We report a polarization-maintaining fiber in which the birefringence is due to artificially introduced anisotropy in the core material. The beat length was measured by direct observation at three different wavelengths, giving a shortest result of 85 µm at a wavelength of 543 nm. The measured phase-index birefringence is about one third of that expected, which is explained by diffusion between the core layers, which are each less than 200 nm thick. By taking account of this diffusion, we can accurately model the experimental beat length and differential group delay over a wide wavelength range.
© 2005 Optical Society of America
Conventional circularly symmetric optical fibers do not maintain the polarization state of the guided mode along their length. Polarization-maintaining (PM) fibers can be formed by intentionally introducing a high birefringence to the guided modes. Two methods have been used to achieve the required birefringence. The shape of the refractive index profile defining the waveguide core has been made non-circular (shape or form birefringence) or the material forming the fiber has itself been made birefringent by introducing stresses (stress birefringence) [1,2]. PANDA  and bow-tie  fibers achieve high birefringence through induced stress, while fibers with an elliptical core  and side air holes  present a high birefringence due to asymmetry in core geometry. In this paper we report a PM fiber in which the birefringence is introduced by artificially structuring the core on a sub-wavelength scale.
It is well known that the birefringent properties of crystals can be explained in terms of the anisotropic electrical properties of the molecules of which the crystals are formed . Birefringence may, however, arise from anisotropy on a scale much larger than molecular, namely when there is an ordered arrangement of similar particles of optically isotropic material on a size scale large when compared with the dimensions of molecules, but small compared to the wavelength of light. In our fiber, we have formed such a structure using two commercial glasses from Schott, SF6 (refractive index 1.79) and LLF1 (refractive index 1.54). A multilayer stack formed from these two glasses, and reduced in scale by fiber drawing, behaves as a uniaxial crystal with its optical axis perpendicular to the plane of the plates.
In this paper, we introduce a lamellar-core fiber with very high birefringence caused by such artificially introduced anisotropy. We used direct observation  to measure the beat length at three different wavelengths, with the shortest beat length observed to be 85 εm at wavelength of 543 nm. This corresponds to a phase-index birefringence of 6.4×10-3 at this wavelength, to our knowledge the largest birefringence reported in an optical fiber. Using low coherence interferometry , we have also measured the differential group delay (DGD) for the two polarization states, deducing the group-index birefringence of 8.8×10-3 at the wavelength of 1540 nm. The measured phase-index birefringence is about one third of that expected, which we explain by the diffusion of material across the interfaces between the two different materials. Accounting for this diffusion in our model allows us to model the experimental beat lengths and DGD results over a wide wavelength range.
To make the lamellar core fiber we first cut the 3 mm thick Schott SF6 and LLF1 glass plates to 21mm×50mm rectangular pieces and then polished both sides. 7 plates (SF6: 3 plates, LLF1: 4 plates) were stacked together and fused by placing them in a furnace at 650 °C for 3 hours. Due to the similar thermal properties of these two glasses , they fused to form a lamellar glass block with the dimension of 21mm×21mm×50mm, which was then ground and polished into a cylindrical glass rod. We drew this glass rod down to a diameter of around 1mm on a fiber-drawing tower, and then inserted it into a jacketing tube formed from LLF1 glass before drawing it down to fiber of the required size in several steps.
Figure 1(a) shows an optical micrograph of the preform with one jacketing tube. This was jacketed and drawn two more times to obtain a fiber with 1.2 μm core size and 50 μm outer diameter, as shown in the electron micrograph in Fig. 1(b). A close-up of the core region of the fiber in Fig. 1(b), recorded using backscattered electrons, is displayed in Fig. 1(c). The lamellar structure in the core is easily visible in this micrograph. The bright regions in Fig. 1(c) are SF6 and the dark regions are LLF1. The thickness of the layers has been decreased to less than 200 nm, smaller than the wavelength of visible light. The small overall core diameter was chosen to ensure that the fiber is single-mode or few-moded (depending on the wavelength), and is not expected to be important for the birefringence obtained.
3. Properties of guided mode
3.1 Waveguiding properties & expected birefringence
We measured the attenuation of the fiber at the wavelength of 632 nm by the cutback method, yielding around 10 dB/m. The intrinsic losses of the SF6 and LLF1 glass are less than 1 dB/m in the visible and near-infrared spectral regions, and the high attenuation in the fiber is attributable to contamination of the internal and external interfaces during the formation of the core material, which leads to increased scattering losses.
A simple analysis  of the expected birefringent properties of the lamellar material suggests that the birefringence can reach 0.018, and that the single mode cut-off wavelength is around 1.0 μm for the fiber with 1.2 μm core diameter. Since the thickness of each layer is smaller than the visible light wavelength, we can consider the structured core as being formed from an anisotropic material.
3.2 Beat length measurement
We have used direct observation to measure the beat length of our lamellar core fiber at several different wavelengths. The periodic light pattern can be seen by exciting both polarisation modes equally and then observing the fiber from the side at an angle of 45° to the birefringent axes. Figure 2 shows an optical micrograph of the beat pattern using a green HeNe laser source (543 nm wavelength), from which 85 μm beat length was deduced. The same measurement method was used at other two wavelengths, 632 nm and 781 nm, and the beat lengths of 100 μm and 140 μm were obtained respectively, as shown in Fig. 3. Note that the beat length in this fiber rises with wavelength. From the measured beat length, we can obtain the phase-index birefringence of 6.4×10-3 at the wavelength of 543 nm.
3.3 Differential group delay (DGD) measurement
The differential group delay between the two polarization fundamental modes was measured by low coherence interferometry for a piece of 80 mm long lamellar core fiber in some wavelengths from 850 nm to 1600 nm. The measured DGD, about 29.3 ps/m at a wavelength of 1540 nm, is shown in Fig. 4, deducing the group-index birefringence of 8.8×10-3 at this wavelength.
4. Numerical modeling
4.1 Modeling based on bulk material constants
A commerical beam propagation method [10–12] tool (BeamProp) was used to compute the effective indices for the two fundamental polarization modes, as shown in Fig. 5. The refractive index distribution we used in the computation is shown in Fig. 6 (dotted black line), with the SF6 being assigned a refractive index value 1.79 and the LLF1 index assumed to be 1.54 (corresponding to their known values at a wavelength of 706 nm). We can see that, when the ratio of wavelength and core diameter is around 0.5, the birefringence reaches a peak value of 0.018. This modeling result is similar to the birefringence obtained for layers formed from infinite plates , implying that the outside shape of the core is not the main contributor to the birefringence.
4.2 Accounting for the effects of diffusion
From the measured beat lengths in Section 3.2 we estimate that the birefringence at 543 nm wavelength is about 6.4×10-3, roughly one third of the expected value of 0.018. We believe that diffusion during the fiber drawing process has decreased the contrast of refractive indices between the two glasses. Energy dispersive x-ray analysis (EDAX) was used to measure the concentration of lead (one of elements in SF6 glass) in the interface region of two glass plates in the fiber preform and we found evidence of diffusion, but the spatial resolution of our EDAX system is insufficient to perform such measurements in the actual fibers. Such diffusion is not expected to have much effect on the cut-off wavelengths for the higher-order modes because the average core index remains very similar. A relatively modest change in the refractive index contrast between the two phases (eg, 1.74:1.59 rather than 1.79:1.54) would be sufficient to explain the measured decrease in birefringence, so we used the refractive index contrast of 1.74:1.59 to compute the effective indices for the two fundamental modes in the fiber using BeamProp. The refractive index distribution assumed is presented in Fig. 6. From the output of the software (the effective indices for the two fundamental guided modes at different wavelengths) we have computed the beat lengths and differential group delays, as plotted in Fig. 3 and 4 (solid lines). The excellent agreement between the experimental results and the modeling provides strong supporting evidence that significant diffusion did occur within the fiber core during the drawing process.
We have described a highly birefringent lamellar-core fiber. The beat length of the fiber was measured by direct observation of scattered light, and found to be 85 μm at a wavelength of 543 nm. The differential group delay was also measured, using low coherence interferometry. We have computed the modal indices using a commercial beam propagation tool, and find that the measured values are not consistent with preservation of the bulk refractive indices within the multilayer stack forming the core. The decreased refractive index contrast within the fiber core can be attributed to diffusion of components within the multilayer structure. When accounting for such diffusion, the modeling results fit well with the experimental results. Aside from their intrinsic interest, we expect such fibers to be useful in the design of more advanced structures such as, for example, a robust single-polarization fiber based on the use of a photonic bandgap cladding.
The authors appreciate useful comments from Tim Birks, David Bird and Philip Russell. The glass plates were polished by Wendy Lambson. This work was partly funded by the UK Engineering and Physical Sciences Research Council.
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