Development of a Thulium Fiber Laser for an Atomic Spectroscopy Experiment

Home , Fiber laser, Output coupler, Thulium

fibers

Article Development of a Thulium Fiber Laser for an Atomic Spectroscopy Experiment

Ronnie Currey *, Ali Khademian and David Shiner

Department of Physics, University of North Texas, Denton, TX 76203, USA; [email protected] (A.K.); [email protected] (D.S.) * Correspondence: [email protected]

Received: 20 December 2019; Accepted: 9 February 2020; Published: 15 February 2020

Abstract: A convenient thulium fiber laser source is described with 3 W of output power operating at a wavelength of 2059 nm with a slope efficiency of 49% with respect to input pump power and 60% with respect to absorbed pump power. The laser was applied in an atomic helium spectroscopy 3 4 1 experiment to quench He (2058.63 nm) and He (2058.69 nm) meta-stable singlets (2 S0), allowing for further investigation of the helium fine structure. The customized laser effectively eliminates the singlet counts to well below a background level (1%). A simplified analysis describes the basic laser performance with fitted constants in reasonable agreement with previous work.

Keywords: fiber; laser; fiber laser; thulium; thulium fiber laser; optics; rare-earth elements; spectroscopy

1. Introduction The key benefits of double clad single transverse mode fiber lasers have been well established, such as efficient and powerful pumping, alignment ease and stability, good heat dissipation due to large surface area to volume ratio, and excellent beam quality [1,2]. For spectroscopic applications, small diameters (typically 250 µm) and long fiber lengths allow for both compact designs and dense mode spacing to conveniently excite very narrow spectral lines. Fiber Bragg gratings are frequently employed to create the laser cavity inside the fiber and select the necessary wavelength and bandwidth. Grating centers can be tuned with temperature for fine control of output wavelength ( 0.02 nm/C for ≈ 2 µm). ≈ Silica (Si) with rare-earth (RE) do-pants provide very broad homogeneous fluorescent emission. When placed in a silica glass host, thulium (Tm) has several different absorption bands, located at 3 3 790 nm, 1210 nm, and 1670 nm [3,4]. The emission spectrum for the F4- H6 transition spans about 400 nm, ranging between 1700 nm to 2100 nm [5]. This emission range extends into the eye-safe regime and has many applications such as laser detection and ranging (LIDAR) for wind shear detection radar, remote sensing, atmospheric pollution monitoring, surgery, range finders, as well as for inducing transitions in atomic spectroscopy experiments [6]. Fiber coupled laser diodes emitting around 790 nm are capable of generating high signal powers especially when employing cladding pumped schemes [7–9].Thulium can be pumped at any of the wavelength bands shown in Figure1, but the 790 nm band is of particular interest because at high doping ( 4%–6%) it yields a near 2 for 1 cross relaxation process populating the upper lasing level, ≈ where the cross relaxation efficiency can be defined as the average number of lasing levels created per pump photon absorbed and increases the overall efficiency that would otherwise be limited to the usual quantum defect between lasing and pump frequencies [10]. Efficiencies have been reported to exceed 60% [3,11].

Fibers 2020, 8, 12; doi:10.3390/ﬁb8020012 www.mdpi.com/journal/ﬁbers Fibers 2020, 8, 12 2 of 7 Fibers 2020, 8, x 2 of 7

FigureFigure 1.1. Energy Levels of Thulium.Thulium. 2. Materials and Methods 2. Materials and Methods 2.1. Laser Design 2.1. Laser Design The laser described in this report is pumped with a diode module centered at 793 nm with a maximumThe laser output described power in of this 8 W report (BWT Beijing),is pumped see wit Figureh a diode2. This module pump lasercentered is fiber at 793 coupled nm with with a 105maximumµm/125 outputµm NA power= 0.15 of fiber 8 W and (BWT has aBeijing), bandwidth see Figure of 3 nm. 2. ItThis also pump is built laser with is feedback fiber coupled protection with between105 µm/125 1900–2000 µm NAnm. = 0.15 The fiber diode and module has a bandwidth is fused to of a 3 (2 nm.+ 1) It also1 multi-mode is built with pump feedback combiner protection (ITF × Technologies)between 1900 to–2000 facilitate nm. The launching diode themodule pump is powerfused intoto a the(2 + active 1) × 1 fiber. multi For-mode this pump experiment, combiner only (ITF one ofTechnologies) the combiner’s to facilitate input ports launching was used. the pump The input power was into designed the active to match fiber. For the pumpthis experiment, laser fiber only and soone had of the 105 combiner’sµm/125 µm input NA = ports0.15 fiberwas used. on the The input input pump was side.designed The signalto match side the had pump 10 µ mlaser/125 fiberµm lowand indexso had double 105 µm/125 clad NAµm =NA0.46 = 0.15 fiber fiber to matchon the theinput active pump fiber. side. We The measured signal side 95% had pump 10 µm/125 beam µm low index double clad NA = 0.46 fiber to match the active fiber. We measured 95% pump beam combiner efficiency and 99% transmission efficiency between the combiner signal ports (called Tc below).combiner Launching efficiency the and pump 99% powertransmission from the effic combineriency between into the the 10 µcombinerm/130 µm signal low indexports Tm(called active Tc fiberbelow). was Launching more diffi thecult pump than we power had expected.from the combiner The 3 cm into of the low 10 index µm/130 recoat µm was low determined index Tm active to be ≈ responsiblefiber was more for mostdiffic ofult the than coupling we had loss.expected. With improvementsThe ≈3 cm of low in cleanlinessindex recoat and was technique, determined the to loss be wasresponsible reduced for to most 5%, as ofverified the coupling by cutback loss. With experiments. improvements Nevertheless, in cleanliness simple and observation technique, withthe loss an opticalwas reduced microscope to 5%, indicates as verified the by index cutback uniformity experiments. of the recoated Nevertheless, fiber was simple not nearlyobservation as uniform with an as theoptical commercial microscope fiber. indicates The active the index fiber consists uniformity of 2.15 of the m ofrecoated thulium fiber doped was 10 notµ mnearly/130 µ asm uniform low index as the commercial fiber. The active fiber consists of 2.15 m of thulium doped 10 µm/130 µm low index NA = 0.46 fiber (Nufern, East Granby, CT, USA) designed to give a truly single-mode profile (TEM00). TheNA thulium= 0.46 fiber fiber (Nufern has a, claddingEast Granby, absorption CT, USA of) 4.6designed dB/m atto 793give nm. a truly This single fiber-mode is expected profile to (TEM absorb00). nominallyThe thulium 90% fiber of the has pump a clad lightding launched absorption into of the 4.6 gain dB/m fiber at (7%793 wasnm. measuredThis fiber exitingis expected the back to absorb which isnominally consistent 90% with of athe 90% pump absorption light launched and the subsequentinto the gain losses fiber through (7% was grating measured and exiting recoat sections).the back Thewhich gain is length consistent was with chosen a 90% basically absorption by balancing and the the subsequent cost of lost losses pump through photons grating versus andthe cost recoat of additionalsections). The Tm gain fiber. length The frequency was chosen mode basically spacing by ofbalancing the overall the cavitycost of length lost pump (c/2nL photons= 150 MHz)versus was the alreadycost of additional dense enough Tm tofiber. overlap Thethe frequency broad spectral mode featurespacing (300 of the MHz overall FWHM), cavity so nolength additional (c/2nL length = 150 MHz) was already dense enough to overlap the broad spectral feature (300 MHz FWHM), so no was needed. The absorbed pump power Pabs in terms of the diode power Pdiode is given by: additional length was needed. The absorbed pump power Pabs in terms of the diode power Pdiode is

given by: P = ηp P (1) abs ∗ diode 푃abs = 휂p ∗ 푃diode (1) Fibers 2020, 8, x 3 of 7

Fiberswith 2020an ,absorption8, 12 efficiency ηp of 81%, given by the product of the beam combiner (0.95), launch3 of 7 (0.95),Fibers 20 and20, 8 , absorptionx (0.90) efficiencies. 3 of 7 withwith anan absorptionabsorption eefficiencyﬃciency ηηpp of 81%,81%, givengiven byby thethe productproduct ofof thethe beambeam combinercombiner (0.95),(0.95), launchlaunch (0.95),(0.95), andand absorptionabsorption (0.90)(0.90) eefficiencies.ﬃciencies.

Figure 2. Thulium Fiber Laser Schematic.

The laser cavity is created by employing a highly reflective fiber Bragg gating (R1 ≈ 99.7% FigureFigure 2.2. Thulium Fiber Laser Schematic.Schematic. inferred from an optical spectrum analyzer measurement of T1 = 0.3% as supplied by the vendor, O/E

Land).The It laseris centered cavity isat created2058.45 by nm employing with a bandwidth a highly reflective of 1.2 nm. fiber The Bragg grating gating is fused (R1 to99.7% the back inferred end The laser cavity is created by employing a highly reflective fiber Bragg gating≈ (R1 ≈ 99.7% fromof the an active optical fiber spectrum and the analyzer Fresnel measurement reflection of ofR2T =1 3.3%= 0.3% forms as supplied the output by the coupler vendor, at O the/E Land).front end. It is inferred from an optical spectrum analyzer measurement of T1 = 0.3% as supplied by the vendor, O/E centeredThe fiber at Bragg 2058.45 grating nm with (FBG) a bandwidth was designed of 1.2 to nm. insure The grating the laser is bandwidthfused to the easily back end overlapped of the active the Land). It is centered at 2058.45 nm with a bandwidth of 1.2 nm. The grating is fused to the back end fiberrequired and the transitions Fresnel reflection even allowing of R2 = for3.3% large forms grating the output centering coupler errors at the and front without end. The any fiber grating Bragg of the active fiber and the Fresnel reflection of R2 = 3.3% forms the output coupler at the front end. gratingtemperature (FBG) control. was designed to insure the laser bandwidth easily overlapped the required transitions The fiber Bragg grating (FBG) was designed to insure the laser bandwidth easily overlapped the even allowing for large grating centering errors and without any grating temperature control. 2.2.required Atomic transitions Helium Beam even allowing for large grating centering errors and without any grating 2.2.temperature Atomic Helium control. Beam The above laser was designed for use in a high precision measurement of fine and hyper-fine structure2.2. AtomicThe abovein Hel theiumlaser stable Beam was isotopes designed (3He for and use 4 inHe a) high of the precision helium measurement atom. Metastable of fine helium and hyper-fine is created structurethrough collisional in the stable excitation isotopes with (3He electrons and 4He) produced of the helium by thermionic atom. Metastable emission heliumfrom ais tungsten created The above laser was designed for use in a high precision measurement of fine and hyper-fine throughfilament collisional, see Figure excitation 3. This produces with electrons approximately produced by equal thermionic sublevel emission populations from a in tungsten the singlet filament, and structure in the stable isotopes (3He and 4He) of the helium atom. Metastable helium is created seetriplet Figure states.3. This produces approximately equal sublevel populations in the singlet and triplet states. through collisional excitation with electrons produced by thermionic emission from a tungsten filament, see Figure 3. This produces approximately equal sublevel populations in the singlet and triplet states.

Figure 3. Helium Atomic Experiment. Figure 3. Helium Atomic Experiment. The atomic beam is collimated through slits, approximately 4 mils wide, to reduce Doppler The atomic beam is collimated through slits, approximately 4 mils wide, to reduce Doppler broadening. The above laser and a 1083 nm laser depopulate the singlet and the m = 0 magnetic broadening. The above laser andFigure a 1083 3. Heliumnm laser Atomic depopulate Experiment the. singlet and the m = 0 magnetic sublevel respectively. Separating the m = 0, +1, and 1 sublevels is done with a set of Stern-Gerlach sublevel respectively. Separating the m = 0, +1, and −1 sublevels is done with a set of Stern-Gerlach magnets,The atomicwhich allowsbeam is for collimated selective detection through slits, of the approximately m = 0 state via 4 mils electron wide, ejection to reduce from Doppler a gold magnets, which allows for selective detection of the m = 0 state via electron ejection from a gold plated platedbroadening. grazing The surface above (surface laser and Penning a 1083 ionization nm laser or depopulate Auger deexcitation). the singlet The and resulted the m electrons= 0 magnetic emit grazing surface (surface Penning ionization or Auger deexcitation). The resulted electrons emit and andsublevel are collected respectively by a. Separating continuous the electron m = 0, multiplier. +1, and −1 Asublevels signal is is detected done with by usinga set of a spectroscopicStern-Gerlach are collected by a continuous electron multiplier. A signal is detected by using a spectroscopic modulatedmagnets, which laser allow of 1083s for nm selective to allow detection for observations of the m of = the0 state J = via0, 1, electron 2 states ejection and the from comparison a gold plated of the modulated laser of 1083 nm to allow for observations of the J = 0, 1, 2 states and the comparison of spacinggrazing ofsurface these levels(surface allow Penning for measurements ionization or of Auger the ﬁne deexcitation). and hyper-ﬁne The structure. resulted electrons The remaining emit and gas the spacing of these levels allow for measurements of the fine and hyper-fine structure. The isare circulated collected through by a continuous a liquid nitrogen electron dewar multiplier. to remove A signal background is detected gas andby using to reuse a spectroscopic the rare and expensivemodulated3 He.laser of 1083 nm to allow for observations of the J = 0, 1, 2 states and the comparison of the spacing of these levels allow for measurements of the fine and hyper-fine structure. The Fibers 2020, 8, x 4 of 7 remaining gas is circulated through a liquid nitrogen dewar to remove background gas and to reuse 3 theFibers rare2020 and, 8, 12expensive He. 4 of 7

3. Results 3. Results 3.1. Laser Characterization 3.1. Laser Characterization Upon testing the laser, the threshold was found to be 1.7 W with a bandwidth of 70 GHz (50 °C). The laserUpon produces testing thean output laser, the of thresholdover 3 W corresponding was found to be to 1.7 a slope W with efficiency a bandwidth of 60% of with 70 GHz respect (50 ◦toC). absorbedThe laser power produces and anfollows output a TEM of over00 profile 3 W corresponding. to a slope efficiency of 60% with respect to absorbedThe laser power shows and followsa fairly aabrupt TEM00 thresholdprofile. and a fairly uniform slope efficiency, see Figure 4. UnderThe such laser conditions shows a simplified fairly abrupt analysis threshold may be and adequate a fairly to uniform determine slope if the effi laserciency, is operating see Figure as4 . expected,Under such see conditionsfor example a simplified[12]. It is important analysis may to point be adequate out that to more determine detailed if theand laser complete is operating laser modelsas expected, have see been for example developed [12 ]. and It is reported important in to literature point out that[4,9], more and detailed they help and completemotivate laser the simplificationsmodels have been taken developed below. Toand estimate reported the in literature slope efficiency, [4,9], and a they homogeneously help motivate broadened the simplifications lasing transitiontaken below. is assumed To estimate with the no slope parasitic efficiency, pump a homogeneouslyor laser absorption, broadened no excited lasing state transition absorption, is assumed hole burning,with no etc. parasitic In steady pump state, or laserany attempt absorption, at additional no excited population state absorption, in the lasing hole burning,level above etc. threshold In steady resultsstate, anyin a attemptshortened at lifetime additional through population stimulated in the emission. lasing level Hence above, the threshold slope efficiency results η inslope a is shortened written aslifetime through stimulated emission. Hence, the slope efficiency ηslope is written as

h (2) η휂 ℎ휈푙푎푠푒푟νlaser slope푠푙표푝푒 = (퐶푅(CR)휂푒푥)ηex (2) ℎ휈hν푝푢푚푝pump

FigureFigure 4. 4. LaserLaser Output Output vs. vs. Absorbed Absorbed Input Input..

InIn addition addition to to the the cross cross relaxation relaxation effi ciency efficiency (CR) (CR) and the and quantum the quantum defect, defect,the extraction the extraction efficiency efficiency(ηex) indicates (ηex) indicates the fraction the fraction of the stimulated of the stimulated photons photons that exit that the exit cavity the andcavity form and the form laser the output. laser output.Because Because the output the couplingoutput coupling of 96.7% of is 96.7% so large, is so the large, additional the additional internal 2.4% internal loss has2.4% only loss a has small only eff ecta smallof laser effect operation of laser (note operation the nonuniform (note the laser nonuniform intensity within laser inttheensity cavity within reduces the sensitivity cavity reduces to losses sensitivityfrom the backto losses side from of the the laser back in side contrast of the to laser the threshold in contrast estimate to the threshold below). With estimateηex = below).0.974, the With CR ηterm,ex = .974, which the wasCR term, not independently which was not determined, independently was simplydetermined, adjusted was to simply 1.6 to yield adjusted the measured to 1.6 to yield slope theeffi measuredciency. This slop valuee efficiency. of 1.6 is compositionThis value of dependent 1.6 is composition (particularly dependent the Al and (particularly Tm concentrations) the Al and [7 ], Tmand concentrations) is less than the [7], best and reported is less valuesthan the of best approximately reported values 1.8 [3 of,9]. approximately 1.8 [3,9]. TheThe threshold threshold of of the the laser occurs whenwhen thethe roundround trip trip gain gain G G from from inversion inversion equals equa thels the round round trip 28 2 26 2 losses. The gain is found using the absorption (σa = 2.8 10 −2m8 )2 and emission (σe = 9 10−26 m2 ) trip losses. The gain is found using the absorption (σa = 2.×8 × 1−0 m ) and emission (σe = 9 ×× 10− m ) cross sections at 2059 nm taken from published data on similar fibers [13–16]. The data agreed to 10%. cross sections at 2059 nm taken from published data on similar fibers [13–16]. The data agreed± to σ ±10%.The variation The variation could could be partially be partially attributed attributed to composition to composition dependence. dependence. The value The for valuea was for σ verifieda was to within 7% by measuring the fiber absorption at 2059 nm (assuming negligible parasitic absorption). Also the modal overlap with the core (Γ = 0.75), the fiber core area A, and the Tm concentration density Fibers 2020, 8, 12 5 of 7

(3 1026 m3) are required. To good approximation, the population is primarily only in the ground × and lasing levels, nt = n1 + n2. The round trip loss is determined by the refectivities, the coupler transmission and the typical splice transmission Ts, experimentally measured through the cut back 4 2 technique to be approximately 99%. At threshold the gain is ﬁxed by R1R2Ts Tc G = 1, and the upper state population N2 is then determined by

R 2Γ Γ (n (x)σe n (x)σa)dx (N σe N σa) G = e 2 − 1 = e A 2 − 1 (3)

Notably, G is better expressed in terms of the total level populations, since the pumping and resulting populations are not uniform along the ﬁber length. The threshold is determined by ﬁnding the pump power at threshold, Pth, required to balance the sum of the density dependent decay rates from the excited levels:

Z 2 (CR)Pth N2 N2 = (γ0 + 2kn2)n2dV = γ0N2 + 2k (1.2) = (4) hνpump 2V τeﬀ

The standard definition for the thulium cross relaxation coefficient (k = k1310) has been used [4]. To simplify the expression, we used the fact that n2 is small compared to n1 and that n2 is approximately αz determined by the local pump power (n2 = n0e− ). The integration factor of 1.2 would be 1.0 in the limit of long fiber length compared to absorption length. The low density lifetime (τ0 = 1/γ0) was measured by electrical pulse pumping and fluorescent monitoring of the decay at long time scales. For times greater than about 500 µs, the decay rate was a simple exponential and gave a lifetime of 480 µs. This is approximately consistent with the range and composition dependent values for the lifetime reported in the literature [17]. The parameters in Equations (3) and (4) that were not measured by us for this fiber were σe and k. To fit our measured values for threshold, σe has to be reduced by 40%, assuming the fitted value of k (1.5 10 23 m3s 1) taken from [4] is correct for our fiber. This k × − − value gives an effective lifetime τeff of 380 µs for our fiber at threshold.

3.2. Atomic Spectroscopy The above laser was designed for convenient optical quenching in an atomic spectroscopy experiment in helium [18]. The fiber laser operating at 2058.65 nm is used for quenching transitions 3 4 1 in He (2058.63 nm) and He (2058.69 nm) singlets (2 S0). The atomic beam of meta-stable helium is created by electron collisions and has an approximately room temperature thermal distributions of velocities (vavg 1500 m/s). The quenching is accomplished when the atoms cross the 3 mm diameter ≈ 1 ≈ laser beam and undergo laser transitions to the fast decaying 2 P0 state (Figure5). With high-power (>0.5 W), the broad emission spectrum is sufficiently stable and continuous to allow for efficient quenching of 3He and 4He simultaneously, insensitive to temperature and alignment fluctuations and drifts. At low power, the inefficient quenching of the states leads to sensitivity to the size of the beam, the power applied, and the transit time of atoms across the laser beam. Also, near threshold, the laser does not produce a uniform and stable frequency spectrum. Thus, the atomic quenching does not follow a simple exponential decay versus overall applied laser power, see Figure5. The bandwidth of the laser is an important design parameter which is approximately given by the FWHM of the output grating given sufficient high input pumping above threshold. When applied to the atomic beam, the laser can quench the singlet states down to a background level (<1%) as shown (Separate experiments indicate the residual signal is from UV background photons) [19]. Fibers 2020, 8, 12 6 of 7 Fibers 2020, 8, x 6 of 7

FigureFigure 5. 5.Quenching Quenching of of the the Singlet Singlet States. States.

4.4. Discussion Discussion ThisThis paper paper describes describes the use the of use a thulium of a thulium fiber laser fiber operating laser operatingat 2059 nm atin an 2059 atomic nm spectroscopy in an atomic experiment.spectroscopy The experiment. laser effectively The laser quenches effectively the quenches singlet states the singlet of atomic states helium, of atomic while helium, being verywhile insensitivebeing very to insensitive laboratory to temperature laboratory andtemperature alignment and changes, alignment making changes, it a very making convenient it a very and convenient reliable solution.and reliable These solution. results indicate These results that customized indicate that Tm double customized clad fiber Tm double lasers might clad providefiber lasers effective might solutionsprovide effective in similar solutions optical pumpingin similar andoptical spectroscopy pumping and applications. spectroscopy The applications. simplified The analysis simplified and publishedanalysis and cross-sections published support cross-sections readily s feasibleupport readily laser designs feasible between laser designs 1900 and between 2100 nm. 1900 The and paper 2100 showsnm. The a simple paper andshows eff aect simple fiber laserand effect source fiber that laser utilizes source readily that utilizes available readily materials available to accomplish materials to scientificaccomplish experiments. scientific experiments.

Author Contributions: This article was supported by D.S. through writing—review and editing, supervision, resources,Author Contributions: and validation. This A.K. article contributed was supported through validationby D.S. through and conceptualization. writing—review R.C.and wasediting, responsible supervision, for writing-originalresources, and draftvalidation. preparation, A.K. contributed formal analysis, through data validation curation,methodology. and conceptualization. All authors R. haveC. was read responsible and agreed for towriting the published-original version draft preparation, of the manuscript. formal analysis, data curation, methodology.

Funding:Funding:This This research research was was supported supported by by NSF NSF award award number number 1404498. 1404498.

ConﬂictsConflicts of of Interest: Interest:The The authors authors declare declare no no conﬂict conflict of of interest. interest.

ReferencesReferences

1.1. Richardson,Richardson, D.J.; D.J.; Nilsson, Nilsson, J.; J.; Clarkson, Clarkson, W.A. W.A. High High power power fiber fiber lasers: lasers: Current Current status status and and future future perspectives. perspectives. J.J. Opt. Opt. Soc. Soc. Am. Am. B B2010 2010, ,27 27, B63–B92., B63–B92. [ CrossRef] 2.2. Zervas,Zervas, M.N.; M.N.; Codemard, Codemard, C.A. C.A. High High power power fiber fiber lasers: lasers: A A review. review.IEEE IEEE J. J. Sel. Sel. Top. Top. Quantum Quantum Electron. Electron.2014 2014, , 2020, 219–241., 219–241. [CrossRef ] 3.3. Moulton,Moulton, P.F.;P.F.; Rines, Rines, G.A.; G.A.; Slobodtchikov, Slobodtchikov, E.V.; E.V.; Wall, Wall, K.F.; K.F.; Frith, Frith, G.; G.; Samson, Samson, B.; B.; Carter, Carter, A.L.G. A.L.G. Tm-doped Tm-doped fiberfibe lasers:r lasers: Fundamentals Fundamentals and and power power scaling. scaling.IEEE IEEE J. Sel.J. Sel. Top. Top. Quantum Quantum Electron. Electron.2009 2009, 15,, 15 85–92., 85–92. [CrossRef ] 4.4. Jackson,Jackson, S.D.;S.D.; King,King, T.A. Theoretical modeling modeling of of tm tm-doped-doped silica silica fiber fiber lasers. lasers. J. Light.J. Light. Technol. Technol. 19991999, 17, 94817, – 948–956.956. [CrossRef] 5.5. Hanna,Hanna, D.;D.; Percival,Percival, R.M.;R.M.; Smart, Smart, R.G.; R.G.; Tropper, Tropper, A.C. A.C. E ffiEfficientcient and and tunable tunable operation operation of of a a tm-doped tm-doped fibre fibre laser.laserOpt.. Opt. Commun. Commun.1990 1990, 75, 75, 283–286., 283–286. [ CrossRef] Fibers 2020, 8, 12 7 of 7

6. Huang, Y.; Jivraj, J.; Zhou, J.; Ramjist, J.; Wong, R.; Gu, X.; Yang, V.X.D. Pulsed and cw adjustable 1942 nm single-mode all-fiber tm-doped fiber laser system for surgical laser soft tissue ablation applications. Opt. Express 2016, 24, 16674–16686. [CrossRef][PubMed] 7. Jackson, S.D.; King, T.A. High-power diode-cladding-pumped tm-doped silica fiber laser. Opics Lett. 1998, 23, 1462–1464. [CrossRef][PubMed] 8. Walbaum, T.; Heinzig, M.; Schreiber, T.; Eberhardt, R.; Tunnermann, A. Monolithic thulium fiber laser with 567 w output power at 1970 nm. Opt. Lett. 2016, 41, 2632–2635. [CrossRef][PubMed] 9. Frith, G.; Carter, A.; Farroni, J.; Farley, K.; Tankala, K. Efficient and reliable 790nm-pumped Tm lasers from 1.91 to 2.13 µm. In Proceedings of the SSDLTR, Albuquerque, NM, USA, 4 June 2008. 10. Jackson, S. Cross relaxation and energy transfer up-conversion processes relevant to the functioning of 2 µm tm3+-doped silica fibre lasers. Opt. Commun. 2004, 14, 197–203. [CrossRef] 11. Christensen, G.F.S.; Samson, B. Developments in thulium-doped fiber lasers offer higher powers. In Proceedings of the 21st Annual Meeting LEOS, IEEE Lasers Electro-Optics Society, Newport Beach, CA, USA, 9–13 November 2008. 12. Siegman, A. Lasers; Chapter 12; University Science Books: Mill Valley, CA, USA, 1986. 13. Walsh, B.; Barnes, N. Comparison of tm: Zblan and tm: Silica fiber lasers; spectroscopy and tunable pulsed laser operation around 1.9 µm. Appl. Phys. B 2004, 78, 325–333. [CrossRef] 14. Agger, S.D.; Povlsen, J.H. Emission and absorption cross section of thulium doped silica fibers. Opt. Express 2006, 14, 50–57. [CrossRef][PubMed] 15. Romano, C.; Tench, R.; Jaouen, Y.; Williams, G. Simulation and design of a multistage 10w thulium-doped double clad silica fiber amplifier at 2050 nm. In Fiber Lasers XIV: Technology and Systems; International Society for Optics and Photonics: San Francisco, CA, USA, 2017; p. 10083. 16. Peterka, P.; Kasik, I.; Dhar, A.; Dussardier, B.; Blanc, W. Theoretical modeling of fiber laser at 810 nm based on thulium-doped silica fibers with enhanced 3h4 level lifetime. Opt. Express 2011, 19, 2773–2781. [CrossRef] [PubMed] 17. Cajzl, J.; Paterka, P.; Kowalczyk, M.; Tarka, J.; Sobon, G.; Sotor, J.; Aubrecht, J.; Honzatko, P.; Kasik, I. Thuliumdoped silica fibers with enhanced fluorescence lifetime and their application in ultrafast fiber lasers. Fibers 2018, 6, 66. [CrossRef] 18. Smiciklas, M.; Shiner, D. Determination of the fine structure constant using helium fine structure. Phys. Rev. Lett. 2010, 105, 123001. [CrossRef][PubMed] 19. Rezaeian, N.H. A Precise Few-Nucleon Size Difference by Isotope Shift Measurements of Helium; University of North Texas: Denton, TX, USA, 2015.

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).