PHYSICS OF PLASMAS 21, 100901 (2014) The extreme nonlinear optics of gases and femtosecond optical filamentationa) H. M. Milchberg,b) Y.-H. Chen, Y.-H. Cheng, N. Jhajj, J. P. Palastro, E. W. Rosenthal, S. Varma, J. K. Wahlstrand, and S. Zahedpour Institute for Research in Electronics and Applied Physics, University of Maryland, College Park, Maryland 20742, USA (Received 21 June 2014; accepted 8 September 2014; published online 10 October 2014) Under certain conditions, powerful ultrashort laser pulses can form greatly extended, propagating filaments of concentrated high intensity in gases, leaving behind a very long trail of plasma. Such filaments can be much longer than the longitudinal scale over which a laser beam typically diverges by diffraction, with possible applications ranging from laser-guided electrical discharges to high power laser propagation in the atmosphere. Understanding in detail the microscopic proc- esses leading to filamentation requires ultrafast measurements of the strong field nonlinear response of gas phase atoms and molecules, including absolute measurements of nonlinear laser-induced polarization and high field ionization. Such measurements enable the assessment of filamentation models and make possible the design of experiments pursuing applications. In this paper, we review filamentation in gases and some applications, and discuss results from diagnostics devel- oped at Maryland for ultrafast measurements of laser-gas interactions. VC 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4896722] I. INTRODUCTION from millimeters to hundreds of meters, depending on the medium and laser parameters. The phenomenon is ubiqui- The filamentation of intense femtosecond laser pulses in tous for femtosecond pulses at the millijoule level in gases transparent solid, liquid, and gas media is an area of expand- and at the microjoule level in liquids and solids,1 where ing research activity.1 It has promise for exciting applica- P 10 MW. “Filament” describes both the extended propa- tions and involves examination of fundamental nonlinear cr gation of the intense optical core and the residual plasma optical physics.1–3 This paper will focus on filamentation in density track, which are typically 100 lm in diameter.6 In gases, with emphasis on experiments at the University of air, for example, k ¼ 800 nm pulses with energy 1 mJ and Maryland. The filament formation process is initiated when pulsewidth 100 fs can typically be induced to form single the electric field strength of a propagating laser pulse is large filaments with a clean and well-defined transverse density enough to induce a nonlinear response in the gas’s constitu- profile, as this laser peak power is not too in excess of P . ent atoms or molecules, leading to an ensemble-averaged cr Pulses with peak powers beyond several P tend to form dipole moment nonlinearly increasing with field strength. cr multiple filaments owing to the transverse modulational This nonlinear refractive index perturbation propagates with instability,1 with filament transverse locations that can vary the pulse as a self-lens. Once the laser pulse peak power, for shot-to-shot. a Gaussian beam, exceeds a critical value, The filamentation of a femtosecond pulse can be viewed P > P ¼ 3:77k2=8pn n 2–10 GW in gases,1,4,5 the self- cr 0 2 as occurring on a temporal slice-by-slice basis. Time slices induced lens overcomes diffraction and focuses the beam, early in the pulse envelope must propagate longer distances leading to plasma generation when the gas ionization inten- before they accumulate sufficient nonlinear phase front cur- sity threshold is exceeded. Here, k is the laser central wave- vature to overcome diffraction and collapse, ionizing the gas length, n is the unperturbed gas refractive index, and n is 0 2 and then refracting, whereas later time slices near the peak the nonlinear index of refraction, defined in Gaussian units of the pulse envelope propagate shorter distances before col- by n ¼ 12p2vð3Þ=n2c, where vð3Þ is the third order nonlinear 2 0 lapse, ionization, and refraction. The overall effect by the scalar susceptibility of the medium.4 full pulse envelope is a tight high intensity core of laser light According to the “standard model” of filamentation and generated plasma, surrounded by a less intense reservoir (more on that later), the on-axis concentration of free elec- of nonlinear-phase-shifting light, which is both converging trons then defocuses the beam, and the dynamic interplay on the core from self-focusing and diverging from it owing between self-focusing and defocusing leads to self-sustained to refraction from the plasma. These dynamics can result in propagation of a tightly radially confined high intensity temporal pulse splitting and axially nonuniform plasma region (the “core”) accompanied by electron density tracks channels.6–8 over distances greatly exceeding the optical Rayleigh range This paper is organized as follows. Section II briefly corresponding to the core diameter. The tracks can extend reviews some applications of femtosecond filaments. It is by no means comprehensive but tends toward relatively recent a)Paper PT3 1, Bull. Am. Phys. Soc. 58, 236 (2013). highlights. Section III discusses filament diagnostics, with b)Invited speaker. emphasis on two diagnostics used by our group, ultrashort 1070-664X/2014/21(10)/100901/11/$30.00 21, 100901-1 VC 2014 AIP Publishing LLC This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 130.58.223.147 On: Fri, 10 Oct 2014 15:03:33 100901-2 Milchberg et al. Phys. Plasmas 21, 100901 (2014) pulse spatial interferometry, and single shot supercontinuum conversion efficiencies of 10À4–10À3. Recently, phase spectral interferometry (SSSI). These diagnostics have matching in 2-color filament-based THz generation has been proved crucial in elucidating the ultrafast nonlinear proc- demonstrated,20 with the yield scaling linearly with plasma esses underlying femtosecond filamentation and settling a length, suggesting that further extending filaments is a prom- related debate. In Sec. IV, we review this debate and discuss ising scheme for THz generation. the role our measurements have played in it. Section V Another concept for radiation generation at a distance, briefly covers recent efforts to extend the length of filaments. to be used for remote sensing applications, is filament- Finally, Sec. VI reviews the post-filament gas dynamics initiated atmospheric backward lasing, with schemes for 21 induced by the nonlinear energy deposition and discusses both O2 (in the near-infrared) and N2 (in the ultravio- applications of the gas response. let).22 A filament-pumped backward-directed laser would enable probing of the intervening atmosphere. Some N2 schemes are based on two pulses: the filament pulse II. FILAMENT APPLICATIONS weakly ionizes the air to 1016 cmÀ3, and then a co- One of the more spectacular effects accompanying fila- propagating “heater” pulse heats these electrons, which mentation is supercontinuum (SC) generation, a coherent, then pump the molecular transition, with preliminary ultra-broadband optical beam co-propagating with the fila- experiments using a k ¼ 0.8 lm filament and a 9,10 23 ment, resulting from ultrafast nonlinear phase evolution of k ¼ 1.064 lm heater pulse. Meanwhile, backward N2 las- the pulse as it propagates through the fast material response it ing has been demonstrated in a high pressure (6 atm) N2/Ar induces in the medium. This lightcanbeusedforfilament- gas cell driven only by a k ¼ 3.9 lm laser pulse,24 with the based white light LIDAR of the atmosphere from filamentation laser transition upper state populated via a different mecha- at large distance scales11 or generated by filamentation in sealed nism than in Ref. 22. A different remote sensing approach, gas cells, where it can be accompanied by self-compression with molecular specificity, has been achieved by exploiting and spatial mode cleaning of the filamenting pulse.10 the extreme bandwidths and short pulses generated in fila- The long ionization tracks left by filaments have stimu- ments to impulsively pump characteristic vibrational states lated work in guided high voltage discharges,12 and the and then probe them with a narrower bandwidth, non- related dream of laser filament-guided atmospheric light- filamenting pulse to generate a stimulated Raman spectrum ning.13 However, both the low electron density in typical for analysis.25 The same group also directly measured the extended filaments (<few 1016 cmÀ3 (Ref. 6)) and the nano- extreme optical pulse shortening, which takes place inside second plasma lifetime14 have made filament-guided dis- a filament core.26 charges much longer than 1 m difficult. Even at a meter Since the first demonstration of femtosecond filamenta- length, such discharges had not been reproducible or uni- tion in air,27 filaments typically have been generated using form. Recently, meter long, uniform discharges in air sus- millijoule-level k ¼ 0.8 lm pulses of duration 100 fs from tained by a compact low jitter Tesla coil have been Ti:Sapphire lasers. Recently, the development of new high generated.15 The same group has demonstrated that laser fila- power mid-infrared (MIR) laser sources have made possible 28 ments can coax high voltage discharges to occur far from the generation of filaments using k ¼ 3.9 lm. Since Pcr / their normal path, even forcing them to follow right angle k2/N, where N is the atomic/molecular density of the propa- paths in free space.16 Even longer discharges await a more gation medium, at 1 atm this scaling demands MIR pulse continuous filament with a higher and much longer-lived energy exceeding the laser output. A high pressure gas cell electron density. Femtosecond filaments in gases are a bur- was used to decrease Pcr to allow filamentation with 7 mJ geoning source of coherent THz radiation with clear advan- pulses.