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Abstract
New measurements of the thermo-optic coefficients (TOCs) in ternary GeO2 and B2O3 co-doped silica core optical fibers are presented. Material additivity models are applied to the measurements to shed more light on the relative contributions by each constituent. Three of the ternary fibers studied are drawn at different temperatures, but from the same preform, providing insight into the influence of fabrication conditions. It is found that the TOC of the B2O3 constituent is somewhat less negative than previously reported and trends towards more negative values with increasing draw temperature. Two approaches are taken in determining the TOC of one of the fibers, including measuring the LP11 cutoff wavelength as a function of temperature. The latter suggests an attractive application for fiber cores with a TOC lower than the cladding: fibers whose V-number intrinsically decreases with increasing temperature. Such thermally-mode-reducing optical fibers could be of great consequence for high-energy laser applications.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Transverse mode instability (TMI) is defined as kHz fluctuations in the output beam of a high-power fiber amplifier or laser. This effect is considered deleterious and is understood to largely restrict the power scalability of large mode area (LMA) Yb-doped fiber amplifiers [1,2]. It has been shown that a thermally induced index grating, owing to quantum defect heating of the active fiber, causes dynamic energy transfer between modes [3,4]. Several models for TMI have been proposed and presented [5,6], generally pointing to a conclusion that lowering the thermo-optic coefficient (dn/dT or TOC) of the core glass can raise the threshold power for the onset of TMI.
Lowering the positive-valued TOC of SiO2 can be achieved by introducing materials with negative-valued TOC into it. Such dopants include P2O5 [7], B2O3 [8], SrO [9], and F [10]. The first two are particularly interesting since they can be incorporated in high concentrations [11,12] into fibers fabricated via conventional means (e.g., modified chemical vapor deposition, MCVD). Furthermore, based on literature data and considering the results in [7] for P2O5 in fiber, B2O3 has the lowest TOC value of the four materials listed above, which is reported to be -35.0 × 10−6 K−1 [8]. Therefore, it is attractive to consider doping B2O3 into the core of a fiber as an efficient means to lowering the TOC. However, since B2O3 has a lower refractive index than silica, the addition of index-raising dopants, such as GeO2 or P2O5, to the core becomes necessary for conventional fibers with pure silica claddings.
Here, the TOCs of ternary GeO2 and B2O3 co-doped silica fibers are investigated to better understand the individual contributions by each of these constituents. This compositional family is consistent with photosensitive fibers [13,14] used in the fabrication of fiber gratings, and therefore the results presented herein will be useful for tailoring the thermal characteristics of such devices. The individual TOCs for the three components are determined through the investigation of five different fibers. One of these has a binary GeO2 doped silica core, while the remaining four have ternary core compositions, and all have pure silica claddings. The investigative approach is as follows: by making TOC measurements on one of the ternary fibers in two different ways, the TOC of pure silica could be determined. Then, by adopting this value for SiO2, that of GeO2 was determined from the binary germanosilicate core fiber. Finally, these two bulk TOCs were applied to measurements on the remaining ternary fibers to determine the TOC of B2O3. The three remaining fibers were drawn at different temperatures from the same preform to investigate any influence thermal history might have on fiber TOC. It is found that, at least in this glass family, the TOC of B2O3 is somewhat less negative than previously reported, and trends towards more negative values with increasing draw temperature. Discussions of next steps and applications are provided at the end.
2. Optical fibers
Five optical fibers were employed in this study, including two that are commercially available: 1) UHNA3 (Coherent|Nufern) and 2) F-SBG-13/15 (Newport Corp.). The remaining three are custom fibers originally fabricated by Coherent|Nufern [15]. They are drawn from the same preform but at three different temperatures: 3) 1900°C, 4) 1950°C, and 5) 2150°C. Hereafter, these fibers will be referred to by number as ascribed above. Composition analysis was performed using wavelength dispersive X-ray (WDX) analysis for all but Fiber 2. As will be discussed later in the paper, the composition of this fiber was not entirely relevant. Fiber refractive index profiles (RIPs) were measured using a spatially resolved Fourier transform interferometer (Interfiber Analysis, LLC) with a sub-micron spatial resolution [16]. Results of these measurements are shown in Fig. 1. To summarize, Fiber 1 was doped only with GeO2 while all the other fibers were doped with both B2O3 and GeO2. The compositions of Fibers 3–5 (provided by Coherent|Nufern) were similar since they were derived from the same preform.
Fig. 1. RIPs and compositions for fibers a) 1, b) 2, c) 3, d) 4, and e) 5. Note that the Fiber 2 composition was not measured.
3. Measurements of TOC
3.1 Modal TOC
The apparatus used to measure the modal TOC of the fibers is described in [17], which is constructed as a ring laser configuration where the fiber-under-test (FUT) forms part of the cavity. By changing the temperature of the FUT, which is kept in a heated thermal water bath, and monitoring the change in laser free spectral range (FSR), the modal thermo-optic coefficient (TOC, dn/dT) can be characterized [17]. As shown in Fig. 2, a 976 nm laser diode was used to pump an erbium doped fiber (EDF), resulting in laser action at a wavelength of 1555 nm. The isolator was employed to guarantee a unidirectional propagation of the light in the ring. Finally, the output signal was sent into a visible-infrared photodetector through the output coupler and an electrical spectrum analyzer (ESA) was used to interrogate the resulting output signal. A typical ESA spectrum showed beating of the longitudinal laser modes and so was characterized by a series of delta functions spaced by the FSR. The test fiber in the setup was typically 4 to 5 meters in length.
The FSR of a ring laser can be found from FSR = c/(n1L1+n2(T)L2(T)), where n is the modal refractive index and L is fiber length. Both are functions of temperature (T) for the FUT (subscript ‘2’). The unheated portion of the cavity is denoted by the subscript ‘1,’ with all the remaining (and various types of) fibers comprising the cavity being lumped into n1 and L1. Then the temperature derivative of the FSR (dFSR/dT) can be calculated as
The change in FSR with temperature is quite small due to the relatively short length of the FUT relative to the remainder of the cavity. However, since numerous longitudinal modes are excited in the ring laser, it becomes convenient to measure the change in FSR for higher order beat harmonics with changing temperature. Doing so enhances the apparent change in FSR by a factor equal to the harmonic number. A typical set of data obtained using this methodology is provided in Fig. 3. The modal TOC can then be revealed by fitting the model represented by Eqs. (1)–(3). Table 1 shows the modal TOCs measured for all five fibers. The measurements of Fibers 3–5 were repeated several times, which enabled the quantification of uncertainty.
Fig. 3. Free spectral range (FSR) versus temperature utilizing ring laser setup in Fig. 2 for Fiber 1 (beat harmonic = 1000).
Table 1. TOCs for Fibers 1 to 5 using the setup in Fig. 2.
3.2 Material TOC
Fibers 2–5 possess cores with TOC values less than that of silica, but still positive-valued. Accordingly, both the core and cladding refractive indices will increase with increasing T, but that of the core increases at a lesser pace with increasing temperature. As a result, the numerical aperture (NA) of the fibers will decrease with increasing temperature, resulting in the same trend for the LP11 cutoff wavelength. The relationship between material TOC and change of (single mode) cutoff wavelength (λc) can be illustrated by taking the derivative with respect to temperature of λc = 2πaNA/2.405, where a is the core radius and 2.405 is the first zero of the Jo Bessel function. This derivative can be rearranged to yield
The LP11 cutoff wavelength can be measured using a standard method [19]. The setup is shown schematically in Fig. 4. Referring to the diagram, light from a tungsten-halogen lamp (Ocean Optics, Inc.) is launched into the test fiber after passing through a multimode fiber. The resulting transmission spectrum was obtained with an optical spectrum analyzer (OSA). The test fiber (typically 2 to 3 m in length) was coiled to a diameter of 15 cm and again held in a water bath to accurately change its temperature. The loss spectrum was obtained by subtracting (using a logarithmic scale) the output spectrum from the white light source spectrum. Unfortunately, only Fiber 2 provided adequate temperature-dependent change in the cutoff wavelength to provide meaningful data. The result is shown below in Fig. 5. In summary, λc changed linearly with temperature, decreasing by around 11 nm as the temperature of fiber was increased from 40°C to 89°C. Analysis of the data obtained from this measurement will be provided in Section 4.2. For the remaining fibers, the change in cutoff wavelength was less than a few nm, which was deemed here to be insufficient in the temperature range (ΔT ≈ 50°C) to ascribe reliability to the measurement. For Fiber 1, this resulted from its relatively large NA0. For Fibers 3–5, it was the relatively lower value of the left-hand-side of Eq. (4) that limited Δλc, or in other words, the core and cladding TOC values were too similar.
Fig. 5. Loss spectrum for Fiber 2 from 40 °C to 89 °C. The cutoff wavelength drops around 11 nm in this range.
4. Determination of constituent TOC
4.1 Modeling TOC in optical fibers
4.1.1 Material TOC
The TOC of a bulk multicomponent glass depends on the TOC values of its N different constituents. This relationship can be expressed via a material additivity model [20] as
where ni is the index and dni /dT is TOC for a specific constituent i. The additivity parameter, xi, in this case, is the volume fraction of that constituent in the multicomponent glass. It is generally more convenient to express xi in terms of mole or weight percent to match typical compositional data obtained through electron microprobe analysis, for example.Although Eq. (5) is suitable for bulk glass, the CTE should be taken into consideration in calculating the TOC as the core is clad in pure silica. Since SiO2 has a relatively low CTE compared to B2O3 and GeO2 [21], thermal expansion of the core will be restricted by the cladding [22], manifesting as pressure when the temperature is increased. In this case, a correction term [23] can be added into Eq. (2) which then becomes
4.1.2 Modal TOC
It is clear from Fig. 1 that the RIPs for all the five fibers are not step index. Therefore, the refractive index of the core, ncore, cannot be taken to be single-valued (nor can its thermal derivative, dn/dT, value for that matter). Instead, the RIP (and compositional profile) is approximated by a six-layer step structure (as in [24]). Equation (5) (for the index) with Eq. (9) then can be employed in all six layers. From this approximate RIP, the modal index can be found as a function of temperature, which is given by n(T) = β(T)λ/(2π), where β(T) is the propagation constant in the fiber and λ is the vacuum optical wavelength. Finally, the modal TOC can be found from dn/dT = [n(T1) – n(T2)]/(T1 – T2), where T1,2 are simply two different temperatures in a linear regime for the TOC. Therefore, by determining the temperature-dependent modal effective index using the RIP of the core [25], and then by comparing the computed modal TOC with measurement results, the TOC of the constituent can be used as a fitting parameter and subsequently determined. Finally, the maximum index difference is not uniform across Fibers 3–5 since they were drawn at different temperatures and seem to have slightly different compositions. It should be noted that the approach taken here characteristically considers the distribution of the optical mode(s) within the waveguide, especially as the fundamental mode diameters decrease as Δn increases.
4.2 SiO2
Previously, a value for the thermo-optic coefficient of SiO2 was determined to be 10.4 × 10−6 K−1 [18]. In the present work, however, it is found that using this value for analysis was not entirely suitable, leading to some inconsistencies between measurements. Therefore, to obtain the benchmark value for SiO2, Fiber 2 was more closely analyzed. As described above, two TOC measurements were made on this fiber: 1) modal TOC using the method outlined in Sections 3.1 and 2) material TOC using the method outlined in Section 3.2. These two measurements together, independent of the composition of the Fiber 2 core, can be used to estimate the TOC of SiO2 for this fiber.
The procedure to do so is straight-forward. First, although the composition of the core is unknown, it is understood to be a B2O3 and GeO2 co-doped photosensitive glass. The assumption is made that the relative concentrations of these two dopants are in equal proportion throughout the fiber core. In other words, Ψ = [B2O3]/[GeO2] (the brackets indicate a molar concentration) is a constant although the absolute composition is varying in the radial direction. Second, since both the TOC and refractive index are additive in the same way [see Eq. (5)], the TOC values in the core are taken to be linearly proportional to the local refractive index difference. Critical to this assumption is the prior notion that Ψ is constant in the radial direction. Hence, a TOC value at one radial position in the core, along with the RIP, completely defines the TOC distribution in the radial direction. This reduces the problem to two unknowns: 1) the TOC of the SiO2 cladding and 2) the TOC at one point in the core (such as at the peak of the RIP).
Since there are two distinct measurements on this fiber, the two unknown TOC values may be determined, even without knowledge of the absolute core composition. First, the fiber was modeled, and its cutoff wavelength was calculated using the six-layer approximation described above. Bending loss (using the model in [24]) was included in the modeling since coiling the fiber necessarily caused a shift of the cutoff wavelength to lower values relative to an unbent fiber. The cutoff is defined here to be where the propagation constant transitions from real to complex-valued. The change in cutoff wavelength depends primarily on the relative TOCs in the core and cladding, and not necessarily their absolute values [see Eq. (4)]. Therefore, the temperature-dependent cutoff measurement essentially gives the difference between the core and cladding TOCs but does not set an absolute cladding value. This difference was iterated upon until the change in cutoff wavelength matched the 11 nm change observed over the temperature range shown in Fig. 5. Note that the pure silica refractive index used in these calculations is taken to be wavelength-dependent using the Sellmeier coefficients found in [26].
From this point, the modal TOC measurement is used. Since the difference in the TOCs between the core and cladding are already determined per the cutoff measurement, the remaining unknown is the TOC for the SiO2 cladding. This value then was used as a fitting parameter and adjusted until the calculated modal TOC (again using the six-layer procedure outlined above) matched that of the measurement. The result is 7.52 × 10−6 K−1 for the core (at the peak of the RIP) and 9.96 × 10−6 K−1 for the cladding. This is 4.2% different than previously identified [8,18]. This new value for the SiO2 cladding is used in all subsequent calculations.
As a final note, a comment is made with respect to chromatic dispersion in dn/dT and the disparate wavelengths used in the two TOC measurements, specifically 1555 nm for the modal value and roughly 1100 nm for the material value (cutoff method). With help from theory found in [27], along with values taken from [28], the TOC is calculated to vary by less than 1% (decreasing with increasing wavelength) in the wavelength range considered here, and therefore the assumption is made hereafter that the TOC for silica, to good approximation, is a constant.
4.3 GeO2
The TOC value for the SiO2 cladding found above is assumed to be the same for the silica component in the core glass. Since Fiber 1 is doped with GeO2 only, it can be used to determine the TOC of the GeO2 component. Due to the large NA of this fiber, the contrast between cutoff wavelengths at different temperatures was largely dominated by measurement uncertainty, rendering it unreliable to evaluate the material TOC using the procedure in Section 3.2. However, the known composition and RIP made it possible to determine the radial TOC distribution in the fiber. Using the Fiber 1 modal TOC data and the six-layer procedure, the TOC for GeO2 was determined to be 19.5× 10−6 K−1.
4.4 B2O3
Since the compositions of Fibers 3-5 are known, the modal TOC measurements can be used to determine that for the boria (B2O3) component. Unfortunately, as discussed above, the contrast between cutoff wavelengths at the different measurement temperatures were again insufficient to reliably determine a relative material TOC directly for these fibers using the procedure in Section 3.2. But, as before, the TOC for boria was calculated using the measured data provided in Table 1 and a six-layer approximation of RIP. The TOCs for SiO2 and GeO2 came from Sections 4.2 and 4.3, respectively. All the required properties for this calculation are given in Table 2 and the final results are provided in Table 3. The values determined here are higher compared to the TOC value of B2O3 provided in [8,22], by about 36%, 30% and 23% for Fibers 3, 4, and 5, respectively. Some error analysis was also implemented and the uncertainty in the TOC for B2O3 was formulated based on the uncertainty in the modal TOC measurements. More specifically several measurements were made and averaged, and the uncertainty was taken to be the difference from the average value to the maximum excursion from this value.
Table 2. Required properties for the TOC calculation.
Table 3. TOC for B2O3 determined from Fibers 3–5.
4.5 Discussion
First, the relatively large errors in the B2O3 TOC values (Fibers 3–5) result from the fibers being somewhat lightly doped. Therefore, relatively small errors in the modal TOC measurement (∼ few %) necessarily lead to larger errors in determining constituent values as they are present in lower concentrations. This source of error can be reduced by decreasing the SiO2 concentrations in the core glass. Should error associated with the determination of the GeO2 TOC from Fiber 1 be included in this analysis, this would further compound the error. The same is true of errors associated with the composition, which is very difficult to quantify.
Second, there is a clear trend observed in the TOC values provided in Table 3, with the magnitude of the TOC increasing, becoming more negative with increasing draw temperature. Given the level of uncertainty, the trend may not necessarily be statistically relevant. However, that said, it is interesting to consider the possibility of the effect of a fictive temperature, Tf, [29] on the fiber. With this thought, a calculation was performed where the TOC of B2O3 was held fixed and that of SiO2 was adjusted to match the modal TOC data provided in Table 1. The result was that the TOC of SiO2 would have to be decreasing with increasing draw temperature. This can also be understood from the data in Table 3, which derives from the fact that the material TOC is decreasing in going from Fiber 3 → 4 → 5. If the TOC of B2O3 were constant, then to achieve the reduced material TOC in Fibers 4 and 5 relative to that of Fiber 3, the silica TOC must therefore decrease in going from Fiber 3 → 4 → 5. However, the TOC of SiO2 is well known to increase with increasing temperature [30] and therefore presumably it also increases with increasing Tf. If Tf indeed monotonically increases with increasing draw temperature in the present case, it seems unlikely that the observed trend finds its origins in an increasing Tf with respect to the silica component. Rather, Tf should be decreasing with increasing draw temperature. An alternate explanation may relate to changes in B2O3 properties with Tf, as was previously observed for the viscoelastic damping coefficient [31]. Unfortunately, efforts to deduce relative fictive temperatures from Raman measurements [29] (Renishaw µPL, 785 nm) have so far been inconclusive. A conceptually different explanation would link dn/dT to draw-induced stress as the draw temperature varied across the fibers [32], or perhaps to an effect related to the concentration of B2O3, which increases slightly in the order Fiber 5 → 4 → 3. Work is currently underway to develop a fiber with much higher dopant concentration in order to decrease the uncertainties associated with the measurements, thereby shedding more light on the observations presented here.
5. Applications
A tantalizing application for a decrease in fiber NA with increasing temperature emerges for high power fiber lasers. Clearly, one can imagine a fiber that is doped with yet larger concentrations of materials that lower the TOC when added to silica or, instead, one where GeO2 is replaced by P2O5. An increase in T would then have a much greater impact on blue shifting the cutoff wavelength in such a fiber. As previously discussed, Eq. (4) further suggests that this process becomes more significant with decreasing NA, an advantage for the large mode area fiber configurations common to the commercial marketplace (NA ∼ 0.06).
Coming at it a different way, if the NA of a multimode fiber can be made to decrease more significantly with increasing T, it is possible that the number of modes in the fiber also decreases as temperature increases. To illustrate this point, a simple example calculation is presented. Assumed is a step-index fiber possessing a core diameter of 25 µm, an NA of 0.06, and a pure silica cladding (and, therefore, a cladding TOC of 9.96 × 10−6 K−1). Figure 6 provides the V-number for this fiber versus T for three different core TOC values. On this graph, the LP11 cutoff condition is identified, suggesting that modal behavior can be controlled through a balanced combination of core composition and not-unreasonable operating temperature. This could be beneficial from the standpoint of managing TMI. Note that the critical point where the V-number is zero is the transition to an optically anti-guiding fiber. Bending loss experienced by the higher-order modes too should be considered as the temperature is increased. As an example, bending loss for the fiber described above (LP11 mode) is calculated [33] as a function of T for a coil diameter of 20 cm for the same core TOC values used in the previous simulation, with the results provided in Fig. 7. This calculation suggests that robust single mode operation can be achieved at temperatures lower than those predicted in Fig. 6, but, more importantly, greater selective loss to the higher-order modes may again be beneficial with respect to avoiding TMI.
Fig. 6. V-number versus temperature for fibers with core TOCs of 4 × 10−6 K−1 (black), 5 × 10−6 K−1 (red), and 6 × 10−6 K−1 (blue) for a fiber with pure silica cladding.
Fig. 7. Bending loss (dB/m) for the LP11 mode versus temperature for fibers with core TOCs of 4 × 10−6 K−1 (black), 5 × 10−6 K−1 (red), and 6 × 10−6 K−1 (blue), pure silica cladding, and 10 cm bending radius.
A few comments regarding the above analysis are now in-order. While the calculations illustrated an additional degree-of-freedom in the design of fibers for the high-power laser application, an idealized uniform temperature distribution had been assumed, which is more consistent with an air-cooled fiber [34]. In a realistic fiber configuration, active cooling and thermomechanical arrangement can have a significant impact on the radial temperature profile in the fiber [35], which, in turn, can significantly impact the RIP [36] and therefore fiber guiding characteristics. Although a fiber with a radially tailored TOC profile can assist in controlling this thermo-optic effect, several system-level design considerations are therefore needed in order to successfully integrate the fiber. With the assumption that such a fiber can reliably be fabricated in a uniform and repeatable fashion, several other such factors include active dopant concentration, pumping and lasing wavelengths (setting quantum defect heating), fiber surface temperature, requisite power, etc. A detailed analysis of the impact of each of these are beyond the scope of this paper but will be provided as active fibers are developed and investigated in laser assemblies.
Next, using the additive model, along with data found in [7], a calculation is presented illustrating the effect of replacing GeO2 with P2O5 (one-for-one in molar units) in Fiber 4. The material TOC of the core (in this case at the point in the core with minimum SiO2 concentration) decreases from about 8.7 × 10−6 K−1 to 5.3 × 10−6 K−1. Roughly doubling the B2O3 concentration would bring this value to below 4 × 10−6 K−1 while rendering a fiber with room temperature NA close to 0.06, consistent with the stated goals above, and not unreasonable from the standpoint of conventional (i.e., MCVD) fiber fabrication. In this spirit, a lightly co-doped (∼ few mole% total of B2O3 and P2O5 in addition to roughly 1 wt% Yb2O3) fiber was fabricated. This fiber had an NA of 0.06 and diameter of around 16 µm and was interrogated using the setup in Fig. 4, with the result provided in Fig. 8. Note that, in this case, the fiber was coiled to approximately an 8 cm diameter and held on a hot plate to achieve higher fiber temperatures. The cutoff wavelength shifted by roughly 40 nm after raising the temperature by 114 °C. This proof-of-concept exercise indicates that practical concerns include any associated increased bending loss to the fundamental mode, especially under very tight bending conditions. Work is currently underway to continue scaling the dopant concentration in an Yb-doped optical fiber and results are forthcoming. An important goal of that on-going work is to verify that the additivity mode employed here scales to lower silica (or higher dopant) concentrations.
Fig. 8. Loss spectrum from 20°C to 134°C. The cutoff wavelength drops by roughly 40 nm in this range.
6. Conclusion
New measurements of the thermo-optic coefficients (TOC) in ternary GeO2 and B2O3 co-doped silica core fibers were presented. By making a TOC measurement on one of the ternary fibers (Fiber 2) in two different ways, the TOC of pure silica was first determined. Then, by adopting this value for SiO2, that of GeO2 was found from a binary germanosilicate-core fiber. Finally, these two bulk TOCs were applied to measurements on the remaining ternary fibers to determine the TOC of the B2O3 component. The three remaining ternary fibers were drawn at different temperatures from the same preform in order to investigate that influence on fiber TOC. The modal TOC was evaluated using the ring laser configuration described in Section 3.1 for all five fibers of this study, while the material TOC for Fiber 2 was found through measurements of the dependence of the LP11 cutoff wavelength on temperature.
To implement modeling, a six-layer stepwise approximation to the core was applied. Each layer has a unique composition, and therefore TOC value. Since the temperature-dependent refractive index can be calculated for each layer, the modal TOC for the fiber could easily be modeled and compared with measurements. An established material additivity model was applied to calculate the relevant parameters (for each layer) as a function of composition. Error analysis also was carried out in the calculation of the TOC of B2O3, with the associated uncertainty based only on that of the modal TOC measurement. More specifically, several such measurements were made and averaged, and the error was taken to be the difference between the average value and maximum excursion from this value.
A potentially transformative application for a decrease in NA with increasing T emerges for high power fiber lasers. If a fiber is doped with yet larger concentrations of materials that lower the TOC when added to silica, an increase in T would have a much greater impact on blue shifting the cutoff wavelength. In this case, the number of modes in the core of the fiber may also decrease with increasing T. As such, it appears to be possible to realize a simple core / clad optical fiber that is multimode at room temperature and that becomes single mode at a (slightly) higher operating temperature. A proof-of-concept was realized using a lightly doped borophosphosilicate fiber. In this spirit, development of P2O5 and B2O3 co-doped active silica fibers is ongoing and further results are forthcoming.
Funding
U.S. Department of Defense Joint Directed Energy Transition Office (DE JTO) (N00014-17-1-2546).
Disclosures
The authors declare no conflicts of interest.
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