Dramatic Spectral Broadening of Ultrafast Laser Pulses in Molecular Nitrogen Ions

Jin-Ming Chen(陈锦明)$^{1,3,4}$, Jin-Ping Yao(姚金平)$^{1\hyperlink{s}{**}}$, Zhao-Xiang Liu(刘招祥)$^{1,3}$, Bo Xu(许波)$^{1,3}$,\\ Fang-Bo Zhang(张方波)$^{1,3}$, Yue-Xin Wan(万悦芯)$^{1,3}$, Wei Chu(储蔚)$^{1}$, Zhen-Hua Wang(王振华)$^{2}$, \\ Ling-Ling Qiao(乔玲玲)$^{1}$, Ya Cheng(程亚)$^{1,2,5\hyperlink{s}{**}}$

doi:10.1088/0256-307X/36/10/104204

⇦Chinese Physics Letters, 2019, Vol. 36, No. 10, Article code 104204⇨ Dramatic Spectral Broadening of Ultrafast Laser Pulses in Molecular Nitrogen Ions * Jin-Ming Chen (陈锦明)1,3,4, Jin-Ping Yao (姚金平)1**, Zhao-Xiang Liu (刘招祥)1,3, Bo Xu (许波)1,3, Fang-Bo Zhang (张方波)1,3, Yue-Xin Wan (万悦芯)1,3, Wei Chu (储蔚)1, Zhen-Hua Wang (王振华)2, Ling-Ling Qiao (乔玲玲)1, Ya Cheng (程亚)1,2,5** Affiliations 1State Key Laboratory of High Field Laser Physics, Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai 201800 2State Key Laboratory of Precision Spectroscopy, East China Normal University, Shanghai 200062 3University of Chinese Academy of Sciences, Beijing 100049 4School of Physical Science and Technology, ShanghaiTech University, Shanghai 200031 5Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006 Received 12 August 2019, online 21 September 2019 ^*Supported by the National Key Research and Development Program of China under Grant No 2018YFB0504400, the National Natural Science Foundation of China under Grant Nos 11822410, 11734009 and 61575211, the Strategic Priority Research Program of the Chinese Academy of Sciences under Grant No XDB16030300, the Key Research Program of Frontier Sciences of the Chinese Academy of Sciences under Grant No QYZDJ-SSW-SLH010, the Key Project of the Shanghai Science and Technology Committee under Grant No 18DZ1112700, the Shanghai Rising-Star Program under Grant No 17QA1404600, and the Youth Innovation Promotion Association of the Chinese Academy of Sciences under Grant No 2018284.
^**Corresponding author. Email: jinpingmrg@163.com; ya.cheng@siom.ac.cn Citation Text: Chen J M, Yao J P, Liu Z X, Xu B and Zhang F B et al 2019 Chin. Phys. Lett. 36 104204 Abstract We investigate nonlinear interaction of nitrogen molecules with a two-color laser field composed by an intense 800 nm laser pulse and a weak 400 nm laser pulse. It is demonstrated that the spectrum of 400 nm pulses is dramatically broadened when the two beams temporally overlap. In comparison, the spectral broadening in argon is less pronounced, although argon atoms and nitrogen molecules have comparable ionization potentials. We reveal that the dramatic spectral broadening originates from the greatly enhanced nonlinear optical effects in the near-resonant condition of interaction between the 400 nm pulses and the nitrogen molecular ions. DOI:10.1088/0256-307X/36/10/104204 PACS:42.65.Re, 42.50.Hz, 42.65.Jx © 2019 Chinese Physics Society Article Text Ultrafast nonlinear optics in gaseous media has been intensively investigated in the past few decades due to its important applications in the generation of novel coherent light sources, remote sensing, pulse compression, etc.[1–7] Today, femtosecond laser fields with strengths comparable to that of Coulomb fields in various atoms and molecules can be routinely generated, opening up an exciting area of extreme nonlinear optics.[8,9] Interestingly, most investigations on extreme nonlinear optics focus on neutral atoms and molecules, whereas the nonlinear optics in ions is largely unexplored for the reasons below. First, in strong field atomic and molecular physics, the density of ions is typically much lower than that of neutral species owing to the small ionization probability in gaseous media with ultrafast laser fields. Second, the nonlinear susceptibility of singly ionized atoms or molecules is usually much smaller than that of neutral atoms or molecules. Consequently, the nonlinear signals from ions are usually too weak to be separated from the strong background of the nonlinear signals contributed by the neutral atoms or molecules. Up to now, nonlinear optics in ions is still a field largely unexplored. Recently, free-space N$_{2}^{+}$ lasing initiated by intense femtosecond laser pulses has aroused great interests owing to its mysterious physical mechanism and potential applications in remote sensing.[10–22] In addition, strong nonlinear optical effects have been observed in N$_{2}^{+}$ ions during the generation of N$_{2}^{+}$ lasing.[23–26] This happens because the resonant interaction of the laser pulses with N$_{2}^{+}$ ions dramatically promotes the nonlinear susceptibility of ions. Here, we experimentally investigate the spectral broadening of ultrafast laser pulses in nitrogen ions. The comparative measurements in nitrogen and argon gases clearly reveal the key contribution of electronic resonance to observation of the nonlinear optical response of ions. The experiment was performed using a two-color laser field with the controllable time delay. The experimental setup is shown in Fig. 1. The laser beam (1.6 mJ, 800 nm, 40 fs, 1 kHz) from a commercial Ti:sapphire laser system (Coherent, Legend Elite Duo) was launched into a 0.1-mm-thick beta barium borate (BBO) crystal to generate a two-color pulse. The polarizations of the fundamental pulse ($\omega $) centered at 800 nm and frequency-doubled pulse (2$\omega $) centered at 400 nm were perpendicular to each other. Two pieces of 2-mm-thick calcite crystals were placed after the BBO crystal to provide the negative time delay, which makes the $\omega$ beam to lag behind the 2$\omega$ beam. After the calcite crystal, an uncoated BK7 wedge pair was used to finely control the phase delay of two-color fields. It was realized by moving one wedge using a motorized translation stage to change the total optical path. The relative phase delay between $\omega$ and 2$\omega$ laser pulses was calculated through the relationship $\tau =\Delta l\Delta n\tan\theta /c$, where $\Delta l$ is the displacement of the motorized translation stage with respect to the position at the zero delay of two pulses, $\Delta n$ the difference between the refractive indices of BK7 glass at the wavelengths of 400 nm and 800 nm, $\theta$ the wedge angle, $c$ the light speed in vacuum. A half-wave plate (HWP) at 800 nm wavelength is used to rotate the polarization of the $\omega$ beam parallel to the 2$\omega$ beam. Then the two-color laser field was focused by a gold-coated concave mirror (GCM) with a focal length of 30 cm into a gas chamber filled with nitrogen or argon gas and collimated by another GCM. After the first GCM, the total energy of the two beams is about 0.85 mJ, and the 2$\omega$ beam is about one order of magnitude weaker than the $\omega$ beam. After the spectral filtering, the generated nonlinear optical signals were completely collected into an imaging spectrometer (Shamrock 500i, Andor) using a plano-convex lens for spectral analysis.

Fig. 1. Schematic of experimental setup.

Fig. 2. (a) The original spectrum of the 2$\omega$ beam measured in the vacuum (the gray shaded curve). The spectrum of the 2$\omega$ beam exiting from 20 mbar nitrogen gas at (b) $\tau =0$ and (c) $\tau =60$ fs. The spectra in three regions were measured independently with different filters, and the intensity ratios of the spectral component near 400 nm (the blue shaded curve) to the generated spectral components at 358 nm and 428 nm are indicated, which are calculated by considering the transmittance of these filters.

First, we measured the spectrum of the 2$\omega$ beam after the two-color laser field interacts with the 20 mbar nitrogen gas. The original 2$\omega$ spectrum in Fig. 2(a) was significantly broadened when the time delay of two-color laser field was close to zero, as shown in Fig. 2(b). For clarity, the broadened spectrum in Fig. 2(b) was divided into three regions by choosing suitable filters, and their relative intensities were roughly estimated by calibrating the transmittance of these filters at the wavelength of $\sim$358 nm and $\sim$428 nm. In comparison to the original spectrum, the blue-shifted and red-shifted spectral components are about 7 and 3 orders of magnitude weaker, respectively, whereas the spectrum near 400 nm only shows a small distortion. Meanwhile, two prominent peaks centered at $\sim$358 nm and $\sim$428 nm overlap on the broadened spectrum, which correspond to the transitions of $B^{2}{\it \Sigma} _{\rm u}^{+}(v'=1)\to X^{2}{\it \Sigma} _{\rm g}^{+}(v=0)$ and $B^{2}{\it \Sigma} _{\rm u}^{+}(v'=0)\to X^{2}{\it \Sigma} _{\rm g}^{+}(v=1)$ of N$_{2}^{+}$ ions, respectively. When the 2$\omega$ beam is launched 60 fs after the $\omega$ beam (i.e., $\tau =60$ fs), the spectral broadening becomes less effective, as illustrated in Fig. 2(c). This means that the intense $\omega$ field itself cannot be effectively broadened to the spectral regions in the low-pressure gas if no weak 2$\omega$ field is injected.

Fig. 3. The comparison of (a) blue-shifted and (b) red-shifted spectral components obtained in the 20 mbar nitrogen and argon.

We performed the same measurement in argon due to its comparable ionization potential to that of nitrogen molecules. We quantitatively compared the red-shifted and blue-shifted 2$\omega$ spectra in nitrogen and argon. As shown in Fig. 3(a), the spectrum in argon is only blue shifted to 375 nm. In comparison, the spectrum in nitrogen can be extended to 350 nm, and shows a strong N$_{2}^{+}$ radiation at $\sim$358 nm. Similarly, the 2$\omega$ spectrum is red-shifted to longer wavelength in nitrogen as compared to argon, and the broadened spectrum accompanies generation of another N$_{2}^{+}$ spectral line. It is noteworthy that these N$_{2}^{+}$ coherent radiations in the two-color scheme are much stronger than that obtained by the 800 nm laser field alone. The comparative measurements clearly illustrate that the nitrogen gas has a significant advantage in spectral broadening, which is different from the previous study.[27]

Fig. 4. The integral intensity of (a) 360–370 nm and (b) 375–385 nm spectral components obtained in nitrogen and argon as a function of gas pressure.

To gain insight into the difference in the broadened spectra in two gases, we further investigated the evolution of the broadened spectra by increasing the pressure. According to the measured results in Fig. 3(a), we chose two parts of the blue-shifted spectrum for quantitative analysis. One part is the spectrum in the 360–370 nm region (labeled as R–I region), which is far away from the original spectrum. The other part is the spectrum in the 375–385 nm region (labeled as R–II region), which is close to the blue tail of the original spectrum and thus is easily generated in the low-pressure argon gas. Figures 4(a) and 4(b) show that integral intensities in two spectral regions follow different tendencies with increasing the gas pressure, and the results obtained in nitrogen and argon are distinctly different. In argon, the signal in the R–I region remains on the level of noise at relatively low gas pressures and begins to grow exponentially until the gas pressure is higher than 40 mbar. Nevertheless, in nitrogen, the signal in the R–I region increases rapidly from 0 mbar to 40 mbar, followed by a slow growth at higher pressure. Thus, in comparison with argon, nitrogen exhibits significant advantages for the spectral broadening in the shorter-wavelength spectral region (i.e., R–I). Unlike the signal in R–I region, the signal in the R–II region can be generated at very low gas pressures in both nitrogen and argon gases, and their intensities are comparable at the gas pressures below 70 mbar, as shown in Fig. 4(b). At higher pressures above 70 mbar, the signal in argon is stronger than that in nitrogen. We also investigated the broadened spectrum (i.e., 360–370 nm) and N$_{2}^{+}$ radiations at $\sim$358 nm and $\sim$428 nm as a function of the relative phase delay between $\omega$ and 2$\omega$ laser fields. As shown in Figs. 5(a)–5(c), all spectral components generated by the nonlinear interaction reach maxima around zero time delay, and decay with the temporal separation of two laser fields. Meanwhile, some periodic modulations can be clearly observed in the evolution curves. The modulation periods of the selected three radiations are close to the optical period of the 4$\omega$ laser field.

Fig. 5. Intensities of (a) 358 nm, (b) 360–370 nm, and (c) 428 nm radiations as a function of the relative phase delay between two-color laser fields.

Based on these experimental results, we discuss the physical mechanism responsible for the dramatic spectral broadening in nitrogen. The spectral broadening induced by a femtosecond laser beam in gaseous media is usually attributed to self-phase modulation, self-steepening, and plasma-induced nonlinear phase shift.[28] In the two-color field scheme, the interaction of two beams can give rise to cross-phase modulation (XPM) and coherent Raman scattering (CRS), which also make generation of new spectral components. As shown in Fig. 2, the spectral broadening strongly depends on the time delay between the 800 nm and 400 nm pulses. This is a strong indication that the generation of these new frequencies results from the synergetic interaction of the two laser pulses with the medium. Another key observation is that at the low gas pressures, the spectral broadening of 2$\omega$ pulses is more significant in nitrogen than in argon, as illustrated in Figs. 3 and 4. This means that the spectral broadening caused by the plasma effect is also negligible, otherwise the similar ionization potentials of argon atoms and nitrogen molecules should result in comparable spectral blue shifts. Consequently, XPM and CRS are the most likely mechanisms of the spectral broadening observed in our experiment. It is known that the spectral broadening induced by XPM is proportional to the real part of three-order nonlinear susceptibility $\chi^{(3)}(-2\omega; \omega, -\omega, 2\omega )$. The nonlinear susceptibility is greatly enhanced in N$_{2}^{+}$ ions, because the input $2\omega$ laser field covers the wavelength of the electronic transition between the $B^{2}{\it \Sigma} _{\rm u}^{+}(v'=0)$ state and the $X^{2}{\it \Sigma} _{\rm g}^{+}(v=0)$ state of N$_{2}^{+}$ ions (i.e., 391.4 nm). The resonance-enhanced XPM makes the spectral broadening in nitrogen more efficient. When the 2$\omega$ spectrum is extended to the frequency covering the transition between the $B^{2}{\it \Sigma}_{\rm u}^{+}(v'=0)$ state and the $X^{2}{\it \Sigma} _{\rm g}^{+}(v=1)$ state, the corresponding radiation at wavelength $\sim$428 nm will be amplified due to the population inversion between the two states.[29] Furthermore, the spectrum of the $\omega$ laser field would be significantly broadened during its nonlinear propagation. When its spectral bandwidth covers $v=0$ and $v=1$ vibrational levels of $X^{2}{\it \Sigma} _{\rm g}^{+}$ states, the vibrational coherence of N$_{2}^{+}$ ions will be created. In this case, coherent radiations at wavelengths 358 nm and 428 nm can also be generated by coherent anti-Stokes and Stokes Raman scatterings, respectively. These coherent Raman scatterings are dramatically enhanced at electronic resonance wavelengths.[24–26] As a result, two strong N$_{2} ^{+}$ spectral lines appear in the broadened spectra. Finally, Fig. 5 shows that the spectral broadening occurs most efficiently with the temporal overlap of two laser pulses, which provides another evidence on the explanation based on XPM. It is also noteworthy that the ionization probability of nitrogen molecules strongly depends on the delay of the two-color laser fields. Thus, two strong N$_{2}^{+}$ spectral lines at $\sim$358 nm and $\sim$428 nm, which could mainly originate from the resonance-enhanced CRS process, also show a strong dependence on the delay. Furthermore, the modulations of all spectral components in Figs. 5(a)–5(c) could be due to the periodic change of ionization probability with the relative phase of the two-color laser fields. In conclusion, we have experimentally observed significant spectral broadening in the low-pressure nitrogen gas. The comparative investigation on the spectral broadening in nitrogen molecules and argon atoms, which have similar ionization potentials, reveals that the spectral broadening mainly originates from the resonance-enhanced cross phase modulation and coherent Raman scattering in molecular nitrogen ions. The observed enhancement of nonlinear optical effects near the electronic resonance of molecular ions can potentially be employed for remote sensing and nonlinear wavelength conversion. References Femtosecond filamentation in transparent mediaThe propagation of powerful femtosecond laser pulses in opticalmedia: physics, applications, and new challengesTunable Ultrashort Laser Pulses Generated through Filamentation in GasesBright Coherent Ultrahigh Harmonics in the keV X-ray Regime from Mid-Infrared Femtosecond LasersWhite-Light Filaments for Atmospheric AnalysisDifferential absorption Lidar (DIAL)Generation of intense, carrier-envelope phase-locked few-cycle laser pulses through filamentationExtreme Nonlinear Optics: Coherent X rays from LasersHigh-brightness switchable multiwavelength remote laser in airRemote creation of coherent emissions in air with two-color ultrafast laser pulsesLasing of ambient air with microjoule pulse energy pumped by a multi-terawatt infrared femtosecond laserRotational Coherence Encoded in an “Air-Laser” Spectrum of Nitrogen Molecular Ions in an Intense Laser FieldForward lasing action at multiple wavelengths seeded by white light from a femtosecond laser filament in airPopulation dynamics of molecular nitrogen initiated by intense femtosecond laser pulsesVibrational and electronic excitation of ionized nitrogen molecules in intense laser fieldsPopulation Redistribution Among Multiple Electronic States of Molecular Nitrogen Ions in Strong Laser FieldsSub-10-fs population inversion in N2+ in air lasing through multiple state couplingSignificant Enhancement of

N_{2}^{+}

Lasing by Polarization-Modulated Ultrashort Laser PulsesRecollision-Induced Superradiance of Ionized Nitrogen MoleculesUnexpected Sensitivity of Nitrogen Ions Superradiant Emission on Pump Laser Wavelength and DurationTesting the Role of Recollision in

N_{2}^{+}

Air LasingNear-Resonant Raman Amplification in the Rotational Quantum Wave Packets of Nitrogen Molecular Ions Generated by Strong Field IonizationGeneration of Raman lasers from nitrogen molecular ions driven by ultraintense laser fieldsVibrational Raman scattering from coherently excited molecular ions in a strong laser fieldStimulated-Raman-scattering-assisted superfluorescence enhancement from ionized nitrogen molecules in 800-nm femtosecond laser fieldsCharacterization of the supercontinuum radiation generated by self-focusing of few-cycle 800 nm pulses in argonFree-space Ν2+ lasers generated in strong laser fields: the role of molecular vibration

[1]	Couarion A and Mysyrowicz A 2007 Phys. Rep. 441 47
[2]	Chin S L, Hosseini S A, Liu W et al 2005 Can. J. Phys. 83 863
[3]	Théberge F, Aközbek N, Liu W et al 2006 Phys. Rev. Lett. 97 023904
[4]	Popmintchev T, Chen M C, Popmintchev D et al 2012 Science 336 1287
[5]	Kasparian J, Rodriguez M, Mejean G et al 2003 Science 301 61
[6]	Xu H L and Chin S L 2011 Sensors 11 32
[7]	Hauri C P, Kornelis W, Helbing F W et al 2004 Appl. Phys. B 79 673
[8]	Kapteyn H C, Murnane M M and Christov I P 2005 Phys. Today 58 39
[9]	Wegener M 2005 Extreme Nonlinear Optics (Berlin: Springer)
[10]	Yao J P, Zeng B, Xu H L et al 2011 Phys. Rev. A 84 051802
[11]	Yao J P, Li G H, Jing C R et al 2013 New J. Phys. 15 023046
[12]	Point G, Liu Y, Brelet Y et al 2014 Opt. Lett. 39 1725
[13]	Zhang H S, Jing C R, Yao J P et al 2013 Phys. Rev. X 3 041009
[14]	Wang T J, Daigle F, Ju J J et al 2013 Phys. Rev. A 88 053429
[15]	Wang P, Wu C Y, Lei M W et al 2015 Phys. Rev. A 92 063412
[16]	Zhong X Q, Miao Z M, Zhang L L et al 2017 Phys. Rev. A 96 043422
[17]	Yao J P, Jiang S C, Chu W et al 2016 Phys. Rev. Lett. 116 143007
[18]	Xu H L, Lötstedt E, Iwasaki A et al 2015 Nat. Commun. 6 8347
[19]	Li H L, Hou M Y, Zang H W et al 2019 Phys. Rev. Lett. 122 013202
[20]	Liu Y, Ding P J, Lambert G et al 2015 Phys. Rev. Lett. 115 133203
[21]	Liu Y, Ding P J, Ibrakovic N et al 2017 Phys. Rev. Lett. 119 203205
[22]	Britton M, Laferriere, Ko D H et al 2018 Phys. Rev. Lett. 120 133208
[23]	Liu Z X, Yao J P, Chen J M et al 2018 Phys. Rev. Lett. 120 083205
[24]	Yao J P, Chu W, Liu Z X et al 2018 New J. Phys. 20 033035
[25]	Xu B, Yao J P, Wan Y X et al 2019 Opt. Express 27 18262
[26]	Miao Z M, Zhong X Q, Zhang L L et al 2018 Phys. Rev. A 98 033402
[27]	Kosma K, Trushin S A, Fuß W et al 2008 J. Mod. Opt. 55 2141
[28]	Alfano R R 2006 The Supercontinuum Laser Source II (New York: Springer)
[29]	Xu B, Jiang S C, Yao J P et al 2018 Opt. Express 26 13331