1. Introduction

High power lasers have many applications in material processing, aerospace and defense. Using optical fiber as a gain medium offers many advantages such as high gain efficiency, large gain window, high power output, diffraction limited beam quality, compactness and reliability. However, because of the small core size and long interaction length, nonlinear effects, such as Stimulated Brillouin scattering (SBS), Stimulated Raman Scattering, and optical Kerr effect can limit the laser performance. For narrow linewidth lasers, the main limitation to achieving high power is SBS because it is normally incurred at a lower threshold than other nonlinear effects [1]. SBS results from the interaction of optical wave with acoustic wave through electrostriction, a phenomenon in which a material is compressed in the presence of an electrical field. The material density variations form an index grating to scatter the incident light in the backward direction through Bragg diffraction. The scattered light is downshifted in frequency due to the Doppler shift associated with the grating moving at the acoustic velocity. SBS is not desirable for high power lasers because it limits the amount of output optical power.

One well-known approach to reduce the SBS effect is to make fibers with large mode area (LMA) [2]. The mode area is increased by lowering the core numerical aperture (NA) and increasing the core diameter. However, when the core diameter is larger than 20 μm, the fiber becomes multimoded even with NA as low as 0.05. Modal discrimination, for example, induced by bending the fiber, can be used to achieve single mode operations. A side effect of this method is that for large core size, bending deforms the mode field distribution and thus reduces the mode area [3, 4].

Another approach of reducing SBS is to reduce the overlap integral between the optical and acoustic fields as accomplished by proper profile design [5, 6, 7]. For transmission fibers, SBS improvement of more than 3 dB has been reported [6]. However, this approach is not effective for LMA fibers since the NA of the LMA fibers is already very low and therefore there is little room to change the index profile. Furthermore, a non-step index profile will cause a non-Gaussian mode field distribution, which is not desirable for high laser beam quality.

Acoustic properties of the glass used to make fibers can be affected by different glass dopants [8]. SBS suppression with Al doped cladding has been reported [9]. In this paper, we report a new LMA fiber design to increase the SBS threshold by using Aluminum and Germanium (Al/Ge) co-doping in the core of the LMA fibers. The design is validated by numerical modeling results. The design is also demonstrated experimentally by an actual fiber with significant improvement in SBS threshold.

2. Fiber design

To understand fiber parameters that affect the SBS, we have developed a model using the coupled mode formalism. The threshold of SBS, P_th , is affected by a few factors [4, 5]:

where α_u is the acoustic attenuation coefficient for the acoustic mode of order u, A_eff is optical effective mode area, G(ν_max) is the effective gain coefficient at the peak frequency, K is the polarization factor, and Ī^a0 _u is the normalized overlap integral between the electric and acoustic fields,

where E ₀ is the optical field associated with the fundamental mode, and ρ_u is the field of a longitudinal acoustic eigen-mode of order u. The above equation indicates that, in addition to the mode area, the SBS threshold can be increased by increasing the acoustic loss, or by decreasing the overlap integral and the maximum gain coefficient. The overlap integral can be controlled by fiber refractive index profile design and acoustic velocity profile design. The acoustic loss can be changed by glass composition design.

The equation that determines the longitudinal acoustic eigen-modes can be obtained from the nonlinear acoustic equation [5] by neglecting the damping factor. The acoustic modes that contribute to the SBS associated with the optical fundamental mode are the modes with no azimuthal variation. The radial distribution of such a mode satisfies,

where Ω_u is the acoustic frequency and the β_u is the propagation constant of the acoustic mode, V_L (r) is the longitudinal acoustic velocity profile across the fiber. The optical mode is backscattered efficiently by the acoustic mode when the phase-match condition, β_u = 2β, is fulfilled, where β is the propagation constant of the optical field. β is related to the optical wavelength λ and the effective refractive index n ^o _eff, $\beta =k_o{n}_{o,\mathrm{eff}}=\frac{2\pi }{\lambda }{n}_{o,\mathrm{eff}}$. By introducing a few terms similar to those used in the scalar wave equation for optical fields, we can cast the problem of solving the eigenmodes for the longitudinal acoustic modes into a problem similar to solving the conventional optical scalar wave equation. We define longitudinal acoustic index n_a(r), and effective longitudinal acoustic index n_a,eff,

where V_clad is the longitudinal velocity in the cladding. As a result, the effective longitudinal acoustic index is related to the effective longitudinal velocity V_clad by $n_{a,\mathrm{eff}}=\frac{V_{\mathrm{clad}}}{V_{\mathrm{eff}}}$. We further define the acoustic wave number k_a and acoustic wavelength λ’ so that

With the introduction of the new terms, the equations for optical and the longitudinal acoustic fields can be written in the similar form,

where the subscript ‘o’ stands for the optical field and subscript ‘a’ stands for the acoustic field. Higher order acoustic modes with azimuthal variation are ignored as the overlap integral between these acoustic modes and the fundamental optical mode are practically zero. C in Eq. (7) is equal to n ² _a,eff. Here we use a different notation just for the convenience of simplifying the equation. In the first order approximation C can take the value of 1 so that Eq. (6) and Eq. (7) are of the same form. In this case, the calculated eigen-modes can already yield accurate results for calculating the overlap integral in Eq. (2). For more accurate results, in the subsequent iteration, C can take the value of n ² _a,eff obtained from the previous iteration. The value of n ² _a,eff quickly converges after a few rounds of iteration. With the newly defined terms for acoustic wave, the wave guiding effects of acoustic wave can be understood in a manner similar to the optical wave guided in a fiber. In addition, the adoption of these terms makes it possible to utilize the solver implemented for optical scalar wave equation to solve for the longitudinal acoustic field with minimum modifications.

To reduce the overlap between the optical and acoustic fields, the simple step index profile contributed by GeO₂ doping is not suitable because the fundamental optical and acoustic modes have very similar field distributions and the overlap integral defined in Eq. (2) is about 1 [5]. More sophisticated profile designs were used to change the optical and acoustic fields [4, 5, 6]. However this approach is not very effective for LMA fibers because for this type of fiber, the difference between the refractive index change in the core and in the inner cladding is very small. There is little room to manipulate the refractive index profile for improved SBS performance. In addition, the mode field distributions for refractive index profiles without step-like structure may deviate from the Gaussian shape. A non-Gaussian power distribution will increase the M² value [11], resulting in poorer beam quality.

 

Fig. 1. Dopant designs that can reduce the overlap between the optical and acoustic fields

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In this paper, we propose a different approach, which uses different dopants in the core to reduce the overlap integral. We achieve the SBS performance improvement by adjusting the relative contributions of refractive index profiles from different dopants while keeping a step index profile for the core. This is possible because the effects of the different dopants on optical and acoustic properties are different. Table 1 lists some common dopants that can be used for making silica glass based fibers as well as their effects on optical and acoustic refractive indices [8]. Among the dopants listed in Table 1, the first three dopants increase both the optical and acoustic indices, while the last three dopants have opposite effects on the optical and acoustic indices. In this paper, we choose GeO₂ and Al₂O₃ as two dopants in the core of the fiber to manipulate the SBS behavior. As the focus of this paper is to manipulate the interaction between the acoustic and optical modes to achieve SBS performance improvement, the best way to illustrate it is through showing the overlap between the optical and longitudinal acoustic fields affected by corresponding optical and acoustic waveguides. Many other factors such as those shown in Eq. (1) play relatively minor roles in contributing to the change of SBS threshold. Figure 1(a) and Fig. 1(b) schematically illustrate a couple of situations where one can incur significantly different field distributions between the fundamental optical field LP01 and the lowest order longitudinal acoustic field, L01. In Fig. 1(a), the first (inner) core region is doped with more Al₂O₃ while the second (outer) core region is doped with more GeO₂. The optical refractive index profile is kept to be a step, but the acoustic index profile becomes an inversed W-shape. As a result, the optical field resides in the whole composite core region whereas the acoustic field is confined in the second core region only, yielding a reduced value for the overlap integral. In Fig. 1(b), the first (inner) core region is doped with GeO₂ while the second (outer) core region is doped with Al₂O₃, although both GeO₂ and Al₂O₃ co-exist across the whole fiber core region. The optical refractive index profile is selected to be a step, but the acoustic index profile becomes a W-shape. The acoustic field is confined in the first core region only. As a result, the overlap integral is reduced significantly.

Table 1. Trend of optical and acoustic refractive index change of different dopants in silica

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An alternative way to manipulate dopants for reducing the SBS is to design a fiber using different dopants that guides the optical wave but anti-guides the acoustic wave. This can be accomplished, for example, by choosing a dopant in the core such as Al₂O₃ to increase the optical index but decrease the acoustic index or by choosing a dopant in the cladding such as F to decrease the optical index but increase the acoustic index. The resultant optical and acoustic refractive index profiles are shown schematically in Fig. 1(c). Because the acoustic wave is not guided in the core region, the interaction between the optical and acoustic waves is reduced. SBS improvement using this approach has been demonstrated [9].

We further illustrate the design ideas schematically shown in Fig. 1(a) and Fig. 1(b) through detailed numerical examples. To determine the SBS threshold increase from a specific fiber design, we solve the optical and acoustic wave equations Eqs. (6, 7) to obtain the field of the fundamental optical mode LP01 and the fields of the lowest orders of acoustic modes. The overlap integrals between the fundamental optical mode and lowest orders of the longitudinal acoustic modes are then calculated. To quantify the SBS threshold improvement, the largest value of overlap integrals of a co-doped design is compared with that of a fiber of the same refractive index profile doped with GeO₂ only. The improvement of the SBS threshold is further expressed in dB unit. Figure 2 shows an optical index delta profile of a step index fiber with the core doped with GeO₂ only and the associated fundamental LP01 field and the longitudinal acoustic fields of the lowest orders. Note that the delta profiles are used to describe the relative refractive index profile. For optical field the refractive index of pure silica is chosen as the reference and for longitudinal acoustic field, the index of the cladding is chosen to be reference. The delta value of the reference is set to be zero._ In this paper, we have adopted such concepts for both the optical field, and the acoustic fields. The definitions of the optical delta profile and acoustic delta profiles are shown below,

where ‘i’ can either be ‘o’ standing for optical field or be ‘a’ standing for acoustic field. n_i represents the index of the core, and n_ic stands for the index of the cladding. The fiber in Fig. 2 (a) has a core NA of 0.065 and a core radius of 10 μm. This fiber serves as a reference fiber in the examples below to gauge the SBS threshold improvement. It can be noticed in Fig. 2(b) that the fundamental acoustic field is essentially perfectly overlapping with the LP01 fundamental optical field, resulting in an overlap integral of 0.986, very close to one. It should also be noted because of the oscillating of higher order modes, resulting in a very small value of the overlap integral, the contribution of the SBS effects from the higher order mode is typically an order of magnitude smaller.

 

Fig. 2. (a). Optical delta profile of a step index file with core doped with GeO₂ only. (b) The fundamental optical field LP01 and the two lowest order acoustic fields.

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Fig. 3. (a). Acoustic delta profile of a fiber with more Al₂O₃ doped in the inner region of the core. (b). Field distributions of the fundamental optical field LP01 and the two lowest order acoustic fields of the fiber with optical delta profile shown in Fig. 2(a) and acoustic delta profile shown in Fig. 3(a).

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Figure 3 shows a GeO₂ and Al₂O₃ co-doped fiber design according to Fig. 1(a). Figure 3(a) is the acoustic delta profile. The core has the same optical delta profile as shown in Fig. 2(a). The central portion from 0 to 7 μm is co-doped with Al₂O₃ contributing 0.1% delta and GeO2 contributing to 0.45% delta. From 7–10 μm, the GeO₂ contributes 0.55% delta. The overall optical delta profile is the same as the reference fiber shown in Fig. 2(a). On the other hand, because Al₂O₃ dopant decreases the acoustic index and the GeO₂ dopant increases the acoustic index, the acoustic delta (index) profile is no longer a simple step, which is shown in Fig. 3(a). Figure 3(b) shows the field distributions of optical mode and two lowest order acoustic modes. It can be found that the fundamental mode of optical field is guided in the whole step core region, while the acoustic modes are guided only in the outer core region, which is quite different from those in Fig. 2(b). The overlaps between the optical and acoustic fields are much less in the GeO₂ and Al₂O₃ co-doped fiber than that in the GeO₂ doped fiber. The reduced overlapping is achieved by pushing the fundamental acoustic field away from the central region of the core to reduce the overlapping in the central core region. The overlap integrals Ī^ao _u between the fundamental optical mode and lower orders of acoustic modes are: 0.19 for the L01 mode and 0.016 L02. The highest contribution of SBS is the interaction between fundamental optical field LP01 and fundamental acoustic field L01. Comparing to the reference fiber with a GeO₂ doped core and same optical delta profile, the SBS threshold is increased by 7.15 dB.

Figure 4 shows a GeO₂ and Al₂O₃ co-doped fiber design according to Fig. 1(b). Figure 4(a) is the acoustic delta profile. Again, the core has the same optical delta profile as shown in Fig. 2(a). The central portion from 0 to 2.5 μm is only doped with GeO₂. From 2.5 to 10 μm, the Al₂O₃ contributes 0.1% optical delta and the GeO₂ contributes 0.45% delta. The overall optical delta profile is the same as the reference fiber shown in Fig. 2(a). The acoustic delta (index) profile is no longer a simple step as shown in Fig. 4(a). Figure 4(b) shows the field distributions of optical mode and the lowest order acoustic mode. It can be found the fundamental acoustic mode is confined in the central region of the core. The reduced overlap is achieved by the lack of the presence of the fundamental acoustic field in the outer region of the core. The overlap integral between the fundamental optical mode and lower order acoustic modes is 0.246, which leads to the SBS threshold improvement over the reference fiber by 6.1 dB.

 

Fig. 4. (a). Acoustic delta profile of a fiber with more Al₂O₃ doped in the outer region of the core. (b). Field distributions of the fundamental optical field LP01 and the two lowest order acoustic fields of the fiber with optical delta profile shown in Fig. 2(a) and acoustic delta profile shown in Fig. 4(a).

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Fig. 5. (a). The acoustic delta profile when the concentration of Al₂O₃ is linearly ramped down from the center of the core to the edge of the core. (b) the Schematic of a double clad fiber with Yb, Ge, and Al co-doped in the core.

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One practical issue in the two segment core design with Al₂O₃ and GeO₂ is the manufacturing difficulty in realizing a true optical flat index-profile among the different core composition-layers. With the low-NA (~0.06) core requirement for the overall double-clad fiber design for fiber lasers, it makes the task even harder in practice. To avoid the optical layer-interface, while still to manage a reduced overlap between the acoustic and the optical field distribution in the fiber core profile design, we propose a new ‘interface-free’ Al/Ge fiber-core composition profile. The Al₂O₃ concentration level is linearly ramped down from the center of the fiber core to the edge of the core, while the GeO₂ concentration level is linearly ramped up across the fiber core in order to maintain the overall step refractive index profile illustrated in Fig. 2(a). In this way, the acoustic fields are primarily guided or distributed towards the edge of the core but a sharp interface is avoided. A specific example of the acoustic delta profile is shown in Fig. 5(a). As a result, the overlap integral Ī^ao _u is reduced to 0.225 leading to a SBS threshold improvement of 6.5 dB.

In addition, any defect in the interface will affect the laser performance. To illustrate the effect of the interface, we have made two passive fibers one with sharp material transition in the middle of the core, and one with smooth change of the co-doping. We measured the fiber loss at a convenient wavelength of 1550nm. The fiber with the interface shows an attenuation of 5dB/km. In contrast, the loss of the interface free fiber shows a much reduced loss of 0.4dB/km, which clearly shows the benefit of interface free design. Although the total loss for practical fiber lasers using typically less than 20 meters of fiber is less than 0.1 dB, which seems very minor, the defects at the interface may become a source of laser failure at high power. It is also expected with the introduction of Yb doping in the active double clad fiber, the detrimental role of the interface can be even greater.

In the practical implementation of an active double clad laser fiber, the fiber core is also uniformly doped with active media, Ytterbium. Although in the above examples, we have ignored the effects of Yb, we expect that the SBS threshold improvement still to occur. Note that the Yb contributes only a small fraction of the overall delta in the core. With the Yb effect factored into the acoustic delta profile, the overall delta in the core may be shifted relative to that of the inner cladding. This may quantitatively change the SBS threshold, but will not alter the illustrated mechanism. A schematic of the overall implementation of an active double clad fiber is shown in Fig. 5(b).

3. Experimental results

A Yb-doped all-glass double-clad fiber according to the design shown in Fig. 5(b) was made by the outside vapor deposition (OVD) process. In fiber fabrication, the flat optical-index profile can be conveniently achieved by up-doping Germania-content and at the same time down-grading Alumina-concentration in order to maintain the overall refractive index profile to be a step-like structure. The slope of the Germania up-doping is about ~30% greater than that of Alumina down-doping due to the latter’s higher refractive index contribution in silica. To be able to validate the SBS improvement in the LMA fiber, one other fiber was also made with a standard step index profile using GeO₂ doping but without Al₂O₃ as the co-dopant.

Table 2. Properties of fibers for SBS threshold measurement

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The properties of the two fibers are summarized in Table 2. Both fibers have a 30 μm diameter core, a 300 μm flat-to-flat hexagonal inner cladding and were doped with 0.5 wt-% of Ytterbia. The core and inner cladding numerical apertures are 0.06 and 0.32, respectively. To verify the acoustic profile of the fiber, the acoustic velocity across the preform was measured using a Scanning Acoustic Microscope (SAM). The result of this measurement is shown in Fig. 6, where we observe the higher acoustic velocity (lower acoustic index) toward the center of the fiber preform and the lower acoustic velocity (higher acoustic index) guiding region toward the edge of the core. It can also be found that from the center of the core to the edge of the core, the longitudinal acoustic velocity linearly decreases, which is the result of the linear decrease of the Al₂O₃ concentration level proposed to avoid the undesired interface effect.

 

Fig. 6. Acoustic velocity profile of fiber preform with reduced acousto-optic overlap

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Fig. 7. SBS threshold measurements

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We further constructed two high power amplifiers using the Yb-doped double clad fibers. The SBS characteristics of the two LMA Yb-doped fibers were measured in a two-end-pumped amplifier configuration. The details of experimental setup and fiber laser performance based on the proposed fiber design have been reported in Ref.[10]. The amplifier was pumped by a maximum of 350 W LD operating at 976 nm from each end. The seed source at 1.064 nm with a 3 kHz linewidth was launched into the fundamental mode and was amplified to 4 W output by a pre-amplifier. A beamsplitter was placed between the two amplifier stages to monitor the power entering the second stage and the backward propagating power and spectrum. The SBS threshold was recorded as the forward output power at which the backward propagating power dramatically increases. The results of the SBS threshold measurements are shown in Fig. 7. The standard LMA fiber (LMA-1) using GeO₂ doping in the core exhibits a SBS threshold of approximately 40 Watts while the fiber with reduced acousto-optic overlap (LMA-2) using Ge/Al co-doping in the core shows a threshold of between 150 and 200 Watts. The SBS threshold is thus increased by about 6 dB. This measurement clearly demonstrates the feasibility of raising the SBS threshold through dopant profiling in the core of the fiber. In fact, with the LMA-2 fiber, a 3 KHz narrow linewidth high power optical fiber amplifier with over 500 W of power in a single mode beam has been demonstrated [12]. Furthermore, an analysis of the amplifier results indicates that the fiber is capable of achieving over 1 kW for the same linewidth [13].

4. Conclusion

We have proposed a novel approach of making large effective area laser fiber with higher threshold for the stimulated Brillouin scattering (SBS) using Al/Ge co-doping in the fiber core. The increased SBS threshold is achieved by designing a fiber to have a reduced value of the acoustic-optic overlap integral Ī^ao _u. The manipulation of the overlap is done by adjusting the relative doping level between Al₂O₃ and GeO₂ in the core of the fiber while keeping the target step index structure of the fiber. We illustrated the mechanism through detailed numerical modeling and showed how the co-doping scheme could alter the field distributions of the lowest orders of longitudinal acoustic modes by either having more Al₂O₃ doped in the central portion of the fiber core or in the outer region of the fiber core. By recognizing the interfacing issue in the practical implementation of the fibers, we further proposed a practical fiber design by ramping down the Al₂O₃ concentration from the center of the core to edge of the core while keeping the overall step index profile. An Yb-doped double clad fiber with the core co-doped with Al₂O₃ and GeO₂ was fabricated by the OVD process. An experimental measurement using scanning acoustic microscope verified that the acoustic velocity in the fiber core changes as the design. A high power amplifier was also constructed and tested. By comparing to a fiber made without the Al/Ge co-doping, we have demonstrated that the proposed fiber has about 6 dB higher SBS threshold.