atoms

Article Opacity Corrections for Resonance Silver Lines in Nano-Material -Induced Plasma

Ashraf M. EL Sherbini 1, Ahmed H. EL Farash 2, Tharwat M. EL Sherbini 1 and Christian G. Parigger 3,*

1 Laboratory of Laser and New Materials, Faculty of Science, Cairo University, Giza 12613, Egypt 2 Engineering Physics Department, Military Technical College, Cairo 11766, Egypt 3 Department of Physics and Astronomy, University of Tennessee, University of Tennessee Space Institute, Center for Laser Applications, 411 B. H. Goethert Parkway, Tullahoma, TN 37388, USA * Correspondence: [email protected]; Tel.: +1-931-841-5690

 Received: 21 June 2019; Accepted: 29 July 2019; Published: 31 July 2019 

Abstract: Q-switched laser radiation at of 355, 532, and 1064 nm from a Nd: YAG laser was used to generate plasma in laboratory air at the target surface made of nano-silver particles of size 95 10 nm. The emitted resonance spectra from the neutral silver at wavelengths of 327.9 nm ± and 338.2 nm indicate existence of self-reversal in addition to plasma self-absorption. Both lines were identified in emission spectra at different laser irradiation wavelengths with characteristic dips at the un-shifted central wavelengths. These dips are usually associated with self-reversal. Under similar conditions, plasmas at the corresponding bulk silver target were generated. The recorded emission spectra were compared to those obtained from the nano-material target. The comparisons confirm existence of self-reversal of resonance lines that emerge from plasmas produced at nano-material targets. This work suggests a method for recovery of the spectral line shapes and discusses practical examples. In addition, subsidiary calibration efforts that utilize the Balmer series Hα-line reveal that other Ag I lines at 827.35 nm and 768.7 nm are optically thin under variety of experimental conditions and are well-suited as reference lines for measurement of the laser plasma electron density.

Keywords: laser-induced plasma; atomic ; self-reversal; self-absorption; nanoparticles; silver; hydrogen

1. Introduction Self-absorption as well as self-reversal of radiation from optically thick plasma occur due to processes of re-absorption in the outer-cooler region or in shockwave-induced density variations. The plasma produced by focusing of pulsed laser light on suitable targets suffers from strong inhomogeneity, even when using a well-defined TEM00 laser mode [1]. Plasma inhomogeneities lead to strong gradients of plasma parameters (electron density and temperature) from the hot central core to peripheries that is in contact with surrounding air. This cooler plasma peripheries contain large population of atoms in lower atomic states, especially in the ground state. These peripheral atoms are often causing plasma re-absorption [2]. The plasma opacity manifests itself in form of homogeneous absorption of the spectral line that is labelled self-absorption. Effects of self-absorption include an apparent increase of the emitted line full-width at half-maximum (FWHM) and a decrease in spectral line height [3]. Line shape recovery is possible, only if one employs a standard, reliable measure of the true plasma electron density, which is offered by the optically thin Hα- and Hβ- lines [3,4], yet frequently the Hα-line is utilized. For instance, line-of-sight measurements of laser-induced plasma at or near an ice surface [4,5] show self-reversal dips at the un-shifted resonance of the hydrogen alpha line of the Balmer series. Typical “fingerprints” due to re-absorption include

Atoms 2019, 7, 73; doi:10.3390/atoms7030073 www.mdpi.com/journal/atoms Atoms 2019, 7, x FOR PEER REVIEW 2 of 9 plasmaAtoms 2019 at, or7, 73near an ice surface [4,5] show self-reversal dips at the un-shifted resonance wavelength2 of 9 of the hydrogen alpha line of the Balmer series. Typical “fingerprints” due to re-absorption include self-reversal and self-absorption [4–11]. In this work, self-absorption and self-reversal parameters, SR self-reversal and self-absorption [4–11]. In this work, self-absorption and self-reversal parameters, SR and SA, respectively, distinguish between these re-absorption effects. and SA, respectively, distinguish between these re-absorption effects. There are significant challenges when considering self-reversed lines, especially for resonance There are significant challenges when considering self-reversed lines, especially for resonance lines, for the evaluation of the electron density measured from the full-width-at-half-maximum, and lines, for the evaluation of the electron density measured from the full-width-at-half-maximum, and the determination of the temperature that is a function of the spectral radiance. Moreover, spectral the determination of the temperature that is a function of the spectral radiance. Moreover, spectral line intensities from nano-based materials show differences from the corresponding bulk signals [12]. line intensities from nano-based materials show differences from the corresponding bulk signals [12]. The theoretical descriptions of self-absorption and self-reversal [5–11] rely on the computation of the The theoretical descriptions of self-absorption and self-reversal [5–11] rely on the computation of the emitted radiation when modeling the emitters by a specific distribution. emitted radiation when modeling the emitters by a specific distribution. However, strong enhanced plasma emission was noticed when focusing laser radiation onto However, strong enhanced plasma emission was noticed when focusing laser radiation onto targets made of pure nanomaterials [12–14]. This enhanced emission was related to the sudden targets made of pure nanomaterials [12–14]. This enhanced emission was related to the sudden increase of the population density of the ground state atoms in the same ratio of the amount of increase of the population density of the ground state atoms in the same ratio of the amount of nano bulk nano bulk nano enhanced emission Iλ0 nano/Iλ0 ≈bulkNλ0 /Nλ0nano [12–14],bulk i.e., more of cold atoms, N0 , exist at nanothe outer enhanced emission Iλ /Iλ Nλ /Nλ [12–14], i.e., more of cold atoms, N , exist peripheries of plasma produced0 0 from≈ nanomaterials0 0 [14], but without further increase in the0 plasma at the outer peripheries of plasma produced from nanomaterials [14], but without further increase excitation temperature [2]. This enhanced emission enables the spectral line intensity Iλ0Nano of the in the plasma excitation temperature [2]. This enhanced emission enables the spectral line intensityNano resonanceNano lines to exceed the corresponding, upper-limit black body radiation intensity Iλ0 ≥ Iλ0 of the resonance lines to exceed the corresponding, upper-limit black body radiation intensity B(λ0Nano,Tex), Iλ0 B(λ0,Tex), ≥ 2hc2hc2 11 BB(λλ,T,T ) = , ,(1) (1) 0 ex 5 λλ expexphc/hcλ/λkkTTex−11 0 { 0 B } − becausebecause of of the the relatively relatively local local temperature, temperature, T Texex, ,in in this this plasma plasma region. region. Therefore, Therefore, and and as as elaborated elaborated by by FujimotoFujimoto [2], [2], i.e., i.e., the the measured measured radiation radiation intensities intensities of of the the resonance resonance lines lines are are only only those those that that emerge emerge fromfrom the the outer outer plasma plasma regions regions at whichwhich thethe plasmaplasma opticaloptical depthdepth isis unity, unity, hence hence self-reversal self-reversal starts starts to toact act at at the the central central un-shifted un-shifted wavelengths wavelengths of resonance of resonance lines thatlines terminate that terminate at the groundat the ground state. Figure state.1 Figureillustrates 1 illustrates a homogenized a homogenized central core,central cold core, periphery, cold periphery, the emanating the emanating “distorted” “distorted” line shape line and shape the andupper the limitupper of limit spectral of spectral intensity intensity imposed imposed by the blackby the body black radiation body radiation “tilted horizontal“tilted horizontal thick line”. thick line”.

FigureFigure 1. 1. AnAn illustration illustration to to the the effect effect of of plasma plasma opacity opacity on on spectral spectral line line shape shape vi viaa self-reversal self-reversal (red) (red) in in comparisoncomparison to to the undistortedundistorted shape shape (), (blue), together together with with the the black blac bodyk body spectral spectral intensity intensity limit (blacklimit (blacklines) lines) for a specificfor a specific excitation excitation temperature temperature at outer at regionouter region of the of plasma. the plasma.

ThereThere are are three three effects effects that that modify modify the the line line shap shape:e: First, First, the the excessive excessive enlargement enlargement of of line line FWHM; FWHM; second,second, reduction ofof spectralspectral radiance radiance imposed imposed by theby the black black body body radiation radiation limit; andlimit; third, and thethird, reversal the reversalin the emitted in the emitted line-shape. line-shape. ThisThis work work introduces introduces a a method method for for retrieving retrieving the the original original undistorted undistorted shape shape of of self-absorbed self-absorbed lineslines that that are are affected affected simultaneously simultaneously by by self-reversal self-reversal and and self-absorption. self-absorption. The The method method is based is based on theon theavailability availability of certain of certain optically-thin optically-thin spectral spectral lines lines that that originate originate from from upper upper states states of of atomic atomic transitions,transitions, viz., viz., Ag Ag I Ilines lines at at 827.35 827.35 and and 768.7 768.7 nm. nm. These These Ag Ag lines lines are are investigated investigated first first by by comparison comparison ofof the the determined determined electron electron density density with with that that obtained obtained from from H Hαα, ,and and then then serve serve as as gauge gauge for for other other optically-thickoptically-thick Ag Ag lines. lines. AtomsAtoms2019 2019, 7,, 7 73, x FOR PEER REVIEW 33 ofof 9 9

2. Materials and Methods 2. Materials and Methods In the experiments, an Nd:YAG laser device(Quantel model Brilliant B) operates at the fundamentalIn the experiments, wavelength an Nd:YAG of 1064 lasernm and device(Quantel the two harmonics model Brilliant at 532 and B) operates 355 nm, at with the fundamental output laser wavelengthenergy per of pules 1064 of nm 370 and ± the5, 100 two ± harmonics4, and 30 ± at 3 532mJ, andrespectively. 355 nm, with The output corresponding laser energy spot per sizes pules at ofthe 370target5, surface 100 4, amount and 30 to3 0.5 mJ, ± 0.05, respectively. 0.44 ± 0.05, The and corresponding 0.27 ± 0.03 mm. spot An sizes optical at the fiber target of 400 surface μm diameter amount ± ± ± tocollects 0.5 0.05, the 0.44radiation0.05, andfrom 0.27 the plasma.0.03 mm. An An echell opticale fibertype ofspectrograph 400 µm diameter (SE200) collects with the an radiation average ± ± ± frominstrumental the plasma. bandwidth An echelle of 0.12 type nm, spectrograph and an attach (SE200)ed intensified with an average charge-coupled instrumental device bandwidth (Andor iStar of 0.12DH734-18F) nm, and anacquire attached the intensifieddata. The spectral charge-coupled pixel reso devicelution (Andor and pixel iStar area DH734-18F) amount to acquire 0.02 nm the and data. 196 Theµm spectral2, respectively. pixel resolution A xyz-holder and pixel allows area one amount to position to 0.02 the nm optical and 196 fiberµm 2at, respectively.distance of 5 A mm xyz-holder from the allowslaser-induced one to position plasma. the optical fiber at distance of 5 mm from the laser-induced plasma. TheThe time time delay delay and and gate gate width width amount amount to to 2 2µ sµs for for all all experiments experiments reported reported in in this this work. work. ICCD ICCD KestrelSpecKestrelSpec®®software softwaresubtracts subtractsthe the background background stray stray light light contributions. contributions. The The measured measured electronic electronic noisenoise level level amounts amounts to to 20 20 ±7 7 counts counts acrossacross wavelengthwavelength rangerange ofof 250–850250—850 nm. nm. The The measurements measurements of of ± incidentincident laser laser energy energy at at each each laser laser shot shot utilize utilize a quartz a quar beamtz beam splitter splitter to direct to direct the reflected the reflected part (4%)part to(4%) a calibratedto a calibrated power-meter power-meter (Ophier (Ophier model model 1z02165). 1z02165). A 25 ps A fast25 ps response fast response photodiode photodiode in conjunction in conjunction with digitalwith digital storage storage CRO (type CRO Tektronix (type Tektronix model TDS model 1012) TD measuresS 1012) measures the laser pulsethe laser width pulse of 5 width1 ns. of A 5 set ± 1 ± ofns. calibrated A set of calibrated neutral density neutral filters density adjusts filters the adju energysts the/pulse. energy/pulse. The DH2000-CAL The DH2000-CAL lamp (Ocean lamp Optics (Ocean SN037990037)Optics SN037990037) allowed usallowed to correct us forto thecorrect sensitivity for the of sensitivity detection systemof detecti composedon system of spectrograph, composed of intensifiedspectrograph, camera intensified and optical camera fiber. and A 500 optical kg/cm 2fiber.press A prepared 500 kg/cm the silver2 press nanomaterial prepared the powder silver (fromnanomaterial MKNANO powder®) to produce(from MKNANO a less brittle®) to tabletproduce without a less brittle further tabl purificationet without orfurther heat treatments.purification Theor heat nanoparticle treatments. size The equals nanoparticle 95 10 size nm, equals as confirmed 95 ± 10 nm, from as confirmed measurements from withmeasurements a transmission with a ± electrontransmission microscope. electron microscope.

3.3. Results Results and and Discussion Discussion AnAn example example of of the the self-reversed self-reversed resonance resonance lines lines from from the the neutral neutral silver silver atoms atoms is is presented presented in in FigureFigure2 after2 after laser laser irradiation irradiation with with di differentfferent wavelengths, wavelengths, namely, namely, Figure Figure2a,d: 2a,d: 355 355 nm, nm, Figure Figure2b,e: 2b,e: 532532 nm, nm, and and Figure Figure2c,f: 2c,f: 1064 1064 nm. nm.

FigureFigure 2. 2.The The e ffeffectect of of self-reversal self-reversal on on the the resonance resonance Ag Ag I transitionI transition from from nano-silver nano-silver plasmas plasmas with with respectrespect to to bulk bulk target target (black). (black). Di Difffferenterent laser laser irradiation irradiation wavelengths wavelengths are are indicated indicated by by di differentfferent colors. colors. (a(,ad,)d blue) blue for for 355 355 nm, nm, (b (,be,)e green) green for for 532 532 nm, nm, and and (c ,(fc),f red) red for for 1064 1064 nm. nm. Atoms 2019, 7, x FOR PEER REVIEW 4 of 9

In Figure 2, the upper self-reversed spectral lines emerge from plasma generated at the surface AtomsAtoms2019 2019, ,7 7,, 73 x FOR PEER REVIEW 4 ofof 99 of the nano-silver target. The lower black spectra are the corresponding lines for the same transition and Inunder Figure the 2, samethe upper experimental self-reversed conditions spectral butlines from emerge the from bulk-silver plasma generatedtarget. One at thecan surfacenotice In Figure2, the upper self-reversed spectral lines emerge from plasma generated at the surface of significantlyof the nano-silver more target. self-reversal The lower of the black plasma spectra created are the from corresponding nano-silver linesthan for theplasma same from transition bulk- the nano-silver target. The lower black spectra are the corresponding lines for the same transition and silver.and under the same experimental conditions but from the bulk-silver target. One can notice under the same experimental conditions but from the bulk-silver target. One can notice significantly significantlyFor the moreresonance self-reversal transitions of theof theplasma Ag Icreated lines atfrom 327.9 nano-silver and 338.2 than nm, forFigures plasma 3–5 from illustrate bulk- more self-reversal of the plasma created from nano-silver than for plasma from bulk-silver. recordedsilver. and fitted nano-material silver lines with central dips at line center. For the resonance transitions of the Ag I lines at 327.9 and 338.2 nm, Figures3–5 illustrate recorded TheFor twothe resonancesets of spectra transitions show the of results the Ag captured I lines atfrom 327.9 nano-material and 338.2 nm, silver Figures targets 3–5 with illustrate 355 nm and fitted nano-material silver lines with central dips at line center. radiation.recorded and The fitted self-reversal nano-material of plasma silver radiationlines with from central nano-silver dips at line material center. is typically absent in The two sets of spectra show the results captured from nano-material silver targets with 355 nm investigationsThe two sets of laser-inducedof spectra show plasma the results with capturedbulk-silver from targets nano-material for otherw silverise similar targets experimental with 355 nm radiation. The self-reversal of plasma radiation from nano-silver material is typically absent in conditions.radiation. The Figure self-reversal 3 shows well-developedof plasma radiation spectral from dips. nano-silver Accordingly, material Figure is 4typically displays absentrecorded in investigations of laser-induced plasma with bulk-silver targets for otherwise similar experimental spectrainvestigations obtained of withlaser-induced 532 nm harmonic plasma withlaser excitation.bulk-silver targets for otherwise similar experimental conditions. Figure3 shows well-developed spectral dips. Accordingly, Figure4 displays recorded conditions. Figure 3 shows well-developed spectral dips. Accordingly, Figure 4 displays recorded spectra obtained with 532 nm harmonic laser excitation. spectra obtained with 532 nm harmonic laser excitation.

Figure 3. AgI (a) 327.9 nm and (b) 338.2 nm lines, 355-nm excitation, fluences of 13.5, 9.6, 5 and 2.1 FigureJ/cm2. 3. AgI (a) 327.9 nm and (b) 338.2 nm lines, 355-nm excitation, fluences of 13.5, 9.6, 5 and 2.1 J/cm2. Figure 3. AgI (a) 327.9 nm and (b) 338.2 nm lines, 355-nm excitation, fluences of 13.5, 9.6, 5 and 2.1 J/cm2.

Figure 4. Ag I (a) 327.9 nm and (b) 38.2 nm lines, 532-nm excitation, fluences of 13.5, 11.5, 8, and 6 J cm2. Figure 4. Ag I (a) 327.9 nm and (b) 38.2 nm lines, 532-nm excitation, fluences of 13.5, 11.5, 8, /and 6 J/cm2. Figure4 indicates diminished self-absorption when compared to Figure3. For 1064 nm laser excitation,Figure Figure 4. Ag 5I displays(a) 327.9 nm even and smaller (b) 38.2 self-absorption nm lines, 532-nm phenomena excitation, fluences for the twoof 13.5, silver 11.5, lines. 8, and 6 Figure 4 indicates diminished self-absorption when compared to Figure 3. For 1064 nm laser J/cm2. excitation, Figure 5 displays even smaller self-absorption phenomena for the two silver lines. Figure 4 indicates diminished self-absorption when compared to Figure 3. For 1064 nm laser excitation, Figure 5 displays even smaller self-absorption phenomena for the two silver lines. Atoms 2019, 7, 73 5 of 9

Atoms 2019, 7, x FOR PEER REVIEW 5 of 9

Atoms 2019, 7, x FOR PEER REVIEW 5 of 9

Figure 5. AgI (a) 327.9 nm and (b) 338.2 nm lines, 1064-nm excitation, fluences of 13.5, 11.5, 8, Figure 5. AgI (a) 327.9 nm and (b) 338.2 nm lines, 1064-nm excitation, fluences of 13.5, 11.5, 8, and andFigure 6 J/cm 5.2 AgI. (a) 327.9 nm and (b) 338.2 nm lines, 1064-nm excitation, fluences of 13.5, 11.5, 8, and 6 J/cm2. 6 J/cm2. In view of Figures3–5, one can see that it would be challenging to extract the full-width at In view of Figures 3–5, one can see that it would be challenging to extract the full-width at half- half-maximumIn view of for Figures determination 3–5, one can of electron see that density.it would Itbe would challenging be required to extract to extract the full-width the FWHM at half- of the maximum for determination of electron density. It would be required to extract the FWHM of the linemaximum after opacity for determination corrections due of electron to self-reversal density. andIt would self-absorption be required eff toects. extract the FWHM of the line after opacity corrections due to self-reversal and self-absorption effects. lineAn after accurate opacity electron-density corrections due to measure self-reversal of the and nano-material self-absorption plasma effects. is required for the design of An accurate electron-density measure of the nano-material plasma is required for the design of self-absorptionAn accurate correction electron-density procedures. measure The of reliable the nano Hα-materialline was plasma supposed is required to provide for the a measuredesign of for self-absorptionself-absorption correctioncorrection procedures.procedures. The The reliable reliable H Hα lineα line was was supposed supposed to provideto provide a measure a measure for for electron density [3], but unfortunately, the Hα line is absent when employing green and blue laser electron density [3], but unfortunately, the Hα α line is absent when employing green and blue laser beamselectron for density plasma [3], generation but unfortunately, with nano-silver. the H line Consequently, is absent when one employing needs to green identify and other blue suitablelaser beamsbeams forfor plasmaplasma generation withwith nano-silver.nano-silver. Consequently, Consequently, one one needs needs to identifyto identify other other suitable suitable optically thin lines. In this work, opacity corrections for self-reversed and self-absorbed Ag lines are opticallyoptically thin thin lines.lines. In this work,work, opacityopacity corrections corrections for for self-reversed self-reversed and and self-absorbed self-absorbed Ag Aglines lines are are based on other optically-thin Ag lines. basedbased on on other other optically-thinoptically-thin AgAg lines.lines. In the process of locating suitable lines in place of Hα, an extensive examination of emission InIn thethe processprocess of locating suitablesuitable lines lines in in place place of of H Hα, αan, an extensive extensive examination examination of emissionof emission spectral lines from the neutral silver discovers that only two Ag I lines at 827.35 or 768.7 nm are suitable spectralspectral lineslines fromfrom the neutral sisilverlver discoversdiscovers that that only only two two Ag Ag I linesI lines at 827.35at 827.35 or 768.7or 768.7 nm nmare are candidates for reliable measurement of the ‘true’ electron density. The inferred electron densities suitablesuitable candidatescandidates for reliable measurementmeasurement of of the the ‘true’ ‘true’ electron electron density. density. The The inferred inferred electron electron compare nicely with the corresponding values obtained from analysis of the hydrogen alpha line of the densitiesdensities comparecompare nicely with thethe correspondingcorresponding va valueslues obtained obtained from from analysis analysis of theof thehydrogen hydrogen Balmer series. Figure6 illustrates the results, and Table1 shows the comparisons. alphaalpha line line of of thethe BalmerBalmer series. FigureFigure 6 6 illustra illustratestes the the results, results, and and Table Table 1 shows 1 shows the the comparisons. comparisons.

FigureFigure 6. 6.Recorded Recorded spectraspectra forfor (a)H) Hα atat 656.28 656.28 nm, nm, (b ()b Ag) Ag I at I at827.35 827.35 nm, nm, and and (c) (Agc)Ag I at I 768.7 at 768.7 nm. nm. LaserFigureLaser fluence fluence6. Recorded 9.6 9.6 J /J/cmcm spectra2,2, 1064-nm1064-nm for ( excitation.excitation.a) Hα at 656.28 nm, (b) Ag I at 827.35 nm, and (c) Ag I at 768.7 nm. Laser fluence 9.6 J/cm2, 1064-nm excitation. 17 3 TableTable 1. 1.Electron Electron densities, densities, n ne,e, inin unitsunits ofof 101017cmcm-3− forfor different different fluence, fluence, 1064-nm 1064-nm excitation. excitation. 17 -3 Table 1. Electron2 densities, ne, in units of 10 cm for different fluence, 1064-nm excitation. LaserLaser Fluence Fluence (J/cm )(J/cm2)n e:Hne: αH656.28α 656.28 nm nm n nee: :Ag Ag I I 827.35 827.35 nm nm ne: Ag ne I: 768.7 Ag I 768.7 nm nm Laser9.94 Fluence9.94 (J/cm2) ne: H 1.64α1.64 656.28 nm ne: Ag1.66 1.66 I 827.35 nm ne: Ag1.76 I 768.7 1.76 nm 7.469.947.46 0.760.761.64 0.77 0.771.66 0.761.76 0.76 5.97.465.9 0.630.630.76 0.66 0.660.77 0.700.76 0.70 4.47 0.57 0.55 0.58 4.475.9 0.570.63 0.550.66 0.580.70 4.47 0.57 0.55 0.58 ThereThere is is excellent excellent agreement agreement ofof thethe measured electron electron density density from from the the H Hα andα and the the two two optically optically thin silver lines. The two silver lines Ag I at 827.35 and 768.7 nm are suitable for electron density thin silverThere lines. is excellent The two agreement silver lines of the Ag measured I at 827.35 electron and 768.7 density nm from are suitable the Hα and for electronthe two optically density determination in nano- and bulk- material for the following reasons: First, the Ag lines emerge from thin silver lines. The two silver lines Ag I at 827.35 and 768.7 nm are suitable for electron density determination in nano- and bulk- material for the following reasons: First, the Ag lines emerge from Atoms 2019, 7, 73 6 of 9 determination in nano- and bulk- material for the following reasons: First, the Ag lines emerge from Atomsthe upper 2019, 7, states x FOR 4dPEER106s-4d REVIEW105p with almost empty lower and highly excited state 4d106s that minimizes6 of 9 the possibility of plasma re-absorption by highly populated low atomic states. Second, both lines are theobserved upper states in emission 4d106s-4d spectra105p with of neutral almost silver empty under lower nearly and highly all conditions. excited state 4d106s that minimizes the possibilityThe experimental of plasma evaluationre-absorption included by highly change populated of the low incident atomic laser states. fluence Second, in the both range lines from are observed5 to 10 J /incm emission2 and measurement spectra of neutra of thel silver emission under spectra nearly during all conditions. IR laser irradiation. The lines are Voigt-fittedThe experimental to recorded evaluation spectral radiances included aschange indicated of the by incident the solid laser black fluence lines in in the Figure range6. Thefrom Stark 5 to 10broadening J/cm2 andparameters measurement for bothof the lines emissi areon archived spectra in during Stark tables IR laser [15 ]:irradiation. At the reference The lines electron are densityVoigt- ref 17 3 AgI AgI fittedof N eto =recorded10 cm −spectral, the Stark radiance broadenings as indicated parameter, by theω Ssolid, amounts black lines to ωinS Figure= 0.18 6. The0.06 Stark nm. AgI ± broadeningThe Lorentzian parameters components for both of the lines emitted are lines,archivedλS in, wereStark extracted. tables [15]: The At electron the reference densities electron listed in ref 17 −3 AgI AgIref AgI AgI AgI densityTable1 wereof Ne evaluated = 10 cm with, the the Stark help ofbroadening the expression, parameter, n e ωSNe , amounts(λ /ω to ωS), and = 0.18 then ± compared0.06 nm. ≈ S S Thewith Lorentzian the corresponding components values of the obtained emitted from lines, H αλ.SAgI, were extracted. The electron densities listed in Table For1 were analysis evaluated of the with self-absorbed the help spectraof the expression, in Figure2, n noticeeAgI ≈ N lineeref reversal(λSAgI/ωS atAgI the), and center then wavelength, compared with the corresponding values obtained from Hα. λ0, and weaker effects in the wings that lead to distortions. The transmittance [3,6], T(τλ0 ), is related to For analysis of the self-absorbed spectra in Figure 2, notice line reversal at the center wavelength, the escape factor [3,6] and it depends on the optical thickness of the plasma, τλ0 . λ0, and weaker effects in the wings that lead to distortions. The transmittance [3,6], T(τ , is related The transmittance, T(τλ0 ), is modeled with a Lorentzian spectral line shape, ϕ(λ), to the escape factor [3,6] and it depends on the optical thickness of the plasma, τ.   Z λ The transmittance, T(τ ), is modeledτλ ϕ(λ with)/ϕ0 a Lorentzian spectral1 line0.5 shape,∆ S φ(λ), T τλ = ϕ(λ)e− 0 dλ, ϕ(λ) = , (2) 0 π (λ λ )2 ( λ )2 / .0 + 0.5 ∆ S Tτ= φ λ e dλ, φ λ = − , (2) . where ∆λs denotes the full-width at half-maximum (FWHM) of the normalized spectral line shape of where Δλs denotes the full-width at half-maximum (FWHM) of the normalized spectral line shape of magnitude ϕ0 at line center. The plasma optical thickness at line center, τλ0 , 0 magnitude φ at line center. The plasma optical thickness at line center,τ, Z 0 τ = κλ dℓ, (3) τλ0 = ℓ κ(λ0)d`, (3) ` is defined in terms of integrated absorption coefficient,− κ (λ), of a spectral line measured along the κ λ is defined in terms of integrated absorption coe0 fficient, ( ), of a spectral line measured along the line-of-sight, ℓ, at the transition wavelength, λ . Figure 7 illustrates results for τ ranging from 0.25 line-of-sight, `, at the transition wavelength, λ . Figure7 illustrates results for τλ ranging from 0.25 to to 2 at equal steps of 0.25, and for fixed Lorentzian0 FWHM of Δλs = 0.5 nm. The0 line shape indicates 2 at equal steps of 0.25, and for fixed Lorentzian FWHM of ∆λs = 0.5 nm. The line shape indicates a flat a flat top for unity optical thickness, i.e., τ =1. For values higher than unity, self-absorption affects top for unity optical thickness, i.e., τ = 1. For values higher than unity, self-absorption affects the the line shape primarily at the center λ[2].0 line shape primarily at the center [2].

τ/ϕ(λ) ϕ Figure 7. Line shapes φλe λ0 / vs.0 wavelength, λ, for fixed Δλs = 0.5 nm. Values of τ range Figure 7. Line shapes ϕ(λ)e− vs. wavelength, λ, for fixed ∆λs = 0.5 nm. Values of τλ0 range fromfrom 0.25 0.25 to to 2.0 2.0 in in steps steps of of 0.25. 0.25.

TheThe fitting fitting of of the the argument argument in in Equation Equation (2) (2) to to the the experimentally experimentally measur measureded line line shape shape can can be be formulatedformulated with with two two line-shape line-shape parameters, parameters, na namely,mely, the the self-absorbed self-absorbed Lorentzian Lorentzian FWHM, FWHM, Δλ∆λS1S1, ,and and τ thethe optical optical depth, depth, τλ0,, at at line line center center [2]. [2]. The self-reversal parameter, SR, is introduced for a quantitative description of the measured line shapes. The parameter SR indicates the ratio of transmitted and of weakly (κ (λ) ℓ << 1) affected intensities at line center, Atoms 2019, 7, 73 7 of 9

The self-reversal parameter, SR, is introduced for a quantitative description of the measured line Atoms 2019, 7, x FOR PEER REVIEW 7 of 9 shapes. The parameter SR indicates the ratio of transmitted and of weakly (κ (λ) ` << 1) affected intensities at line center, τλ 1−1 ee− 0 SR == − 11 ,, (4) (4) τλ ≤ τ0 or in terms of the transmittance, SR = T(τλ0 ). Self-reversal diminishes the peak spectral radiance as or in terms of the transmittance, SR = T(τ). Self-reversal diminishes the peak spectral radiance as well. In In comparison with self-absorption, self-rev self-reversalersal causes causes further further appa apparentrent enlargement of the FWHM, ∆λ , with ∆λ > ∆λ . In analogy with the derivation of self-absorption [3], one can write FWHM, ΔλS2 S2 S1S1 , withα Δλ > Δλ . In analogy with the derivation of self-absorption [3], one can write ∆λS2 = ∆λS1 SR . The value for the exponent is taken to be α = –0.54, in analogy to previously Δλ =Δλ SR . The value for the exponent is taken to be α = –0.54, in analogy to previously reported self-absorptionreported self-absorption studies [3]. studies The [self-reversal3]. The self-reversal factor, SR, factor, is functionally SR, is functionally identical identical to that to for that the for self- the α self-absorption factor [3], SA, ∆λ = ∆λS0 SA . Here, ∆λ and ∆λS0 indicate the FWHM of spectral absorption factor [3], SA, Δλ = Δλ SA . Here, Δλ and ΔλS0 indicate the FWHM of spectral lines with lines with and without self-absorption, respectively. and without self-absorption, respectively. Figure 88 summarizessummarizes twotwo typicaltypical examplesexamples ofof thethe discusseddiscussed spectralspectral lineline shapeshape analysisanalysis forfor thethe measured Ag I lines at 327.9 and 338.2 nm. Figure Figure 88aa,d,d display self-reversed data,data, FigureFigure8 8b,eb,e portray portray corrected lines that are still self-absorbed, and Figu Figurere 88c,fc,f illustrateillustrate thethe retrievedretrieved line-shapesline-shapes whenwhen using data from the optically thin line at 827 nm.

Figure 8. Line shapes (a) self-reversed ΔλS2 = 0.37 nm, SR = 0.3, T(λ) = 33%; (b) Self-absorbed ΔλS1 = Figure 8. Line shapes (a) self-reversed ∆λS2 = 0.37 nm, SR = 0.3, T(λ) = 33%; (b) Self-absorbed 0.2∆λ nm,= n0.2e1 = nm, 4.2 × n 1018= cm4.2−3, SA10 =18 0.01;cm (3c,) Reconstructed SA = 0.01; (c) 327.9-nm Reconstructed optically 327.9-nm thin line: optically ΔλS0 = 0.017 thin line:nm, S1 e1 × − n∆e1λ = 3.5= 0.017× 1017 cm nm,−3, nSA == 1.3.5 (d) Δλ10S217 = 0.32cm 3nm,, SA SR= = 1.0.38, (d T() ∆λ)λ =40%,= 0.32 (e) Δλ nm,S1 =SR 0.19= nm,0.38, SA T( =λ 0.01,) = 40%, and S0 e1 × − S2 (fe)) 338.2-nm∆λ = 0.19 line: nm, Δλ SAS0 == 0.0170.01, nm, and n (fe1) = 338.2-nm 3.5 × 1017 line: cm−3∆, λSA = 1.0.017 Light nm, pulses n = for3.5 (a) 10and17 (cmd) of3, fluence SA = 1. S1 S0 e1 × − 13.5Light J/cm pulses2 at 355 for (nma,d) generated of fluence laser 13.5 Jplasma./cm2 at 355Reconstruction nm generated for laser (c) and plasma. (f) isReconstruction accomplished with for (c data,f) is fromaccomplished the 827-nm with line. data from the 827-nm line.

The measured widths and plasma transmission percentages (typically (typically 33% 33% and 40% for the reported experiments) are included in the figurefigure captions.captions. The theoretical, asymptotic form for the transmittance of a Lorentzian line profileprofile [2,6] [2,6] equals T τ ~ 1/ π τ T (τ ) 1/ √π τ (5)(5) theory SR ∼ SR The theoretical transmittances are compatible with SR factors of 0.32 and 0.38. The measured line shapesThe theoretical are well-described transmittances by are the compatible fitted Lorent withzians. SR factors However, of 0.32 for and sake 0.38. of The simplicity, measured this line shapes are well-described by the fitted Lorentzians. However, for sake of simplicity, this discussion discussion omits Gaussian components due to instrumental broadening of Δλinstrument ~0.12 nm. Figure omits Gaussian components due to instrumental broadening of ∆λ ~0.12 nm. Figure8a,d 8a,d show a significant reduction in intensity along with an apparentinstrument increase in broadening (ΔλS2). The self-reversal coefficients are relatively small (SR = 0.32 and SR = 0.38), but due to line center effects [2,5–10] dips occur. Noteworthy in this work, self-reversal (quantified by the coefficient SR) is almost independent of the laser fluence, but self-absorption (SA) changes monotonically with laser fluence. Atoms 2019, 7, 73 8 of 9

show a significant reduction in intensity along with an apparent increase in broadening (∆λS2). The self-reversal coefficients are relatively small (SR = 0.32 and SR = 0.38), but due to line center effects [2,5–10] dips occur. Noteworthy in this work, self-reversal (quantified by the coefficient SR) is almost independent of the laser fluence, but self-absorption (SA) changes monotonically with laser fluence. In this example, the self-reversal peak separation provides values for ∆λS2, using the FWHM of lines with the dip would cause even larger discrepancies for the electron density, ne. From Equation (5), computed ∆λS1 would show electron densities that are ~ ten times higher than obtained from the optically thin line that was retrieved by comparison with 827-nm results. When using lower fluence α levels for these two lines, larger variances occur in inferred ne values. From ∆λ = ∆λS0 SA , a factor of ten higher electron density means that the self-absorption factor is of the order of SA ~ 0.01. For self-absorption, the magnitude of the peak spectral irradiances can be evaluated [3] using I0(λ0) ~ I1(λ0)/SA, leading to two orders of magnitude higher irradiances. Such discrepancy indicates significant self-absorption and line reversal for the selected example.

4. Conclusions Self-absorption may lead to a decrease in the peak line intensity up to two orders of magnitude, including appearance of self-revered lines. Even after taking into consideration the line shape effects, occurrence of self-absorption for a measured line contraindicates plasma electron density and temperature measurements from that line. The experimentally measured transmission factors for the 327.9 and 338.2 nm lines change with incident laser fluence. The theoretical analysis predicts transmittance values consistent with the measured ones within the experimental margins of error. The optically thin, 827-nm silver line allows one to determine the electron density showing decreases as expected from 3.5 1017 to 1.1 1016 cm 3 with decreasing laser fluence. However, as self-absorption × × − of the silver 338.2 nm line decreases with decreasing fluence, the variations of inferred electron densities are larger than anticipated, or the 338.2 nm line shows a larger standard deviation than the 827 nm line. The Ag I line at 338.2 nm disappears for a laser fluence of 2.1 J/cm2. Finally, plasma opacity manifests itself as a combination of self-absorption and self-reversal effects, and line recovery would require results from an optically thin line, or in other words, self-absorbed or self-reversed lines are ill-suited as electron density diagnostic of laser plasma.

Author Contributions: A.M.E.S. conceived and performed the experiments. A.M.E.S. analyzed the result together with C.G.P., and all authors contributed to the writing of the article. Funding: This research received no external funding. Conflicts of Interest: The authors declare no conflict of interest.

References

1. Eidmann, K.; Sigel, R. Second-Harmonic Generation in an Inhomogeneous Laser-Produced Plasma. Phys. Rev. Lett. 1975, 34, 799–802. [CrossRef] 2. Fujimoto, T. Plasma Spectroscopy; Clarendon Press: Oxford, UK, 2004. 3. El Sherbini, A.M.; El Sherbini, T.M.; Hegazy, H.; Cristoforetti, G.; Legnaioli, S.; Palleschi, V.; Pardini, L.; Salvetti, A.; Tognoni, E. Evaluation of self-absorption coefficients of aluminum emission lines in laser-induced breakdown spectroscopy measurements. Spectrochim. Acta Part B At. Spectrosc. 2005, 60, 1573–1579. [CrossRef] 4. Parigger, C.G.; Surmick, D.M.; Gautam, G.; El Sherbini, A.M. Hydrogen alpha plasma diagnostic. Opt. Lett. 2015, 40, 3436–3439. [CrossRef][PubMed] 5. Parigger, C.G.; Surmick, D.M.; Gautam, G. Self-absorption characteristics of measured laser-induced line shapes. J. Phys. Conf. Ser. 2017, 810, 012012. [CrossRef] 6. Irons, F.E. The escape factor in plasma spectroscopy—I. The escape factor defined and evaluated. J. Quant. Spectrosc. Radiat. Transf. 1979, 22, 1–20. [CrossRef] 7. Holstein, T. Imprisonment of Resonance Radiation in Gases. Phys. Rev. 1947, 72, 1212–1232. [CrossRef] Atoms 2019, 7, 73 9 of 9

8. Holstein, T. Imprisonment of Resonance Radiation in Gases. II. Phys. Rev. 1951, 83, 1159–1168. [CrossRef] 9. Cowan, R.D.; Dieke, G.H. Self-Absorption of Spectrum Lines. Rev. Mod. Phys. 1948, 20, 418–455. [CrossRef] 10. Kielkopf, J.F.; Allard, N.F. Shift and width of the Balmer series Hα line at high electron density in a laser-produced plasma. J. Phys. B At. Mol. Opt. Phys. 2014, 47, 155701. [CrossRef] 11. Moon, H.-Y.; Herrera, K.K.; Omenetto, N.; Smith, B.W.; Winefordner, J.D. On the usefulness of a duplicating mirror to evaluate self-absorption effects in laser induced breakdown spectroscopy. Spectrochim. Acta Part B At. Spectrosc. 2009, 64, 702–713. [CrossRef] 12. EL Sherbini, A.M.; Parigger, C.G. Wavelength dependency and threshold measurements for nanoparticle-enhanced laser-induced breakdown spectroscopy. Spectrochim. Acta Part B At. Spectrosc. 2016, 116, 8–15. [CrossRef] 13. EL Sherbini, A.M.; Parigger, C.G. Nano-material size dependent laser-plasma thresholds. Spectrochim. Acta Part B At. Spectrosc. 2016, 124, 79–81. [CrossRef] 14. El Sherbini, A.M.; Hagrass, M.M.; Rizk, M.R.M.; El-Badaway, E.A. Plasma ignition threshold disparity between silver nanoparticle-based target and bulk silver target at different laser wavelengths. Plasma Sci. Technol. 2019, 21, 015502. [CrossRef] 15. Dimitrijevi´c,M.S.; Sahal-Bréchot, S. Stark broadening of Ag I spectral lines. At. Data Nucl. Data Tables 2003, 85, 269–290. [CrossRef]

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