A novel method for measuring the resonant absorption coefficient of rare-earth-doped optical fibers
RResearch Article 1
A novel method for measuring the resonant absorptioncoefficient of rare-earth-doped optical fibers M OSTAFA P EYSOKHAN , E
SMAEIL M OBINI , B
EHNAM A BAIE , AND A RASH M AFI Department of Physics & Astronomy, University of New Mexico, Albuquerque, NM 87131, USA Center for High Technology Materials, University of New Mexico, Albuquerque, NM 87106, USA * Corresponding author: mafi@unm.eduCompiled February 12, 2019
A non-destructive method for measuring the resonant absorption coefficient of rare-earth-doped opticalfibers is introduced. It can be applied to a broad range of fiber designs and host materials. The methodcompares the side-collected spontaneous emission at two arbitrary locations along the fiber as a functionof the pump wavelength to extract the absorption coefficient. It provides an attractive and accurate al-ternative to other available techniques. In particular, the proposed method is superior to the cut-backmethod, which destroys the sample and is prone to inaccuracies due to the cladding mode contamination.Moreover, because it does not involve any mechanical movement, it can be used for fragile optical fibers. © 2019 Optical Society of America
OCIS codes: (230.2285) Fiber devices and optical amplifiers; (140.3615) Lasers, ytterbium; (160.5690) Rare-earth-doped materials; (120.4530)Optical constants. http://dx.doi.org/10.1364/ao.XX.XXXXXX
1. INTRODUCTION
Fiber lasers and amplifiers are widely adopted in industry andscientific research because of their high power, good beam qual-ity, and ease of operation [1, 2]. In order to design and optimizefiber lasers and amplifiers, it is essential to know the geometricaland optical properties of the optical fiber gain medium to a highdegree of accuracy [3–6]. Such characteristics may be consider-ably different from those anticipated from the fiber preform andcan be altered during the fiber drawing process. Therefore, it isimportant to accurately measure these characteristics directly inthe fiber. An important property of a rare-earth-doped opticalfiber is the resonant absorption coefficient α r ( λ ) , which can bedetermined from the dopant density N and the absorption crosssection σ abs ( λ ) . However, σ abs ( λ ) is strongly dependent on thehost glass, which can be affected during the preform fabricationand drawing. The dopant density profile can also be modifiedduring the fiber drawing because of diffusion; therefore, it isimperative to determine α r ( λ ) directly using the optical fiber.In this work, we present a novel method that can be used toaccurately determine α r ( λ ) in the presence of rare-earth ions inan optical fiber at all relevant wavelengths. The method is basedon analyzing the emitted side-light, which contains both fluores-cence and pump scattering at different locations along the fiber.It is a universal technique that can be applied to single-mode,multi-mode, large-mode-area, photonic crystal, and double-cladrare-earth-doped optical fibers. It is also applicable to fibersmade from different materials such as ZBLAN, silica, or chalco- genides. Because the method does not involve the movement ofany mechanical or optical components during the measurementprocess, it can be readily applied to fragile fibers [7], includinghighly tapered fibers [8].The presented method is an alternative to the cut-backmethod, which is widely used to measure the absorption co-efficient of optical fibers [9]. In the cut-back method, the outputpower from the fiber is measured by gradually cutting backthe fiber from the end and reducing its length [9]. The cut-back method is destructive; therefore, it cannot be employedin experiments that need to be performed on a single piece ofoptical fiber. In a sensitive experiment, e.g. for laser cooling,even a slight sample-to-sample variation can affect the outcome;therefore, two pieces of the same fiber may not perform thesame way and must be characterized individually [10–12]. An-other issue involves the excitation of the cladding modes thatcontaminate the cut-back measurements in short pieces of thefiber [13]. Moreover, in the cut-back measurements of highlyabsorbing rare-earth-doped optical fibers, because the core mustbe pumped well below the saturation intensity, the output sig-nal can be quite weak and even comparable to the claddingpower contamination. Finally, the cut-back method involvesundesirable mechanical processing such as cleaving, polishing,and inspecting the fiber that at best can be quite elaborate, andin cases involving fragile fibers totally impractical.We already mentioned that our proposed method is highlyadvantageous for characterizing fibers for laser cooling. In a a r X i v : . [ phy s i c s . op ti c s ] F e b esearch Article 2 similar context, the accurate determination of α r ( λ ) is essentialfor designing radiation-balanced lasers (RBLs) [14–24]. RBLshave been proposed as a way to mitigate the thermal issuesin high-power fiber lasers, which have hindered the progressin power-scaling because of the thermally induced transversemode instability [25–29]. RBLs operate based on the fluorescencecooling principle, in which the rare-earth-doped optical fiber ispumped at a wavelength, which is higher than the mean fluores-cence wavelength of the active ions; therefore, the anti-Stokesfluorescence removes some of the excess heat [14]. In RBLs,the heat generated due to the quantum defect, parasitic back-ground absorption of the pump and laser, and the non-radiativerelaxation of the excited rare-earth ions is balanced against thefluorescence cooling. RBLs pose stringent requirements on thetypes and levels of dopants, as well as the host materials. Inparticular, the parasitic background absorption ( α b ) must bequite small for RBLs to work. Our proposed method, when com-bined with the laser-induced temperature modulation spectrum(LITMoS) test developed in Sheik-Bahae’s research group [12],allows us to also accurately determine α b for the doped fiber andthe cooling efficiency of rare-earth doped fibers [10, 11].
2. THEORY
We refer to this new technique as “measuring the absorptioncoefficient via side-light analysis” (MACSLA). This method isbased on the fact that when a rare-earth doped optical fiberis pumped far below the saturation intensity, the spontaneousemission power emitted from the side of the fiber is directlyproportional to the pump power. The method compares the side-collected spontaneous emission at two arbitrary locations alongthe fiber as a function of the pump wavelength and employsthe McCumber theory [30] to extract the spectral form of theabsorption coefficient.
Fig. 1.
Schematic of the propagation of the pump power in theoptical fiber and the collection of the spontaneous emissionfrom the side of the rare-earth-doped optical fiber.Figure 1 shows a schematic of the proposed method. Thepump propagates through the core of the optical fiber fromleft to right. The pump wavelength is assumed to be in theproximity of the peak absorption wavelength such that α r ( λ ) is much larger than α b . The pump intensity in the fiber coreis assumed to be far below the saturation intensity; therefore,the pump power propagating in the core, P core ( z ) , attenuatesexponentially due to the absorption by the rare-earth dopants: P core ( z ) = P exp ( − α r ( λ ) z ) , (1) where P is input pump power in the core at z = A and B along the fiber, which are separated bya distance ∆ z . The collection points A and B and their distance ∆ z remain unchanged through the experiment. The collectionefficiencies of the two multimode fibers may be slightly differentdue to inevitable misalignments. Therefore, we can write P coll ( z A ) = γ A P core ( z A ) , (2a) P coll ( z B ) = γ B P core ( z B ) , (2b) where P coll ( z A ) and P coll ( z B ) are the collected powers at points A and B , respectively. γ A and γ B are coefficients that relatethe propagating power in the core to the collected spontaneousemission power, which also incorporate the coupling efficienciesto the multimode fibers at points A and B , respectively. We nowdivide Eq. 2b by Eq. 2a, take the natural logarithm of both sides,and obtain: r ( λ ) = ln ( γ B / γ A ) − α r ( λ ) ∆ z , (3) where r ( λ ) = ln (cid:18) P coll ( z B ) P coll ( z A ) (cid:19) . (4) In Eq. 3, α r ( λ ) follows a strict spectral function of the form(see Appendix A): α r ( λ ) ∝ λ S ( λ ) exp (cid:18) hc λ k B T (cid:19) , (5) where S ( λ ) is the emission power spectral density measured bythe optical spectrum analyzer, h is the Planck constant, k B is theBoltzmann constant, and c is the speed of light in vacuum. Wealso assume that the ratio γ B / γ A is wavelength independentover the narrow range of wavelengths used in this experiment.Therefore, the left-side in Eq. 3, r ( λ ) , must also follow the spec-tral form in Eq. 5 when the pump wavelength is varied. Becausethe spectral shape of α r ( λ ) is obtained from Eq. 5, all that isneeded is to find its overall magnitude by balancing the left-side and right-side in Eq. 3 over the respective wavelengths.Therefore, we replace α r ( λ ) in Eq. 3 with α pr × (cid:101) α r ( λ ) , where (cid:101) α r ( λ ) is the absorption coefficient normalized to its peak value, α pr = α r ( λ peak ) . This way, we can determine both γ B / γ A and α pr through a fitting procedure that involves measurements of r ( λ ) and (cid:101) α r ( λ ) at multiple wavelengths near the peak absorptionwavelength.
3. EXPERIMENT
In our experiment, we used a commercial Yb-doped optical fiber(SM-YSF-LO-HP, Nufern, Inc.) to demonstrate the utility of theMACSLA method. SM-YSF-LO-HP is a low-doped Yb-silicasingle-mode and single-clad optical fiber. As we mentionedin the previous section, in order to use the Beer-Lambert expo-nential decay form in Eq. 1, the pump intensity must be keptconsiderably below the saturation intensity. As such, we firstmeasured the pump saturation power ( P sat ) by pumping thecore of the doped fiber ( P core ) and measuring the side sponta-neous emission power ( P spont ) for different values of the pumppower at 976 nm wavelength. The measurements were fitted tothe functional form of the saturated power in a doped fiber [31] P spont ( P core ) ∝ P core + P core / P sat . (6) esearch Article 3 For our fiber, the saturation power was determined to be 966 µW.In our later experiments, P core was kept below 5% of the satura-tion power to make sure that Eq. 1 could be reasonably applied(see Appendix B). Fig. 2.
Experimental setup for measuring the absorption co-efficient using the MACSLA method. LP stands for linear po-larizer, OSA for optical spectrum analyzer, LPF for long-passfilter, PD for photodetector, and SMF for single-mode fiber.The experimental setup that is used in MACSLA for mea-suring the absorption coefficient is shown in Fig. 2. The fiberwas pumped by a tunable continuous-wave (CW) Ti:Sapphirelaser and the side spontaneous emission power was collected atpoints A and B using two multimode fibers (M124L02, Thorlabs,Inc.), which were connected to InGaAs Detectors (DET08CFC,Thorlabs, Inc.). Long-pass filters ( ≥ A and B , ∆ z , must be substantiallylarger than the typical length of the Yb-doped fiber segment, L ,from which the side spontaneous emission is collected by eachlight-collecting multimode fiber. This is to ensure that the collec-tion segment can be considered a point for all practical purposesrelative to ∆ z . The length of the fiber segment is approximatelygiven by L = D + d tan θ , sin θ = NA, (7) where D is the diameter of the core of the multimode fiber, d isthe distance between the input tip of the light-collecting mul-timode fiber and the core-cladding interface of the Yb-dopedfiber, θ is the maximum acceptance angle of the light-collectingmultimode fiber, and NA is the numerical aperture of the light-collecting multimode fiber, as shown in Fig. 3. Using typicalvalues for our experiment in Eq. 7, one concludes that L is onthe order of 0.5mm and ∆ z (cid:29) D = = d ≈ d was comparable to theradius of the Yb-doped fiber. At the same time, ∆ z must be suf-ficiently large to allow for a distinct nontrivial collected powerratio in the form of r ( λ ) , while it must be small enough to ensurethat the signal to noise ratio at point B is not much different fromthat of point A , because the signal drops exponentially with ∆ z .For our experiment, we chose ∆ z = Fig. 3.
Schematic of the fluorescence emission collected by themultimode fiber from the side of the Yb-doped fiber for theestimation of the fiber segment length, L , from which the sidespontaneous emission is collected (see Eq. 7).The detectors were connected to a lock-in amplifier that wasused to extract the weak spontaneous emission signal from thenoisy background. In order to use the lock-in amplifier, thepump was modulated at 1 KHz with a commercial chopper. Twolinear polarizers were used to attenuate the pump power andkeep the core power far below the saturation. A beam-splitterand a power-meter were used to measure the input power, andanother power-meter was placed at the end of the doped fiberto monitor the output power as a secondary check to makesure that the fiber core power remained far below saturationthroughout the experiment. The pump power was coupled toa passive single-mode fiber by a 20X microscope objective, andthe single-mode fiber was fusion-spliced to the doped fiber todeliver the pump power. As the pump wavelength is varied,the input pump power changes slightly; however, the MACSLAmethod relies only on the power ratios collected at points A and B and is not affected by such power variations.For the fitting procedure, we chose seven different pumpwavelengths near the absorption peak wavelength for the Yb-silica fiber ( λ peak = 977 nm) by tuning the operating wavelengthof the CW Ti:Sapphire laser. For each wavelength, the emissionsignal power was measured at positions A and B over suffi-cient time windows until the desired signal-to-noise-ratio wasachieved and the error-bars were obtained from the lock-in am-plifier. The distance between points A and B was also measuredby a digital caliper. The power spectral density S ( λ ) of the Yb-silica fiber is shown in Fig. 4. The inset shows the resonantabsorption coefficient, which is normalized to its peak value,and is calculated by using the McCumber theory [30].
4. RESULTS AND DISCUSSION
The fitted line over the experimental measurements related toEq. 3 are shown in Fig. 5. The points (with error-bars) indicatethe values of r ( λ ) measured at seven different wavelengths, andthe fitting curve comes directly from the resonant absorptionspectrum shown as the inset in Fig. 4. The outcome of the fit-ting procedure was the peak value of the resonant absorptioncoefficient α pr = ± − . While unimportant to theprocedure, the fitting also resulted in γ B / γ A = α pr should be compared with the value reported by thevendor, which is 0.220 ± − . We also performed the cut-back as a point of comparison for measuring the peak value ofthe resonant absorption coefficient. We used the CW Ti:Sapphirelaser as the pump operating at the peak resonant absorptionwavelength of the Yb-doped fiber and coupled its output usingan objective lens to a 50 cm segment of a passive single-modefiber (HP-980, Nufern), while the other end the single-mode fiberwas fusion-spliced to the Yb-doped fiber. esearch Article 4 Fig. 4.
The emission power spectral density S ( λ ) , which ismeasured by the optical spectrum analyzer is plotted in ar-bitrary units. The inset shows the resonant absorption coeffi-cient, which is normalized to its peak value, and is calculatedby using the McCumber theory [30].The intermediate step of using a passive single-mode fiberto couple light to the Yb-doped fiber provided two main ad-vantages: first, it reduced the amount of pump coupling to thecladding modes of the gain fiber for enhanced accuracy; and sec-ond, it allowed for the inevitable moving and bending as a resultof the incremental cleaving of the gain fiber without having toworry about the fiber alignment to the pump. We also appliedindex matching gel on the cladding of the Yb-doped fiber toreduced cladding light contamination of our measurement. Ourcareful cut-back method measurement of the peak value of theresonant absorption coefficient resulted in α pr = − ,which is closer to the value provided by the MACSLA method(see also Appendix B for potential corrections to the result fromMACSLA). While the experimental results reported here arefor a single segment of the Yb-doped silica fiber, we performedthe same procedure on a segment of a Yb-doped ZBLAN fiberand the results came in agreement with those reported by thevendor. We also note that the results are insensitive to the actualvalue of ∆ z –while we reported ∆ z = ∆ z = α r ( λ ) . In their procedure, thedoped fiber is pumped at a fixed wavelength and the sponta-neous emission is measured at different positions along the fiberby using an optical spectrometer. They measure α r at the re-spective wavelength by fitting the side-collected power to theBeer-Lambert exponential decay form in Eq. 1. In their method,the coupling efficiency to the side-collecting fiber is assumed toremain unchanged at different locations along the doped fiber.This assumption is likely to result in measurement inaccuracies ifthe gain fiber is single-mode with a small core. The fitting to theBeer-Lambert exponential decay form necessitates mechanicalmovement to obtain measurements at multiple points; therefore,optical alignment may become an issue and it will be hard tomaintain a uniform coupling efficiency to the side-collecting Fig. 5.
The points with error-bars indicate the values of r ( λ ) from Eq. 4 measured at seven different wavelengths near thepeak of the resonant absorption coefficient. The fitting curvecomes directly from the resonant absorption spectrum shownas the inset in Fig. 4. The fitting parameters are α pr and γ B / γ A .fiber at all points. Moreover, the requirement to keep the pumppower far below the saturation power, which is on the order of1 mW in single-mode fibers, necessitates high-sensitivity spec-trometers for adequate signal-to-noise-ratio.
5. SUMMARY AND CONCLUSION
In summary, the MACSLA method provides an attractive and ac-curate alternative to other techniques for measuring the resonantabsorption coefficient in rare-earth-doped optical fibers. In par-ticular, it is superior to the cut-back method, which destroys thesample and is prone to inaccuracies due to the cladding modecontamination. When combined with the LITMoS test [12, 33],the MACSLA method allows one to also determine the parasiticbackground absorption coefficient ( α b ). In laser cooling experi-ments and RBLs, the cooling efficiency is improved by reducingthe ratio of background absorption coefficient to the resonantabsorption coefficient ( α b / α r ) [10–12, 33–36]. Our techniques en-ables an accurate determination of α b that is essential to designand interpret such fluorescence cooling experiments.One of the main advantages of the MACSLA method is thefact that it does not require precise alignments, which makes itsuitable for commercial applications. Moreover, the techniquedoes not require an accurate knowledge of the actual coupledpower into the medium, hence one is not worried about sur-face reflections and scatterings. In practice, the lock-in ampli-fier may not be required if one uses a high-sensitivity detectorsuch as a low threshold avalanche photodiode. We verified thisin a separate measurement for a multimode Yb-doped opticalfiber, where the side-collected spontaneous emission signal wasstronger than that of a single-mode Yb-doped fiber due to ahigher value of pump power. Finally, we would like to empha-size that while the MACSLA method is used to extract the peakvalue of the resonant absorption coefficient, when combinedwith the emission power spectral density S ( λ ) , which is mea-sured by the optical spectrum analyzer as in Fig. 4, provides afull characterization of the resonant absorption coefficient at allrelevant wavelengths and is not limited to the vicinity of thepump wavelength. esearch Article 5 APPENDIX A
In this Appendix, we would like to justify the form of Eq. 5. Westart with the McCumber theory, which relates the absorptioncross section ( σ abs ( ν ) ) and emission cross section ( σ em ( ν ) ) ofdopants in solid-state media [30]: σ abs ( ν ) = σ em ( ν ) exp (cid:18) h ν − (cid:101) k B T (cid:19) . (8) ν is the frequency of light, and (cid:101) is the so-called “zero-line”energy. The emission cross section can be formally obtainedfrom [37]: σ em ( ν ) = A g ( ν ) λ π n , (9) where the A is the Einstein A-coefficient , g ( ν ) is the normalizedlineshape function, λ is the free space wavelength, and n isthe refractive index of the medium. The resonant absorptioncoefficient, α r ( λ ) , can be expressed as α r = N σ abs − N σ em ≈ N σ abs , (10) where N ( N ) is the population density of the lower (upper)manifold of the dopant ions, and N = N + N is the dopantion number density. The approximation in the right hand sideof Eq. 10 holds when the gain material is pumped well belowthe saturation intensity such that N ≈ N ≈ N . Theobserved spectral florescence intensity, I ( ν ) , is given by [37]: I ( ν ) = A g ( ν ) h ν N = λ c S ( λ ) , (11) where S ( λ ) is the emission power spectral density, previouslyintroduced in the main part of the manuscript, and the right-most part of Eq. 11 comes from noting that I ( ν ) d ν ≡ S ( λ ) d λ .Combining Eqs. 8–11, we obtain α r ( λ ) ≈ exp (cid:18) − (cid:101) k B T (cid:19) (cid:18) N / N π hc n (cid:19) λ S ( λ ) exp (cid:18) hc λ k B T (cid:19) , (12) where the wavelength-dependent part gives Eq. 5. APPENDIX B
In this Appendix, we estimate the impact of the finite ratio ofthe P core to P sat on our results. In the low emission signal limit,which is valid in our setup, the pump propagation is describedby dP core ( z ) dz = − α r ( λ ) P core + P core / P sat , (13) where α r ( λ ) = N σ abs ( λ ) . The formal solution to Eq. 13 isgiven by P core ( z ) = P sat × W (cid:18) P P sat e P / P sat e − α r ( λ ) z (cid:19) , (14) where W ( y ) is the Lambert W-function (product logarithm func-tion) defined as the principal solution for W in y = W e W . Thezeroth order term in Taylor expansion of Eq. 14 in P / P sat givesEq. 1.If we calculate r ( λ ) from Eq. 4 and keep terms to the firstorder of Taylor expansion in P / P sat , we obtain r ( λ ) = ln ( γ B / γ A ) − α r ( λ ) ∆ z (15) + ( P / P sat ) e − α r ( λ ) z A ( − e − α r ( λ ) ∆ z ) , The actual expansion parameter for the correction term inEq. 15 relative to Eq. 3 is the ratio of P exp ( − α r z A ) / P sat ,due to the fact that P is the input power to the fiber but P exp ( − α r z A ) is the power at the first point of spectral mea-surement. Employing the fitting procedure using Eq. 15 with P exp ( − α r z A ) / P sat =
5% gives the peak value of the absorp-tion coefficient at α pr = ± − , which must becompared with α pr = ± − obtained from fittingwith Eq. 3, which is a 4% correction. Such an upward correctionis understandable because the increase in the denominator inEq. 13 due to a finite value of P core / P sat must be compensatedby an increase in the numerator in the form of rescaling α r ( λ ) toa larger value. FUNDING INFORMATION
This material is based upon work supported by the Air ForceOffice of Scientific Research under award number FA9550-16-1-0362 titled Multidisciplinary Approaches to Radiation BalancedLasers (MARBLE).
ACKNOWLEDGMENT
The authors would like to thank M. Sheik-Bahae, R. I. Epstein,and A. R. Albrecht for illuminating discussions.
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