Two-wavelength beam deflection technique for electrondensity measurements in laser-produced plasmas
Gregory W. Faris and HAkan Bergstr6m
We describe the use of a two-wavelength beam deflection technique in the measurement of electron densityand expansion velocity in a laser-produced plasma. Beam deflection measurements are made with a spatialresolution of 250 ,um, temporal resolution of 25 ns, and a dynamic range of 1000. Several techniques fordetermining the spatial and temporal variation of the electron density from beam deflection measurementsare described. Key words: Beam deflection, electron density, laser-produced plasma, two-wavelength two-color tomography, plasma expansion velocity.
1. Introduction
Laser-produced plasmas',2 and laser ablation are ofcurrent interest for a number of applications, includ-ing the production of atomic species of low vapor pres-sure species for spectroscopy 3 and new laser sources4 ;the production of clusters5 ; the production of VUVradiation6 and soft x-ray radiation for optically pump-ing soft x-ray lasers, 7 for microscopy, 8 and for lithogra-phy9; collisional excitation of soft x-ray lasersl; depo-sition of diamond1 and superconducting films12; andthe etching of polymers.'3 Better understanding ofthese processes is assisted by useful diagnostic tech-niques for measuring parameters within the plasma.A simple plasma diagnostic that may be implementedwith apparatus found in many laboratories is the beamdeflection technique.
When a laser beam is passed through a region withvarying index of refraction it is deflected by gradientsin the index of refraction. The deflection angle adepends on the integrated gradient of the index ofrefraction and is given to a good approximation by' 4
a (y) =-Jndx, (1)n dy
When this work was done both authors were with Lund Instituteof Technology, Physics Department, P.O. Box 118, S-221 00 Lund,Sweden; G. W. Faris is now with SRI International, Molecular Phys-ics Laboratory, 333 Ravenswood Avenue, Menlo Park, California94025.
where n is the index of refraction, no is the ambientindex of refraction, x is the direction of the laser beampropagation, and y is the direction of the deflection.Measured deflection angles may be used to reconstructthe spatially resolved index of refraction in the probedregion, which may then be related in various condi-tions to electron density, 3"15"16 gas density,1 7 speciesconcentration,' 8 or temperature.' 8 In this regard, thetechnique is similar to the path integrated imagingtechniques of schlieren, interferometry, and hologra-phy, except that the measurements give a time historyof the integrated index along a single line instead of a 2-D image at a single time as obtained with a pulsedimaging technique. The beam deflection technique isattractive because of its simplicity in implementationand analysis.'4 Beam deflection measurements havebeen used to perform electron density and gas densitymeasurements in laser-produced plasmas3"5 16 andother plasmas19 -2 2 as well as a diagnostic for laser abla-tion and associated density variations.23 -26
The many components in a plasma make the inter-prbtation of index of refraction measurements compli-cated.27 When electron density neis well below thecritical density n,, the index of refraction for free elec-trons is approximately
1 nen = 1 2 n,
The critical density is given bylrmec2
e2A
(2)
(3)
where me is the mass of the electron, c is the speed oflight, e is the charge of the electron, and X is thewavelength of the light. Thus the index of refraction
for electrons is less than one and varies rapidly withwavelength. This is in contrast to the index of refrac-tion for the other components of the plasma (ions,neutral atoms, molecules, and particles), which isgreater than one for visible and infrared wavelengthsand, except near optical resonances, slowly varying.By using a two-wavelength technique the contribu-tions from the electrons can be separated from theother components. In this paper we describe a two-wavelength beam deflection technique for the mea-surement of electron density in laser-produced plas-mas.
II. Experiment
The apparatus used for our beam deflection mea-surements is shown in Fig. 1. To avoid the effects ofbackground gas on the measurements, the plasma isformed in a chamber evacuated to 10-7 mbar. Theplasma is formed by using a 250-mm lens to focus 25-50 mJ of 1.06-Am radiation from a Q-switchedNd:YAG laser (Quanta-Ray DCR) to an intensity of_1010 W/cm2 on a rotating target. The position of the
focus is moved between measurements to maintain aclean surface on the target for each measurement.Targets made of boron, graphite, silicon, iron, tanta-lum, and tungsten were used.
A He-Ne laser and a He-Cd laser, operating at 632.8and 441.6 nm, respectively, were used as probe lasers.An air-cooled Ar+ laser was used instead of the He-Cdlaser for early measurements 5 but vibrations causedby the fan were found to significantly reduce the sensi-tivity of the measurements. The He-Ne and He-Cdlasers differ by about a factor of 2 in the index ofrefraction for the electrons [Eqs. (2) and (3)], and thecritical densities for these wavelengths (2.78 X 1021 and5.72 X 1021 cm-3 for the He-Ne and He-Cd wave-lengths, respectively) are well above those found in theplasmas. Thus Eq. (2) is valid and the absorption bythe electrons is very small. A dichroic mirror is used tocombine the two lasers and a 500-mm lens is used tofocus both beams in the plasma. The two laser spotswere carefully overlapped in the plasma region to avoidsystematic errors. The distance of the He-Cd laser
from the dichroic mirror is varied to give focal spots ofthe same size (250,um) to within 5%. Accurate overlapof the two laser beams is obtained using the two quad-rant detectors. The detector at the left is used tooverlap the beams at the dichroic mirror, while thedetector at the right is used to overlap the beams overtheir lengths. The adjustment of these positions isdecoupled by using a tilted optical flat (window)placed in front of the He-Ne laser. Changing theangle of the optical flat allows translation of the He-Nebeam without changing the beam's direction, whiletilting the dichroic mirror allows changing the beamdirection with minimal change in overlap at the mirror.
The He-Ne and He-Cd lasers used for the deflectionmeasurements have little noise at frequencies over 10kHz and little beam-pointing drift after being warmedup (1 h). Thus, there is little noise on the time scalesof a beam deflection measurement, which is performedover 2.5 As. There is also little mechanical vibration atthese frequencies, and although the experiments wereperformed on the third floor of a building, good resultswere obtained with the two lasers and the detector allon separate tables (of which none was an optical table).Normal optical interferometry would not be possiblein these conditions. The He-Ne laser, with mirrorshard-sealed onto the tube, was particularly stable, andwe have measured deflection angles to 200 nrad in aplasma when averaging 100 laser shots. This is equiv-alent to a variation of -13,000th of an interferencefringe over the spot size of 250 Am.
For best results, the beam waists (focal spots) of theprobe lasers are placed at the center of the plasma.The beam waist spot size then determines the spatialresolution, the minimum measurable deflection angle,and the maximum deflection angle measurable withgood linearity. Reducing the beam waist size im-proves the spatial resolution until a point is reachedwhere the resolution at the edges of the measurementregion begins to be significantly degraded due to dif-fraction. This occurs for a Gaussian beam at a spotsize given by' 4
W= <7r (4)
HeNeleser
Fig. 1. Experimental arrangement for two-wave-length measurement of beam deflection angles in a
where w0 is the 1/e2 beam radius of the probe intensityat the beam waist, and is the length of the measuredregion. When using a segmented detector such as asplit (bicell) or quadrant detector to measure deflec-tions, the deflection signal has the form of an errorfunction, Vmar erf(V-ywff), where Vmax is the voltagefrom the entire laser beam, y is the deflection distance,and wff is the far field spot size, wff = Xx/hrw, at adistance x from the focal spot. The signal is linear towithin 5% for deflections up to laylwff = 0.39. (Al-though lateral detectors give linear signals over largedeflections, they are too slow for measurements inlaser-produced plasmas.) The maximum deflectionsignal size with good linearity is thus
0.39 aex --O4_2_r W0
(5)
Co
-a
0)
0
a,
= 1a,
c]
-200 1-200 0 200
Time (ns)
The slope of the error function signal is dVldy =4Vmax/V7wff. If the limiting noise may be expressedas a voltage, Vmin, as is the case for noise from theelectronics or from laser intensity fluctuations, theminimum detectable deflection is
min = 1 Vmin X(6)24; Yrax wU
For the measurements here, focal spots of w0 = 2 50,mwere used. As the measurement region in the plasmais 20 mm or less, Eq. (4) shows there is no resolutiondegradation. This spot size allows linear measure-ments up to deflection angles of 220 Mrad, while thelargest deflection angles we have measured in the plas-mas was 300 rad. With the 200 nrad as the smallestdetectable deflection, the dynamic range is >1000. Atransform lens placed between the measurement vol-ume and the detector eliminates errors from beamdisplacements on traversing a sample.1 4 Because ofthe large distance between the plasma and the detector(2.2 m), no transform lens was used. Although using atransform lens affects the spot size at the detector, it iseasily shown that the maximum and minimum mea-surable deflections are still determined by the focalspot size in the measurement region according to Eqs.(5) and (6).
To eliminate the intense light from the Nd:YAGlaser and the plasma, an interference filter is placed infront of the quadrant detector. The filter is ex-changed to allow measurement of either the 632.8- or441.6-nm beams. Two of the outputs of the quadrantdetector are individually ac coupled and amplified twotimes each in fast amplifiers (EG&G Ortec model 574amplifiers, 4.5 gain, 1.2-ns rise time) and input to thedifferential inputs of a Biomation model 8100 tran-sient digitizer (10-ns sample time, 3 dB at 25 MHz).The transient digitizer is triggered using light from theNd:YAG laser pulse. For all the measurements pre-sented here, zero time corresponds to the leading edgeof the Nd:YAG laser pulse, which is digitized separate-ly on the transient digitizer. The data are transferredto an IBM AT computer for signal averaging, storage,and analysis. Typically, 100 laser shots are averagedfor a beam deflection measurement. The signal detec-
Fig. 2. Example of temporal beam deflection profile in a laser-produced plasma measured at 0.5 mm from a silicon target. Thesolid line corresponds to the He-Ne measurement, the dashed line is
for He-Cd.
tor is mounted on a micrometer-driven translationstage. By translating the detector horizontally, a cali-bration of detector voltage vs deflection distance isobtained for calculation of the deflection angle.
An example of a beam deflection measurement per-formed in a silicon plasma at a distance of 0.5 mm fromthe target is shown in Fig. 2. The He-Ne signal isshown as a solid line, and the He-Cd signal as a dashedline. Negative deflections correspond to deflectionaway from the target. From the two-wavelength mea-surements, the interpretation of the beam deflectionmeasurement is straightforward. From Eqs. (2) and(3) it is apparent that the index of refraction contribu-tion for electrons at the two wavelengths used shoulddiffer by a factor of -2. As the deflection angle givenin Eq. (1) scales linearly with the index of refraction,the deflection angles will also differ by a factor of 2.For the small deflection approximation of Eq. (1), thedeflections due to electrons and the remainder of theplasma may be added. Thus the initial, negative sig-nal in Fig. 3 is due predominantly to electrons. Thelater, positive part of the deflection has about equalsignal sizes at the two wavelengths. Thus, this signalis primarily the result of neutral species. This positivepart of the beam deflection was only present within -1mm from the target and was not present for the tanta-lum and tungsten targets. A large positive deflectionwas found for the He-Cd measurements with an irontarget, apparently because of enhancement from theproximity of a strong resonance at 441.51 nm in Fe I(Ref. 28) to the He-Cd wavelength of 441.6 nm. Thepresence of the positive signal approximately corre-lates with the boiling points of the target material,which tends to support a delayed vaporization of thetarget as described by Allen.29 The separation of thebeam deflection signal into portions with dominantand minimal contributions from electrons is fortunate(this was typical for all the targets studied). In spite ofthe care in matching the laser beam probes, irreprodu-
Fig. 3. Electron density profiles for a laser-produced plasma with agraphite target, reconstructed from a composite of many temporal
beam deflection curves.
cibility of the plasma and, for larger distances from thetarget, excess noise for the He-Cd measurements didnot allow separation of electron and nonelectron sig-nals with good signal to noise. Instead, the electrondensity calculations below were made with the He-Newavelength measurements alone, and the positive sig-nal was set to zero. The measurements with the He-Cd were used as a check for the accuracy of this simpli-fication.
For distances less than -500 Am from the target,absorption of the probe laser was often present, ap-pearing as an asymmetry between the signals from thetwo sides of the quadrant detector. When this oc-curred, the two signals were digitized separately, and asingle deflection signal was subsequently calculatedwhich was corrected for the effects of absorption of theprobe laser.
To accurately reconstruct the electron density in theplasma requires recording deflection curves such asthat in Fig. 2 at many distances from the target. If theplasma is reproducible, these data may be taken with asingle laser beam. This was done by translating boththe target and focusing lens for the 1.06-Mm radiation.Then, if the plasma may be approximated as spherical-ly symmetric, the index of refraction may be calculatedby using a tomographic reconstruction technique.'4
In this case, the same projection (deflection angle as afunction of distance at a fixed time) is used 100 times.While the plasma is not strictly spherically symmetric,the error in the reconstructed densities is estimated tobe less then a factor of 2. The result of applying thistechnique to beam deflection measurements in a plas-ma produced from a graphite target is shown in Fig. 3.The peak electron densities agree well with those mea-sured interferometrically for comparable focused laserintensities.2
As the data acquisition and analysis for the recon-struction technique above are lengthy, it is of interestto examine simpler techniques to provide estimates ofelectron densities. If it is assumed that the plasma
expansion obeys a self-similar behavior30 with a con-servation of the total number of electrons,3 ' an elec-tron density profile may be obtained using a singledeflection measurement. For a self-similar expan-sion, we write the electron density ne as
n(rR) = (R8 , (r\ (7)
where r is the distance from the pulsed laser focus, R isa variable that scales with the size of the plasma, he is anormalized density profile, and ne0 is the peak densitywhen R = R0. Because the deflection angle scales onlyas the peak index of refraction,'4 the deflection angle ahas the same scaling relationship as for the electrondensity:
a(y,R) = R3 0 - (8)
The scaling variable may be written as the product ofan expansion velocity v and the duration the plasmahas been expanding t; R = vt. If velocity v is constant(this is shown to be approximately valid below), asingle deflection curve, such as the one in Fig. 2, con-tains information on the plasma electron density at alltimes for a self-similar expansion. Such a curve de-fines a(rR) = a(r,vt) for r fixed and varying time t.The normalized deflection curve as a function of dis-tance &(r/R) can be recovered by multiplying the de-flection curve as a function of time by t3, where t = 0should correspond to the initiation of the plasma, andthen plotting the curve as a function of lit. Scaling ofthe axes is determined by ensuring that the deflectionat a given distance and time for the new curve agreewith the same time and distance in the original curve.In principle, the time for the deflection curve found inthis manner can be chosen arbitrarily. However, thesignal to noise is best when reconstructing for timeswhere the deflection angle in the original curve is rela-tively large. The results when this technique is ap-plied, together with tomographic reconstruction forthe same data used for Fig. 3, are shown in Fig. 4. Theagreement with the results in Fig. 3 is quite good,except for the curve reconstructed at 10 ns. The self-similar approximation is not valid at 10 ns because thetotal number of electrons is still growing.
Determination of electron density profiles may besimplified further if, in addition to the assumption ofself-similar behavior, it is assumed that the functionalform of the electron density vs distance from the targetis known. Then the deflection measurement may beused to scale the distribution. For example, if theelectron density is given by a Gaussian distribution,32
and the peak deflection measured as a function of timeat a position y* is a*, it may be shown that the electrondensity is given by
n = 4g a*n, exp(-2r 2/y*
2 ). (9)
This equation was used together with the data used forFigs. 3 and 4 to calculate the electron density profilesshown in Fig. 5. Electron density curves are only
Fig. 4. Electron density profiles for a laser-produced plasma with agraphite target, reconstructed from single temporal beam deflectioncurves. The 10-ns profile is calculated from a measurement made at0.5 mm from the target. The correspondences for the other timesare 50 ns at 1.4 mm, 100 ns at 3.7 mm, 200 ns at 5.0mm, and 300 ns at
5.5 mm.
10
10
E
-.7Ca)0)
005
il
10
10
10
100 2 4 6
Distance (mm)
Fig. 5. Electron density profiles for a laser-producedgraphite target, calculated from peak deflection ang]
Gaussian density dependence.
shown for 50, 100, and 200 ns because thedata containing peaks at earlier or latergood signal to noise. As indicated in Eq. (1deflection for a temporal deflection curvepoint where the electron density (and th(angle) is small compared to their peak vabecause of the 1R 3 factor in Eqs. (7) an4calculated electron densities shown in Ffairly well with those found from the motechniques for Figs. 3 and 4.
Calculation of the peak electron densityextent is not that sensitive to the exact funcof the electron distribution. For example,en of the twelve hypothetical electron densitions given by Keilmann 3 3 (his distributionhas no beam deflection peak for finite time
10
8-
E
0)C)
co
0
2-
0 100 200 300 400 500Time (ns)
Fig. 6. Distance from the target vs time for the peak deflectionangle for a number of targets.
deflection for a fixed position deflection curve occursat a position
y* = (0.915 : 0.06)R, (10)
where Keilmann defines R by h(R) = 0.1 h(0).peak deflection angle is given by
The
a* = (0.683 : 0.26) , (11)n,
where ne(r = 0) is the peak electron density at thatmoment.
The fixed position deflection curves allow simpledetermination of the expansion velocity of a laser-produced plasma. To the degree that the shape of theplasma does not change (as is true for a self-similarexpansion, for example), the time for a peak deflectionat a given distance determines the expansion velocity.As an example, the measurement distance as a func-
8 1 0 tion of the peak deflection time is shown for a variety oftargets in Fig. 6. The data were taken for approxi-
plasma with a mately equivalent power densities from the Nd:YAG[es assuming a laser. For times after -50 ns, the velocities are about
constant in the 20-100-km/s range. The correspond-ing ion kinetic energies we have measured are in therange of 800 eV to 1 keV for the tantalum and tungsten
re were no targets and the 200-400-eV range for the other targets.0)thes withk This is in agreement with the results obtained by By-), the peak kovskii et al. 3 4 using a mass spectrometer.
occurs at adeflection
lues; this is 1ll- Discussion
i (8). The The sensitivity of the beam deflection technique'ig. 5 agree may be enhanced fairly simply. The temporal resolu-re involved tion was primarily limited by the large area of the
quadrant detector. This could be improved by using aand spatial smaller split detector, although a faster transient digi-ctional form tizer would also be required. Because there is littleusing elev- laser noise in the measurement bandwidth, beam de-ty distribu- flections can be measured using a very fast single ele-
n number 11 ment detector (up to -50-ps rise time is available) ins), the peak conjunction with a razor blade to block half of the laser
beam. A collection lens can be placed between therazor blade and the detector to collect all the lightwhich passes the razor blade onto the small detectorarea. If desired, the laser power can be monitoredwith a beam splitter and another fast detector to im-prove the signal to noise. Because the index of refrac-tion is inversely proportional to the square of the de-tection wavelength, using infrared lasers such as laserdiodes35 for the deflection measurement enhances thesensitivity for small electron densities while still main-taining the validity of the approximation in Eq. (2).
Although the experiments described here were notsuccessful in completely separating the contributionsof electrons from the remaining plasma components,improvements in the apparatus should make this pos-sible. By using a second dichroic mirror to separatethe beams just before the detector, measurementscould be taken at both wavelengths simultaneously.The relative stability of the two beams could be as-sured by passing both beams through a single pinholeor optical fiber and using an achromat lens to image thepinhole or fiber end into the center of the plasma.
The apparatus for beam deflection measurements ina laser-produced plasma can be very simple. We mea-sured deflection angles close to the target by couplingthe unamplified detector signal directly into an oscillo-scope. Thus the minimum equipment needed is a He-Ne or similar laser, a fast photodiode, a razor blade,and an oscilloscope.
A possible method to measure fixed time beam de-flection curves might be to use a differential interfer-ometer. Reference 36 describes the similarity be-tween differential interferometer measurements andbeam deflection measurements as well as a simpledifferential interferometer with tunable sensitivitythat would be well suited for laser plasma measure-ments. Time resolution could be obtained by using apulsed laser or by using a diode array with a gatedimage intensifier.
We have applied a two-color beam deflection tech-nique to the measurement of the electron density inlaser-produced plasmas. The rapid time scales of theplasma allow reduced stability requirements and lownoise. Although the reproducibility of the measure-ments did not permit complete separation of the con-tribution of the electrons to the beam deflections (orindex of refraction) from that of the ions and neutrals,the two-color technique established that the earlierpeak consisted almost entirely of electrons and thatthe later peak had little electron contribution. Sever-al techniques for reconstruction of the electron densitywere compared. These varied from tomographic re-construction of data from stacked fixed position beamdeflection curves (with uncertainty of less than a factorof 2) to simple estimates based on the peak deflectionangles which yield uncertainty of <1 order of magni-tude. The technique allows straightforward measure-ment of the expansion velocity of the leading edge ofthe plasma.
This work was supported by the National SwedishBoard for Technical Development and the National
Science Foundation. We would like to acknowledgehelpful conversations with Sune Svanberg, HansLundberg, Anders Persson, and Ake Bergsquist.
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