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In this letter, we propose a new method that uses the stress applying parts (SAPs) in the polarization maintaining fibers (PMFs) cladding to realize the self-alignment of the side-polished face and the slow axis. This method enables the polarizers to be fabricated directly onto PMFs, and there are no interruptions to the optical path and no internal interfaces to reflect light. The polarizers offer a high polarization extinction ratio (PER) and high temperature stability. Theoretical and experimental results show that the new method dramatically reduces the polarization axis alignment (PAA) error and increases the success rate of making side-polished PMF polarizers with PER > 23 dB from 18.8% to 65.0%.
©2010 Optical Society of America
1. Introduction
PMF devices, such as in-line PMF polarizers and couplers/splitters [1–4], have generated great interest in high-speed coherent fiber optic communications systems, fiber optic gyroscopes (FOG) and interferometric sensors [5–7]. It is easy to make side-polished in-line single mode fiber (SMF) devices, such as in-line SMF polarizers and couplers/splitters, and the PER of SMF polarizers can be over 40 dB [8–10]. However, it is very difficult to produce side-polished in-line PMF polarizers with a high PER, because the PER of side-polished in-line PMF polarizers depends on the accuracy of the alignment between the side-polished face and the slow or fast axis of the PMFs [11–13].
Side-polished PMF polarizers are made in two ways. The first is to use the PMF as the input and output fibers and an SMF as the side-polished section. The main disadvantages of this method include: too many production steps, high insertion loss and back reflection, and poor temperature stability. The second method is to make a side-polished face on a PMF directly [14]. The main advantages of this method are lower insertion loss and excellent temperature stability. The key challenge is to ensure accurate alignment between the side-polished face and the slow or fast axis of the PMF, especially for PMFs of 80 μm and 40 μm cladding diameter.
The following theoretical analysis demonstrates how the SAPs in the PMF cladding may be used to promote the self-alignment of a side-polished face and the slow axis of a PMF and consequently greatly reduce the PAA error. This principle can also be used in producing other PMF devices.
2. Theory
The new method is best illustrated by following the production steps of a side-polished in-line PMF polarizer. A PANDA-style PMF of 80 μm cladding diameter and one meter length is stretched over the curved face of an aluminium substrate prior to firmly bonding as shown in Fig. 1 . The top surface of the substrate is curved along the length of the substrate, and is as smooth as possible. The length, radius of curvature, and the width of the substrate are about 25 mm, 250 mm, and 2 mm, respectively. F is the stretching force, and T1 and T2 are the tensions in SAP1 and SAP2, respectively.
Fig. 1 PMF stretched over a curved aluminium substrate and bonded. F is the stretching force, and T1 and T2 are the tensions in SAP1 and SAP2, respectively. θ is the wrap angle, and R is the radius of curvature of the substrate.
Figure 2 shows the structure of a PANDA-style fibre, a polishing wheel, and an aluminium substrate. The surface of the polishing wheel and the aluminium substrate are parallel to the x axis. ϕ is the angle between the slow axis and the x axis. It is very important to bond the PMF correctly. An alignment angle of ϕ =0 ° or ϕ =90 ° yields the ideal PAA result. The maximum possible output PER of a side-polished in-line PMF polarizer is thus limited by [15]:
Fig. 2 Cross sectional view from A-A of the PMF, the polishing wheel and the aluminium substrate. a is the radius of the SAP; b is the distance between the center of the fiber core and the center of the SAP; c is the radius of the cladding; ϕ is the angle between the slow axis and the x axis; and N is the normal force component of T.
In order to make a side-polished in-line PMF polarizer with an output PER greater than 20 dB, the angular misalignment must be less than 5.7 °. For an output PER greater than 30 dB, the angular misalignment must be less than 1.8 °, according to Eq. (1). The angular alignment is very hard to realize especially for the PMFs with smaller cladding diameters, such as 80 μm or 40 μm. This kind of small form-factor fibre with a cladding diameter of 80 µm or 40 μm is well known in FOG applications [11].
As shown in Fig. 1, the original length of the fiber is L = R⋅θ, where R is the radius of curvature of the substrate and θ is the wrap angle. F is the force applied to the PMF pulling the fibre over the aluminium substrate and stretching it by ΔL. The original length of the micro-section of the fiber is dL = R⋅dθ. The increase in micro-section is a function of y, and can be expressed as l + y⋅dθ, where the micro-section is stretched by l at y = 0. Therefore, the stress σ is not uniformly distributed over the cross section of the PMF, and can be written as:
Where Y is the Young’s modulus of the SAP. Obviously, as shown in Fig. 2, the tensions of the two SAPs are different, because they have different changes in length. Using Eq. (2), the tensile force exerted by the material when stretched by ΔL on the SAP can be expressed as: Where T 1 and T 2 are the tensions in SAP1 and SAP2 respectively; S = πa 2 is the cross-sectional area of the SAP; c is the radius of the cladding; and b is the distance between the center of the fiber core and the center of the SAP.As shown in Fig. 1 and 2, the normal force component N, which leads to the rotation of the PMF, can be expressed as:
The normal force is proportional to tension T, so dN 1>dN 2 (when ϕ is not zero). Inserting Eq. (3)a) and Eq. (3)b) into Eq. (4), the summation of moments about the core, M, can therefore be expressed as:
The moment of force is proportional to cosϕ⋅sinϕ according to Eq. (5). Therefore if the side polished face is exactly parallel to the slow axis (ϕ =0 °) or fast axis (ϕ =90 °), the sum of moments will be zero and the fibre will be in steady state. The maximum possible value of the output PER of the side-polished PMF polarizer would be infinity. However, this ideal angular alignment is very hard to realize in practice. It is necessary to point out that in our model, for simplicity, we focus on the moments caused by the SAPs and ignore the moments caused by the cladding.
If the side polished face is parallel to the slow axis (ϕ ≈0 °), the moment of force M tends to return the PMF to its original position of equilibrium even if there is a small angular misalignment, because it is a stable equilibrium. Conversely if the side polished face is parallel to the fast axis (ϕ ≈90 °) the moment of force M tends to turn the PMF away from the equilibrium position if there is a small angular misalignment, because the equilibrium is unstable. In other words, as shown in Fig. 2, ϕ ≈0 ° is the position of minimum potential energy, and ϕ ≈90 ° is the position of maximum potential energy. This means that the choice between making the side-polished face parallel to the slow axis or the fast axis is crucial.
Unfortunately, in almost all cases, side-polished in-line PMF polarizers or couplers are made with the side-polished face parallel to the fast axis (ϕ ≈90 °), thus leaving the slow axis to be the transmission axis. This method will increase the PAA error and decrease the PER of PMF polarizers or couplers, as demonstrated in the above theoretical analysis.
For making high extinction ratio in-line PMF polarizers it is therefore clear that a better approach is to make the side-polished face parallel to the slow axis (ϕ ≈0 °) of a PMF, while leaving the fast axis to be the transmission axis. Thus using the stresses within PMFs for polarization axis self-alignment, we can dramatically decrease the PAA error and increase the PER of PMF polarizers.
3. Experiments and discussion
A PANDA-style PMF of 80 μm cladding diameter and one meter length is prepared by stripping off 20mm of the fiber coat and placing the fiber on two fiber holders as show in Fig. 3 . The fiber is lit from above and viewed via a CCD camera. The fiber is slowly turned until the characteristic image of either the slow or fast axis appears (depending on what is desired), and the fiber holders are then closed. The fiber can now be firmly bonded onto the aluminium substrate which is carefully aligned with the fiber holders. However, experimentation shows that closing the fiber holders tends to slightly rotate the fiber away from the ideal position of ϕ =0 ° or ϕ =90 °, obviously limiting the PER and the production success rate of side-polished PMF polarizers. The new method overcomes this problem as the fiber will tend to self-align when stretched over the aluminium substrate (provided ϕ ≈0 ° has been chosen) even when subject to a rotational perturbation.
In order to demonstrate the new strategy of making side-polished PMF polarizers, we fabricated three batches of PMF polarizers, one with the side-polished face parallel to the fast axis (ϕ ≈90 °) and two with the side-polished face parallel to the slow axis (ϕ ≈0 °) but with different stretching forces. It is worth reiterating that side-polished in-line PMF polarizers or couplers are customarily always made with the side-polished face parallel to the fast axis (ϕ ≈90 °), thus leaving the slow axis to be the transmission axis.
The experimental setup used to monitor the optical intensity during polishing is shown in Fig. 4 . One end of the PMF is connected to a superluminescent light emitting diode (SLED) and the other end to a power meter. The fibre’s output power should be monitored carefully to ensure that the evanescent field has been reached and the core of the PMF is not penetrated. In order to minimize the insertion loss of the side-polished PMF polarizers, we deposited an aluminium film of 40 nm in thickness on a portion of the polished face [12, 14].
The experimental setup used to measure the output PER of the side-polished PMF polarizers is shown in Fig. 5 . The low PER light from an SLED at a wavelength of 850 nm is launched into the fibre polarizers to be tested. A high quality crystal polarizer, a Glan-Taylor (G-T) prism, was placed at the output end of the fibre polarizer to evaluate the polarization dependence of the output power. The G-T prism reflects o-ray at an internal air-gap, transmitting only e-ray. The output light intensity from the polarizer was measured using an optical detector attached to a power meter. The G-T prism was rotated in steps of 10 degrees, and the output power P recorded for each rotation of the prism. The output PER of a side-polished in-line PMF polarizer can be written in Eq. (6):
The polar plot of the normalized output light intensity of the side-polished fibre polarizer, No. 0907, as a function of G-T prism angles in steps of 10 ° is shown in Fig. 6a . The PER of the polarizer is over 35 dB at room temperature. Figure 6b shows the temperature stability of side-polished PMF polarizer No. 0907. The absolute offset of PER is about 0.4 dB over the temperature range of 75 °C.
Fig. 6 Experimental results for the side-polished PMF polarizer No. 0907. a. Polar plot of the normalized output light intensity of the polarizer. b. Temperature stability of the polarizer.
Table 1 shows the experimental results of the sample batches, each batch has 20 to 24 samples. The first batch of PMF polarizers is fabricated according to the old method with the side-polished face parallel to the fast axis (ϕ ≈90 °) and a low stretching force, and the other two batches are fabricated following the new method with the side-polished face parallel to the slow axis (ϕ ≈0 °) but with a low and high stretching force respectively to separately show the improvements in PER due to first selecting the slow axis and then increasing the stretching force. Note that increasing the stretching force with the side-polished face parallel to the fast axis (ϕ ≈90 °) would be expected to lead to a reduction in PER
Table 1. Experimental results of 3 batches of side-polished PMF polarizers.
The experimental results prove that with the fast axis as the transmission axis (ϕ ≈0 °) and an adequate stretching force F, the PER and the success rate can be dramatically improved. Using our new method for making side-polished PMF polarizers, the expectation of misalignment angle Δϕ, standard deviation of misalignment angle Δϕ, and the expectation of the PER are improved from 6.42 ° to 4.07 °, 3.52 ° to 2.23 °, and 20.40 dB to 24.16 dB, respectively. The success rate for making the side-polished PMF polarizers with PER > 23 dB increased from 18.8% to 65.0%.
4. Conclusion
In summary, we report theoretical and experimental investigations into a new method of making side-polished in-line PMF polarizers. This method enables the polarizers to be fabricated directly onto PMFs, and there are no interruptions to the optical path and no internal interfaces to reflect light. The polarizers offer a high extinction ratio and high temperature stability over a temperature range of 75 °C. This unique method can dramatically decrease the PAA error and improves the production success rate for side-polished PMFs polarizers with PER > 23 dB from 18.8% to 65.0%. The unique features of this new method, combined with its low-cost fabrication, could enable an entire suite of production applications for other PMF devices.
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