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We present Brillouin spectroscopy of YAG-derived optical fibers. It is found that the addition of yttria and alumina both tend to raise the acoustic velocity when added to silica, with the change due to yttria being much weaker. The temperature-dependence of the Stokes’s shift in the YAG-derived fibers is also measured, disclosing a lesser temperature dependence than conventional Ge-doped fibers. These fibers are found experimentally to have a substantially larger acoustic attenuation coefficient relative to that of bulk silica, and assuming a photoelastic constant of amorphous YAG similar to that of pure crystalline YAG, a much-reduced Brillouin gain coefficient as a result. A 40 weight percent yttria and alumina fiber has a Brillouin gain coefficient estimated to be roughly one sixth of pure silica. We also show that the addition of Er to the YAG-derived system decreases the acoustic velocity and broadens the Brillouin spectrum.
©2010 Optical Society of America
1. Introduction
Optical fibers are being employed under increasingly more extreme conditions. One example of this is high energy laser systems where multi-kilowatts of optical power are propagated down single fibers. These fibers principally are large-mode area analogs to those originally developed as amplifiers for the telecommunications industry. There exist tremendous opportunities for new materials, or combinations of materials, to yield the revolutionary advances necessary for achieving the performance criteria required for use in future directed energy systems.
Recently, novel optical fibers have been fabricated from yttrium aluminum garnet (YAG) [1,2] Even though these fibers ultimately result in an amorphous yttrium aluminosilicate core, such YAG-derived fibers constitute a new class of optical fibers with compositions not achievable using conventional chemical vapor deposition processes. Optical fibers made from such highly modified compositions show several advantageous properties that make them worth further study for potential use in high energy laser systems.
Presented here, for the first time to the best of our knowledge, is the Brillouin spectroscopy of YAG-derived silica optical fibers. Stimulated Brillouin scattering (SBS) poses a very significant power limitation in narrow linewidth high-power laser systems [3]. Recently, SBS suppression has been achieved through a careful tailoring of the doping profile, leading to acoustic waveguide losses [4] and a reduction in the acousto-optic scattering integral [5,6]. Investigation of novel fiber materials may lead to additional degrees of freedom in the design of these fiber types. This is true not only in terms of changes to the acoustic velocity of the material comprising the fiber, but also in the utilization of dopants that have relatively large acoustic damping coefficients and low photoelastic constants relative to the conventional silica optical fibers.
More specifically, spontaneous Brillouin spectra (SpBS) are measured in the vicinity of 1550 nm and the acoustic velocities from these YAG-derived optical fibers are deduced from the measured Stokes’ shift. A simple model then is used to fit the data, leading to an approximation of the longitudinal acoustic velocity, acoustic damping coefficient, mass density, and index of refraction for the bulk (amorphous) material. A sample of erbium-doped YAG-derived silica also is measured in order to investigate the effect of Er doping on the system. Also included as a reference is a conventional erbium doped, aluminum co-doped optical fiber in order to demonstrate that yttrium appears to increase the acoustic velocity when added to silica, but at a rate much lower than that of aluminum. Finally, the Brillouin gain coefficient, gB (m/W) is estimated. It is found that YAG-derived fibers have a substantially weaker Brillouin interaction than silica, possibly paving the way for novel ultra-low-SBS fibers. In particular, it is estimated that the gain coefficient of the material comprising one of the YAG-derived fibers is about 1/6 the value of pure silica, with much lower values expected for greater yttria and alumina concentrations.
2. Experimental procedures
2.1 Fabrication of YAG-derived optical fibers
Commercial-grade single crystals of either undoped, 0.25 weight percent Er-doped, or 2 weight percent Er-doped YAG were provided by Northrop Grumman Synoptics (Charlotte, NC). YAG rods were core-drilled from the single crystal boule (Ceramare, Piscataway, NJ) to a diameter of 3 mm and a length of 40 mm. Optical quality silica glass (Heraeus Tenevo F300, Buford, GA) was used as the cladding. The YAG core rod then was placed in the center of the capillary silica cladding tube and a series of fiber sizes were drawn. All fibers were drawn at approximately 2025 °C using the custom Heathway fiber draw tower at Clemson University. The undoped and 0.25% Er-doped fibers were the same fiber as described in [1]. Hereafter, the fibers are referred to as Fiber 1 (0.25% Er-doped), Fiber 2 (2% Er-doped), and Fiber 3 (undoped); see Table 1 .
Table 1. Summary Properties of YAG-Derived Fibers
For comparison, a fourth fiber (Fiber 4) was included in the set of measurements as a reference fiber. This fiber was doped with 0.05 mol% of Er2O3 and 7.08 mol% Al2O3 (data provided by the manufacturer, INO of Canada) and has a core diameter of about 18 μm. This fiber also contains approximately 0.25 mol% P2O5, but this level can be considered as a negligible contribution for the present analysis [7]. Using this fiber as a baseline, the effect of Y2O3 doping on silica can be compared with that of Al2O3. Both yttria and alumina have an acoustic velocity for the pure bulk material that is greater than that of silica [8,9]. Finally, the tested lengths of Fibers 1 – 4 are 50 m, 20 m, 50 m, and 25 m, respectively.
2.2 Stimulated Brillouin scattering spectroscopy
An optical heterodyne approach was used to acquire the Brillouin spectra of the YAG derived fibers. The setup is described in greater detail in [10], but a simple overview is provided here. Referring to Fig. 1 , a narrow linewidth (< 100 kHz) seed source (15XX nm, Agilent 81682A) is power-boosted by an erbium doped fiber amplifier (EDFA) chain. The seed laser is tunable, and the wavelength was optimized for the heterodyne signal for each of the test fibers. The specific test wavelengths can be found in Table 1.
Fig. 1 Experimental setup used to acquire the spontaneous Brillouin spectra. A narrow linewidth external cavity laser diode is amplified and sent through a circulator and into the test fiber (Port 2). The back-reflected Brillouin and local oscillator signals then pass into Port 3, are optically pre-amplified, and finally heterodyned on a fast detector. An electrical spectrum analyzer measured the spectra.
The amplified signal is then passed from port 1 to port 2 of an SMF-28TM-based optical circulator and into the test fiber. The circulator had a fiber extension spliced to the fiber-under-test (FUT) port 2. It was found that the extension fiber has a slightly different peak Brillouin frequency shift than the original circulator fiber. This is clearly evident from the data, and will be discussed in more detail later in the paper. The well-known SMF peak was used as a reference for studying the temperature dependencies of the Brillouin spectra.
The FUT was spliced directly to the circulator using a Fitel S182PM fusion splicer via an automatic alignment program. A visual streak was always evident at the resulting splice, probably resulting from the extreme dissimilarity between the two fibers: standard single mode fiber versus the YAG-derived fiber. Regardless, splices were reasonable enough to obtain decent Brillouin spectra. In addition, sufficient local oscillator (LO) signal for successful heterodyning was obtained from the reflection at the splice, due to the large index difference between the fibers. The index of refraction is described in more detail in the next section. Finally, the output end of the FUT was not cleaved or prepared, just simply clipped with a pair of wire cutters since the LO signal is retrieved from the splice.
The Stokes’ signal resulting from Brillouin scattering in the FUT (including the circulator port 2 fiber) and the LO signal reflected from the splice then pass into Port 3 of the circulator. A final EDFA was used to increase the raw optical signals (small signal amplification) thereby increasing the resulting heterodyne signal. The signals were heterodyned using a New Focus 1434 detector and the spectra were measured with an Agilent PSA series electrical spectrum analyzer (ESA). An electrical amplifier was not used in the setup. The current arrangement allows for the detection of spontaneous Brillouin spectra from single mode fibers that have lengths << 1 meter, and thus the circulator signature was always observed in the resulting experimental data. Additionally, the power launched into the test fibers was at a level low enough to avoid any SBS gain-narrowing effects [11], confirmed by the fact that the spectra did not change shape or broaden with a decrease in power launched into the test fiber.
The refractive index profile (RIP) of the undoped-YAG-derived fiber (Fiber 3) was measured at 903 nm by Interfiber Analysis Inc. using a spatially resolved Fourier Transform technique [12]. More detail can be found in [12], but the measurement system comprises placing the fiber transversely in the sample arm of a Mach-Zehnder interference microscope, and using a translating wedge to introduce a known phase shift between the two interferometer arms.
3. Results and discussion
3.1 Index of refraction
The observed peak Brillouin frequencies (presented in the next section) are a linear function of the index of refraction. In particular, the Brillouin frequency is related to the acoustic mode velocity (Vm), optical mode index (nm), and optical wavelength (λ) via νB = (2Vmnm)/λ. Therefore, the index of refraction of the core needs to be known in order to obtain a reasonably accurate estimation of its acoustic velocity. The refractive index of crystalline YAG has been characterized in the literature [13], however it is not clear that this data reliably represents the present case due in part to the amorphous nature of the core as well as the fact that the composition is known to change due to diffusion of silica from the cladding into the molten core upon fiber draw and depends on the core size (i.e., diffusion distance) [1,14].
Figure 2 provides the refractive index profile measured for both the horizontal and vertical directions of a length of the undoped YAG-derived fiber (Fiber 3). This data was used to estimate the RIPs of both of the other two YAG-derived fibers. The optical mode indices, nm, were then calculated from the RIPs. From Fig. 2, it is clear that the index profile is graded. This can most likely be attributed to the diffusion of silica from the surrounding cladding into the molten core melt during the fiber fabrication process [1]. It is worth noting that data beyond 903 nm was not provided and that this wavelength seemed to optimize the RIP signal-to-noise ratio. However, the estimated refractive index difference between the undoped YAG-derived core and the pure silica cladding was within ± 2.5 × 10−3 of 0.117 across the wavelength range of 500 nm to 1000 nm.
Fig. 2 Refractive index profile (RIP), measured at 903 nm, showing orthogonal linescans across the YAG-derived fiber. The core is found to have a high degree of circularity. The shape can be attributed to the silica in-diffusion process.
This observation is used then to justify a reasonable extrapolation of the measured index difference to the 15XX nm region. The Sellmeier equations for pure YAG [13] and for pure silica [15] were used to calculate the index difference (nYAG – nSiO2) across the wavelength range 500 nm to 1560 nm. In the range of 500 nm to 1000 nm, the index difference between that of pure YAG and silica changes by about −0.014. Since the fiber characterized in Fig. 2 contains approximately 40% yttrium and aluminum oxides by weight, this is in fairly good agreement with the refractive index measurements from which a total change of about 0.005 was estimated across that wavelength range.
The computed index difference between pure silica and YAG for wavelengths 903 nm and 1560 nm is 0.366578 and 0.36295, respectively with a difference of < 0.004. In order to extrapolate to 1560 nm for the YAG-derived fiber, the index difference in the glass fiber is assumed to scale downward by the ratio of the silica-YAG index difference at the two wavelengths as Δn1560 = (0.36295/0.366578) Δn903. This yields a maximum index difference of about 0.115 at 1560 nm in the YAG-derived fiber, which is very close to the 0.117 value measured at 903 nm. Finally, the index differences for the other YAG-derived fibers were found by assuming a linear relationship between the index difference at the center of the core and measured molar content of yttrium and aluminum oxides [14,15]. It is assumed that all the YAG-derived fibers have similar RIP shapes from which the mode indices were calculated. This is a reasonable approximation and introduces a negligible error since, for highly multimode fibers, the modal index is very close to the material index at the core center, as will be seen with the calculated [16] mode indices provided in the next section.
3.2 Stimulated Brillouin scattering spectra
Table 1 provides a summary of the measured and calculated properties of the YAG-derived fibers including core diameter (2a), index difference (peak value in the core), measurement wavelength, calculated mode index, measured peak Brillouin frequency (νB), measured Brillouin spectral width (ΔνB), and acoustic velocity (Vm). The optical properties of the conventional Er:Al-doped reference fiber (Fiber 4) that are stated in Table 1 were provided by the manufacturer, while the acoustic properties were measured as part of this work. The data provided in parentheses for Fiber 1 are the calculated material values for this fiber. This is described in more detail later in the paper. However, we point out that since each of the YAG-derived fibers has a core acoustic velocity that is greater than that of the cladding, they are acoustically antiguiding [4]. This can result in a measured spectral width and acoustic velocity that are both larger than the material values.
Figure 3 provides the Brillouin spectrum of undoped Fiber 3 shown as an example, or ‘typical,’ spectrum obtained. A Lorentzian fit to the data is also shown (dashed line). The Brillouin signals were weak; in particular, about 10 dB weaker for Fibers 2 and 3 than the signal originating from the roughly one meter of fiber on circulator port 2. Regardless, a distinct Lorentzian lineshape function is observed, establishing a high degree of confidence in the measured peak spectral shift and approximate spectral width. The spectral line-widths and peak Brillouin frequency shifts of each of the four fibers were determined equivalently by fitting a Lorentzian line-shape to the measured data.
Fig. 3 Brillouin spectrum of the undoped YAG-derived optical fiber provided as an example spectrum. The signal is weak and noisy, but a distinct Lorentzian lineshape is still observed. The spectrum was taken at 1534 nm. The Lorentzian fit is also shown (dashed line).
The effect of temperature on the observed Brillouin frequency shift was also investigated for Fibers 1 - 3 by placing the fibers into a heated thermal chamber (up to 100 °C). The results for Fiber 1 are shown in Fig. 4 in the form of two measured Brillouin gain spectra. It is found that for the 0.25 weight % Er-doped YAG-derived fiber (Fiber 1) the frequency increases with increasing fiber temperature, as with standard SMF. As a control, a small segment of the circulator’s standard SMF was also inserted into the chamber. It can be seen that Fiber 1 has a Brillouin frequency shift that increases at a lesser rate with increasing temperature than for standard single mode fiber. In particular, the observed temperature dependencies were found to be + 1.09 MHz/K for SMF and + 0.65 MHz/K for Fiber 1.
Fig. 4 Brillouin gain spectra of the 0.25 weight % Er:YAG-derived fiber measured at a wavelength of 1555 nm at temperatures of 23 °C and 100 °C. Also visible is the gain spectrum that of the circulator (located between 10.8 GHz and 11 GHz), which is made from standard single mode fiber (SMF). A small segment of the circulator fiber was placed in the thermal chamber as a control.
Interestingly, no frequency shift was observed for either Fibers 2 or 3 as the temperature was increased to 100 °C. This result coupled with a weaker temperature-dependent shift relative to SMF for Fiber 1 may lead one to conclude that amorphous YAG counteracts the increasing frequency with increasing temperature for the silica glass [17]. One may further conclude that the concentrations, as they are in Fiber 3, somehow balance the net change in frequency between silica (increasing with increasing temperature) and the amorphous yttrium aluminosilicate glass (i.e., silica-diffused into the YAG melt during draw) such that the net result is a nearly zero change in acoustic velocity. This very interesting result is the subject of continued studies.
It is worthy of note that any influences of residual strain on the observed Brillouin frequency shifts of the fibers are being neglected in this work [18,19]. Table 2 provides a detailed analysis of the fiber compositions. The average dopant compositions are provided in various units. The averages of the distributions were weighted against the acoustic power distribution as θave = 0∫∞ u(r)θ(r)u*(r)rdr, where u(r) is the normalized (power-normalized) acoustic field and θ(r) is the radial distribution of the dopant of interest (i.e., Al2O3 or Y2O3). The acoustic field is calculated using the theory outlined elsewhere [10] using a step-wise approximation of the graded profile. The radial step size was reduced until the solution converged to the frequency defined by the Bragg condition.
Table 2. Average Fiber Dopant Composition in Various Units
Table 3 provides some analytical data. Specifically, the second column provides the acoustic velocities of the acoustic mode (Vm) and the third column notes the percentage increase in acoustic velocity relative to pure silica (assuming 5,970 m/s [10]). In the fourth column, the percentage change in acoustic velocity per weight percent alumina is noted. This information will be used to qualitatively investigate how the addition of yttria influences the acoustic velocity of silica fibers. Based on [8] and [9], the acoustic velocities of bulk amorphous alumina and yttria are 10,820 m/s and 6,931 m/s, respectively. As such, the YAG-derived fiber would be expected to exhibit an increase in the acoustic velocity of the core relative to that of pure silica (5,970 m/s). However, of additional interest is the possibility that yttria increases the net acoustic velocity when added to silica, perhaps introducing an alternative to aluminum doping [7].
Table 3. Comparison of the Observed Acoustic Velocity with That of Pure Silica
The row describing Fiber 1 has an additional set of numbers. It turns out that the fibers of the present investigation are acoustically anti-guiding to the longitudinal acoustic waves. In this case, the resulting acoustic propagation constant is complex-valued and can take on a waveguide loss coefficient comparable to, or even greater than, that of the material damping coefficient [4]. In addition, assuming that the propagation constant takes on the form β = ka – jγwg, where ka = λ/2nm and γwg is the waveguide attenuation coefficient (m−1), the solutions to the wave equation occur at modal acoustic velocities that are greater than the material value in the core. This effect was determined to only be significant for Fiber 1. The modal and material acoustic velocities are found to be within 1 m/s of each other for the remaining fibers.
Utilizing the model in [4], the calculated acoustic velocity of the Fiber 1 core is provided in the fifth column, with the resulting percentage change over pure silica provided in column six. The seventh column provides the new percentage expressed as a per weight percent of alumina. From the model, it was determined that the modal acoustic velocity lies 22 m/s above the core material value, and the acoustic mode has an attenuation coefficient of about 4.5 × 104 m−1. This additional loss is a broadening mechanism for the Brillouin spectrum. As a result, it is desirable to remove this component from the measured value to reveal the bulk (material) spectral width. The spectral width resulting from the extra attenuation term is found to be about 87.3 MHz based on ΔνΒwg = (Vm × γwg)/π. This is subtracted from the measured spectral width provided in Table 1 with the result (40.7 MHz in parenthesis) corresponding to the material damping term. This will be used to estimate the effect of yttrium and aluminum oxide contents on the acoustic damping coefficient. The remaining fibers, due to their large size and velocity contrast between the core and cladding, have an acoustic waveguide attenuation coefficient that is much less than material damping (< 103 m−1), and can thus be neglected in the present analysis. By the same argument, the modal acoustic velocity is approximately equal to the material value in the core (these were calculated to be within 1 m/s of each other for Fibers 2 – 4). This is noted in Table 3.
From the analysis of the conventional Fiber 4 in Table 3 (reference fiber, no yttria), we see that the acoustic velocity increases at a rate of about 0.31%/wt% of Al2O3. However, the YAG-derived Fibers 1 and 3 have an acoustic velocity that grows at a rate of 0.37 to 0.39%/wt% of alumina. As a result, we can conclude that the addition of yttria to the glass acts to increase the acoustic velocity relative to pure silica, however clearly at a much lower rate than alumina. This is consistent with the observed acoustic velocities of the pure bulk materials reported in the literature [8,9]. The sound velocity of pure alumina is nearly double that of pure silica, while the acoustic velocity of yttria is only about 16% larger than that of silica [8,9]. Due to its relatively small apparent effect on the acoustic velocity of pure silica, while providing a sizeable index change, yttria may prove to be a useful alternative to alumina in designing acoustically antiguiding optical fibers. Fiber 2 is a special case due to its Er content and will be considered later. We note that Fiber 1 has an Er content that is considered to be negligible for this analysis.
In order to analyze the effects of the yttrium and aluminum oxide doping in the YAG-derived fibers on the acoustic properties of silica, we assume the amorphous YAG unit cell. In other words, a complete molecule of YAG, Y3Al5O12, with a molar weight of 593.6 g/mol, is assumed to be well-mixed in the silica glass. We will designate this unit cell as ЦYAG. The assumption, then, is that the length scale over which the compositional fluctuations exist is much less than the acoustic wavelength and so we treat this as if YAG + SiO2 follows a rule of mixtures. We assume the YAG unit cell (rather than taking the species separately) since Al is known to influence the local bonding structure of some co-dopants, especially the lanthanides [20], and this will permit consideration of such compositional effects into a fit to data. Equation (1), from [21], is used to compute the acoustic velocity as follows:
whereand M represents the molar weight, ρ is the mass density, V is the acoustic velocity, and [YAG] is the mole fraction (mol%) of ЦYAG. The subscript ‘s’ corresponds to silica and ‘y’ to ЦYAG. The values of 593.6 g/mol and 60.1 g/mol are used for the molar mass of ЦYAG and silica, respectively. Further, the values of 2,200 kg/m3 and 5,970 m/s are used for the mass density and acoustic velocity of pure silica, respectively.Referring to Eqs. (1) and (2), there are only two unknowns, Vy and ρy. The analysis is not further simplified by assuming the values for crystalline YAG since this is probably not appropriate given the amorphous nature of the fiber core. Instead the measured acoustic velocities for Fibers 1 and 3 are used, resulting in two equations with two unknowns by converting the concentration data in Table 2 into mol% of ЦYAG. The result of this conversion is that [YAG] is 1.49 mol% for Fiber 1, 6.57 mol% for Fiber 2, and 6.20 mol% for Fiber 3. For clarity it is noted that one mole of ЦYAG contains five moles (elemental, not oxide) of Al and three moles of Y. The result of this calculation is that Vy = 7,649 m/s and ρy = 3,848 kg/m3.
Using these fit parameters, Eq. (1) is plotted in Fig. 5 as a function of [YAG] along with the data points for Fibers 1 – 3. Since the model was fit to only two existing data points, the fit is exact, but does not take into consideration any uncertainties in the elemental compositional scans of the fibers. Fiber 2 appears to have an acoustic velocity that lies below the pure ЦYAG line. This is attributed to the erbium concentration in the fiber. From the data, we can deduce that the Er decreases the acoustic velocity by about 0.76%/wt% of Er2O3. This is an observation consistent with [10], where Nd, another rare earth, was found to decrease the acoustic velocity of Ge-doped silica.
Fig. 5 Acoustic velocity vs. ЦYAG content (mol%) modeled using Eq. (1) and the deduced density and acoustic velocity for pure ЦYAG. The experimental data points are also shown on the plot.
Next, using the index difference defined as Δn = m(ny – ns) [10] a model can be fit to the index of refraction data provided in Table 1. Retaining each of the parameters assumed or determined above, a value of ny = 1.868 is obtained. A plot of the index difference at the center of the core is provided in Fig. 6 at a wavelength of 1534 nm along with the data points from Table 1. Finally, the model for material damping is fit in order to estimate the damping coefficient for bulk ЦYAG (αy in units of m−1). The model can be found in [21] as αnet = (νa/11 GHz)2[αym + αs(1-m)] where νa is determined as noted above with the material values substituted for the modal index and acoustic velocity values. The scaling term, (νa/11GHz)2, accounts for the frequency-squared dependence of the acoustic attenuation coefficient [22], and invokes some value of the acoustic attenuation at some reference frequency. A convenient reference frequency of 11 GHz was selected since it marks the location of the Brillouin frequency shift of standard SMF at 1534 nm.
Fig. 6 Index difference at core center vs. ЦYAG content (mol%) fit using the deduced density. We obtain ny = 1.868 for the fit. The data points from Table 1 are also shown on the plot.
Using the spectral width for pure bulk silica determined in [21] as 23.2 MHz at 11 GHz (αs = 1.16 × 104 m−1), the model was fit to the measured data. The results are shown in Fig. 7 for a fixed optical wavelength of 1534 nm. Each of the spectral widths of Table 1 are also shown, however they have been extrapolated from their measurement wavelength to 1534 nm scaling with the wavelength squared (approximately acoustic frequency squared). We calculate that αy = 10.4 × 104 m−1, or that the material damping coefficient is roughly an order of magnitude greater for ЦYAG than for silica at the reference acoustic frequency (11 GHz).
Fig. 7 Brillouin spectral width vs. ЦYAG content (mol%) fit using the deduced density ρy. We obtain αy = 10.4 × 104 m−1 for the fit. The data points from Table 1 are also shown on the plot.
It can be seen that the spectral width of Fiber 2 lies above the pure ЦYAG fit. This can be attributed to the erbium content in this fiber. It is clear that the addition of erbium to the glass has broadened the spectrum, an observation again consistent with [10]. Clearly, the much higher acoustic attenuation coefficient of ЦYAG will result in a bulk Brillouin gain coefficient that is lower than that of pure silica. The Brillouin gain can be calculated [21] from gB(νB) = (2πn 7 p12 2)/(cλ 2 ρVaΔνB) where each of the parameters is for the bulk material. Each of the quantities in the equation for gB can be calculated from the above analysis. However, the photoelastic constant, p 12, for the yttrium aluminosilicate glass remains unknown. A speculation on this value is based on that of bulk crystalline YAG and silica; p 12 = 0.022 [23] and 0.271, respectively. Given the amorphous nature of the YAG in the present investigation, this may have significant errors. This is described below. However, this assumption seems reasonable given the similarity of p 12 for fused silica [24] to that of α-quartz [25]. Assuming that the photoelastic constant follows p12 = m(p12y – p12s) + p12s, the results shown in Fig. 8 are obtained. The Brillouin gain coefficient calculated for Fiber 3 is in the vicinity of 0.49 × 10−11 m/W, or roughly 1/6 the value of pure silica (~2.9 × 10−11 m/W from Fig. 8). Due to the waveguide attenuation that is present in Fiber 1, its Brillouin gain coefficient is expected to be comparable to the Fiber 3 value.
Fig. 8 Calculated Brillouin gain coefficient vs. ЦYAG content (mol%) using the photoelastic constant of crystalline YAG.
While all but one of the parameters used in calculating gB was derived from experimental data, the estimate for p12 may introduce some error in the present calculation. As a limiting case, if the photoelastic constant of the YAG-derived fiber is instead assumed be that of pure silica (i.e. p12y = 0.271) then the gain coefficient is calculated to be 0.86 × 10−11 m/W. This is still a sizeable decrease relative to silica, owing mainly to the relatively large acoustic attenuation coefficient. For lower yttria and alumina contents the change in gB by assuming the pure silica photoelastic constant is much less. For Fiber 1, it is in the vicinity of 16%.
A considerable decrease in the gain coefficient may be experienced as the yttrium and aluminum oxide contents are increased. For example, when [YAG] = 20 mol%, the gain coefficient is calculated to fall below 0.1 × 10−11 m/W, roughly 30 times lower than that of pure silica. This is due in part to the assumed value of p 12 y, the monotonically increasing spectral width, larger mass density, and increasing acoustic velocity with increasing [YAG], all of which cooperate to result in a considerable reduction of the Brillouin gain relative to pure silica, only partly offset by the higher index of refraction. Validating the curve in Fig. 8 requires further experimental work, but the results suggest that the YAG-derived fibers may be a promising core material for the realization of low-SBS optical fibers. The largest source of uncertainty presently lies in our assumed values of p 12, with larger values leading to slightly increased calculated gB values.
The monotonically decreasing Brillouin gain coefficient in the YAG-derived fibers results from the fact that ЦYAG increases the acoustic velocity and that an inverse relationship exists between acoustic velocity and gain coefficient. Increasing the velocity also increases the Brillouin frequency shift, which results in greater acoustic attenuation (or a broadening of the spectrum). In contrast to the present case, according to the results in [21], Ge-doped fibers have a gain coefficient that reaches an absolute minimum value at some Ge concentration. This results from the fact that Ge doping decreases the acoustic velocity, resulting in a relative increase in the Brillouin gain. This property of YAG-derived silica can be very advantageous in the design of fibers with a weakened strength of Brillouin scattering.
4. Conclusions
We have shown for the first time, to the best of our knowledge, Brillouin spectroscopy of YAG-derived silica fibers. We have experimentally verified that the addition of yttrium to silica fiber increases the acoustic velocity, consistent with observations for the bulk in the literature [9]. Our measurements suggest that, for the purposes of tailoring or designing the acoustic profile of these fiber types, the acoustic velocity of the YAG-derived core glass (pure amorphous YAG) is in the vicinity of 7,650 m/s, the mass density around 3,850 kg/m3, and index of refraction at around 1.868. Furthermore, the acoustic attenuation coefficient was found to be roughly nine times larger for YAG-derived glass than silica at an acoustic frequency of 11 GHz. We have also shown that the addition of Er to the YAG-derived system decreases the acoustic velocity and broadens the Brillouin spectrum.
Assuming p 12 for crystalline YAG, we have provided an estimate of the expected Brillouin gain coefficient for YAG-derived fibers. Modeling results suggest that the gain coefficient of the material comprising Fiber 3 is about 1/6 the value of pure silica, with much lower values expected for greater concentrations of ЦYAG. This implies that YAG-derived fibers can form at least one basis for optical fibers with extremely low Brillouin gain coefficients. Validation of these results is warranted via Brillouin gain measurements, however the optically multimoded nature of the present fibers makes these measurements very difficult and subject to significant experimental errors. A focus of present studies includes other fiber geometries/configurations in order to lower the number of guided modes in the core to obtain a more reliable set of measurements.
Acknowledgements
The fabrication of the YAG-derived fibers was originally supported in part by the Joint Technology Office (JTO) through their High Energy Laser Multidisciplinary Research Initiative (HEL-MRI) programs at Clemson University: “High Power Fiber Lasers” under an ARL supplement to ARO contract # W911NF-05-1-0517 and “Eye-Safe Polycrystalline Lasers” under AFOSR contract # FA9550-07-1-0566. Additionally, the authors (J. Ballato, T. Hawkins, and P. Foy) thank Northrop Grumman – Synoptics (Charlotte, NC) for providing at no cost the undoped and doped YAG samples. P. Dragic thanks A. Yablon at Interfiber Analysis Inc. for the RIP measurements and Dr. R. Rice for fruitful discussions. Brillouin work was supported in part by the Joint Technology Office (JTO) through their High Energy Laser Multidisciplinary Research Initiative (HEL-MRI) program entitled “Novel Large-Mode-Area (LMA) Fiber Technologies for High Power Fiber Laser Arrays” under ARO subcontract # F014252.
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