Bend loss as a function of radius of curvature

Loss was measured at 1550 nm as a function of the bend radius for fibres HF1, HF2 and HF₃ using the experiment described in Section 4.4 . These measurements were repeated for several random angular orientations of the fibre and are shown in Figs 4.8 (a), (b) and (c), by the open shapes. Superimposed on each graph is a curve fitted to all the experimental data for each fibre. This enables us to average over the different angular orientations and thus extract an average value for the critical bend radius,R_c. Note that the fibres considered in this section are endlessly single-mode and that Rc ≡R

FM

c , where R FM

c is the critical bend radius of the fundamental mode. This critical radius is found to be 21 mm, 46 mm and 66 mm for holey fibres HF1, HF2 and HF3 respectively, which increases with mode size as expected.

In order to understand the relative contributions that transition loss and pure bend loss make to the net observed loss, these results are compared to theoretical predictions. For one full loop of fibre, there are two transition regions, one at the beginning of the bend and another at the end of the bend, which result in two transition losses. Figs 4.9 (a), (b) and

Table 4.1: Fundamental mode area (AFMeff) for holey fibres HF1 −HF4 and the conventional step-

index fibre C1. The holey fibre parameters are extracted from scanning electron microscope im-

ages. fibre NA a[µm] AFM_eff [µm2] @ 1.55 µm C1 0.11 4.0 126 fibre Λ [µm] d/Λ AFM_eff [µm2_] @ 1.55 µm @ 633 nm HF₁ 7.6 0.23 130 72 HF₂ 9.7 0.23 215 100 HF3 11.3 0.24 230 103 HF4 9.5 0.25 180 98

Figure 4.8: Loss for one loop of fibre as a function of bend radius. Open shapes represent measured bend loss for (a) HF1, (b) HF2 and (c) HF3 for different random angular orientations of the fibre. The solid line

in each graph corresponds to the fitted curve from which the critical radius is extracted.

(c) show the measured bend loss for fibres HF1, HF2 and HF3, as in the previous graph, together with predicted values for the transition loss and pure bend loss. The dotted lines in Figs 4.9 (a), (b) and (c) show the predicted transition loss for one full loop of fibre bent in theφ = 0o_{, 45}o _{and 90}o _{directions for HF}

1, HF2 and HF3 respectively. These predicted values clearly show that transition loss is a small overall contribution to bend loss for these holey fibres in the macro-bend regime at 1550 nm and implies that the majority of loss must be attributed to pure bend loss.

The predicted pure bend loss is shown for each fibre by the solid lines in Figs 4.9 (a), (b) and (c) for bends in the φ = 0o_{, 45}o _{and 90}o _{directions. Recall that in the model of} pure bend loss described in Section 3.5, a constant of proportionality (τ) was introduced

Figure 4.9: Loss as a function of bend radius. Open shapes represent measured bend loss for (a) HF1,

(b) HF2 and (c) HF3 for different random angular orientations of the fibre, while the predicted pure bend

loss is shown by solid lines for bends in theφ= 0o_{, 45}o _{and 90}o _{direction. The predicted transition loss is}

shown by dotted lines for bends in theφ= 0o_{, 45}o _{and 90}o _direction.

in Eq. 3.16. Since the transition loss is a small contribution to the overall loss (Fig. 4.9), this factor can be found by fitting the predicted curves to the experimental data. We find that by choosing τ = 6, we achieve excellent agreement with experimental data for all three fibres, as can be seen in Figs 4.9 (a), (b) and (c). For example, using our scalar model, the critical bend radius of the fundamental mode (RFM_c ), is predicted to be 23 mm, 44 mm and 58 mm for holey fibres HF1, HF2 and HF3 respectively. This compares well with experimental values of RFM_c (given above) of 21 mm, 46 mm and 66 mm for holey fibres HF1, HF2 and HF3 respectively.

As mentioned above, the holey fibres considered within this chapter (HF1, HF2, HF3 and HF4) are not made from a single grade of silica. A lower grade (higher OH content) silica glass was used for the outer jacketing tube in the preform of these fibres. In addition, we find that the bend losses of these fibres are lower than those fibres made from a single grade of silica. This may result from the fact that the refractive index of this lower grade silica is slightly less than the silica used in the rest of the fibre. As a result, the lower index region acts as a secondary cladding and, when the fibre is bent, may act to confine the bent mode to the inner cladding more effectively, enabling the cladding modes to couple back into the core mode more efficiently, resulting in lower bending losses. Consequently, we find that the fitting factorτ is actually greater for these fibres than other holey fibres that have been made entirely from a single, high grade of silica. For all other fibres considered in this thesis, τ = 2.0 is found to produce the best agreement with experiment. For example see Sections 5.4, 5.6, 6.2.4, and 7.3.3.