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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 7 — Apr. 8, 2013
  • pp: 8746–8752
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Identification of the physical mechanism of generation of coherent N2+ emissions in air by femtosecond laser excitation

Jielei Ni, Wei Chu, Chenrui Jing, Haisu Zhang, Bin Zeng, Jinping Yao, Guihua Li, Hongqiang Xie, Chaojin Zhang, Huailiang Xu, See-Leang Chin, Ya Cheng, and Zhizhan Xu  »View Author Affiliations


Optics Express, Vol. 21, Issue 7, pp. 8746-8752 (2013)
http://dx.doi.org/10.1364/OE.21.008746


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Abstract

Recently, amplification of harmonic-seeded radiation generated through femtosecond laser filamentation in air has been observed, giving rise to coherent emissions at wavelengths corresponding to transitions between different vibrational levels of the electronic B2Σu+ and X2Σg+ states of molecular nitrogen ions [Phys. Rev. A. 84, 051802(R) (2011)]. Here, we carry out systematic investigations on its physical mechanism. Our experimental results do not support the speculation that such excellent coherent emissions could originate from nonlinear optical processes such as four-wave mixing or stimulated Raman scattering, leaving stimulated amplification of harmonic seed due to the population inversion generated in molecular nitrogen ions the most likely mechanism.

© 2013 OSA

1. Introduction

For the above-mentioned purpose, in the present work, we perform systematic experimental investigations based on a pump-probe scheme. As shown in Fig. 1(a)
Fig. 1 (a) Typical schematic of the interaction of nitrogen molecules with two color pulses. Inset: the strong and coherent emission with ~0.3 nm bandwidth (FWHM) appearing on the spectrum of the probe pulse. (b) Energy-level diagram of ionized and neutral nitrogen molecules in which the vibrational transition between B2Σu+ (v = 0) and X2Σg+ (v = 0) states corresponding to 391.4 nm wavelength [10] is indicated.
and 1(b), in this scheme, an intense femtosecond laser pulse at 800 nm wavelength serves as the pump for excitation of the molecular system. In such a case, due to the inversion symmetry of air, second harmonic generation of the pump pulses cannot occur in air. Consequently, amplification of self-generated harmonic seed pulses at wavelengths near ~400 nm is impossible. We thus introduce a weak second harmonic pulse generated by a nonlinear crystal to serve as the probe, which can be temporally arranged with an arbitrary delay time behind the 800 nm pump pulse. The amplification of the seed critically depends not only on the temporal delay between the pump and probe pulses [18

18. J. Yao, G. Li, C. Jing, B. Zeng, W. Chu, J. Ni, H. Zhang, H. Xie, C. Zhang, H. Li, H. Xu, S. L. Chin, Y. Cheng, and Z. Xu, “Remote creation of strong and coherent emissions in air with two-color ultrafast laser pulses,” New J. Phys. 15(2), 023046 (2013). [CrossRef]

], but also on the intensity, spectrum, and the incident direction of the probe pulse as we will show in this study. Below, we present three pump-probe experimental investigations by manipulating the (1) incident direction, (2) spectral property, and (3) intensity of the probe pulses. These investigations provide rich information on the physics behind the coherent emissions generated in air by femtosecond laser excitation.

2. Experiments and results

2.1. Seed amplification in the counter-propagating case of the probe and the pump pulses

Figure 2(b) shows the spectrum of the probe pulse recorded. In the absence of the pump pulses, the spectral profile of the probe pulses appears smooth and does not exhibit any emission lines at wavelength ~391 nm. In contrast, when the pump pulse is sent into the molecular system ahead of the probe pulse, a strong, narrow-bandwidth emission located at 391.4 nm appears on the top of the probe spectrum, indicating amplification of the probe pulse at 391.4 nm even when it counterpropagates with respect to the pump pulse. The amplified signal intensity is measured with varied delay times as depicted in Fig. 2(c). The zero delay is defined as the occurrence of the amplification. Positive delay time suggests the pump pulse interact with medium at an earlier time than the probe pulse.

2.2. Dependence of the coherent emission on the spectral property of the probe pulse

It can be seen in Fig. 3(b) that when the 391.4 nm wavelength, which corresponds to the transition between the B2Σu+ (v = 0) and X2Σg+ (v = 0) states coincides with the dip of the modulated harmonic spectrum, there is no amplification of the probe pulse. Since the probe pulse was severely diffracted by the plasma formed by the pump pulse, the spectral amplitude of the probe pulse in the presence of the pump pulse (solid black curve) is weaker than its original spectrum (dash red curve). Apart from amplitude attenuation due to diffraction, the spectrum of the probe pulse after the plasma appears to be slightly blue shifted by comparing the positions of peaks in the black and red curves. We currently speculate that the blue shift in the spectrum is attributed to the passage of the probe pulses through the weak plasma region, which has been explained in Ref [20

20. S. L. Chin, Femtosecond Laser Filamentation (Springer, Berlin, 2010).

]. In contrast of the failure of amplification in Fig. 3(b), in Fig. 3(c), when the 391.4 nm wavelength coincides with one of the peaks of the spectrum of the seed pulses, a strong signal with a bandwidth (FWHM) of ~0.3 nm centered at the wavelength of 391.4 nm is superposed on top of the spectrum of the probe pulse. This observation indicates that the amplified emission is strongly dependent on the spectral intensity at 391.4 nm of the probe pulse. To achieve distinct amplification, the spectrum of the probe pulse must cover the frequency that corresponds to the transition of molecular ions.

2.3. Influence of the probe power on the coherent emission

Lastly, we study the dependence of the coherent 391.4 nm signal intensity on the input power of the probe pulse. In this experiment, the probe pulse co-propagates with the pump pulse. The experimental setup is described in detail in section 2.2. In this case, the input pump pulse energy is 1.7 mJ. The focal length of the focusing lens is 30cm. The laser spark generated by the pump pulse is of ~6 mm length. The thickness of the BBO crystal is 400 µm. The polarization of the probe is perpendicular to that of the pump. The power of the probe pulse is varied by rotating a half-wave plate placed before a Glan-Taylor prism. The amplified signal at 391.4 nm intensity is measured by a spectrometer.

The spectrum of the probe pulse after passing through the laser spark is presented by the red line in Fig. 4(a)
Fig. 4 (a) Measured spectra of the probe pulse in the present and absent of the pump pulse. (b) Measured dependence of the 391.4 nm output signal on the input probe power.
, while its original spectrum measured before the laser spark is shown by the black line. The amplified signal intensity, Ss, is defined as Ss = Stotal-Sharmonic, where Stotal represents the spectral peak intensity at 391.4 nm and Sharmonic is the signal intensity of the smooth harmonic spectrum at 391.4 nm, as illustrated in Fig. 4(a). In Fig. 4(b), the signal intensity, Ss, is plotted as a function of the input power of the probe pulse, which demonstrates a perfect linear dependence, as fitted by the solid line.

3. Discussion

Since the first observation of the generation of ultrafast forward coherent emissions in air by the infrared femtosecond filament [10

10. J. Yao, B. Zeng, H. Xu, G. Li, W. Chu, J. Ni, H. Zhang, S. L. Chin, Y. Cheng, and Z. Xu, “High-brightness switchable multiwavelength remote laser in air,” Phys. Rev. A 84(5), 051802 (2011). [CrossRef]

], a consensus about its underlying mechanism has not been reached yet. Currently, it is concluded that three schemes including four-wave parametric amplification [21

21. R. W. Boyd, M. G. Raymer, P. Narum, and D. J. Harter, “Four-wave parametric interactions in a strongly driven two-level system,” Phys. Rev. A 24(1), 411–423 (1981). [CrossRef]

], stimulated resonant Raman amplification [22

22. A. S. Kwok and R. K. Chang, “Stimulated resonance Raman scattering of Rhodamine 6G,” Opt. Lett. 18(20), 1703–1705 (1993). [CrossRef] [PubMed]

], and seed amplification based on the population inversion [10

10. J. Yao, B. Zeng, H. Xu, G. Li, W. Chu, J. Ni, H. Zhang, S. L. Chin, Y. Cheng, and Z. Xu, “High-brightness switchable multiwavelength remote laser in air,” Phys. Rev. A 84(5), 051802 (2011). [CrossRef]

,15

15. W. Chu, B. Zeng, J. Yao, H. Xu, J. Ni, G. Li, H. Zhang, F. He, C. Jing, Y. Cheng, and Z. Xu, “Multiwavelength amplified harmonic emissions from carbon dioxide pumped by mid-infrared femtosecond laser pulses,” Europhys. Lett. 97(6), 64004 (2012). [CrossRef]

17

17. S. L. Chin, H. Xu, Y. Cheng, Z. Xu, and K. Yamanouchi, “Natural population inversion in a gaseous molecular filament,” Chin. Opt. Lett. 11(1), 013201–013203 (2013). [CrossRef]

] are the most likely candidates that could lead to this interesting phenomenon.

However, four-wave parametric amplification and stimulated resonance Raman scattering are all third-order nonlinear optical processes which greatly differ from lasing actions based on population inversion. The first difference between four-wave parametric amplification and lasing action based on population inversion is that the former is a parametric process that strongly depends on phase matching condition and thus on the propagation direction of the probe pulses, while the latter is able to occur for both the co-propagation and counter-propagation cases of the pump and probe pulses even when the pump and probe are temporally separated (no phase matching). As shown in Figs. 2(b) and 2(c), the generation of the coherent emission at 391.4 nm can be achieved in the counter-propagation case of the pump and probe pulses, as well as in the case of temporally separated pump and probe pulses. This excludes the possibility of four-wave mixing as the mechanism to generate the coherent emission at 391.4 nm. Furthermore, the above observation can be regarded as the first evidence for the population inversion mechanism with picosecond population inversion lifetime and stimulated emission cross section σ=6.76×108m2s1 [23

23. I. M. Littlewood and C. E. Webb, “Excitation mechanisms of the N2+ laser,” J. Phys. D Appl. Phys. 14(7), 1195–1206 (1981). [CrossRef]

], leading to the seed amplification at 391.4 nm.

The second difference between a lasing action based on population inversion and nonlinear frequency conversion processes (e. g., four-wave mixing and stimulated Raman scattering) lies in the spectral property of the probe pulse. For population inversion induced amplification, the spectrum of the probe pulse has to cover the transition between the two levels to achieve a high gain. For the two nonlinear frequency conversion processes mentioned above, the spectrum of the probe pulse does not need to overlap exactly with the transition frequency. Therefore, the observation that the amplified emission at 391.4 nm appears in Fig. 3(c), but disappears in Fig. 3(b) indicates that the spectrum of the probe pulse covering the vibrational transition frequency between B2Σu+ (v = 0) and X2Σg+ (v = 0) states is a prerequisite for generation of the coherent emission at 391.4 nm. This can be regarded as the second evidence for the population inversion mechanism.

Last but not least, stimulated Raman gain is exponentially proportional to the seed signal intensity, Iseed. On the other hand, a laser signal intensity resulted from the seed amplification in a population inversion system is linearly proportional to Iseed [22

22. A. S. Kwok and R. K. Chang, “Stimulated resonance Raman scattering of Rhodamine 6G,” Opt. Lett. 18(20), 1703–1705 (1993). [CrossRef] [PubMed]

]. Therefore, the linear dependence observed in Fig. 4(b) clearly shows that the mechanism due to stimulated resonance Raman scattering can be safely excluded. As a consequence, the observation can serve as the third evidence for the mechanism of the seed amplification based on the population inversion.

4. Summary

To summarize, we have systematically investigated the physical mechanism of generation of coherent emissions induced by femtosecond laser excitation in air using a series of pump–probe experiments. By manipulating the propagating direction, spectral property, and intensity of the probe pulse, it is found that the coherent N2+ emission at 391.4 nm results neither from the parametric process of four-wave mixing nor from stimulated Raman scattering. The results further suggest that the population inversion in nitrogen molecular ions established by femtosecond laser filamentation is the most likely mechanism.

Acknowledgments

This work is financially supported by National Basic Research Program of China (Grant 2011CB808102), National Natural Science Foundation of China (Grant Nos. 11134010, 11074098, 61235003, 60825406, 10974213, and 11204332), NCET-09-0429 and the Fundamental Research Funds of Jilin University. We thank Andrius Baltuška of Vienna University of Technology for the valuable discussion.

References and links

1.

A. Couairon and A. Mysyrowicz, “Femtosecond filamention in transparent media,” Phys. Rep. 441(2-4), 47–189 (2007). [CrossRef]

2.

S. L. Chin, S. A. Hosseini, W. Liu, Q. Luo, F. Théberge, N. Aközbek, A. Becker, V. P. Kandidov, O. G. Kosareva, and H. Schroeder, “The propagation of powerful femtosecond laser pulses in optical media: physics, applications, and new challenges,” Can. J. Phys. 83(9), 863–905 (2005). [CrossRef]

3.

L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J.-P. Wolf, “Ultrashort filaments of light in weakly ionized, optically transparent media,” Rep. Prog. Phys. 70(10), 1633–1713 (2007). [CrossRef]

4.

M. Rodriguez, R. Bourayou, G. Méjean, J. Kasparian, J. Yu, E. Salmon, A. Scholz, B. Stecklum, J. Eislöffel, U. Laux, A. P. Hatzes, R. Sauerbrey, L. Wöste, and J.-P. Wolf, “Kilometer-range nonlinear propagation of femtosecond laser pulses,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69(3), 036607 (2004). [CrossRef] [PubMed]

5.

K. Stelmaszczyk, P. Rohwetter, G. Mejean, J. Yu, E. Salmon, J. Kasparian, R. Ackermann, J. P. Wolf, and L. Woste, “Long-distance remote laser-induced breakdown spectroscopy using filamentation in air,” Appl. Phys. Lett. 85(18), 3977–3979 (2004). [CrossRef]

6.

H. Xu, H. Xiong, R. Li, Y. Cheng, Z. Xu, and S. L. Chin, “X-shaped third harmonic generated by ultrashort infrared pulse filamentation in air,” Appl. Phys. Lett. 92(1), 011111 (2008). [CrossRef]

7.

M. Kolesik, E. M. Wright, and J. V. Moloney, “Dynamic nonlinear X waves for femtosecond pulse propagation in water,” Phys. Rev. Lett. 92(25), 253901 (2004). [CrossRef] [PubMed]

8.

N. Aközbek, A. Iwasaki, A. Becker, M. Scalora, S. L. Chin, and C. M. Bowden, “Third-harmonic generation and self-channeling in air using high-power femtosecond laser pulses,” Phys. Rev. Lett. 89(14), 143901 (2002). [CrossRef] [PubMed]

9.

F. Théberge, N. Aközbek, W. Liu, A. Becker, and S. L. Chin, “Tunable ultrashort laser pulses generated through filamentation in gases,” Phys. Rev. Lett. 97(2), 023904 (2006). [CrossRef] [PubMed]

10.

J. Yao, B. Zeng, H. Xu, G. Li, W. Chu, J. Ni, H. Zhang, S. L. Chin, Y. Cheng, and Z. Xu, “High-brightness switchable multiwavelength remote laser in air,” Phys. Rev. A 84(5), 051802 (2011). [CrossRef]

11.

Q. Luo, W. Liu, and S. L. Chin, “Lasing action in air induced by ultra-fast laser filamentation,” Appl. Phys. B 76(3), 337–340 (2003). [CrossRef]

12.

A. Dogariu, J. B. Michael, M. O. Scully, and R. B. Miles, “High-gain backward lasing in air,” Science 331(6016), 442–445 (2011). [CrossRef] [PubMed]

13.

D. Kartashov, S. Ališauskas, G. Andiukaitis, A. Pugžlys, M. Shneider, A. Zheltikov, S. L. Chin, and A. Baltuška, “Free-space nitrogen gas laser driven by a femtosecond filament,” Phys. Rev. A 86(3), 033831 (2012). [CrossRef]

14.

L. Yuan, K. E. Dorfman, A. M. Zheltikov, and M. O. Scully, “Plasma-assisted coherent backscattering for standoff spectroscopy,” Opt. Lett. 37(5), 987–989 (2012). [CrossRef] [PubMed]

15.

W. Chu, B. Zeng, J. Yao, H. Xu, J. Ni, G. Li, H. Zhang, F. He, C. Jing, Y. Cheng, and Z. Xu, “Multiwavelength amplified harmonic emissions from carbon dioxide pumped by mid-infrared femtosecond laser pulses,” Europhys. Lett. 97(6), 64004 (2012). [CrossRef]

16.

J. Ni, W. Chu, H. Zhang, C. Jing, J. Yao, H. Xu, B. Zeng, G. Li, C. Zhang, S. L. Chin, Y. Cheng, and Z. Xu, “Harmonic-seeded remote laser emissions in N₂-Ar, N₂-Xe and N₂-Ne mixtures: a comparative study,” Opt. Express 20(19), 20970–20979 (2012). [CrossRef] [PubMed]

17.

S. L. Chin, H. Xu, Y. Cheng, Z. Xu, and K. Yamanouchi, “Natural population inversion in a gaseous molecular filament,” Chin. Opt. Lett. 11(1), 013201–013203 (2013). [CrossRef]

18.

J. Yao, G. Li, C. Jing, B. Zeng, W. Chu, J. Ni, H. Zhang, H. Xie, C. Zhang, H. Li, H. Xu, S. L. Chin, Y. Cheng, and Z. Xu, “Remote creation of strong and coherent emissions in air with two-color ultrafast laser pulses,” New J. Phys. 15(2), 023046 (2013). [CrossRef]

19.

A. H. Chin, O. G. Calderón, and J. Kono, “Extreme midinfrared nonlinear optics in semiconductors,” Phys. Rev. Lett. 86(15), 3292–3295 (2001). [CrossRef] [PubMed]

20.

S. L. Chin, Femtosecond Laser Filamentation (Springer, Berlin, 2010).

21.

R. W. Boyd, M. G. Raymer, P. Narum, and D. J. Harter, “Four-wave parametric interactions in a strongly driven two-level system,” Phys. Rev. A 24(1), 411–423 (1981). [CrossRef]

22.

A. S. Kwok and R. K. Chang, “Stimulated resonance Raman scattering of Rhodamine 6G,” Opt. Lett. 18(20), 1703–1705 (1993). [CrossRef] [PubMed]

23.

I. M. Littlewood and C. E. Webb, “Excitation mechanisms of the N2+ laser,” J. Phys. D Appl. Phys. 14(7), 1195–1206 (1981). [CrossRef]

OCIS Codes
(190.7110) Nonlinear optics : Ultrafast nonlinear optics
(260.5950) Physical optics : Self-focusing

ToC Category:
Nonlinear Optics

History
Original Manuscript: February 6, 2013
Revised Manuscript: March 13, 2013
Manuscript Accepted: March 25, 2013
Published: April 2, 2013

Citation
Jielei Ni, Wei Chu, Chenrui Jing, Haisu Zhang, Bin Zeng, Jinping Yao, Guihua Li, Hongqiang Xie, Chaojin Zhang, Huailiang Xu, See-Leang Chin, Ya Cheng, and Zhizhan Xu, "Identification of the physical mechanism of generation of coherent N2 + emissions in air by femtosecond laser excitation," Opt. Express 21, 8746-8752 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-7-8746


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References

  1. A. Couairon and A. Mysyrowicz, “Femtosecond filamention in transparent media,” Phys. Rep.441(2-4), 47–189 (2007). [CrossRef]
  2. S. L. Chin, S. A. Hosseini, W. Liu, Q. Luo, F. Théberge, N. Aközbek, A. Becker, V. P. Kandidov, O. G. Kosareva, and H. Schroeder, “The propagation of powerful femtosecond laser pulses in optical media: physics, applications, and new challenges,” Can. J. Phys.83(9), 863–905 (2005). [CrossRef]
  3. L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J.-P. Wolf, “Ultrashort filaments of light in weakly ionized, optically transparent media,” Rep. Prog. Phys.70(10), 1633–1713 (2007). [CrossRef]
  4. M. Rodriguez, R. Bourayou, G. Méjean, J. Kasparian, J. Yu, E. Salmon, A. Scholz, B. Stecklum, J. Eislöffel, U. Laux, A. P. Hatzes, R. Sauerbrey, L. Wöste, and J.-P. Wolf, “Kilometer-range nonlinear propagation of femtosecond laser pulses,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.69(3), 036607 (2004). [CrossRef] [PubMed]
  5. K. Stelmaszczyk, P. Rohwetter, G. Mejean, J. Yu, E. Salmon, J. Kasparian, R. Ackermann, J. P. Wolf, and L. Woste, “Long-distance remote laser-induced breakdown spectroscopy using filamentation in air,” Appl. Phys. Lett.85(18), 3977–3979 (2004). [CrossRef]
  6. H. Xu, H. Xiong, R. Li, Y. Cheng, Z. Xu, and S. L. Chin, “X-shaped third harmonic generated by ultrashort infrared pulse filamentation in air,” Appl. Phys. Lett.92(1), 011111 (2008). [CrossRef]
  7. M. Kolesik, E. M. Wright, and J. V. Moloney, “Dynamic nonlinear X waves for femtosecond pulse propagation in water,” Phys. Rev. Lett.92(25), 253901 (2004). [CrossRef] [PubMed]
  8. N. Aközbek, A. Iwasaki, A. Becker, M. Scalora, S. L. Chin, and C. M. Bowden, “Third-harmonic generation and self-channeling in air using high-power femtosecond laser pulses,” Phys. Rev. Lett.89(14), 143901 (2002). [CrossRef] [PubMed]
  9. F. Théberge, N. Aközbek, W. Liu, A. Becker, and S. L. Chin, “Tunable ultrashort laser pulses generated through filamentation in gases,” Phys. Rev. Lett.97(2), 023904 (2006). [CrossRef] [PubMed]
  10. J. Yao, B. Zeng, H. Xu, G. Li, W. Chu, J. Ni, H. Zhang, S. L. Chin, Y. Cheng, and Z. Xu, “High-brightness switchable multiwavelength remote laser in air,” Phys. Rev. A84(5), 051802 (2011). [CrossRef]
  11. Q. Luo, W. Liu, and S. L. Chin, “Lasing action in air induced by ultra-fast laser filamentation,” Appl. Phys. B76(3), 337–340 (2003). [CrossRef]
  12. A. Dogariu, J. B. Michael, M. O. Scully, and R. B. Miles, “High-gain backward lasing in air,” Science331(6016), 442–445 (2011). [CrossRef] [PubMed]
  13. D. Kartashov, S. Ališauskas, G. Andiukaitis, A. Pugžlys, M. Shneider, A. Zheltikov, S. L. Chin, and A. Baltuška, “Free-space nitrogen gas laser driven by a femtosecond filament,” Phys. Rev. A86(3), 033831 (2012). [CrossRef]
  14. L. Yuan, K. E. Dorfman, A. M. Zheltikov, and M. O. Scully, “Plasma-assisted coherent backscattering for standoff spectroscopy,” Opt. Lett.37(5), 987–989 (2012). [CrossRef] [PubMed]
  15. W. Chu, B. Zeng, J. Yao, H. Xu, J. Ni, G. Li, H. Zhang, F. He, C. Jing, Y. Cheng, and Z. Xu, “Multiwavelength amplified harmonic emissions from carbon dioxide pumped by mid-infrared femtosecond laser pulses,” Europhys. Lett.97(6), 64004 (2012). [CrossRef]
  16. J. Ni, W. Chu, H. Zhang, C. Jing, J. Yao, H. Xu, B. Zeng, G. Li, C. Zhang, S. L. Chin, Y. Cheng, and Z. Xu, “Harmonic-seeded remote laser emissions in N₂-Ar, N₂-Xe and N₂-Ne mixtures: a comparative study,” Opt. Express20(19), 20970–20979 (2012). [CrossRef] [PubMed]
  17. S. L. Chin, H. Xu, Y. Cheng, Z. Xu, and K. Yamanouchi, “Natural population inversion in a gaseous molecular filament,” Chin. Opt. Lett.11(1), 013201–013203 (2013). [CrossRef]
  18. J. Yao, G. Li, C. Jing, B. Zeng, W. Chu, J. Ni, H. Zhang, H. Xie, C. Zhang, H. Li, H. Xu, S. L. Chin, Y. Cheng, and Z. Xu, “Remote creation of strong and coherent emissions in air with two-color ultrafast laser pulses,” New J. Phys.15(2), 023046 (2013). [CrossRef]
  19. A. H. Chin, O. G. Calderón, and J. Kono, “Extreme midinfrared nonlinear optics in semiconductors,” Phys. Rev. Lett.86(15), 3292–3295 (2001). [CrossRef] [PubMed]
  20. S. L. Chin, Femtosecond Laser Filamentation (Springer, Berlin, 2010).
  21. R. W. Boyd, M. G. Raymer, P. Narum, and D. J. Harter, “Four-wave parametric interactions in a strongly driven two-level system,” Phys. Rev. A24(1), 411–423 (1981). [CrossRef]
  22. A. S. Kwok and R. K. Chang, “Stimulated resonance Raman scattering of Rhodamine 6G,” Opt. Lett.18(20), 1703–1705 (1993). [CrossRef] [PubMed]
  23. I. M. Littlewood and C. E. Webb, “Excitation mechanisms of the N2+ laser,” J. Phys. D Appl. Phys.14(7), 1195–1206 (1981). [CrossRef]

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