resonance Raman enhancement are satisfied in the CFWM process.

The figure confirms that the broad input spectrum can be replicated to most of the sidebands. The structures seen in Fig. 3 originate mainly from those present in the input spectrum that is shown in Fig. 1. The sidebands do gradually get narrower at higher anti-Stokes orders when increasing dispersion towards the blue side of the spectrum naturally tightens the phase-matching bandwidth. A distinctive feature in Fig. 3 is that there is significant overlap in the spectra of all the adjacent sidebands as was initially conjectured. Every frequency is present in at least two different CFWM sidebands. The pulse energy of sidebands higher than the tenth falls off rapidly as dispersion causes CFWM to become far from being phase-matched.

The frequency span of the combined sidebands is larger than 13000 cm−1, spanning more than one octave. This spectral width is sufficient for the Fourier synthesis of single isolated few-cycle to single-cycle transient fields. Matter of fact this generated total bandwidth is similar to previously reported CFWM work cited above. However the difference is that in the present case there is better spectral continuity and coverage with few periodic structural peaks. Such discrete structures are inevitable when inputs narrower than the Raman spacing were used as pump. Suppression of these structural peaks due to the improved continuity in spectral coverage that is achieved in this experiment will help to realize pedestal-free femtosecond transient fields.

The sidebands generated by CFWM are expected to be mutually coherent. Since the sidebands overlap there should be optical interference when heterodyning pairs of adjacent sidebands. We set up a Michelson interferometer to demonstrate this effect. The beam of the first anti-Stokes sideband (AS1) pulses was aligned collinearly with that of the second anti-Stokes sideband (AS2). The combined beam was fiber-coupled to the spectrometer-diode array detector system. The resulting spectrum was recorded while the AS1 pulse was delay-scanned with respect to the AS2 pulse. The result is a two-dimensional multi-wavelength interferogram that simultaneously records the interference of many wavelengths as a function of time delay between the two anti-Stokes sideband pulses as shown in Fig. 4
Fig. 4 Result of phase coherence tests of the generated sidebands: (a) Spectrum of AS1 and AS2 recorded separately (red: AS1; green: AS2) and combined with the two temporally separated (blue); (b) Spectrally-resolved intensity pattern of combined AS1 and AS2 from 670 nm to 685 nm as a function of relative time delay between the two sidebands. Relative delay time of zero is when the phases are aligned at all wavelengths; (c) portion of (b) expanded in time to show the result of optical interference. (d) to (f) are repeat of (a) to (e) for AS3 and AS4 with similar result.
. The blue curve in Fig. 4(a) is spectrum recorded when AS1 and AS2 pulses were temporally separated. This spectrum is simply the sum of the individual spectra of the AS1 and AS2 pulses. Figure 4(a) also shows that the spectra of AS1 and of AS2 overlap for as much as 90 nm, from ~620 nm to ~710 nm.

As the two pulses began to overlap in time, interference in the form of a beat signal across the overlapping spectral region of AS1 and AS2 can clearly be discerned. The portion from 670 nm to 685 nm where the largest modulation depths were produced is shown in Fig. 4(b). A portion of Fig. 4(b) is expanded for display in Fig. 4(c) to show clear oscillations at every resolvable wavelength. The slanted pattern in Figs. 4(b) and 4(c) is an expected consequence of different phase-coherent wavelengths propagating simultaneously in space. The interferograms shown in Fig. 4 took several minutes to complete. The clarity of the interference patterns indicates that the phase locking between the two pulses is extremely stable.

We repeated the measurements for the third (AS3) and fourth (AS4) sidebands and obtained similar results (Figs. 4(d)4(f)). By induction the result can be used to interpret that phases are locked simultaneously at all wavelengths across the entire supercontinuum. While phase coherence is fully expected from a CFWM process, this is the first time that the coherence and its stability are displayed by experiment over a broad spectral region simultaneously. From the interferogram, relative spectral phase across many wavelengths can be determined. Thus, these measurements demonstrate that for sidebands generated by broad-bandwidth CFWM it is sufficient to use simple spectral interferometry to determine the relative phases without having to resort to nonlinear optical processes that are a lot less efficient. This technique can eventually be used to set or correct the relative phase of all the anti-Stokes sidebands by inclusion of phase adjustment devices such as spatial light modulators [25

25. M. Zhi, K. Wang, X. Hua, and A. V. Sokolov, “Pulse-shaper-assisted phase control of a coherent broadband spectrum of Raman sidebands,” Opt. Lett. 36(20), 4032–4034 (2011). [CrossRef] [PubMed]

] or chirp mirrors to facilitate compression to an ultrafast field transient.

The measured average power of the output were 344 μW, 68 μW, 20 μW, 6 μW, 4.8 μW, and 3.6 μW for the first to the sixth anti-Stokes sideband respectively. This is >13% power conversion from the pump pulse to the anti-Stokes sidebands. The power of higher anti-Stokes sidebands were less than 1μW and are not listed here. These sideband powers are scalable with the input power.

By the nature of off-angle phase-matched four-wave mixing, the generated sidebands exit the diamond crystal at slightly different angles and are spatially chirped in the phase-matching plane. These effects have to be compensated when it comes time to synthesize ultrashort pulses with these sidebands. One solution is to bring the sidebands together in a focused region with a pair of parabolic mirrors similar to the arrangement exercised in Ref. [21

21. R. Weigand, J. T. Mendonca, and H. M. Crespo, “Cascaded nondegenerate four-wave-mixing technique for high power single-cycle pulse synthesis in the visible and ultraviolet region,” Phys. Rev. A 79(6), 063838 (2009). [CrossRef]

] and Ref. [25

25. M. Zhi, K. Wang, X. Hua, and A. V. Sokolov, “Pulse-shaper-assisted phase control of a coherent broadband spectrum of Raman sidebands,” Opt. Lett. 36(20), 4032–4034 (2011). [CrossRef] [PubMed]

] or use MEMS mirrors to perform the compensation. An alternative is to substitute off-angle mixing with collinear four-wave mixing. This however is an inferior solution due to a lower efficiency and some reduction in bandwidth of the continuum.

4. Summary

Acknowledgments

We thank Yu-Jung Tsou, Bo-Han Chen, Hong-Yu Chen, and Yu-Chen Cheng for technical assistance. This work is supported by the Academia Sinica, the National Science Council of Taiwan (grants NSC 100-2120-M-007-007 and NSC 101-2112-M-001-008), the National Science Foundation of the United States (award number PHY-1307153) and the Welch Foundation (grant number A1547).

References and links

1.

E. E. Serebryannikov, E. Goulielmakis, and A. M. Zheltikov, “Generation of supercontinuum compressible to single-cycle pulse widths in an ionizing gas,” New J. Phys. 10(9), 093001 (2008). [CrossRef]

2.

A. Wirth, M. Th. Hassan, I. Grguraš, J. Gagnon, A. Moulet, T. T. Luu, S. Pabst, R. Santra, Z. A. Alahmed, A. M. Azzeer, V. S. Yakovlev, V. Pervak, F. Krausz, and E. Goulielmakis, “Synthesized light transients,” Science 334(6053), 195–200 (2011). [CrossRef] [PubMed]

3.

M. Th. Hassan, A. Wirth, I. Grguraš, A. Moulet, T. T. Luu, J. Gagnon, V. Pervak, and E. Goulielmakis, “Invited Article: Attosecond photonics: Synthesis and control of light transients,” Rev. Sci. Instrum. 83(11), 111301 (2012). [CrossRef] [PubMed]

4.

S. E. Harris and A. V. Sokolov, “Subfemtosecond pulse generation by molecular modulation,” Phys. Rev. Lett. 81(14), 2894–2897 (1998). [CrossRef]

5.

A. V. Sokolov, D. R. Walker, D. D. Yavuz, G. Y. Yin, and S. E. Harris, “Raman generation by phased and antiphased molecular states,” Phys. Rev. Lett. 85(3), 562–565 (2000). [CrossRef] [PubMed]

6.

H. S. Chan, Z. M. Hsieh, W. H. Liang, A. H. Kung, C. K. Lee, C. J. Lai, R. P. Pan, and L. H. Peng, “Synthesis and measurement of ultrafast waveforms from five discrete optical harmonics,” Science 331(6021), 1165–1168 (2011). [CrossRef] [PubMed]

7.

A. Nazarkin, G. Korn, M. Wittmann, and T. Elsaesser, “Generation of multiple phase-locked Stokes and Anti-Stokes components in an impulsively excited Raman medium,” Phys. Rev. Lett. 83(13), 2560–2563 (1999). [CrossRef]

8.

H. Crespo, J. T. Mendonça, and A. Dos Santos, “Cascaded highly nondegenerate four-wave-mixing phenomenon in transparent isotropic condensed media,” Opt. Lett. 25(11), 829–831 (2000). [CrossRef] [PubMed]

9.

M. Zhi and A. V. Sokolov, “Broadband coherent light generation in a Raman-active crystal driven by two-color femtosecond laser pulses,” Opt. Lett. 32(15), 2251–2253 (2007). [CrossRef] [PubMed]

10.

J. Takahashi, Y. Kawabe, and E. Hanamura, “Generation of a broadband spectral comb with multiwave mixing by exchange of an impulsively stimulated phonon,” Opt. Express 12(7), 1185–1191 (2004). [CrossRef] [PubMed]

11.

E. Matsubara, K. Inoue, and E. Hanamura, “Dynamical symmetry breaking induced by ultrashort laser pulses in KTaO3,” J. Phys. Soc. Jpn. 75(2), 024712 (2006). [CrossRef]

12.

H. Matsuki, K. Inoue, and E. Hanamura, “Multiple coherent anti-Stokes Raman scattering due to phonon grating in KNbO3 induced by crossed beams of two-color femtosecond pulses,” Phys. Rev. B 75(2), 024102 (2007). [CrossRef]

13.

M. Zhi and A. V. Sokolov, “Broadband generation in a Raman crystal driven by a pair of time-delayed linearly chirped pulses,” New J. Phys. 10(2), 025032 (2008). [CrossRef]

14.

M. Zhi, X. Wang, and A. V. Sokolov, “Broadband coherent light generation in diamond driven by femtosecond pulses,” Opt. Express 16(16), 12139–12147 (2008). [CrossRef] [PubMed]

15.

J. Liu and T. Kobayashi, “Cascaded four-wave mixing in transparent bulk media,” Opt. Commun. 283, 1114–1123 (2010). [CrossRef] [PubMed]

16.

W. Liu, L. Zhu, L. Wang, and C. Fang, “Cascaded four-wave mixing for broadband tunable laser sideband generation,” Opt. Lett. 38(11), 1772–1774 (2013). [CrossRef] [PubMed]

17.

F. C. Turner, A. Trottier, D. Strickland, and L. L. Losev, “Transient multi-frequency Raman generation in SF6,” Opt. Commun. 270(2), 419–423 (2007). [CrossRef]

18.

Z. Cui, M. Chaturvedi, B. Tian, J. Ackert, F. C. Turner, and D. Strickland, “Spectral red-shifting of multi-frequency Raman orders,” Opt. Commun. 288, 118–121 (2013). [CrossRef]

19.

H. Kawano, Y. Hirakawa, and T. Imasaka, “Generation of high-order rotational lines in hydrogen by four-wave Raman mixing in the femtosecond regime,” IEEE J. Quantum Electron. 34(2), 260–268 (1998). [CrossRef]

20.

O. Shitamichi and T. Imasaka, “High-order Raman sidebands generated from the near-infrared to ultraviolet region by four-wave Raman mixing of hydrogen using an ultrashort two-color pump beam,” Opt. Express 20(25), 27959–27965 (2012). [CrossRef] [PubMed]

21.

R. Weigand, J. T. Mendonca, and H. M. Crespo, “Cascaded nondegenerate four-wave-mixing technique for high power single-cycle pulse synthesis in the visible and ultraviolet region,” Phys. Rev. A 79(6), 063838 (2009). [CrossRef]

22.

E. Matsubara, Y. Kawamoto, T. Sekikawa, and M. Yamashita, “Generation of ultrashort optical pulses in the 10 fs regime using multicolor Raman sidebands in KTaO3.,” Opt. Lett. 34(12), 1837–1839 (2009). [CrossRef] [PubMed]

23.

J. He, J. Du, and T. Kobayashi, “Low-threshold and compact multi-colored femtosecond laser generated by using cascaded four-wave mixing in a diamond plate,” Opt. Commun. 290, 132–135 (2013). [CrossRef]

24.

F. Peter, “About refractive indices and absorption constants of the diamond 644-226 nm,” Z. Phys. 15, 358–368 (1923). [CrossRef]

25.

M. Zhi, K. Wang, X. Hua, and A. V. Sokolov, “Pulse-shaper-assisted phase control of a coherent broadband spectrum of Raman sidebands,” Opt. Lett. 36(20), 4032–4034 (2011). [CrossRef] [PubMed]

OCIS Codes
(190.4380) Nonlinear optics : Nonlinear optics, four-wave mixing
(190.5650) Nonlinear optics : Raman effect
(320.6629) Ultrafast optics : Supercontinuum generation

ToC Category:
Nonlinear Optics

History
Original Manuscript: December 3, 2013
Revised Manuscript: February 9, 2014
Manuscript Accepted: February 10, 2014
Published: February 13, 2014

Citation
Chih-Hsuan Lu, Li-Fan Yang, Miaochan Zhi, Alexei V. Sokolov, Shang-Da Yang, Chia-Chen Hsu, and A. H. Kung, "Generation of octave-spanning supercontinuum by Raman-assisted four-wave mixing in single-crystal diamond," Opt. Express 22, 4075-4082 (2014)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-4-4075


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References

  1. E. E. Serebryannikov, E. Goulielmakis, A. M. Zheltikov, “Generation of supercontinuum compressible to single-cycle pulse widths in an ionizing gas,” New J. Phys. 10(9), 093001 (2008). [CrossRef]
  2. A. Wirth, M. Th. Hassan, I. Grguraš, J. Gagnon, A. Moulet, T. T. Luu, S. Pabst, R. Santra, Z. A. Alahmed, A. M. Azzeer, V. S. Yakovlev, V. Pervak, F. Krausz, E. Goulielmakis, “Synthesized light transients,” Science 334(6053), 195–200 (2011). [CrossRef] [PubMed]
  3. M. Th. Hassan, A. Wirth, I. Grguraš, A. Moulet, T. T. Luu, J. Gagnon, V. Pervak, E. Goulielmakis, “Invited Article: Attosecond photonics: Synthesis and control of light transients,” Rev. Sci. Instrum. 83(11), 111301 (2012). [CrossRef] [PubMed]
  4. S. E. Harris, A. V. Sokolov, “Subfemtosecond pulse generation by molecular modulation,” Phys. Rev. Lett. 81(14), 2894–2897 (1998). [CrossRef]
  5. A. V. Sokolov, D. R. Walker, D. D. Yavuz, G. Y. Yin, S. E. Harris, “Raman generation by phased and antiphased molecular states,” Phys. Rev. Lett. 85(3), 562–565 (2000). [CrossRef] [PubMed]
  6. H. S. Chan, Z. M. Hsieh, W. H. Liang, A. H. Kung, C. K. Lee, C. J. Lai, R. P. Pan, L. H. Peng, “Synthesis and measurement of ultrafast waveforms from five discrete optical harmonics,” Science 331(6021), 1165–1168 (2011). [CrossRef] [PubMed]
  7. A. Nazarkin, G. Korn, M. Wittmann, T. Elsaesser, “Generation of multiple phase-locked Stokes and Anti-Stokes components in an impulsively excited Raman medium,” Phys. Rev. Lett. 83(13), 2560–2563 (1999). [CrossRef]
  8. H. Crespo, J. T. Mendonça, A. Dos Santos, “Cascaded highly nondegenerate four-wave-mixing phenomenon in transparent isotropic condensed media,” Opt. Lett. 25(11), 829–831 (2000). [CrossRef] [PubMed]
  9. M. Zhi, A. V. Sokolov, “Broadband coherent light generation in a Raman-active crystal driven by two-color femtosecond laser pulses,” Opt. Lett. 32(15), 2251–2253 (2007). [CrossRef] [PubMed]
  10. J. Takahashi, Y. Kawabe, E. Hanamura, “Generation of a broadband spectral comb with multiwave mixing by exchange of an impulsively stimulated phonon,” Opt. Express 12(7), 1185–1191 (2004). [CrossRef] [PubMed]
  11. E. Matsubara, K. Inoue, E. Hanamura, “Dynamical symmetry breaking induced by ultrashort laser pulses in KTaO3,” J. Phys. Soc. Jpn. 75(2), 024712 (2006). [CrossRef]
  12. H. Matsuki, K. Inoue, E. Hanamura, “Multiple coherent anti-Stokes Raman scattering due to phonon grating in KNbO3 induced by crossed beams of two-color femtosecond pulses,” Phys. Rev. B 75(2), 024102 (2007). [CrossRef]
  13. M. Zhi, A. V. Sokolov, “Broadband generation in a Raman crystal driven by a pair of time-delayed linearly chirped pulses,” New J. Phys. 10(2), 025032 (2008). [CrossRef]
  14. M. Zhi, X. Wang, A. V. Sokolov, “Broadband coherent light generation in diamond driven by femtosecond pulses,” Opt. Express 16(16), 12139–12147 (2008). [CrossRef] [PubMed]
  15. J. Liu, T. Kobayashi, “Cascaded four-wave mixing in transparent bulk media,” Opt. Commun. 283, 1114–1123 (2010). [CrossRef] [PubMed]
  16. W. Liu, L. Zhu, L. Wang, C. Fang, “Cascaded four-wave mixing for broadband tunable laser sideband generation,” Opt. Lett. 38(11), 1772–1774 (2013). [CrossRef] [PubMed]
  17. F. C. Turner, A. Trottier, D. Strickland, L. L. Losev, “Transient multi-frequency Raman generation in SF6,” Opt. Commun. 270(2), 419–423 (2007). [CrossRef]
  18. Z. Cui, M. Chaturvedi, B. Tian, J. Ackert, F. C. Turner, D. Strickland, “Spectral red-shifting of multi-frequency Raman orders,” Opt. Commun. 288, 118–121 (2013). [CrossRef]
  19. H. Kawano, Y. Hirakawa, T. Imasaka, “Generation of high-order rotational lines in hydrogen by four-wave Raman mixing in the femtosecond regime,” IEEE J. Quantum Electron. 34(2), 260–268 (1998). [CrossRef]
  20. O. Shitamichi, T. Imasaka, “High-order Raman sidebands generated from the near-infrared to ultraviolet region by four-wave Raman mixing of hydrogen using an ultrashort two-color pump beam,” Opt. Express 20(25), 27959–27965 (2012). [CrossRef] [PubMed]
  21. R. Weigand, J. T. Mendonca, H. M. Crespo, “Cascaded nondegenerate four-wave-mixing technique for high power single-cycle pulse synthesis in the visible and ultraviolet region,” Phys. Rev. A 79(6), 063838 (2009). [CrossRef]
  22. E. Matsubara, Y. Kawamoto, T. Sekikawa, M. Yamashita, “Generation of ultrashort optical pulses in the 10 fs regime using multicolor Raman sidebands in KTaO3.,” Opt. Lett. 34(12), 1837–1839 (2009). [CrossRef] [PubMed]
  23. J. He, J. Du, T. Kobayashi, “Low-threshold and compact multi-colored femtosecond laser generated by using cascaded four-wave mixing in a diamond plate,” Opt. Commun. 290, 132–135 (2013). [CrossRef]
  24. F. Peter, “About refractive indices and absorption constants of the diamond 644-226 nm,” Z. Phys. 15, 358–368 (1923). [CrossRef]
  25. M. Zhi, K. Wang, X. Hua, A. V. Sokolov, “Pulse-shaper-assisted phase control of a coherent broadband spectrum of Raman sidebands,” Opt. Lett. 36(20), 4032–4034 (2011). [CrossRef] [PubMed]

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