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Abstract
The rapidly-developed high-power mid-infrared 2-5 µm laser technology requires a compact, flexible low-loss glass fiber for power delivery or laser generation. With the broadest bandwidth of low-loss transmission window in mid-infrared region amongst all mid-infrared glass fibers, chalcogenide glass fiber is the best candidate covering the whole 2-5 µm range. Multi-hundred-watt high-power delivery for 5.4-µm CO laser was previously demonstrated in a multimode chalcogenide fiber with a 1-mm-diameter large core, at the cost of giving up one of the most desirable fiber advantages, the flexibility. Indeed, chalcogenide glass fibers with decent flexibility have never exhibited hundred-watt-level power transmitting capability in the 2-5 µm range. In this paper, we have experimentally demonstrated 100-watt-level power transmission in multimode As2S3 chalcogenide fibers, using a customized high-power 2-µm thulium doped silica fiber laser source. With effective forced cooling, the multimode As2S3 fiber with 200 µm core diameter can resist incident laser power of 120 W and deliver transmitted power of 63 W. Nano-sized scattering center related laser damage mechanism and the cylindrical heat transfer model have been proposed to explain the high-power damage process of chalcogenide glass fibers. The calculation is in good agreement with the experiments. It is promising to further enhance the transmitted power above 100 W in flexible chalcogenide glass large-core fibers.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
The mid-infrared (mid-IR, 2-20 µm) region contains two important atmospheric windows, 3-5 µm and 8-12 µm. According to Wien’s displacement law, 3-5 µm window, corresponds to the peak wavelengths of blackbody radiation at the temperature between 300 and 700 °C. It happens to be the typical temperature range of aircraft jet engine exhaust plume, which is widely chosen as the IR signature targets in the guided missiles technology and laser-based infrared countermeasures [1–3]. Secondly, many chemical and biological molecules undergo characteristic absorptions within this 3-5 µm spectral band. Therefore high-power mid-IR laser technology [4–6] has been developed rapidly for a number of applications such as remote detection, security, metrology, medical treatment, optical coherence tomography (OCT) [7], high-precision IR spectroscopy [8], and hyperspectral tissue imaging [9]. It is worth pointing out that the current state-of-the-art pulsed mid-IR fiber source (i.e., mid-IR fiber supercontinuum) is 2 orders of magnitude brighter than the synchrotron in the whole 2-10 µm range [10].
High-power 2-µm and 3-µm lasers are the effective excitation source for generating laser emission expanding into 3-5 µm regime [11,12], and hence they are recognized as the entrance to realize high-power 3-5 µm lasers. So far, the recorded output power of continuous wave (CW) and pulsed 2-µm thulium-doped fiber lasers have both exceeded the level of 1-kW [13,14], while the Cr(II) doped II-VI chalcogenide (e.g., Cr2+-doped ZnS and ZnSe) solid-state lasers have achieved the power level over 100 W [15].
On the other hand, recently quantum cascaded lasers (QCLs) [5] have been developed rapidly. The reported emission wavelength of QCLs covers the broad range from 3 µm to beyond 100 µm. Due to their high room-temperature wall-plug efficiency (up to 30%), QCLs have been viewed as the most promising candidate for efficient, compact mid-IR laser sources [16]. In terms of the power, the output of a single-mode CW QCL has exceeded 8 W [17]. Meanwhile, QCL array technology has been proposed to manufacture high power QCLs with multi-hundred-watt output and near-diffraction-limit beam quality [18]. We optimistically expect that the era of kW-level mid-IR lasers covering the whole 2-5 µm is looming.
Analogue to the optical fiber technology developed in the near-infrared regime, the emerging high-power mid-IR 2-5 µm laser technology also requires compact and flexible optical fiber medium as the base of laser platforms. Chalcogenide glass (ChG) fiber possesses the broadest low-loss spectral range (from near-IR to up to 16 µm), in comparison with any other glass fibers [19]. Note that it is known that fluoride glass fibers are highly hygroscopic in particular under the condition of high power laser operation [20]. Instead, ChG glass (sulfide or selenide glass based) fibers are fairly stable to relative harsh environment. Therefore, ChG fiber is a preferable medium for 2-5 µm high-power usage, e.g., power delivering [21–27] and nonlinear frequency generation [28–34].
Despite the excellent optical performances of ChG glass fiber, its low laser damage threshold, arising from the weak chemical bonds constructing the glass network structure, hinders ChG glass fiber from resisting high power. Previously, multi-hundred-watt high-power delivery for 5.4-µm CO gas laser was reported in a multimode As2S3 glass fiber with 1-mm core diameter [27]. The maximum transmitted power of 226 W was obtained under the incident power of 460 W [27]. However, the fiber with such a large core diameter actually lost the flexibility, one of the most important advantages of optical fibers. Such a rigid component is not helpful for realizing compact and portable optical devices. To date, 2-5 µm hundred-watt-level laser transmission has not been proven in flexible ChG fibers.
In this paper, we have experimentally demonstrated 100-watt-level power-transmission capability of flexible ChG multimode fibers (MMFs). A customized 2-µm high-power thulium doped silica fiber laser is used as the excitation source. An As2S3 glass based MMF with a core diameter of 200 µm is selected. Such a fiber shows decent flexibility. The nano-sized scattering defects related laser damage mechanism of chalcogenide fibers has been proposed. With powerful forced cooling, the multimode As2S3 fiber with 200 µm core diameter is capable of resisting incident laser power of 120 W and delivering transmitted power of 63 W.
2. Fiber fabrication and characterizations
2.1 Fiber fabrication
As-S glass family was selected as the host material of the chalcogenide fiber for high power transmission experiment. First, sulfur-related chemical bond strength in a sulfide glass is stronger than the Se-related bond in a selenide glass and therefore sulfide glass fiber can typically resist higher laser power than the selenide fiber. Second, the material zero-dispersion wavelength of the selenide glass is around 7 µm [33], significantly longer than that of a sulfide glass (at ∼5 µm). For 2-5 µm high power nonlinear frequency generation using chalcogenide fibers, large-mode-area fiber based on sulfide glass will be a reasonable option over the ones based on other chalcogenide glass families, for the convenience of dispersion management.
The core and cladding compositions of the studied large core ChG MMF were As40S60 (atomic (at.) %) and As38S62 (at. %), respectively. The refractive indices (n) of the two glasses have been measured using a J. A. Woollam IR-VASE ellipsometer. Figure 1(a) plots the wavelength-dependent refractive index curves. It is seen that the index contrast between the two glasses is ∼0.03 in the range of 1.7-11.5 µm.
Fig. 1. (a) Measured refractive index curves of core and cladding glasses. (b) Calculated fiber NA and normalized frequency V number of the fiber with core diameter of 200 µm.
High-purity As-S glasses were prepared using multiple steps of distillation. The core rod was directly obtained after melt-quenching the purified As40S60 (at. %) melt in the silica ampoule, while the cladding glass tube was made by rotating the As38S62 (at. %) melt inside the silica ampoule [35]. And the core/cladding preform was made using inserting the core rod into the cladding tube. Thermoplastic polyetherimide (PEI) film (Solvay Ltd, Beijing Branch) was wrapped out of the preform as the protection. The rod-in-tube assemble was then drawn into the MMFs in dry nitrogen atmosphere. The drawing temperature was around 300 °C. The fiber had a core diameter of 200 ± 2 µm and a glass outer diameter (OD) of 250 ± 2 µm. The thickness of the protective PEI layer was 25 ± 5 µm and the resultant OD of the final fiber including the PEI coating was ∼300 µm. The yield of the uniform fiber in the draw was ∼200 meters.
The calculated numerical aperture (NA) and the normalized frequency V number of the As-S glass fiber with a core diameter of 200 µm are shown in Fig. 1(b). At the wavelength of 2 µm, the NA and the V number are ∼0.38 and ∼120, respectively, indicating that the 200-µm diameter core supports more than five thousands of modes, according to the empirical formula, N≈V2/2, where N is the number of the supporting modes [36].
2.2 Fiber loss measurements
The global attenuation of the MMF has been measured using a Bruker Tensor 27 Fourier-transform infrared (FTIR) spectrometer. The cutback length was ∼0.8 m each time. A few cutbacks have been done for determining the loss spectrum. The fiber attenuation at 2 µm was also measured using a 2-µm fiber laser as the light source. The typical cutback length was ∼2 m. The loss was then linearly fitted according to the transmitted power values obtained from 3-4 cutbacks.
Figure 2 illustrates the fiber loss measured at 2 µm (see the scatter), in comparison with the measured global loss spectrum using an FTIR spectrometer in the range of 1.8-7 µm. It is seen that the measured loss of 0.25 ± 0.05 dB/m at 2 µm is consistent with the loss measured by the FTIR spectrometer (∼0.3 dB/m). Note that the peaks at ∼3 µm and ∼4 µm shown in Fig. 2 are due to the residual O-H and S-H impurities respectively in the arsenic sulfide glasses [27,37].
Fig. 2. Loss spectrum of As-S MMF measured using FTIR spectrometer, together with the loss of MMF (scatter) measured at 2 µm.
3. High-power mid-IR laser transmission in ChG MMFs
3.1 Experimental results of high-power laser transmission
A customized diode-pumped 2-µm continuous-wave (CW) thulium doped silica fiber laser (provided by Mid Infrared Laser Technology (Jiangsu) Co., Ltd.) was used as the high power laser source for testifying the laser transmission and fiber damage of large-core ChG fibers. The output fiber pigtail was equipped with a fiber endcap. The beam quality factor M2 of the laser was ∼1.2, and the maximum output power was ∼130 W.
Figure 3 shows the schematic of the experimental setup of laser transmission through the As-S MMF. An uncoated calcium fluoride lens (Thorlabs) with a focal length of 50 mm and a second uncoated calcium fluoride lens with a focal length of 150 mm were used for collimating and then focusing the laser beam into the input end of the As-S MMF. With the above lens combination, the focused beam waist diameter in front of the As-S MMF is estimated to be 180 ± 10 µm, which is ∼90% of the core diameter of the MMF.
As shown in Fig. 3, the input end of the fiber with a length of ∼12 cm was sandwiched between two brass V-grooved plates. Double-sided conductive copper tape was applied on the top surface of the fiber ensuring good contact between the fiber and the metal plates. The V-grooved plates were attached on semiconductor Peltier modules (TEC1 12706), using conductive glue. A thermocouple was allocated next to the center position of As-S MMF section on the lower brass plate. The Peltier modules and the thermocouple were connected to a PC for programming and recording the temperature of the input section of the As-S MMF. A water-cooled aluminum plate was attached below the Peltier modules, for dissipating the heat generated on the opposite side of the cooling face due to the Peltier effect. All the above elements were mounted on three-dimensional (3D) translation stages. The latter was used for precisely adjusting the light coupling into the MMF.
By monitoring the laser power in front of the input end and the output end of the MMF, the transmission efficiency η (η=Pout/Pin, where Pin and Pout are the incident power and output power, respectively) through the MMF with a certain length has been obtained. For each experiment, before Pin is raised to high power, the transmission efficiency η through the tested MMF was maximized by optimizing the launching position of the fiber input at low Pin (∼1.5 W). The launched power was well confined inside the core, confirmed by observing the guidance from the fiber output end using a Tigris-640 MCT-BB high-speed MWIR (1.5-6 µm) camera. A fan-cooled thermal power meter (S322C Thermal Power Head, Thorlabs) with optical power range of 0.1-200 W was used for measuring Pin and Pout. To prevent the scattered laser light from the input end entering the power meter head located at the output end, the fiber input axis and the output axis were nearly perpendicular to each (see Fig. 3). The bending radius of the MMF was between 15 and 30 cm. Within such a bending radius range, the bending loss of an As-S MMF with a core diameter > 100 µm should be negligible [26].
A series of experiments on laser transmission and damage in As-S MMFs has been carried out. For each test, the temperature of the first 12-cm-long input section was cooled by the Peltier modules. The temperature of the fiber input was set at 15 °C, which was ∼10 °C below the ambient temperature of the experiment. The temperature fluctuation of the PID (i.e., Proportional-Integral-Derivative)-loop-controlled temperature was measured to be below ±0.1 °C during the experiment (see Fig. 4).
The length of the tested As-S MMFs was between 40 and 100 cm. Figure 5 shows the relation between the incident power and the transmitted power in four selected samples. The facets of the MMFs used for the transmission experiment were mechanically cleaved before the experiments. Mind that the PEI coating of the fiber ends has been dissolved firstly by dipping in organic solvent, e.g., carbon tetrachloride, for a few minutes before the cleavage.
Fig. 5. Relation between measured incident and transmitted power in selected As-S MMFs with forced cooling. Each colored upward arrow represents the incident power when the sample marked with same color is damaged.
Since As40S60 (at. %) core glass has a refractive index n of ∼2.429 at 2 µm (see Fig. 1(a)), a normal reflection loss (R) at one fiber facet is estimated to be ∼17%, according to the formula of R = [(n-1)/(n+1)]2 [38]. The total Fresnel reflection loss due to the multiple reflections inside the fiber can be calculated to be ∼30%. It is deduced that the theoretical maximum transmission efficiency η (=Pout/Pin) in the As-S MMF is ∼70%. The solid gray line in Fig. 5 represents such a theoretical limit.
In the experiment, the incident power Pin was raised step-by-step by increasing the electric output power percentage of the laser controller. For each set point, the fiber input was exposed to the incident laser for at least 2 minutes. It is seen from Fig. 5 that sample #1 and #3 have got damaged under the incident power of 47 W, while sample #2 has been damaged under the incident power of 65 W. In the case of sample #4, it was damaged under the Pin of 120 W with the transmitted power of 63 W. To the best of our knowledge, either for the incident Pin or the transmitted Pout, it is the highest recorded power in any flexible chalcogenide fibers within the 2-5 µm range. Note that after the incident power has reached 120 W for ∼30 seconds, the fiber started burning in a ∼5-cm-long section just after the 12-cm-long cooled section. One can also see from Fig. 5 that for sample #4, the transmission efficiency η is 55% and with excellent linearity before Pin reaches 91 W, and then the slope drops down to 37% before the fiber is damaged at the point of Pin of 120 W. Such a power saturation behavior just before the damage is consistent with the previous observation in As-S and Ge-As-S MMFs with 1-mm core diameter under the exposure of 5.4-µm CO laser with Pin >300 W [27]. The significant decrease of the Pout/Pin slope before the fiber failure implies that the heat accumulates around where the fiber section will fail and the heat ought to be converted from the reduced fraction of the transmitted power. Same behaviors have been also observed in other samples in our series of experiments. But since the maximum incident power for those samples is much lower than 100 W, the fiber samples are damaged under the incident power level quite close to the turning point. Note that, a colored upward arrow at a certain incident power is plotted for each sample in Fig. 5, representing the damage incident power of the sample marked with same color.
An extra experiment has been carried out to investigate the influence of the ambient temperature on the transmittance of the As-S MMF. The tested MMF had a length of 60 cm. The temperature of the first 12-cm long input part was program-controlled by the Peltier modules. Figure 6(a) plots the measured temperature variation of input section. The sample has been maintained at each set temperature for 3-5 minutes. Figure 6(b) shows the variation of Pout under a constant Pin of 5.40 W. It is seen from Fig. 6(b) that when the temperature of the input section varies between 7 °C and 50 °C, Pout is measured to be 2.94 W with a tiny fluctuation of ±0.04 W. Since the measured Pout variation is within the measurement accuracy of the power meter, it can be deduced that the drop of the efficiency η (=Pout/Pin) in Fig. 5 is due to the localized hot spots with a temperature far more than 50 °C. On the other hand, when the transmitted power or launched laser power, Pout or Pin, is far below the damage threshold of the fiber, the uniformly distributed heat on the entire fiber will hardly change the linearity between the Pin and Pout.
Fig. 6. (a) Measured real temperature of first 12 cm of MMF input and (b) recorded output power of ChG MMF with total length of 60 cm in ∼1 hour time span.
Table 1 summarizes the laser transmission and fiber damage results on As-S MMFs at the wavelength of 2 µm in this work. The data provided in Ref. [27] at the wavelength of 5.4 µm are also listed in the table for comparison. Note that the incident intensity in this work is calculated according to the focal spot size of the incident laser of 180 µm, which is ∼90% of the core diameter, while the incident intensity in Ref. [27] is calculated according to that the spot focused in front the 1-mm core MMF is 500 µm, which is only ∼50% of the core diameter [27].
Table 1. Summary of laser transmission and damage on As-S MMFs at wavelength of 2 µm, in comparison with the data given in Ref. [27] at 5.4 µm.
One can see that the slopes of transmission efficiency η (=Pout/Pin) of the four samples in this work are between 53 ± 3%, which is close to the value of 56% given in Ref. [27]. But sample #4 in our work actually resists incident intensity of 472 kW/cm2 and transmitted intensity of 200 kW/cm2, higher than the values given in Ref. [27] by 100% and near one order of magnitude, respectively. In terms of absolute incident power and transmitted power, our best results are still lower than the ones reported at 5.4 µm [27]. However, the incident power and transmitted power achieved in our work is sufficiently for practical usage, for instance 2-5 µm laser-based countermeasures. What is more, the As-S glass MMFs in this work has an OD of 300 µm, ensuring excellent flexibility of the fiber component for realizing compact devices, while the As-S MMF with 1-mm core diameter used in Ref. [27] virtually possesses no flexibility.
3.2 Observation of high-power laser damage of As-S glass fibers
All the fiber damages that we have observed in the experiment are thermal failure under CW laser irradiation. This is consistent with the conclusion drawn in Ref. [27]. Specifically, in our work the fiber was damaged (i) either at the input end if it is not completely embedded inside the brass plates, or (ii) randomly somewhere along the fiber out of the cooled section.
In the series of laser transmission and fiber damage experiments, either explosion or burning has been observed in the damaged section, when the incident power Pin was enhanced to the damaging power level. Also, it is worth pointing out that all failures occurred after the ratio of the Pout/Pin started decreasing when Pin increases.
Explosion occurs locally inside the fiber and yellow smoke can be seen jetted from the fiber, in particular at the place close to the output end. Figure 7 shows the optical photograph of a cleaved cross section of the As-S MMF after explosion. It is seen that the explosion has initiated from a spot marked with “A”, which has a diameter of ∼10 µm. Then the explosion energy seems to be released through the channels marked with “B” and “C”. The original size of the local defects before the explosion happened ought to be much smaller than 10 µm, otherwise much higher scattering loss should be observed.
Fig. 7. Optical photograph of cleaved fiber cross section after explosion. A: spot where the explosion started; B and C: channels where the explosion energy is released through.
Burning is more often to be observed than explosion in our high-power transmission experiments. All four selected samples, #1-#4, have ended with burning rather than explosion. It should be noted that the fiber input end and output end are not always be damaged in the experiments. Burning occurs at the input end only if the fiber input facet is not well buried inside the brass shield, when it is prominent from the cooled plates for example even by 1 mm.
We have noticed that, in the experiments, fiber damage occurs: (i) where the fiber section was without forced cooling and (ii) where there was mode conversion occurring. The former means that there is heat accumulation in the local section before damage starts there. Second, the forced cooling method can effectively remove the heat and the cooling actually delays the damage to the uncool part. Mode conversion occurs at the input facet when the laser spot is coupled into the fiber, i.e., redistributing spatial light energy from free space to the guided modes in the waveguide. Mode conversion also occurs inside the fiber when the propagating light meets certain perturbations along the fiber. Then the power fraction carried by each guided mode has to be redistributed [36]. The perturbations along the fiber could be distortion of the index profile, sharp bending, twisting, and so on. In general, heat generation can happen when mode conversion occurs, because light guided in the low-loss fiber core will leak into the cladding or coating area with relatively high loss. When the transmitted power is high, the local perturbation-induced heat generation becomes significant. Such an emerging local temperature gradient profile becomes a ‘hot spot’ and intercepts even more fraction of the transmitted power for heat generation until the fiber is damaged locally.
3.3 Proposed high-power damage mechanism of As-S fiber
Because all fiber damage occurred after the linear slope of the Pout/Pin started dropping, where there was no active cooling applied, some types of defects located in the fiber core should be responsible for the local accumulated heat in the damage section under high power. First, under optical microscope, no visible defects have been observed in the tested fiber. From the loss cutback method, the transmitted power (in dB) behaved linearly for all the cutbacks. Thus we can rule out the possibility of large defects with µm size first. Absorbing impurities, either ionic impurities or impurity bondings (e.g., oxygen or hydrogen involved) are also not likely, because they should be distributed in the glass uniformly and no characteristic absorption bands are seen at ∼2 µm in the loss spectrum (see Fig. 1). Therefore such types of defects could be scattering centers with dimensions much smaller than the observing wavelengths (i.e., from visible to 2 µm).
Due to relatively loss of the tested As-S MMFs, the concentration of such types of defects should be low. The observation that the damage section appeared randomly along the uncooled fiber part can be understood by the following model. When the impurity defects are dispersed uniformly in the host and the dopant concentration is high, the impurity concentration can be expressed as a constant with a small amplitude of fluctuation. But when the impurity concentration is low, the amplitude of fluctuation becomes comparable to the real concentration. Then the concentration appears nonuniform along the fiber. Thus the random location of the damage section along the fiber and the observed fact that the samples #1-#4 with the same loss value were damaged at different incident power Pin can be explained.
One type of the possible defects here could be the heterophase inclusions in As-S fiber [24,37,39,40]. The dimension of the heterophase inclusions in As-S glass is typically at the order of tens of nanometers [37], which is ∼2 order of magnitude smaller than the wavelength. Note that the nano-sized heterophase inclusions in As-S glasses typically contain the impurities of oxygen, carbon, hydrogen, and/or silicon [39].
The scattering due to extrinsic defects and impurities can lead in Rayleigh scattering, Rayleigh-Gans scattering, and so on [41]. In the following we borrow the widely accepted Rayleigh scattering formula to build a simple but not precise physical image of the nano-sized extrinsic scattering defects responsible for high-power damage of the As-S MMFs.
When the density fluctuations, or refractive index fluctuation, with dimensions much smaller than the light wavelength, the formula for calculating Rayleigh scattering loss coefficient can be used to estimate the magnitude of the refractive index of the nano-sized defects. The Rayleigh scattering attenuation coefficient (α) can be expressed as [42–45]:
Additionally, based on the data given in Ref. [40], the concentration of the nanometer-scale scattering centers in the As-S fiber with a loss of 0.25 dB/m at 2 µm is estimated to be at the order of 105 cm-3. It means that in the studied As-S MMF with a core diameter of 200 µm, there are a few tens of scattering centers per centimeter. The distribution of such a low concentration of defects certainly cannot be uniform along the fiber. Since the energy distribution in individual modes is determined by the cross-sectional refractive index profile of the fiber core [46], under high power level of transmitted laser, the equilibrium of the energy distribution carried by individual modes in the As-S MMF is broken when the propagating light meets nano-sized scattering defects with relatively high concentration. Extra heat is generated in such an energy redistribution process amongst guided modes. And localized hot spots are formed this way. Ultimately fiber is damaged in such a section once the accumulated heat raises the local temperature approaching or above the glass transition temperature Tg.
In addition, Eq. (1) contains a term of ${(n_s^2/n_m^2 - 1)^2}$, which represents the contribution of index contrast between the scattering centers and the matrix to the scattering loss. If we go to the extreme to assume that all scattering centers are silica particles (i.e., ns = 1.45) here, then the contribution of the ${(n_s^2/n_m^2 - 1)^2}$ term to the loss will increase by a factor of 1018. This is obviously not possible for an As-S fiber with a loss of 0.25 dB/m only. Mind that the existence of silica nanoparticles to the fiber loss is significant. As-S glass containing SiO2 impurity particles with sub-µm size and 106-107 cm-3 concentration shows non-selective loss > 10 dB/m at 2 µm [40]. Therefore, the above calculated index contrast of ∼5 × 10−10 between the scattering centers and the fiber actually indicates that the size of the scattering centers containing the possible impurities of oxygen, carbon, hydrogen, and/or silicon is far smaller than the optical wavelength. Therefore the boundary between the defects and the glass matrix cannot be resolved by the light and the effective index of such index fluctuation becomes close to the glass matrix.
3.4 Thermal loading calculation of As-S fiber under high-power damage
In the case of sample #4, when the incident power Pin is above 91 W, the transmission efficiency η (=Pout/Pin) decreases from 55% to 37%. It indicates that when Pin is raised to 120 W from 91 W, a net power of 5.3 W is converted into heat in the local short section of the tested fiber, according to the decrease of the two linear fitting lines for sample #4 in Fig. 5. On the other hand, ∼15% (i.e., the differential between the theoretical ∼70% limit and the first linear slope of 55%) of the incident power is converted into heat along the entire fiber length. Since the fiber loss in the total length of 0.5 m is only ∼0.13 dB, it is fair to assume that the heat is uniformly distributed along the fiber with an intensity of 0.36 W/cm, when Pin = 120 W. Therefore, at the moment when the fiber is damaged under Pin of 120 W, the total generated heat Q in the localized damaged section with a length of Lx should be 0.36x+5.3 W, where Lx = x cm (see Figs. 8(a) and 8(b)).
Fig. 8. (a) Schematic of heat flow of heat generated in the core conducting through cladding layer in the damage section, where Rc is the core radius, Ro the radius of the outer surface of the cladding, ΔL the length of heat accumulated section, k the thermal conductivity of the cladding material, Tc the temperature of the fiber core, To the temperature of the surface of the cladding, T∞ the temperature of the surrounding, Q1 heat conducting from the core to the cladding outer surface, Q2 heat dissipated from the fiber outer surface to the surrounding, Q total heat generated in the localized damaged section, h heat transfer coefficient of cooling, respectively. (b) Longitudinal schematic of fiber with total length of L, containing cooling section with length of Lc, damaged section with length of Lx, and the rest. Mind that the damage section Lx is randomly located after the section with active cooling (Lc).
As shown in Fig. 8(a), the heat conducting from the core to the cladding outer surface (Q1) can be calculated by [47,48]
where Rc is the core radius, Ro the radius of the outer surface of the cladding, ΔL the length of heat accumulated section, k the thermal conductivity of the cladding material, Tc the temperature of the fiber core, To the temperature of the surface of the cladding, respectively.It is known that the thermal conductivities k of As-S glasses and PEI polymer are in the range of 0.20 ± 0.03 W/(m·K) [49]. Here the k value is chosen to be 0.20 W/(m·K) for all the materials composing the MMF. Therefore, PEI layer can be treated as part of the fiber cladding in the calculation.
The heat dissipated from the fiber outer surface to the surrounding (Q2) can be calculated by Newton’s law of cooling [47],
where h is the heat transfer coefficient to the surrounding, 2πRoΔL the total outer surface area of the fiber cladding (including PEI layer), T∞ the temperature of the surrounding, respectively.In the calculation, the fiber parameters Rc and Ro are set to be 100 µm and 150 µm, respectively. It is assumed that the fiber is damaged at the core temperature Tc of 170 °C, ∼30 °C lower than Tg of the core glass. The temperature of the fiber outer surface To is assumed to be 100 °C, while the surrounding temperature T∞ is set to be 15 °C, assuming that the fiber and the metal heatsink is well contacted.
Figure 9(a) plots the calculated heat flow dissipated to the surrounding versus various length of the damaged section Lx. The thick gray line represents the maximum capability that the heat can be conducted from the core to the cladding under the real fiber structural parameters. The thin lines with various colors represent the maximum capability that the heat can be removed from the fiber outer surface to the surrounding through a certain cooling approach with a given heat transfer coefficients h. Note that in the cases of stagnant air cooling, forced air cooling, and forced water cooling, the typical values of h are 10 [49,50], 500 [49], and 4000 W/(m2·K) [51], respectively. We assume that the h value in our brass heatsink cooling method with constant temperature of 15 °C, 10°C lower than the ambient temperature, is the same as the forced water cooling method, because in our case the fiber surface is well contacted with the cooled heatsink and the thermal conductivity k of brass is as high as 100 W/(m·K) [52].
Fig. 9. (a) Calculated heat flow dissipated to the surrounding versus various length of the damaged section Lx. Note that h is heat transfer coefficient of cooling method. The dashed circle represents the actual section length when damage starts. Note that the fiber core diameter is 200 µm and the outer diameter is 300 µm. (b) Calculated heat flow dissipated to the surrounding versus various length of the damaged section Lx for the case in Ref. [27]. Note that the fiber core diameter is 1 mm and the outer diameter is assumed to be 1.2 mm.
For an efficient cooling approach, first, the conducting capability Q1 arising from the fiber structure should be not lower than the heat Q generated inside the fiber core, otherwise the temperature of the core region will be ultimately ramped to the damage temperature. Second, the heat Q1 approaching fiber surface should be dissipated to the surrounding by a certain forced cooling method with a sufficiently high heat transfer coefficient h; in other words, the heat dissipating capability Q2 of the cooling method should be not lower than Q1 to avoid the heat accumulation causing the damage. The relation of Q1 ≥ Q2 ≥ Q must be satisfied, in order to avoid the fiber damage. Mind that Q1 is proportional to (Tc-To) and Q2 is proportional to (To-T∞). The real To should not be too close to the room temperature, otherwise it means that the fiber is a too poor thermal conductor and the fiber damage will occur by all means even with active cooling. On the other hand, To should not be too close to the upper working limit of the glass (170 °C), otherwise it means that the fiber is a too good thermal conductor and the fiber damage cannot happen even without active cooling. Therefore, in the calculation, we set fiber outer surface To to be 100 °C, which is approximately the medium value of room temperature (25 °C) and the maximum working temperature of As-S glass (170 °C).
It can be seen from Fig. 9(a) that, only the cooling method with heat transfer coefficient h close to 4000 W/(m2·K), i.e., either the forced water cooling or the heatsink method used in this work, can effectively prevent the heat accumulation and the consequent thermal failure within the As-S MMFs under high incident laser power. Second, the actual length of the damaged section in our experiment should be longer than 3 cm (see the dashed circle in Fig. 9(a)). This is consistent with our observation that the burning always starts within a length of 5-10 cm. Quantitatively, such a short section should contain hundreds of nano-sized scattering centers, according to the above estimated nano-defect concentration of ∼105 cm-3. These defects are responsible for the drop of η (=Pout/Pin) from 55% to 37% (see Fig. 5) after Pin reaches the turning point at Pin = 91 W.
It should be pointed out that, although forced cooling with an assumed heat transfer coefficient h of 4000 W/(m2·K) has only been applied on the first 12-cm long section here, the maximum transmitted Pout from a 12-cm long fiber will not be too different from a 1-m-long MMF if the forced cooling is applied to the entire length, because the fiber loss is as low as 0.25 dB/m. Therefore, our above experimental results have actually proved that the minimum transmitted power Pout through the 200-µm core As-S MMF with a length of ∼1 m is 63 W, corresponding to the minimum transmitted power density of 200 kW/cm2.
Figure 9(b) shows our calculation on the data extracted from Ref. [27]. In that work, the tested As-S MMF with a Teflon cladding had a core diameter of 1 mm and an unknown cladding diameter. We assume that the outer diameter of that As-S MMF is 1.2 mm. Because the linear η (=Pout/Pin) was 56% before it dropped [27], the net heat Q generated in the localized section with a length of Lx can be estimated be 0.7x+7 W (where Lx = x cm), when the fiber was damaged under the Pin of 461 W. Since forced N2 gas cooling has been applied for the entire fiber [27], the heat transfer coefficient h is assumed to be 500 W/(m2·K). It can be seen from Fig. 9(b) that the cross point between the generated heat (the thick red line in Fig. 9(b)) and the heat transfer capability of forced air cooling (the thin green line in Fig. 9(b)) is at x= ∼10 cm. Such a length is approximately 2-3 times longer than the one in our experiment (see Fig. 9(a)). It implies that the concentration of the nano-defects in Ref. [27] is lower than that of our fiber. This can be supported by the fact that the loss of the tested As-S MMF in Ref. [27] was only ∼0.1 dB/m at 2 µm, about half of the loss of our fiber. It can be deduced that the heat generated in the damaged section in Ref. [27] was ∼15 W, when the incident power was 461 W. If a heat transfer approach with a high h of 4000 W/(m2·K), e.g., forced liquid (i.e., water) cooling method [53], could be applied in the 1-mm-diameter core fiber used in Ref. [27], the maximum transmitted power Pout can be enhanced by at least a factor of 2, i.e., Pout = ∼500 W or higher, judging from the heat transfer allowance from the fiber conductivity and the heat dissipation capability of the cooling method shown in Fig. 9 (b).
In addition, it can be deduced that, for an As-S MMF with a core diameter of 260 µm, an OD of 300 µm, and the same concentration of nano-sized scattering defects as the one we have tested in this work, the transmitted power of 2-µm laser can be enhanced to 100 W. This is because in such a case, the heat transfer rates of the fiber structure and the forced cooling method are still the same as the fiber with a core diameter of 200 µm and an OD of 300 µm shown in Fig. 9(a). Note that in such a deduction, we assume that the increase of the generated heat in the localized section is proportional to the enhanced laser power.
In the case of the transmitted power Pout of 63 W, the generated heat Q within the 5-cm long local section is ∼7 W (i.e., 0.36x+5.3W, where x = 5 cm). Therefore, in the MMF with a core diameter of 260 µm and an OD of 300 µm, the generated heat Q in the core is estimated to be ∼11 W, when the transmitted power Pout reaches 100 W. Since the cladding layer of the larger core MMF becomes thinner than the 200-µm-core MMF, the conducting capability Q1 of the fiber is also enhanced, in comparison with the one shown in Fig. 9(a). Therefore, the net heat flow Q generated inside the core is still below the capabilities of thermal conducting of the fiber structure and the heat dissipating from the forced cooling method.
Moreover, we expect that if the concentration of the nano-sized defects in our As-S MMF can be further reduced by a factor of 2-3 through deep-level glass purification, 2-5µm laser power delivery beyond 100 W can even be realized in the MMF with 200 µm core diameter and 300 µm OD. This is because in a fiber with lower concentration and concentration fluctuation of nano-sized scattering centers, the same heat generated before the laser damage will be distributed in a longer fiber section and it will ease the heat dissipation issues.
At last, it is well known that Fresnel loss of a chalcogenide glass fiber is 30% or higher, because of the high refractive index of such a glass family. Previous trials using antireflection (AR) coating on As-S fiber have showed that it is difficult to find a low-index coating material with both required refractive index (for antireflection) and the thermal expansion coefficient (for thermal mismatching during high laser power usage). For example, it was seen that under multi-hundred CO laser exposure, the damage incident power level of the As-S fiber with a single-layer PbF2 AR-coating was actually ∼50% lower than that of As-S fiber without the AR-coating [27]. Instead, nanoimprinting approach has been successfully applied on chalcogenide glass fibers with enhanced mid-IR transmission and supercontinuum generation for the very first time [54]. In the case of high-index chalcogenide glass fiber, such a single-material motheye-microstructure technique is obviously advantageous over the previous AR-coating technique requiring a pair of materials with matched high and low refractive index, in particular in the scenario when multi-hundred-watt mid-IR laser is used.
4. Conclusions
In summary, we have experimentally demonstrated that a flexible multimode As2S3 glass fiber with 200 µm core diameter can resist incident 2-µm laser power of 120 W and deliver transmitted power of 63 W. The high-power laser damage mechanism of As-S glass fiber is proposed to be arising from the nano-sized scattering defects inside the glass host. The heat transfer analysis on the high-power damage process of As-S MMFs is in good agreement with the experimental results both in our work at 2 µm and in the previous report on transmitting multi-hundred-watt mid-IR 5.4-µm CO laser through As-S glass MMFs. Finally, it is expected that 2-5 µm laser power transmission beyond 100 W can be realized in a flexible large-core As-S glass multimode fiber either by optimizing the fiber structural parameters or by further lowering the fiber attenuation associated with the concentration and the concentration fluctuation of nano-sized scattering centers.
Funding
National Natural Science Foundation of China (62175096).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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