Bulk-optics–based optical components are a limiting factor for high-power fiber laser systems, whose continuous-wave output power has exceeded the kilowatt level [1]. At the same time, bulk optics–based, fiber-pigtailed optical Faraday components are currently limited to around 20 W because of the material/air interfaces and alignment and epoxy problems. Defects and dirt make material/air interfaces vulnerable to high laser intensity. Heat generated from power loss will soften the epoxy used to fix the bulk-optics components, resulting in their misalignment. To solve these problems, all-fiber Faraday components are required. Because of the small Verdet constant [~1.1 rad/(Tm) at 1064 nm] of standard silica fiber, several meters of fiber are required to build an all-fiber Faraday rotator, which is impractical in terms of magnet size and polarization mixing. Compact all-fiber Faraday rotators have been demonstrated using standard silica fiber coiled multiple turns with several-millimeter diameter to increase the polarization rotation [2,3]. However, bend-induced linear birefringence affects the state of polarization and quenches the desired Faraday effect.

Terbium (Tb) doping is an effective way to increase the Verdet constant in optical fiber [4,5]. Although this concept was proposed two decades ago, the difficulties in cleaving Tb fiber, splicing Tb fiber with silica fiber, and developing other fiber components (such as fiber polarizers) prohibited progress in all-fiber Faraday devices until recently [6,7]. In Ref. 6, a 56-wt%-Tb-fiber with a Verdet constant of –24.5 rad/(Tm) was fabricated. The isolator, with a 9-dB loss, consisted of a 25-cm Tb fiber, a 15 × 15 × 25-cm³ N35 NdFeB magnet, and two commercial fiber polarizers. In Ref. 7, the same fiber Faraday rotator and a fiber Bragg grating (FBG) were used to make a Faraday mirror, with a loss of more than 13 dB.

In this paper, 65-wt%-Tb fiber with a record-high Verdet constant of –32.1 rad/(Tm) in the fiber is reported. This value is 83% of that found in the commercially available crystal [terbium gallium garnet (TGG)] used in bulk-optics–based isolators and 27 × larger than that of standard silica fiber. A compact all-fiber Faraday isolator and all-fiber Faraday mirror are demonstrated using a 4-cm-long Tb fiber and a 4-cm-long magnet tube. The losses of these devices are significantly reduced compared to the previous demonstrations.

Terbium is a good dopant to add to the fiber, not only because it has a high Verdet constant, but also because it has a small absorption coefficient in the visible and IR wavelength regions. Highly terbium doped silicate glasses were designed and fabricated. Boron oxide and aluminum oxide were added into the glass composition to improve the solubility of the terbium oxide. A 65-wt%-terbium-oxide–doped glass was used as the core glass. The rod-in-tube technique was used for single-mode fiber fabrication. The fiber pulling temperature was around 1000°C. The numerical aperture and diameter of the core were 0.083 and 7.4 μm, respectively, and the cladding diameter of the fiber was 125 μm. The propagation loss of the fiber was measured to be 0.024 dB/cm at 1310 nm using the cutback technique. The fiber was fabricated at AdValue Photonics using an in-house fiber drawing tower.

The polarization rotation angle in the Tb fiber was measured using the technique described in Ref. 6. A 4-cm Tb fiber was spliced between two short pieces of single-mode (SM) fiber. Figure 1 shows the measured rotation angle and the corresponding curve fit at the 1053-nm measurement wavelength as the magnet was translated along the length of the fiber. The maximum rotation angle reached 45°. The error in the measured angle was primarily caused by air flow and was determined to be 1° by a polarization stability measurement. The effective Verdet constant was determined to be –32.1 ± 0.8 rad/(Tm), which is 27 × larger than that of silica fiber and the largest measured to date in any optical fiber.

 

Fig. 1 Measured rotation angle (circle) and corresponding curve fit (solid) at a wavelength of 1053 nm as a function of the magnet location along the fiber axis z.

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Figure 2 shows the measured and curve-fit Verdet constants of the 54-wt%-Tb fiber [5], 56-wt%-Tb fiber [6], 65-wt%-Tb fiber, and TGG [5] as functions of Tb³⁺ concentration. From the figure, it is clear that the Verdet constant is proportional to the Tb³⁺ concentration. The Verdet constant of the 65-wt%-Tb fiber was 31% larger than our previously reported results [6] and 83% of the Verdet constant of commercially available crystal (TGG) used in bulk optics–based isolators, which implies that all-fiber Faraday components will be practical in the near future.

 

Fig. 2 Measured (dots) and curve fit (line) Verdet constants of the 54-wt%-Tb fiber, 56-wt%-Tb fiber, 65-wt%-Tb fiber, and TGG as functions of Tb³⁺ concentration.

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Helica in-fiber polarizers from Chiral Photonics are used as fiber polarizers. This fiber polarizer is a chiral scattering grating (CSG) made from a twisted birefringent fiber [8]. Two linear polarized modes from the input end can be converted into two circular polarized modes in the adiabatically twisted region. One circular polarized mode is blocked by the grating and the other propagates. The propagating circular polarized mode is then adiabatically converted back into a single linear polarized mode. In this way, the CSG works as a fiber polarizer. The fiber polarizer used in the experiment had a 4-cm-long CSG with polarization-maintaining (PM) fiber pigtails at both ends. The center wavelength was around 1064 nm, with a bandwidth greater than 50 nm. The polarization extinction ratio of the fiber polarizer was greater than 30 dB, and the insertion loss was less than 2 dB.

The experimental isolator configuration is shown in Fig. 3 . A 4-cm section of Tb-doped fiber, spliced between two short pieces of SM fiber, goes through a magnet tube. The N48 NdFeB magnet tube (residual flux density B _r = 1.35 T) is 4 cm long with inner and outer diameters of 5 mm and 6 cm, respectively. The magnetic field of this magnet was derived in Ref. 9. The N48 magnet has an inside average magnetic field that is 2.2 × larger than that of the N35 magnet used in Ref. 6, and a length that is only 16% of that of the N35 magnet. The two other ends of the SM fibers are each spliced to a fiber polarizer. The polarization directions of the two fiber polarizers are aligned with a rotational difference of 45°.

 

Fig. 3 Experimental configuration of the all-fiber Faraday isolator.

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The two pieces of SM fiber are spliced to the Tb fiber to increase the total Verdet constant. Since the axially integrated magnetic fields inside and outside the magnet tube have opposite signs but identical absolute values, the total Verdet constant consists of two parts, given by V _total = V _Tb–V _silica = –33.3 rad/(Tm), where V _Tb = –32.1 rad/(Tm) and V _silica = 1.2 rad/(Tm) are effective Verdet constants of the Tb and the silica fibers at 1053 nm, respectively. With this increased total Verdet constant, the polarization rotation angle of the Faraday rotator can reach 45°, as shown in Fig. 1. Since the axial magnetic field outside the magnet can be neglected beyond 4 cm past the end of the magnet, the effective length of the Faraday fiber is 12 cm, including 4-cm Tb fiber and two 4-cm pieces of SM fiber. The SM fiber could be eliminated by using a higher-grade (stronger) magnet, for example, an N50 NdFeB magnet, or by increasing the outer diameter of the magnet tube by a few percent. The effective length of the Faraday fiber would then be only 4 cm.

The optical isolation at 1053 nm is measured to be 19 dB at room temperature. The loss of the isolator is 6.1 dB, including 2 dB of insertion loss of each CSG, 0.1 dB of propagation loss in Tb-doped fiber, and 1-dB from each splicing point between the SM and Tb-doped fiber. Recent progress in CSG has demonstrated a reduction of insertion loss in the fiber polarizer to less than 0.5 dB [10]. The 1-dB loss per splice point occurs because the melting points of the terbium-oxide–doped silicate fiber and silica fiber are 1200°C and 1650°C, respectively. This makes it difficult to fuse the fibers together using a conventional fusion splicer. Although this splicing loss is high, it could be decreased further by using a custom setup, for example, using a temperature controllable heating filament. By implementing these improvements, an all-fiber Faraday isolator could be made with less than 1-dB of insertion loss.

The experimental configuration used to test the Faraday mirror is shown in Fig. 4 . A 4-cm section of Tb-doped fiber, spliced between two short pieces of SM fiber, goes through the same magnet tube as mentioned above. A fiber Bragg grating (FBG) is spliced to the other end of one of the SM fiber. The FBG has a center wavelength of 1053 nm, a reflectivity of 97%, and a bandwidth of 1 nm. The SM fiber is short and kept straight to avoid altering the polarization state. A four-port, 3-dB PM coupler is spliced with the other SM fiber for testing purposes. Linearly polarized 1053-nm light is launched into the PM fiber via port 1. It then propagates through the Faraday rotator (Tb fiber), and the polarization state rotates 45°. After it is reflected back by the FBG, the polarization state rotates another 45° through the Faraday rotator, and the total polarization rotation angle through the device reaches 90°. The polarization states of the output and input light are measured at ports 2 and 3, respectively, of the 4-port PM coupler.

 

Fig. 4 Experimental configuration of the all-fiber Faraday mirror.

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When measuring the polarization state, the light goes through a lens and a polarizer and is finally collected by a detector. When the polarizer is rotated by an angle θ, the light intensity I at the detector is a cosine-square function $I/I_0={\cos }^2\left(\theta -{\theta }_0^i\right),$ which is the well-known Malus’ Law [11]. I ₀ is the maximum light intensity received by the detector, and ${\theta }_0^i$ represents the polarization state of the input and the output light (i = input, output). Figure 5 shows the measurement results. Squares and circles are measurement points of the input and output light, respectively. The dashed and solid lines are curve fits of the input and output light, respectively. The polarization rotation angle is calculated to be ${\theta }_0^{\text{output}}-{\theta }_0^{\text{input}}=88\pm 4°.$ The error is determined from a polarization stability measurement of the Faraday mirror configuration, which is different from the Verdet constant measurement configuration.

 

Fig. 5 Polarization-state measurement of the input and output light of Faraday mirror. Squares and circles are measurement points of the input and output light, respectively. Dashed and solid lines are curve fits of the input and output light, respectively.

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The insertion loss of the Faraday mirror is 4.3 dB, including a 0.2-dB propagation loss from Tb fiber (round trip), a 0.1-dB reflection loss from the FBG, and a 1-dB splicing loss per slice point between Tb and SM fiber, which is counted four times. Similar to the isolator, the splicing loss could also be decreased by using a temperature-controllable heating filament, resulting in an all-fiber Faraday mirror with insertion loss of less than 0.5 dB. The FBG can also be written on the Tb fiber directly, which would also reduce the splicing loss. The extinction ratios of the input and output light are 20 and 13 dB, respectively. If the SM fiber between the Tb fiber and FBG were shortened, the extinction ratio of the output light could be increased to the 20-dB input level.

This compact all-fiber Faraday isolator and the Faraday mirror will have the most-significant impact in high-power fiber laser systems. There are no material/air interfaces or epoxy problems as found in bulk optics Faraday components, which increase the damage thresholds required for high-power applications. Since hundreds of pieces of Tb fiber can go through one magnet tube at the same time, many Faraday components can be integrated into a single magnet, reducing the cost and size for large fiber array systems.

In conclusion, a compact all-fiber Faraday isolator and Faraday mirror are demonstrated. The isolator consists of two fiber polarizers and a fiber Faraday rotator. The fiber Faraday rotator is made of a 4-cm-long, 65-wt%-terbium–doped silicate fiber. The effective Verdet constant of the terbium-doped fiber is measured to be –32.1 ± 0.8 rad/(Tm), which is 27 × larger than that of silica fiber. This effective Verdet constant is the largest measured value to date in any fiber and is 83% of the Verdet constant of commercially available crystal (TGG) used in bulk optics–based isolators. The isolation of this fully fusion spliced all-fiber isolator is measured to be 19 dB. The Faraday mirror consists of a same-fiber Faraday rotator and a fiber Bragg grating as a mirror. The polarization state of the reflected light is rotated 88 ± 4°.