Generation of Ultrabroad and Intense Supercontinuum in Mixed Multiple Thin Plates

hv photonics

Communication Generation of Ultrabroad and Intense Supercontinuum in Mixed Multiple Thin Plates

Jing Li, Wenjiang Tan *, Jinhai Si, Zhen Kang and Xun Hou

Key Laboratory for Physical Electronics and Devices of the Ministry of Education, Shaanxi Key Lab of Information Photonic Technique, School of Electronic Science and Engineering, Xi’an Jiaotong University, Xi’an 710049, China; [email protected] (J.L.); [email protected] (J.S.); [email protected] (Z.K.); [email protected] (X.H.) * Correspondence: [email protected]

Abstract: Supercontinuum (SC) generation using multiple thin plates is demonstrated with a femtosecond laser pulse. We propose an improved technique to obtain larger spectrum broadening and higher spectral intensity by employing mixed multiple thin plates with different thicknesses and materials. Furthermore, the spectrum has good stability, which is superior to that of the spectrum induced by the traditional single ﬁlament in bulk material. Our approach offers a route towards simple and stable SC generation for potential applications.

Keywords: femtosecond laser; supercontinuum generation; spectral broadening; multiple thin plates

1. Introduction SC generation is a universal phenomenon produced by the nonlinear propagation of intense femtosecond laser pulses in a transparent medium [1]. SC is characterized by an extremely broad spectrum with frequencies ranging from infrared to ultraviolet. The Citation: Li, J.; Tan, W.; Si, J.; Kang, underlying physics of filament-induced SC generation appears to be a complex process Z.; Hou, X. Generation of Ultrabroad that involves a dynamic interplay of spatial and temporal effects: self-focusing, self-phase and Intense Supercontinuum in modulation, self-steepening, group velocity dispersion, and multiphoton absorption [2–6]. Mixed Multiple Thin Plates. Photonics SC has attracted significant research interest in diverse fields owing to its advantages of 2021, 8, 311. https://doi.org/ ultrabroadband radiation, high spectral brightness, and high spatial coherence, which 10.3390/photonics8080311 are equivalent to those of white-light lasers. It has found wide application in optical frequency combs [7], biomedical imaging [8], molecular fingerprint spectroscopy [9], and Received: 21 June 2021 the generation of few-cycle femtosecond pulses [10]. Accepted: 27 July 2021 In recent years, there have been many ways to generate an ultrabroadband SC. For Published: 3 August 2021 instance, a femtosecond laser pulse is injected into inert-gas-filled hollow-core fibers. This method could enable the compression of pulses with high compression ratios and better Publisher’s Note: MDPI stays neutral spatial modes [11,12]. However, it has some inherent drawbacks, such as low efficiency of with regard to jurisdictional claims in fiber coupling and complexity of adjustment of the experimental apparatus. In addition, published maps and institutional affil- SC can be efficiently generated in a solid-state material due to its higher nonlinear index iations. of refraction. It is a simple and robust method to broaden the spectrum. However, when the peak power of the laser pulse is sufficiently high, self-focusing and multiphoton ionization result in optical breakdown and permanent damage to the material. More recently, a novel technique that generates SCs with multiple thin plates has attracted Copyright: © 2021 by the authors. much attention [13–16]. This technique effectively circumvents energy loss and optical Licensee MDPI, Basel, Switzerland. breakdown. It has been reported in nearly one octave-spanning spectrum ranging and a This article is an open access article few-millijoule pulse energy [17,18]. Different applications place differing demands on the distributed under the terms and characteristics of the SC spectrum. For example, the spectral coherence and a broad spectral conditions of the Creative Commons range are the key factors in pulse compression. In the application of femtosecond transient Attribution (CC BY) license (https:// absorption spectroscopy, high intensity of shortwave components will provide a broad creativecommons.org/licenses/by/ 4.0/). spectral detection range, and better spectral stability will improve the detection sensitivity.

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transient absorption spectroscopy, high intensity of shortwave components will provide a broad spectral detection range, and better spectral stability will improve the detection sensitivity. In addition to supercontinuum generation, the use of thin plates makes it possible to perform more complex manipulations with high-energy ultrashort pulses. A new concept of using thin plates was proposed for spectral broadening with subsequent temporal compression of ultrashort pulses having energy as high as a few hundred Joules [19]. An experiment was reported in which the successful compression of high-energy laser pulses was achieved [20]. The measured spectrum broadening in thin plates together with the fundamental spectrum also allows the reconstruction of the pulse intensity and phase [21].

Photonics 2021, 8, 311 In this paper, we experimentally investigated the generation2 of 8 of SC by mixing multiple thin plates. The broadening and intensity of the SC spectrum in the short-wavelength region was further enhanced through a set of multiple thin plates with different thick- In addition to supercontinuum generation, the use of thin plates makes it possible to nessesperform and more materials. complex manipulations with high-energy ultrashort pulses. A new concept of using thin plates was proposed for spectral broadening with subsequent temporal 2.compression Experiments of ultrashort pulses having energy as high as a few hundred Joules [19]. An experiment was reported in which the successful compression of high-energy laser pulses was achievedThe experimental [20]. The measured apparatus spectrum broadeningof SC generation in thin plates in together multiple with thethin plates is illustrated in Figurefundamental 1. A spectrum Ti:sapphire also allows femtosecond the reconstruction laser of the system pulse intensity operating and phase with [21]. a pulse duration of 50 fs In this paper, we experimentally investigated the generation of SC by mixing multiple andthin central plates. The wavelength broadening and of intensity 800 nm of at the a SCrepetition spectrum in rate the short-wavelengthof 1 kHz was used in our experiment. Aregion neutral was further density enhanced filter through placed a set in of multiplethe beginni thin platesng with was different used thicknesses to control the average power of and materials. the laser beam to obtain a suitable energy per pulse of 520 µJ. The beam diameter was approximately2. Experiments 10 mm. The output pulse was loosely focused onto a set of fused silica thin The experimental apparatus of SC generation in multiple thin plates is illustrated in platesFigure1 with. A Ti:sapphire a convex femtosecond lens (f = laser 2000 system mm). operating The diameter with a pulse durationof the focal of 50 fs point was approximately 410and µm central at wavelength the 1/e of2 width 800 nm at measured a repetition rate by of 1the kHz knife-edge was used in our method. experiment. The peak intensity was approximatelyA neutral density filter 7.9 placed× 1012 in theW/cm beginning2 at the was usedfocal to controlpoint. the The average fused power silica thin plates (Beijing of the laser beam to obtain a suitable energy per pulse of 520 µJ. The beam diameter was Zhongapproximately Cheng 10 mm.Quartz The output Glass pulse Co., was Ltd., loosely BJ, focused CHN) onto used a set of in fused our silica paper thin were squares with sides ofplates 20 mm with aand convex thicknesses lens (f = 2000 mm). of 120 The diameterµm and of 200 the focal µm. point These was approximately plates were placed at the waist of 410 µm at the 1/e2 width measured by the knife-edge method. The peak intensity was theapproximately beam at the 7.9 × Brewster1012 W/cm2 angleat the focal (55.5°) point. to The redu fusedce silica the thin Fresnel plates (Beijingreflection loss at the surfaces. TheZhong generated Cheng Quartz SC Glass spectrum Co., Ltd., Beijing,was collected China) used by in our a paperlens wereon squaresa fiber-coupled spectrometer with sides of 20 mm and thicknesses of 120 µm and 200 µm. These plates were placed at (Oceanthe waist Optics of the beam HR at 4000). the Brewster A filter angle (55.5was◦) toused reduce in the front Fresnel of reflection the spectrometer loss to suppress the fundamentalat the surfaces. Thefrequency generated SClight spectrum at a center was collected wavelength by a lens on of a fiber-coupled800 nm. spectrometer (Ocean Optics HR 4000). A filter was used in front of the spectrometer to suppress the fundamental frequency light at a center wavelength of 800 nm.

Figure 1. Schematic of the experimental setup (NDF: neutral density ﬁlter).

Figure3. Results 1. Schematic and Discussion of the experimental setup (NDF: neutral density filter). Firstly, seven 120 µm thin fused silica plates were applied for SC generation. The 3.first Results thin plate and was Discussion placed 20 cm before the focus of the lens, and the average power was approximately 489 mW after the plate. The spacing between these thin plates was 8 cm, 10 cm,Firstly, 5 cm, 2.5 cm,seven 2.5 cm, 120 2.5 µm cm, respectively. thin fused The silica positions plates of the plateswere were applied determined for SC generation. The first thinby obtaining plate was the broadest placed transmitted 20 cm before spectrum the after focus each plate ofwithout the lens, optical and damage. the average power was ap- The thin plates should be placed in sequence, resulting in the best spectrum broadening. As proximatelythe laser passes through489 mW the thin after plate, the the self-focusingplate. The effect spacing causes thebetween laser beam these to form thin plates was 8 cm, 10 cm,a focal 5 cm, point 2.5 in the cm, air. 2.5 It should cm, be2.5 noted cm, that respectively. the next thin plate The should positions be placed of away the plates were determined from the focal point to effectively avoid material damage. The beam diameter was increased byafter obtaining the seventh plate,the broadest leading to a reductiontransmitted in peak power.spectrum When more after120- eachµm-thin platefused without optical damage. Thesilica thin plates plates were added, should the width be placed of the spectrum in sequence ceased to broaden., resulting The average in the power best spectrum broadening. Asafter the the laser second passes to seventh through plates was the 480 thin mW, 473plate, mW, 458the mW, self-focusing 448 mW, 437 mW, effect and causes the laser beam to 428 mW, respectively. To understand the process of spectrum broadening, the fundamental formspectrum a focal and thepoint SC spectrum in the afterair. eachIt should plate were be recorded,noted that as shown the innext Figure thin2. plate should be placed awayIt was from observed the that focal the broadened point to spectra effectively in the first av threeoid platesmaterial were symmetricdamage. to The beam diameter was the fundamental spectrum, which coincided with the process of self-phase modulation. increasedHowever, the after spectra the were seventh significantly plate, broadened leading from theto fourtha reduction to seventh in thin peak plates, power. When more 120- µm-thinas shown infused Figure silica2b. The plates primary we mechanismre added, responsible the width for spectral of the broadening spectrum was ceased to broaden. The averagethe nonlinear power phase after accumulation the second pass through to seventh the plate, plates leading towas pulse 480 self-steepening. mW, 473 mW, 458 mW, 448 mW, 437 mW, and 428 mW, respectively. To understand the process of spectrum broadening, the fundamental spectrum and the SC spectrum after each plate were recorded, as shown

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in Figure 2. It was observed that the broadened spectra in the first three plates were sym- metric to the fundamental spectrum, which coincided with the process of self-phase modulation. However, the spectra were significantly broadened from the fourth to seventh thin plates, as shown in Figure 2b. The primary mechanism responsible for spectral broad-

Photonicsening2021, 8 ,was 311 the nonlinear phase accumulation pass through the plate, leading to pulse3 self- of 8 steepening. As a comparison, the supercontinnum generation in an 840 µm fused silica plate without filamentation was also investigated. The thickness of this plate was equivalent to the sum of theAs aseven comparison, thin plates the supercontinnum mentioned generation above. inTo an avoid 840 µm the fused filamentation, silica plate without this single plate was placedﬁlamentation 25 cm wasbefore also investigated.the focal point, The thickness and the of thisSC platespectrum was equivalent is shown to the by sum the of the seven thin plates mentioned above. To avoid the ﬁlamentation, this single plate was red dotted line in Figureplaced 252b. cm The before output the focal average point, and power the SC spectrumwas approximately is shown by the 455 red dotted mW. lineThe spectral width inducedin Figure by2 b.the The single output averageplate was power narrower was approximately than that 455 mW.of the The multiple spectral width thin plates due to the lowerinduced input by the laser single intensity. plate was narrower than that of the multiple thin plates due to the lower input laser intensity.

(a) (b)

Figure 2. 2.Spectra Spectra passing passing through through the fused silicathe fused plates. Thesilica “0 piece”plates. indicates The “0 fundamental piece” indicates spectrum. fundamental Red dotted line spec- representstrum. Red the dotted spectrum line generated represents from the the single spectrum 840 µm plate. gene Eachrated spectrum from was the normalized single 840 by its µm maximum plate. value. Each spectrum was normalized by itsWe maximum compared the value. effect of different thicknesses in multiple thin plates on spectral broadening. The spectrum of SC generation with 120 µm and 200 µm thin fused silica plates We compared isthe shown effect in Figure of different3. Seven plates thickne with thesses same in thickness multiple were thin strategically plates placedon spectral at the broadening. The spectrumwaist position of ofSC the generation incident laser with beam. 120 It was µm observed and that200 a µm broader thin spectrum fused couldsilica be obtained with seven pieces of 120 µm thin fused silica plates, and the ﬁnal spectrum plates is shown in Figureextended 3. toSeven approximately plates with 490 nm the in thesame short-wavelength thickness were region. strategically However, the placed cutoff at the waist positionwavelength of the incident in the short-wavelength laser beam. regionIt was was observed approximately that 520a broader nm for 200 spectrumµm thin µ could be obtained withplates. seven In the coursepieces of of the 120 experiment, µm thin it wasfused found silica that plates, 200 mthin and plates the werefinal easily spec- damaged and had poor stability. Essentially, there was a longer optical path inside the trum extended to approximatelythicker plates, which 490 was nm more in pronethe short-wavelength to energy loss from multiphoton region. However, ionization and the cutoff wavelength inoptical the damage,short-wavelength resulting in less region spectral was broadening. approximately However, 520 a thinner nm for plate 200 has µm a thin plates. In the courseshorter optical of the path, experiment, which avoids theseit was disadvantageous found that factors 200 butµm provides thin plates very limited were self-phase modulation. Self-phase modulation is usually characterized by the B-integral. easily damaged and had poor stability.2π R L Essentially, there was a longer optical path inside It is deﬁned as B = λ 0 n2 Idz, where λ is the central wavelength, n2 is the nonlinear the thicker plates, whichrefraction was index, moreI is prone the intensity to energy of incident loss light, fromz ismultiphoton the coordinate ionization along the beam and optical damage, resultingdirection, andin lessL is thespectral thickness broadening. of Kerr medium. However, When the optical a thinner intensity plate is constant, has a the B-integral increases with the propagation distance. The nonlinear refractive index for shorter optical path,fused which silica avoids is 2.4 × 10 these−16 cm disa2/W.dvantageous The estimated value factors of the but B-integral provides is approximately very limited self-phase modulation.3.0 for the 200 Self-phaseµm thin plate modula and 1.8 fortion the is 120 usuallyµm thin characterized plate in our experiment. by the Thus, B-inte- the accumulation2π L of self-phase modulation for the 200 µm thin plate is 1.67 times that of the gral. It is defined as = , where λ is the central wavelength, n2 is the nonlinear BnIdzµ 2 120 m plate.λ 0 We infer that if a set of thin plates with different thicknesses was employed, the SC spectrum would have a more expanded range. refraction index, I is the intensity of incident light, z is the coordinate along the beam di- rection, and L is the thickness of Kerr medium. When the optical intensity is constant, the B-integral increases with the propagation distance. The nonlinear refractive index for fused silica is 2.4 × 10−16 cm2/W. The estimated value of the B-integral is approximately 3.0 for the 200 µm thin plate and 1.8 for the 120 µm thin plate in our experiment. Thus, the accumulation of self-phase modulation for the 200 µm thin plate is 1.67 times that of the 120 µm plate. We infer that if a set of thin plates with different thicknesses was employed, the SC spectrum would have a more expanded range.

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Figure 3. SC spectra after the laser beam propagated through the fused silica thin plates. Each Figurespectrum 3. 3. SCwas SC spectra normalizedspectra after after by the its the laser maximum laser beam beampropagated value. propagated through thro theugh fused the silica fused thin silica plates. thin Each plates. Each spec- spectrumtrum was was normalized normalized byby its its maximum maximum value. value. Normally, the diameter of the spot gradually increased as the number of insetting Normally, the diameter of the spot gradually increased as the number of insetting plates increased, while the peak power density of the laser decreased. Therefore, it is platesNormally, increased, while the diameter the peak power of the density spot ofgradua the laserlly decreased.increased Therefore,as the number it is of insetting advantageous to inset a thicker plate in the back. This can not only accumulate a greater advantageousplates increased, to inset while a thicker the platepeak in power the back. density This can of not the only laser accumulate decreased. a greater Therefore, it is ad- effectvantageouseffect ofof self-phaseself-phase to inset modulationmodulation a thicker butbut alsoalsoplate avoidavoid in somethesome back. adverseadverse This nonlinearnonlinear can not influences,influences, only accumulate andandit it a greater can finally contribute to further spectrum broadening. To provide a better comparison, caneffect finally of self-phase contribute to modulation further spectrum but broadening. also avoid To some provide adverse a better comparison,nonlinear theinfluences, and it sevenththe seventh thin plate thin was plate replaced was replaced with a 200 withµm a thin 200 plate μm based thin plate on the based above on experiments. the above Itcanexperiments. is necessaryfinally contributeIt to is adjust necessary the to positionto further adjust of the spectrum the position new inset ofbroadening. the plate new to inset broaden To plate provide the to spectrumbroaden a better the as comparison, muchthespectrum seventh as possible. as muchthin After plate as possible. passing was replaced After through passing allwith the throu plates,a 20gh0 µm all the the spectrathin plates, plate were the based measured, spectra on were the as above experi- shownments.measured in It Figure, isas necessaryshown4a. Thein Figure spectrato adjust 4a. were The the spectra broader position were than ofbroader those the new of than the insetthose seven ofplate plates the sevento with broaden plates the the spectrum sameaswith much thickness,the same as possible. thickness, which extended Afterwhich to passingextended 470 nm in throughto the 470 short-wavelength nm all in the shortplates, region.-wavelength the In spectra addition, region. were the In measured, as addition, the spectral intensity was significantly increased in the range from 470 nm to spectralshown intensityin Figure was 4a. significantly The spectra increased were in broader the range th froman those 470 nm of to the 650 nmseven compared plates with the same to650 that nm of compared the seven to 120 thatµm of plates. the seven Figure 1204 bμm shows plates. a color Figure photographic 4b shows a imagecolor photographic of the beam profilethickness,image inof thethe whichfar beam field profileextended that was in takenthe to far 470 by field anm digital that in the camera.was sh takenort-wavelength The by most a digital striking camera. region. feature The isIn a mostaddition, red the spec- ringtralstriking surroundingintensity feature wasis a a white red significantly ring circular surro centralunding increased area. a white in circular the range central from area. 470 nm to 650 nm compared to that of the seven 120 µm plates. Figure 4b shows a color photographic image of the beam profile in the far field that was taken by a digital camera. The most striking feature is a red ring surrounding a white circular central area.

(a) (b)

FigureFigure4. 4.( (aa)) SCSC spectrum spectrum afterafter thethe laserlaser beam beam propagated propagated throughthrough aa set set of of thin thin plates plates with with mixed mixed thickness.thickness. ((bb)) TheThe imageimage ofof outputoutput beambeam proﬁle.profile.

WeWe furtherfurther analyzedanalyzed thethe influenceinfluence ofof mixedmixed thinthin platesplates withwith differentdifferent materials materials andand thicknessesthicknesses onon spectralspectral broadening.broadening. Usually,Usually, a a thin thin plate plate of of fused fused silica silica is is used used to to generategenerate SC.SC. The The material material of theof the thin (a thin plates) plates is not is confined not confined to fused to silica. fused Because silica. fluoride Because(b materials ) fluoride havematerials a large have bandgap, a large it bandgap, is possible it tois furtherpossible broaden to further the broaden spectrum the to spectrum the short-wavelength to the short- side.Figurewavelength However, 4. (a )side. SC it spectrumHowever, is susceptible itafter is tosusceptible the optical laser damage beamto optical propagated owing damage to the owing through low damageto thea set low thresholdof damage thin plates with mixed ofthickness.threshold fluoride of material(b ) fluoride The image [22 material]. We of surmisedoutput [22]. Webeam that surmised aprofile. plate with that fluoride a plate withmaterials fluoride placed materials at the placed at the back of multiple thin plates would expand the spectrum to a greater degree. Then,We we further continued analyzed to insert athe 1-mm influence-thick CaF of2 mixedplate ((111), thin Unionplates Optic with Inc different., WUH, materials and thicknesses on spectral broadening. Usually, a thin plate of fused silica is used to generate SC. The material of the thin plates is not confined to fused silica. Because fluoride materials have a large bandgap, it is possible to further broaden the spectrum to the short-wavelength side. However, it is susceptible to optical damage owing to the low damage threshold of fluoride material [22]. We surmised that a plate with fluoride materials placed at the back of multiple thin plates would expand the spectrum to a greater degree. Then, we continued to insert a 1-mm-thick CaF2 plate ((111), Union Optic Inc., WUH, CHN) based

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back of multiple thin plates would expand the spectrum to a greater degree. Then, we on the broadened continuedspectrum to of insert the combined a 1-mm-thick pl CaFates2 withplate ((111),different Union thicknesses. Optic Inc., Wuhan,It should China) based be noted that the CaFon the2 plate broadened was placed spectrum at a distance of the combined of approximately plates with 10 different cm from thicknesses. the last It should fused silica plate tobe avoid noted optical that the damage. CaF2 plate The was position placed of at the a distance new inset of approximatelyplate was adjusted 10 cm from the so that the spectrumlast was fused as silica broad plate as possible. to avoid opticalThe recorded damage. spectra The position are shown of the in new Figure inset plate was 5. The spectrum wasadjusted obviously so that broadened the spectrum to was approximately as broad as possible. 430 nm The in the recorded short-wave- spectra are shown in Figure5. The spectrum was obviously broadened to approximately 430 nm in the length region. Moreover, the intensity of short-wavelength components in the range of short-wavelength region. Moreover, the intensity of short-wavelength components in the 430 nm to 600 nm rangewas greatly of 430 nmincreased. to 600 nm As was a comparison, greatly increased. a 1-mm-thick As a comparison, fused silica a 1-mm-thick plate fused was inserted. The silicaspectrum plate wasno longer inserted. broadened, The spectrum as shown no longer by broadened, the green asline shown in Figure by the 5. green line in In fact, CaF2 had aFigure higher5. Innonlinear fact, CaF 2refractivehad a higher index nonlinear and lower refractive critical index power and lower of self-fo- critical power of cusing [23]. In termsself-focusing of the results [23]. shown In terms in of Figure the results 2, more shown self-phase in Figure 2modulation, more self-phase might modulation be accumulated throughmight be multiple accumulated thinner through CaF2 multipleplates as thinner opposed CaF to2 plates those as that opposed are 1-mm- to those that are thick. If there are thinner1-mm-thick. CaF2 If plates, there are further thinner broadening CaF2 plates, to further wavelengths broadening less tothan wavelengths 400 nm less than 400 nm could be achieved by inserting multiple CaF plates. could be achieved by inserting multiple CaF2 plates. 2

(a) (b)

FigureFigure 5. SC spectrum5. SC spectrum after the after laser the beam laser propagated beam propagated through a through set of mixed a set thin of mixed plates withthin differentplates with materials dif- and thickness.ferent (a )materials Spectra on and a log thickness. scale; (b) Spectra(a) Spectra on a on linear a log scale. scale; (b) Spectra on a linear scale.

The stability of theThe SC stability spectrum of theis an SC im spectrumportant isfactor an important in many factorapplications. in many We applications. in- We vestigated the stabilityinvestigated of the SC the spectrum stability of thein our SC spectrumexperiment, in our which experiment, is crucial which in transient is crucial in transient absorption spectroscopy.absorption In general, spectroscopy. SC is In generated general, SC by is a generated single filament by a single in bulk filament media in bulk in media in most experiments. Thus, a piece of fused silica with the size of 15 mm × 15 mm × 10 mm most experiments.was Thus, used a piece to induce of fused a single sili filamentca with the for comparison.size of 15 mm The × spectra15 mm of× 10 SC mm obtained from was used to inducethe a single bulk fused filament silica for and comp the mixedarison. multiple The spectra thin plates of SC are obtained shown from in Figure the6 a. It was bulk fused silica andobserved the mixed that the multiple spectral intensitythin plates and broadeningare shown forin theFigure bulk 6a. fused It silicawas wasob- inferior to served that the spectralthat for intensity the mixed and multiple broadeni thinng plates. for the A color bulk photographic fused silica was image inferior of the SCto generated that for the mixedfrom multiple the bulk thin fused plates. silica A color was recorded photographic by a digital image camera of the and SC isgenerated shown in Figure6b . from the bulk fusedThe silica transverse was recorded section of by the a beam digital image camera reveals and a typicalis shown conical in Figure emission 6b. pattern. A The transverse sectioncentral of white the beam core wasimage surrounded reveals a by typical colored conical Newton’s emission rings appearingpattern. A in an order central white coreopposite was surrounded to diffraction. by colore Furthermore,d Newton’s the spectral rings appearing stability that in wean measuredorder op- in multiple thin plates was compared to the case of a single filament generated in bulk fused silica. posite to diffraction. Furthermore, the spectral stability that we measured in multiple thin A series of spectra were collected by the spectrometer for 10 min with an acquisition plates was comparedinterval to the time case of of 6 s.a single The spectral filament integral generated intensity in bulk was calculatedfused silica. and A normalized series by its of spectra were collectedmaximum by value.the spectrometer The fluctuations for 10 of min SC arewith represented an acquisition by the interval difference time between the of 6 s. The spectralnormalized integral spectralintensity integral was calculated intensity and and its meannormalized value. Theby spectralits maximum fluctuations with value. The fluctuationscollection of SC time are are represente shown in Figured by 7the. The difference spectrum between induced by the a singlenormalized filament exhibited spectral integral intensitysmall fluctuations, and its mean while, value. in the The case ofspectral multiple fluctuations thin plates, with it was collection relatively stable. In addition, the standard deviation (SD) was used to quantitatively evaluate the stability of time are shown in Figure 7. The spectrum induced by a singleq filament exhibited small N 2 fluctuations, while,the in SC the spectrum. case of multiple The SD was thin defined plates, as it σwas= relatively∑i=1 Ii − stable.I /N, In where addition,N is the number the standard deviation (SD) was used to quantitatively evaluate the stability of the SC N 2 spectrum. The SD was defined as σ =−()I IN, where N is the number of spectra i=1 i collected, Ii indicates each normalized spectral integral intensity, and Ī is the average value of the normalized spectral integral intensity. As the value of SD is smaller, the spectrum is more stable. The SDs of the spectra induced by bulk media, multiple thin plates, and

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¯ ofthe spectra spectrum collected, is moreIi indicates stable. The each SDs normalized of the spectra spectral induced integral by intensity, bulk media, and I ismultiple the thin Photonics 2021, 8, x FOR PEER REVIEW average value of the normalized spectral integral intensity. As the value of SD is smaller,6 of 8 plates, and the fundamental frequency light were calculated to be 0.0398, 0.0285, and the spectrum is more stable. The SDs of the spectra induced by bulk media, multiple 0.0149, respectively. The results indicate that the spectrum induced by multiple thin plates thin plates, and the fundamental frequency light were calculated to be 0.0398, 0.0285, and shows better stability, which is 40 percent higher than that of the spectrum induced by a the0.0149, fundamental respectively. frequency The results light were indicate calculated that the to spectrum be 0.0398, induced 0.0285, by and multiple 0.0149, thin respec- plates single filament in bulk media. The reason is as follows. As is well known, SC generation tively.shows The better results stability, indicate which that the is 40 spectrum percent higherinduced than by multiple that of the thin spectrum plates shows induced better by a stability,singleis a complex filamentwhich is nonlinear in40 bulkpercent media. opticalhigher The than process. reason that isof The as the follows. intensityspectrum As inducedstability is well known, by of a SC single SCwill generationfilament be influenced by in isthebulk a complexnonlinear media. nonlinearThe amplification reason optical is as process.follows.of the input TheAs is intensity pulsewell known, fluctuations. stability SC ofgeneration SC In will terms be is influenced ofa complexthe SC bygeneration nonlinearthemechanism, nonlinear optical amplification theprocess. SC induced The ofintensity the by input the stability pulse thin fluctuations.of plates SC will almost be influenced In terms originated of by the the SCfrom nonlinear generation pure self-phase amplificationmechanism,modulation, of the thewhile SC input induced the pulse SC byinduced fluctuations. the thin by plates bulk In terms almostmedia of theoriginatedmight SC generationbe fromaffected pure mechanism, by self-phase many nonlinear themodulation,optical SC induced processes while by the the besidesthin SC inducedplates the almost by self bulk- phaseoriginated media modulation. might from bepure affected Thus,self-phase by the many modulation, stability nonlinear of the SC optical processes besides the self-phase modulation. Thus, the stability of the SC generated whilegenerated the SC inducedfrom the by multiple bulk media thin might plates be might affected be byshot many-noise nonlinear-limited optical and better pro- than that from the multiple thin plates might be shot-noise-limited and better than that of the SC cesses besides the self-phase modulation. Thus, the stability of the SC generated from the generatedof the SC fromgenerated bulk media. from bulk media. multiple thin plates might be shot-noise-limited and better than that of the SC generated from bulk media.

(a) (a) (b(b) ) FigureFigureFigure 6. ( 6. a6.) (SC a(a)) SCspectra SC spectra spectra generated generated generated from from the from bulk the the bulk fused bulk fused si licafused silica and silica the and mixed and the mixedthe multiple mixed multiple thin multiple plates. thin plates. thin(b) plates. (b) Image(Imageb) Image of the of ofSCthe the beam SC SC beam beamprofile profile proﬁle in the in inbulk thethe fused bulk bulkfused silica. fused silica. silica.

Figure 7. Fluctuation of normalized spectral integral intensity with collection time. σ is the standard Figure 7. Fluctuation of normalized spectral integral intensity with collection time. σ is the standard deviationdeviation of ofnormalized normalized spectral spectral integral integral intensity. intensity. Figure 7. Fluctuation of normalized spectral integral intensity with collection time. σ is the standard 4. Conclusionsdeviation of normalized spectral integral intensity. In summary, we have demonstrated a technique using multiple thin plates to gener- ate4. a Cmoreonclusions intense and broader SC spectrum. This is achieved by a set of solid thin plates with differentIn summary, thicknesses we and have materials. demonstrated The spectrum a te intensitychnique and using spectrum multiple broaden- thin plates to generate a more intense and broader SC spectrum. This is achieved by a set of solid thin plates with different thicknesses and materials. The spectrum intensity and spectrum

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4. Conclusions In summary, we have demonstrated a technique using multiple thin plates to generate a more intense and broader SC spectrum. This is achieved by a set of solid thin plates with different thicknesses and materials. The spectrum intensity and spectrum broadening in the short-wavelength region were significantly increased compared to those of traditional thin plates with identical thicknesses and materials. Furthermore, the spectrum exhibited excellent stability, which is superior to that of the spectrum induced by the single filament. Our results indicate that mixing multiple thin plates might be an interesting substitute for other SC generation techniques. For instance, when SC was generated in bulk material, the spectral broadening and intensity were insufficient. The results can be utilized in a wide range of applications, including femtosecond transient absorption spectroscopy, high-resolution investigation of ultrafast phenomena, and the generation of bright isolated attosecond pulses.

Author Contributions: Conceptualization, J.S. and W.T.; validation, J.S. and W.T.; investigation, J.L and Z.K.; resources, W.T.; writing—original draft preparation, J.L.; writing—review and editing, W.T. and J.L.; visualization, J.L.; supervision, X.H. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by the National Natural Science Foundation of China, grant number 62027822 and 61690221; the National Key Research and Development Program of China, grant number 2019YFA0706402; the Natural Science Basic Research Plan in Shaanxi Province of China, grant number 2018JM6012, and the Fundamental Research Funds for the Central Universities, grant number xzy012019039. Data Availability Statement: Data sharing is not applicable. Conﬂicts of Interest: The authors declare no conﬂict of interest.

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