The mechanism for continuum polarization in laser induced breakdown spectroscopyof Si(111)
John S. Penczak Jr. a, Yaoming Liu a, Richard D. Schaller b,c, Daniel H. Rich d, Robert J. Gordon a,⁎a Department of Chemistry, University of Illinois at Chicago, Chicago, IL 60607‐7061, USAb Argonne National Laboratory, Center for Nanoscale Materials, Argonne, IL 60439, USAc Department of Chemistry, Northwestern University, Evanston, IL 60208, USAd Department of Physics and The Ilse Katz Institute for Nanoscale Science and Technology, Ben-Gurion University of the Negev, P.O.B 653, Beer-Sheva 84105, Israel
a b s t r a c ta r t i c l e i n f o
Article history:Received 22 November 2011Accepted 19 June 2012Available online 26 June 2012
Polarization of the plasma luminescence produced by both nanosecond and femtosecond laser ablation ofSi(111) was analyzed under different conditions of fluence and detection geometry. It is shown that the lu-minescence is partially polarized and is directed in the plane of the crystal. The time evolution of the plasmaemission signal was also investigated with the use of a streak camera. The mechanism for polarization is pro-posed to be preferential reflection of s-polarized light (i.e., light polarized normal to the plane of laser inci-dence) by the melted surface, in agreement with the Fresnel equations. Earlier reports of much strongerpolarization are shown to be erroneous.
Laser-induced breakdown (LIB) spectra generally consist of a se-ries of sharp peaks riding on top of a continuous background [1,2].The peaks arise from fluorescent transitions of ions and neutralatoms and molecules produced in a plasma, whereas the continuumis usually attributed to ion-electron recombination and bremsstrah-lung. Various methods have been implemented to suppress the con-tinuum so as to increase the signal/background ratio. In particular,time-gating of the detected signal can reduce the continuum, whichgenerally decays much more rapidly than the discrete fluorescence.
Several years ago, Liu et al. [3] discovered that under certain condi-tions the continuum emission from Si(111) produced with femtosec-ond (fs) pulses from an 800nm Ti:Sapphire laser is strongly polarized,suggesting the possibility of suppressing the background by simplyplacing a polarizer before the detector. The polarization was found tobe strongest at short wavelengths, increasing to over 90% below350nm. Later studies showed this effect to be a general phenomenon,occurring also for metals [4,5] and dielectrics [5]. Subsequently, Liu etal. [6] and Majd et al. [7] reported that a polarized continuum is gener-ated also by nanosecond (ns) pulses, using, respectively, the 532nmsecond harmonic and the 1.064μm fundamental frequency of a Nd:YAG laser. Most recently, Asgill et al. [8] attempted to repeat these find-ings, using 1.064μm ns pulses at a fluence of 1020J/cm2 to ablate Cu,and found little or no polarization. In an effort to reconcile this discrep-ancy, Penczak et al. [9] extended the fluence range of their earlier ns
studies of Al and found that the magnitude of the polarization, P, de-creases monotonically with fluence between 5.4 and 497J/cm2. Theyalso found that P is greater for an s-polarized laser than forp-polarization. With these differences in mind, they showed that thevarious ns studies are mostly consistent.
Despite the seeming consistency between the findings of the variousgroups, the mechanism for producing strong continuum polarizationremained a mystery. The observations of the Gordon group [3–6,9]have some of the characteristics of scattering of the incident laser beamby the surface. The emission appears in a cone around the specular direc-tion, and the angle of the polarization vector is consistent with dipoleemission from a surface (i.e., a p-polarized laser produced p-polarizedemission, an s-polarized laser produced s-polarization, and intermediatepolarizations produced the corresponding projections onto the observa-tion plane). Nevertheless, the increasing polarization at shorter wave-lengths seemed to rule out a simple reflection or scattering mechanism.Accordingly, they speculated that the polarization is produced either bysome alignment process in the plasma or possibly by some frequencyup-conversion of the laser beam in the plasma. While the findings ofMajd et al. are in general agreement with of those of Gordon andco-workers, they found that the emission is s-polarized and is indepen-dent of the polarization state of the laser [7]. They nevertheless also fa-vored a plasma alignment mechanism. Asgill et al. [8] attributed thevery small s-polarization (P≤5%) that they observed in some experi-ments to selective reflection by the surface of s-polarized light generatedin the plasma, in accordance with the Fresnel equations.
The present study is a further attempt to elucidate the polarizationmechanism and to reconcile the observations of the various groups.We reason that any polarization produced in the plasma itself, either
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by some directed motion of electrons or by frequency up-conversionof the laser beam, would be short-lived, on a time scale comparable tothat of the laser pulse. To test this hypothesis, we used an ultrafaststreak camera to measure the time-dependence of the polarized emis-sion produced by ablating a Si(111) sample with a fs laser. Observationof polarization for periods substantially greater than the laser pulsewould argue strongly against a plasma alignment mechanism.
2. Methods
Three sets of experiments were performed, each with its own ap-paratus. In all the experiments, Si(111) wafers were ablated in airwith single laser shots, and the emitted light was collected and ana-lyzed with a spectrograph. The first set of experiments was per-formed at the University of Illinois at Chicago (UIC), using theapparatus depicted in Fig. 1. Laser pulses of ~65fs duration were gen-erated by a Ti:Sapphire laser (Spectra Physics Tsunami oscillator andSpitfire amplifier). The output of the regenerative amplifier had apeak intensity at 805nm and a bandwidth of 24nm (full width athalf maximum), falling to 1% at 772 and 834nm. A half-wave plateand polarizer were used to reduce the pulse energy, E, to within therange of 10–100μJ, with a shot-to-shot variation of less than 3%. Thepolarization state of the laser was varied using a second half-waveplate. The laser beam was focused onto the sample with a microscopeobjective (10×, NA=0.25). The radius of the focused beam, ω0, wasmeasured with a scanning knife edge and was found to have a valueof 1.8±0.2μm. This quantity is the Gaussian radius of the electricfield, corresponding to an irradiance of
I rð Þ ¼ I0e−2r2=ω0
2
; ð1Þ
and a peak fluence of
F ¼ 2E cosθin=πω02; ð2Þ
where θin is the angle of incidence. The sample was mounted on anautomated sub-μm precision xyz translation stage. The stage ad-vanced 100μm between laser shots to expose a fresh surface foreach pulse, with an average of 20 shots taken for each data point.The angles of incidence and detection (θdet) were manually adjustedby moving the translation stage and laser beam optics. A notch filter(Chroma Technology, E690SPUV6) was used to block scattered laser
light. The filter transmitted >85% of the emitted light between390nm and 595nm and rejected the laser light with transmittancesof 1×10−6, 2.3×10−6, and 2.3×10−5 at 772, 805, and 834nm,respectively.
The ablating pulse generated a plume, consisting of electrons, gro-und state and electronically excited atoms and ions, molecules, andparticulates. Light emission from this plume was focused onto the600μm entrance slit of a spectrograph (Spectrapro 2300i, PrincetonInstruments), in which the spectrum was dispersed by a 300lines/mm grating blazed at 500nm, and was recorded with a non-gated,thermoelectrically cooled CCD (PIXIS 400, Princeton Instruments)camera. A Glan-Thompson polarizer (Red Optronics, GMP-6015)mounted on a motorized rotation stage was inserted in front of theentrance slit of the spectrograph to measure the polarization of theplasma emission.
The second set of experiments was performed at the Center forNanoscale Materials at Argonne National Laboratory (ANL). The pri-mary difference between the apparatus at ANL and UIC is that theANL setup used an ultrafast streak camera (Hamamatsu C5680)mounted on a spectrograph (Acton SP2150) to measure the emittedlight as a function of time, with a resolution of 1.5% of the temporalgate (e.g. 750ps for a time window of 50ns, and a maximum resolu-tion of 3ps for a 140ps window) and a slit width of 60μm. As before, aTi:Sapphire laser (Spectra-Physics MaiTai oscillator and Spitfire Proamplifier, 35fs pulse width) was used to ablate the sample. Thelaser was triggered at a rate of 18Hz, while the sample was translatedcontinuously at a speed great enough to ensure that the irradiatedspots were separated by a minimum of 100μm. The pulse energywas set between 50 and 100μJ by means of a variable neutral densityfilter. The same notch filter and sample controller were used as in theUIC setup.
The third set of experiments, performed at UIC, used the secondharmonic of a Nd:YAG laser (Continuum Surelite, 532nm, 4ns pulsewidth) to ablate the sample. A variable neutral density filter wasplaced before the focusing optics to set the pulse energy of thebeam between 9μJ and 4mJ. The laser was focused onto the sampleby a 100mm focal length convex lens. The focused laser beam had aradius of ω0=22.6±1.4μm, which was measured with a scanningknife edge. An interference filter (Thorlabs, FES0500) was mounteddirectly in front of the entrance slit to block scattered laser light.This filter has a transmission range of 380 to 500nm and a transmit-tance of 1.3×10−5 at 532nm. The sample controller and spectrographwere the same as in the first apparatus, except that the slit width ofthe spectrograph was decreased to 200μm.
Special precautions were taken to ensure that the signal was notcontaminated by artifacts such as scattered laser light or polarizationcontributed by the detection optics. The polarization preference ofthe spectrometer grating was calibrated using an unpolarized whitelight source, so that any effects caused by differences in diffraction ef-ficiencies of s- and p-polarization could be accounted for [10]. As anadditional precaution, an experiment was performed using a 2mlong, single-mode fiber (Ocean Optics, QP600-2-UV–VIS) placed inthe optical path between the polarizer and spectrometer to act as adepolarizer. The degree of linear polarization of the laser source was99.8%. We found that our particular fiber optics geometry resultedin the depolarization of the laser source by ~93%. The polarization ofthe emitted light was then measured with the fiber placed betweenthe polarizer and the spectrograph. We obtained nearly identical re-sults as those using the grating calibration without the fiber, therebyruling out the possibility that the monochromator/detector affectedthe polarization measurements. We also carefully checked the polar-ization properties of the optics (lenses and filter) in the detectionpath to confirm that they did not have any polarization preference.The entrance slit of the spectrometer was widened to 600μm sothat any misalignment of the polarizer would not result in part ofthe signal being lost on the edge of the slit. We also verified the
Fig. 1. Schematic drawing of the apparatus used at UIC, including half wave plates (λ/2), polarizers (P1 and P2), lenses (L1, L2, and L3), and an interference filter (F).
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results using a photomultiplier tube (Hamamatsu R212), utilizing in-terference filters for different wavelength selections in the samerange as the CCD measurements.
3. Results
Fig. 2 shows typical LIB spectra of Si recorded at UIC, using either ans-polarized (upper panel) or p-polarized (lower panel) Ti-Sapphirelaser to ablate Si(111) crystals. In both panels, the upper trace wasobtained using the polarizer to transmit only s-polarized light, whilethe lower trace corresponds to p-polarized transmission. These datashow that the emitted light is preferentially s-polarized. The most in-tense peaks are labeled in panel (a), and the corresponding transitionsare listed in Table 1 [10].
To quantify the magnitude of the polarization, spectra wererecorded with the polarizer angle, α, set at different values in 20° in-tervals. The intensities at each wavelength were fit to the Malus func-tion, A+Bcos2(α−α0), as illustrated in Fig. 3. The magnitude of thepolarization, P, equals B/(2A+B), and the direction of the polarizationis determined from the value of α0. Calibration of the polarizer with alinearly polarized laser gave a value of α0=44° for s-polarized light.(Hereafter we will refer to the polarization angle as α0). The resultingP and α0 spectra are shown in Fig. 4 for s- and p‐laser polarizations.The top panel shows a typical polarization spectrum, in which P isseen to have a background value of 12–20% that increases graduallywithwavelength. The slightly larger value of P for s-polarized excitationis not statistically significant. (In some runs p-polarized excitation gaveslightly larger P.) Superposed on this background are structural
features, some of which are correlated with peaks in the LIB spectrum.Between 395 and 415nm there is a strong maximum in P produced bythe s-polarized laser and a smaller minimum in P produced by thep-polarized laser, which lie in the vicinity of peak ‘c’ of the LIB spectrum(Fig. 2a). Features ‘a’, ‘b’, and ‘d’may also be identifiedwith peaks in theLIB spectrum, whereas the small dip at 448nm does not appear to havea resolvable counterpart in the LIB spectrum.
Fig. 4b shows the polarization angle spectrum obtained from thefitted parameters in the Malus function. The value of α0 lies withina few degrees of the s-plane (i.e., normal to the plane of laser inci-dence) and displays a gradual falloff with increasing wavelength.Some of the structure seen in the P spectrum is evident here as well.
Fig. 5 displays time-resolved measurements of the emission inten-sity, polarization, and polarization angle obtained with the streakcamera at ANL. These data are slices of the full spectra taken at480nm. The top panel shows that the signal reaches a maximum at2.9ns and then falls to 1/e of that value within 1.0ns. The middlepanel shows that P is fairly constant (5–10%) during the first 10nsand increases slowly to a value of 15–25% at 45ns. The bottompanel shows that α0 remains within ±5° of the s-plane throughoutthe measured time range.
Additional experiments were conducted using the ns (Nd:YAG)apparatus at UIC. Spectra produced with s- and p-polarized laserbeams are shown in Fig. 6. Although the fs and ns spectra have fea-tures in common, there are significant differences between them.For example, peaks ‘a’ and ‘b’ in the fs spectrum differ in intensityby almost a factor of 2, whereas in the ns spectra their intensitiesare nearly equal. Also, peak ‘e’ is absent in the ns spectra, and peak‘h’ is present only in the ns spectrum. (Peaks ‘f’ and ‘g’ are blockedby the 532nm filter and therefore cannot be seen in the ns spectrum.)
Fig. 2. Laser-induced breakdown spectra obtained with an (a) s-polarized and(b) p-polarized fs laser. The upper (red) and lower (black) curves correspondto spectra taken with the polarizer set to admit s-polarized or p-polarized light, re-spectively. The peaks were assigned to neutral and ionic transitions, using the NISTatomic line database.
Table 1Assignment of peaks in the LIB spectra.
Label λ(nm)
Assignment Label λ(nm)
Assignment
a 385.6 Si I 3s3p2-3s24p e 462.1 Si II 3s24d-3s27fb 390.6 Si I 3s23p2-3s23p4s f 500.6 Si I 3s23p4s-3s23p6pc 400 Second harmonic of Ti:
Sapphire laserg 505.6 Si II 3s24p-3s24d
d 413.1 Si II 3s23d-3s24f h 455 H′-X (5,0) band of the Sidimer (?)
Wavelengths for lines ‘a–d’ and ‘e–g’ are the values listed in the NIST database, ref. [10].The assignment of feature ‘h’ is from ref. [14].
Fig. 3. A typical plot of the emission intensity as a function of polarizer angle, using the UICfs apparatus. The s-polarized laser has a fluence of 503.6J/cm2 and an angle of incidence of30°, with the detector positioned perpendicular to the incident laser beam. The data arefor a wavelength of 460nm. The curve is a least squares fit of the Malus function.
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The P and α0 spectra shown in Fig. 7 were determined in the samemanner as in the fs experiments and have similar properties. The con-tinuum polarization ranges from 12 to 15% between 380 and 495nm,increasing slightly with wavelength. The polarization angle of thecontinuum lies near the s-plane and varies weakly with wavelength.As before, the difference between s- and p-polarized excitation isnot significant. Both P and α0 have structure correlated with peaksin the LIB spectrum. Closer examination of this structure revealsasymmetric profiles in both P and α0. There is a hint of such asymme-try in the fs data as well, although the poorer signal/noise ratio makesthis effect more difficult to discern. In all the experiments describedso far, the laser was incident at an oblique angle 30° from the normal,and the emission was detected perpendicular to the laser beam. Tofurther characterize the polarized emission, additional measurementswere performed with ns excitation in which the detection angle wasvaried, with θin fixed at 40°. These results are plotted in Fig. 8 for488nm emission. The polarization was found to have a maximumvalue near θdet=80°, falling off to near zero at θdet=0. The polariza-tion direction of the emitted light was always in the s-plane.
In a final set of experiments, wemeasured the fluence dependenceof P. Using the ns apparatus, we varied the fluence from 1J/cm2 toover 400J/cm2. We found that although the general appearance ofthe polarization spectrum is for the most part independent of fluence,the value of P is greatest at low fluences. Fig. 9 shows a slice of thespectra at 460nm as a function of fluence. This plot shows that P re-mains relatively constant at low fluence and then drops monotonical-ly as the fluence is increased past approx. 40J/cm2. The angular studyshown in Fig. 8 was performed in the region of the low fluenceplateau.
4. Discussion
We begin our discussion by comparing the fs and ns LIB spectrashown in Figs. 2 and 6. Most of the features may be explainedsemi-quantitatively on the basis of the line intensities and EinsteinA-coefficients listed on the NIST Atomic Spectra Database. More careis needed, however, to identify peaks ‘c’, ‘e, and ‘h’. The first of these isprominent only in the s-polarized emission produced by thes-polarized fs laser (Fig. 2a). More extensive studies performed withsingle and double pulses at varying angles of incidence [11] providestrong evidence that this peak is the second harmonic (SH) of the800nm Ti:Sapphire laser. The most likely mechanism for producingthis emission is surface SH generation (SSHG [12]), although some con-tribution from the plasma-generated SH is also possible [13]. (The latteris more commonly produced by a p-polarized laser, which couples
Fig. 4. Polarization (panel (a)) and polarization angle spectra (panel (b)), showing themagnitude and angle of polarization measured at each wavelength, taken under thesame conditions as Fig. 2. The vertical tic marks in panel (a) correspond to the locationsof the assigned peaks in Fig. 2a. The horizontal line in the bottom panel corresponds tos-polarized emission. The experimental uncertainty in P is ±1.5%.
Fig. 5. Time-resolved polarization data taken with the ANL fs laser at a fluence of1700J/cm2 and an angle of incidence of 30°. The data are for a wavelength of 480nm.The panels show (a) the signal intensity, (b) the magnitude of the polarization, and(c) the polarization angle. The inset in (b) is a higher resolution scan of the first 2nsof the polarization. The horizontal line in the bottom panel corresponds tos-polarized emission.
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efficiently to the plasma.) The observation of SHG far from the specularangle ismost likely caused by a ripple produced by a Rayleigh-Taylor in-stability in the laser-generated plasma [11]. The shoulder at 400nmseen in the ns spectrum may be assigned to several weak Si+ linesthat coincidentally lie in this region [10].
Feature ‘e’, seen only in the fs spectrum, is assigned to fluores-cence from a highly excited state of Si+, lying at 122,655cm−1. Pop-ulation of this state requires ten 800nm photons and seven 532nmphotons. The observation of this feature only with the fs laser maybe explained by the six orders of magnitude greater irradiance ofthe short pulse. Feature ‘h’, which appears only in the ns spectrum, re-quires a different explanation. Although there is a line in the NIST da-tabase at 455.3nm having a large Einstein coefficient, the very highenergy of the upper level (175,336cm−1) makes it difficult to ratio-nalize its population with the ns and not the fs laser. A more attractiveassignment is to fluorescence from the neutral Si dimer. RecentlyOjha and Gopal [14] discovered several new electronic states of Si2populated by 532nm ablation of Si. The most intense feature intheir spectrum recorded in air matches the 455nm peak in Fig. 6. Al-though we cannot explain its absence in the fs spectrum, it is wellknown that clustering in an ablation plume is sensitive to the tempo-ral properties of the pulse [15,16].
We turn now to the possible sources of the observed polarization.One possibility is that it is derived from the polarization of the laserbeam itself, either by scattering from the surface or by somenon-linear frequency up-conversion process in the plasma. A secondpossibility is that the polarization is caused by an anisotropic velocitydistribution of electrons in the plasma, which, upon recombining
Fig. 6. Laser-induced breakdown spectra obtained with an s-polarized (panel (a)) anda p-polarized (panel (b)) ns laser at a fluence of 27.0J/cm2 and an angle of incidence of30°, with the detector positioned perpendicular to the incident laser beam. The upper(red) and lower (black) curves correspond to spectra taken with the polarizer set toadmit s-polarized or p-polarized light, respectively.
Fig. 7. Polarization (panel (a)) and polarization angle (panel (b)) spectra recordedunder the same conditions as Fig. 6. The vertical tic marks in panel (a) correspond tothe locations of the assigned peaks in Fig. 6a. The horizontal line in the bottom panelcorresponds to s-polarized emission.
Fig. 8. Polarization of 488nm emission as a function of detection angle measured withthe ns apparatus, using either an s- (black symbols) or p-polarized (red symbols) laser.Data were recorded at a fluence of 21.6J/cm2 and an incident angle of 40°. The detec-tion angle is measured with respect to the sample surface normal. Vertical error barsare a single standard deviation of the polarization measurement, and the horizontalerror bars are an estimate of the experimental uncertainty in the detection angle. Thecurves Rs and Rp are the reflectance of liquid Si calculated from the Fresnel equationsfor s- and p-polarized light, respectively, assuming a refractive index of 2.89+4.98i.The curve labeled P is the polarization that would be produced by an unpolarizedbeam reflected from the liquid Si surface, whereas curve P′ is the calculated result ifhalf of the light reaches the detector directly and half is reflected by the surface.
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with the ions, convert their directed motion into polarization of theemitted light [17]. A third possibility is that reflection by the targetsurface of unpolarized emission from the plasma polarizes the outgo-ing radiation in accordance with the Fresnel equations. Lastly, it ispossible that photoluminescence from an intact layer within the crys-tal is polarized. This effect is well-known for semiconductors havinglocal asymmetry caused, for example, by strain induced by latticemismatch between a quantum dot and the substrate on which it isgrown [18,19] or by the cylindrical axis of a nanowire [20].
We rule out the first mechanism immediately because we found thatthe polarization lasts much longer than the pulse duration. We may ruleout the secondmechanismon the same grounds inasmuch as it is difficultto imagine a plasma alignment persisting for several nswithout some ex-ternal means of sustaining it. The observation that the polarization vectorlies in the s-plane (i.e., normal to the plane of laser incidence) regardlessof the laser polarization is further evidence against these two mecha-nisms. The last mechanism is also unlikely because crystalline Si has a di-amond structure, for which the optical selection rules predict isotropicphotoluminescence [20]. (Recently Hu et al. [21] reported that a properlyshaped pulse trainmay induce symmetry-breaking in GaAs that results inpolarized photoluminescence. These specialized conditions are absent inthe experiments reported here.)
We are leftwith the thirdmechanism, namely selective reflection bythe surface of unpolarized light, resulting in an s-polarized outgoingwave. Previously, we ruled out this mechanism because the emissionwas not always observed to be s-polarized. The present study shows,however, that the data in our earlier experiments were obscured byscattered laser light, which appeared as an artifact at shorter wave-lengths. Using notch filters to reject laser scatter and carefully cor-recting for polarization induced by optical components, we now findthat the detected light is always within a few degrees of the s-plane.
We conclude therefore that the most likely mechanism for the po-larized signal is reflection of unpolarized plasma emission by thesample surface. Numerous pump and probe measurements of thetime-resolved reflectance of semiconductors in the melting and abla-tive regimes have been reported [22–26]. Time-resolved microscopyrevealed the formation of a highly reflective liquid phase that persistsfor nanoseconds [27]. We posit that in our experiment a surface layerof liquid Si selectively reflects the s-component of unpolarized emis-sion from the plume. To test this hypothesis, we compared the polar-ization as a function of detection angle with the predictions of theFresnel equations. In our model, the incident angle of the laser doesnot play a role in the reflection mechanism. Rather, we assume that
light from the plume strikes the surface at all angles and is reflectedat the specular angle.
For a transparent material, the Fresnel equations predict thatp-polarized light is totally transmitted at the Brewster angle, so thatthe reflected light is 100% s-polarized. For an absorbingmedium, the re-flectance of p-polarized radiation falls to a non-zero minimum at theBrewster angle, and the reflected beam has maximum s-polarizationat that angle. For a complex index of refraction, n=η+iκ, the Fresnelequations give for the reflectances of s- and p-polarized light
Rs ¼n1 cosθ−n2 cosϕn1 cosθþ n2 cosϕ
� �2ð3Þ
and
Rp ¼ n1 cosϕ−n2 cosθn1 cosϕþ n2 cosθ
� �2; ð4Þ
where θ is the angle of incidence of the plasma luminescence, andϕ is theangle of refraction [28]. Subscripts 1 and 2 refer to themedium of the in-cident wave and the absorbing/reflecting surface, respectively. As shownin Appendix A, Snell's law can be used to eliminate ϕ, yielding reflec-tances that depend solely on the angle of incidence, the real refractiveindex of medium 1, and the complex refraction index of medium 2[29]. Assuming that the vapor pressure of Si above the reflecting surfaceis well below atmospheric during most of the period that light is gath-ered by the detector, we may to good approximation take n1=1, whilefor n2 we take the literature values of η2 and κ2 for liquid Si [30].
If the light emitted by the plasma is unpolarized, the reflected lighthas polarization
P ¼ Rs−Rp
Rs þ Rp: ð5Þ
The problem is complicated by the fact that some of the light travelsdirectly to the detector and some of it is reflected (and absorbed) by thesurface, as depicted schematically in Fig. 10. If we assume that a con-stant fraction, f, is detected directly, the relative signals detected whenthe polarizer is set for maximum and minimum transmission aref+(1−f)Rs and f+(1−f)Rp, respectively, so that the observed polariza-tion is given by
P′ ¼1−fð Þ Rs−Rp
� �
2f þ 1−fð Þ Rs þ Rp
� � : ð6Þ
Fig. 9. Fluence dependence of the polarization obtained using either an s- (blacksquares) or p- (red circles) polarized ns laser. The data were recorded for an angle ofincidence of 30°, with the detector positioned perpendicular to the incident laserbeam. Error bars are a single standard deviation.
Fig. 10. Schematic drawing of light emitted from the plasma plume and detected atangle θdet. Rays R1 and R2 represent, respectively, light emitted directly from the plas-ma without reflection and light emitted from the plasma and subsequently reflected bythe thin liquid Si surface layer. Electric field orientation vectors are shown for rays R1and R2 to illustrate the (i) unpolarized and (ii) s-polarized character of the respectiverays, the latter caused by the Fresnel effect upon reflection. The positions of lenses L1and L2 correspond to the same optical element positions illustrated in Fig. 1.
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In general, f is spatially dependent. Assuming arbitrarily a value off=0.5, we obtain the results for Rs, Rp, P, and P′ plotted in Fig. 8. Inadding the intensities of the direct and reflected rays, we have as-sumed that coherent interference averages to zero [31]. This assump-tion is justified because of spatial averaging of the emissionoriginating from adjacent regions of the plume. Fig. 11 shows the cal-culated variation of P′ with wavelength for a fixed value of θdet=80°.The Fresnel mechanism predicts a gradual increase in polarizationwith wavelength, in qualitative agreement with the data.
The quantitative agreement between P′ and the measured polari-zation in Fig. 8 is most likely fortuitous, considering the arbitrarychoice of f and the assumption that n2 does not vary with time. Nev-ertheless, agreement between the calculated and measured values ofthe maximum angle (~80°) and the near-zero value of P at θdet=0 strongly support the Fresnel mechanism.
Structure in the polarization spectra (Figs. 4a and 7a) associatedwith discrete transitions may be explained by the spatial dependenceof f. It is likely that atomic fluorescence and continuum emission aregenerated at different locations in the plasma, so that the relativecontributions of reflected and directly transmitted waves are differ-ent, leading to maxima or minima in P′ at the discrete lines. The ran-dom structure in Fig. 11 is caused by the much poorer signal/noiseratio at an 80° incidence angle. The strong maximum in P at 400nm(peak ‘c’ in Fig. 4a) produced by the s-polarized fs laser may beexplained by addition of the s-polarization of the SH signal to thes-polarized reflection of the background continuum at that wave-length. The dip in P produced by the p-polarized laser is similarlyexplained by partial cancelation of p-polarized SHG by thes-polarized Fresnel reflection. This effect is naturally absent in thens spectrum (Fig. 7a).
The structure in the polarization angle spectra (Figs. 4b and 7b) ismore difficult to explain. The small but systematic drift in the baselineof α0 in Fig. 4b suggests the existence of a weak birefringence of theplume. If real, this unexpected effect would imply the formation ofsome optically active molecules or clusters that rotate the polariza-tion of continuum radiation passing through the plume, with the ef-fective column length depending on where in the plume differentfree–free transitions occur. Such an effect would not be inconsistentwith the assumption of n1≈1 near the surface. The asymmetric pro-files of α0 are as of yet unexplained, although we note that a shiftfrom s- to p-polarization has been observed in the blue wing of theSH signal produced in a plasma [13].
Direct comparison of our results with those of Majd et al. [7] andHahn et al. [8] is not possible because they worked with Cu and ourpresent study was performed with Si. Nevertheless, the discrepanciesbetween the various groups are mostly resolved, at least qualitatively.In particular, the falloff in P with laser fluence (Fig. 9) is consistent
with our most recent results [6] and with the near-zero value of Preported by Asgill et al. [8] at 1020J/cm2. Possible reasons for theloss in polarization at higher fluences include plasma shielding ofthe surface, which could increase the value of f, and disruption ofthe laminar liquid layer at the Si surface, causing the light to bescattered non-specularly. Likewise, our observation of predominantlys-polarization is in agreement with the finding of Majd et al. [7], al-though their observation of larger P for s-polarized irradiation isunexplained. Within experimental error, we find that P is the samefor both s- and p-polarized excitation.
In summary, the Fresnel mechanism for the reflection of light at asurface provides a semi-quantitative explanation of the observed polar-ization of the continuum in laser-induced breakdown spectroscopy. Inparticular, it explainswhy the polarization is largely s-polarized. The re-sults for fs and ns excitation are largely consistent. There remain, how-ever, some aspects of our data associatedwith the discrete structure in Pand α0 that are not fully understood and which are especially relevantfor application to LIB spectroscopy.
Acknowledgments
This project was supported under Contract Number FA7014-07-C-0047, with the U.S. Air Force Surgeon General's Office (AF/SG)and administered by the Air Force District of Washington (AFDW).Use of the Center for NanoscaleMaterials was supported by theU. S. De-partment of Energy, Office of Science, Office of Basic Energy Sciences,under Contract No. DE-AC02-06CH11357.
Appendix A. Calculation of the polarization
Eqs. (3) and (4) give the polarization of a light beam incident on asurface with incident angle θ and refraction angle ϕ. The latter anglemay be calculated from a generalization of Snell's Law. We start bywriting the wave number as a complex quantity
K→¼k
→þi a
→ ðA1Þ
and the index of refraction as
n ¼ ηþ iκ: ðA2Þ
The components of the wave vector in medium 2 are given by [20]
k2 sinϕ ¼ k0η1 sinθ ðA3Þ
and
k2 cosϕþ ia2 ¼ k0 η2 þ iκ2� �2−η21 sin
2θh i1=2
; ðA4Þ
where k0 is the wave number in a vacuum.Eq. (A4) may be decomposed into real and imaginary components.
We write the argument of the square root as
V ¼ η22−κ22−η21 sin
2θþ 2iκ2η2 ¼ Vj jeiγ : ðA5Þ
The amplitude and phase of V are given by
Vj j2 ¼ η22−κ22−η21 sin
2θ� �2 þ 4κ2
2η22 ðA6Þ
and
tanγ ¼ 2κ2η2η22−κ2
2−μ21 sin
2θ: ðA7ÞFig. 11. Polarization spectrum under the same laser conditions as Fig. 7a, measured at a
detection angle (θdet) of 80°. The smooth curve is the calculated value of P′with f=0.5.
9J.S. Penczak Jr. et al. / Spectrochimica Acta Part B 74–75 (2012) 3–10
Author's personal copy
The real part of Eq. (A3) then becomes
k2 cosϕ ¼ k0ffiffiffiffiV
pcos γ=2ð Þ: ðA8Þ
Using Eq. (A3) to eliminate k2, we obtain the refraction angle,
tanϕ ¼ n1 sinθffiffiffiffiV
pcos γ=2ð Þ ; ðA9Þ
which may be inserted into Eqs. (3) and (4).In the limit of κ2=0, we recover the ordinary form of Snell's Law:
V ¼ η22−η21 sin2θ ðA10Þ
tanϕ ¼ η1 sinθffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiη22−η21 sin
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