Transmission through plasma created by laser-inducedbreakdown of water droplets
Wen-Feng Hsieh,* Jia-biao Zheng, t and Richard K. ChangSection of Applied Physics and Center for Laser Diagnostics, Yale University, New Haven, Connecticut 06520
Received April 5, 1989; accepted June 26, 1989
The temporally and spatially resolved transmission is measured with a green probe beam through the plasmacreated by an intense near-IR beam that is incident upon a water droplet. We report the propagation speed of theexpanding plasma and the evolution of the transmission decrease and recovery at various locations along a line in thedirection of the IR beam.
The propagation of a high-intensity laser beamthrough the atmosphere is affected by atmosphericturbulence, linear absorption of molecular constitu-ents in the atmosphere, thermal blooming resultingfrom linear absorption, and strong attenuation byplasma created by the laser-induced breakdown (LIB)of air and/or water droplets with radius a. LIB isinitiated just within the droplet shadow face for a < 60Am when the laser radiation is in the visible and thewater droplet is at atmospheric pressure.1 The propa-gation velocities of the two emitting plasma plumesalong the laser beam direction (the z axis) have beenstudied theoretically2 with a one-dimensional modeland experimentally with temporally and spatially re-solved plasma emission techniques.3 -8
There are no reports, to our knowledge, on tempo-rally and spatially resolved transmission measure-ments of the attenuation through inhomogeneousplasma. Only the time profile of the spatially inte-grated transmission T(t) = f dx X dyT(x, y, t) hasbeen investigated,9-11 using one laser beam to causeLIB and to measure T(t). The bound-bound transi-tions within the plasma are accepted as the mainsource of attenuation in the visible-wavelength region.Transmission measurements at one wavelength (X =0.532 Am) do not allow us to separate the plasma den-sity and temperature dependences.
We report a new diagnostic technique that providesboth temporally and spatially resolved transmission ofa green probe laser beam propagating through inho-mogeneous plasma created by LIB with a near-IR la-ser beam. Specifically, with a single IR laser shotcreating the plasma, we have measured the time devel-opment of the one-dimensional resolved transmissionof a green beam at different locations along a lineparallel to the IR laser beam direction, e.g., T(z, t) infront of the droplet shadow face and behind thedroplet's illuminated face. Our transmission resultsmay be amenable to comparison with calculationsbased on the present one-dimensional model2 andfuture two-dimensional models for the development ofplasma inside and outside the droplet.12
The experimental arrangement is shown in Fig. 1.A linear stream of monodispersed water droplets (a -40 gm) is produced by a vibrating orifice. The IR
beam (with intensity hiR and spot diameter -200 Am)from a single-mode Q-switched Nd:YAG laser irradi-ates a single water droplet. The green second-har-monic output of this laser (X = 0.532 Mm) is delayed by4.75 nsec relative to the IIR pulse. The greatly attenu-ated green radiation (<100 W/cm2, with diameter-1200 Am) is separated into two parts, a probe beam(IP) and an undeviated reference beam (IR). The in-set in Fig. 1 shows the relative orientation of Ip (alongthe x axis), IIR (along the z axis), and the transmittedprobe beam T(z, t)Ip through the expanding and inho-mogeneous plasma. Both the T(z, t)Ip and IR beamspass through two identical spatial filters, consisting oflenses with 5-cm focal length and apertures with -200-,um diameter. The IR beam is aligned to the T(z, t)Ipbeam but displaced vertically relative to it. An inter-ference filter centered at X = 0.532 gim and a green-glass filter are placed in front of an imaging lens, which
Fig. 1. Schematic of the experimental arrangement used tomeasure the transmission of a green probe beam (Ip)through the LIB-generated plasma caused by a near-IR laserbeam (IR) irradiating a single water droplet. The transmit-ted probe beam [T(z, t)Ip] and the reference beam (IR) areimaged on two portions of the streak-camera slit. The insetshows the orientation of the IIR and Ip beams relative to theexpanding plasma.
September 15,1989 / Vol. 14, No. 18 / OPTICS LETTERS
(a) 11R = 0 GW/Cm2
,2
:L-
(b) IIR = 26 GW/cm2
'V01
0 7Ref
-2 .
8 E n EE Tr td
cE = - =- . Probe
_Il 14-5 nsec
ITime
Fig. 2. Streak-camera output of the reference beam and thetransmitted probe beam (a) with the IR beam blocked (IIR =0) and (b) with IIR = 26 GW/cm 2 . The radius of the waterdroplet is -40 ,gm.
focuses both the IR and the T(z, t)Ip beams onto twodifferent portions of the streak-camera entrance slit(50 ,im wide) with equal magnification. This slit isaligned parallel to the IR laser beam and to the princi-pal diameter of the droplet. The combination of thespatial filters and the imaging lens ensures that thestreak camera measures the extinction and not anyplasma emission.
Figure 2(a) shows the single-laser-shot time profilesof the T(z, t)Ip and IR beams (labeled TransmittedProbe and Ref, respectively) with the IIR blockedalong the streak-camera slit (labeled Distance AlongZ). In Fig. 2 the two streak-camera tracks pertainingto the droplet's illuminated and shadow faces are la-beled I and S, respectively, and the direction of the IRbeam is indicated. With the IIR off, each of the T(z,t)Ip tracks is normalized by the IR tracks to producegoff(z, t).
Figure 2(b) shows the single-laser-shot time profilesof the T(z, t)Ip and IR beams as a function of z whenthe IR beam (with IIR = 26 GW/cm2) causes LIB andthe subsequent development of plasma. The intensi-ties of the T(z, t)Ip tracks with IIR = 26 GW/cm 2 areconsiderably lower than those with IIR = 0 because ofthe attenuation of the expanding plasma (see the insetof Fig. 1). In order to deduce the transmission fromthe curves shown in Fig. 2(b), each of the T(z, t)Iptracks is first normalized by the IR tracks to obtaingo2 (z, t) with IIR = 26 GW/cm 2 . Next, gn(Z, t) isnormalized by goff(z, t) to minimize the spatial nonuni-formity of the optics and streak-camera response.The transmission through the plasma as a function ofz and t is defined as T(z, t) -gn(Z, t)/g0 ff(Z, t).
The time profiles Of IIR and Ip (delayed by 4.75 nsec)are displayed in Fig. 3(a). Using the appearance ofthe plasma emission as the criterion for LIB initiation,we note that LIB occurs at tLIB - 5 nsec after the start
of the IIR pulse. The normalized data shown in Fig.2(b) are replotted in Fig. 3(b) for IR = 26 GW/cm2. InFig. 3(b) the abscissa is the time axis, and each of thetransmission curves at different z is displaced alongthe ordinate axis by an integer number of 2a. At t = 0nsec, well before LIB has occurred, T(z, t) is 100%. InFig. 3(b) X's indicate the time T(z, t) = 80%, and dotsindicate the time when T(z, t) reaches its minimumvalue, which is indicated in each of the curves.
For IIR = 180 GW/cm2, the time delay between thegreen and IR pulses is still set at 4.75 nsec. However,the initiation of LIB occurs sooner [tLIB 2.5 nsec; seeFig. 4(a)]. The T(z, t) curves are shown in Fig. 4(b).The lowest transmission that we can measure is T(z, t)
10%, a limit determined by the dynamic range of thestreak camera.
The propagation speed of the plasma attenuationfront along the +z directions can be extracted from theT(z, t) curves shown in Figs. 3(b) and 4(b). Dashedlines connect groups of X's in Figs. 3(b)and 4(b), andtheir slopes correspond to the speed of the plasmafront. Analogously, the slopes of the dashed linesconnecting groups of dots correspond to the speed ofthe fully developed portion of the plasma.
In the region behind the droplet's illuminated face,Fig. 3(b) shows that the slopes of the dashed linesconnecting the X's have the following values forIIR = 26GW/cm2 : (1) soon after LIB and near the maximum ofthe IR pulse, the slope is nearly vertical, implying a highspeed (-300 km/sec); (2) after the IR pulse has reachedits maximum, the slope decreases, and the speed is 85km/sec, consistent with the speed determined from
(a) I IR = 26 GW/cm'
IA
ILIB1
0 tLIB 10
team
20
Time (nsec)
(b)
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0
ol
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Time (nsec)
Fig. 3. (a) Time profiles of the IR beam (with IIR = 26 GW/cm2) and the probe beam. (b) Time profiles of T(z, t) forvarious distances along z in integral units of the droplet diam-eter. The water droplet's illuminated face (I), the shadowface (S), and the IR laser beam direction are indicated. TheX's denote the time when T(z, t) reaches 80%, and the dotsdenote the time when T(z, t) reaches its indicated minimumvalue. Dashed lines connect groups of X's and dots.
Fig. 4. Same as Fig. 3 except IIR = 180 GW/cm 2. Thelowest limit of our transmission measurement is 10% [see thedots in (b)].
plasma emission measurements for a laser-supportedoptical detonation wave7'8; and (3) toward the end ofthe pulse, the slope decreases even more, and the speedslows to 25 km/sec, implying that the remaining portionof the IR laser pulse can no longer sustain the opticaldetonation wave and the wave returns to a plasma orshock wave.2' 7'8 For the plasma or shock wave ejectedfrom the shadow face, the dashed-line slope corre-sponds to a speed of 10 km/sec.
For 1IR = 180 GW/cM2 and from the slopes of thedashed lines connecting the X's Fig. 4(b) shows thatthe plasma has a speed of 370 km/sec in the regionbehind the droplet's illuminated face and a speed of270 km/sec in the region in front of the shadow face.
A dashed line also. connects groups of dots [for thetime when T(z, t) reaches its minimum]. A time delayof -5 nsec is noted for the plasma transmission todecrease from an optically thin value of 80% to itsminimum, which is optically thick for 1IR = 180 GW/cm2. In the region behind the droplet-illuminatedface, the slopes of the dashed lines connecting the X'sand the dots are nearly equal in Figs. 3(b) and 4(b).This observation indicates that the speeds of the fullydeveloped portion of the plasma and of the plasmafront are equal, consistent with the properties of anoptical detonation wave propagating away from thedroplet's illuminated face toward the laser.2' 3' 7'8
The slopes connecting the X's and dots differ in theregion in front of the droplet shadow face. In Fig. 3(b)the propagation speed of the plasma front is 10 km/sec, and that of the fully developed portion of theplasma [where T(z, t) reaches its minimum] is 30 km/sec. In contrast, in Fig. 4(b), the propagation speed ofthe plasma front is 270 km/sec, and that of the fully
developed plasma is 110 km/sec. The speed of theplasma front is determined by the initial part of theunattenuated IR laser pulse soon after the initiation ofLIB. The speed of the fully developed plasma, whichcan propagate faster or slower than the plasma front,is dependent on the transmission of the remainingportion of the IR laser beam through the plasma in theregion behind the droplet's illuminated face. If theplasma transmission is low (as is the case for IIR = 180GW/cm2), the remaining portion of the IR pulse canno longer reach the plasma wave in front of the dropletshadow face to heat this plasma. Consequently, thefully developed portion of the plasma wave is expectedto slow down relative to the plasma front as the plasmacontinues to expand and to cool by the infusion of thesurrounding air in front of the shadow face.
The recovery of the plasma transmission can also benoted from the curves shown in Figs. 3(b)and 4(b).Far from the droplet's illuminated and shadow faces,T(z, t) eventually recovers from the minimum to T(z,t) = 100% within 5 nsec after the IR laser pulse is off.Figures 3(b) and 4(b) indicate that the transmissionrecovery rate of the plasma farther from the droplet isfaster than that nearer the droplet, suggesting that inthe outer layer of the plasma the temperature coolsand the density decreases more rapidly than in theinner layer. In addition, a comparison of Figs. 3(b)and 4(b) shows that the transmission recovery rate forIIR - 26 GW/cm 2 is faster than that for IIR = 180 GW/cm2, indicating that the plasma in the outer layer ishotter and/or denser at higher 1IR-
We gratefully acknowledge the partial support ofthis research by the U.S. Army Research Office (con-tract DAAL03-88-K-0040).
* Present address, Institute of Electro-Optical En-gineering, National Chiao Tung University, Hsinchu,Taiwan.
t Present address, Department of Physics, FudanUniversity, Shanghai, China.
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