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Fig. 3. From( a) to( e). Cross-sectional images of the tapered section of fiber 1 for 5 different cladding diameters( 125, 97, 80, 67 and 1.6 lm). The yellow dotted lines represent a fit of the external boundary of the fiber with a circle.( f) Measurement of the thinnest part diameter obtained by LC-OCT.( g) Optical microscopy image of the thinnest part of the fiber.
Microscopy( SEM) provides much higher resolution but is far more complex to implement than this optical method. Moreover, in our previous works, we have performed SEM measurements that have shown that our drawing machine yields very good results in terms of diameter accuracy and homogeneity [ 7, 15 ].
In Figure 4a, we report the evolution of the cladding and core diameters along the taper. As the diameters decrease, the reflectivities also decrease due to the progressive diffusion of the Ge: SiO 2 core during the tapering process, leading to a reduction of the step index value. In particular, the smallest core diameter that could be measured is 1.85 lm for a cladding diameter of 67 lm. Below this value, the detection limit of LC-OCT is reached [ 12 ], corresponding
2 Dn to a minimum reflectivity R min ¼’ 10 �9, n core þ n clad which is obtained for a refractive-index step of Dn’ 10 �4.
In Figure 4b, we plot the ratio of the core to cladding
diameters, R ¼ U core
. This ratio is not constant, varying
U clad from 0.064 to 0.05 over the first 4.5 mm in the taper. It then decreases abruptly to 0.027 for the last point that could be measured.
Our hypothesis is that there are two distinct effects occurring during the tapering process: the geometrical reduction of the initial core size and the expansion of the region of higher refractive index, due to the diffusion of Ge into the cladding in the vicinity of the initial core. We still name this region“ core”. These two combined effects could explain the behavior observed in Figure 4b, that can be separated into three parts:
– At the beginning, until z = 2.5 mm, the increase in core size due to diffusion is negligible compared to
the reduction in core size from the fiber stretching, giving an almost constant ratio R.
– After z = 2.5 mm, there is a more pronounced increase in the ratio R until z = 3.5 mm because of a more important diffusion reducing the core diameter decrease speed.
Then after z = 3.5 mm, R decreases sharply because of both the reduction of the geometrical size of the core and the fact that the index difference Dn is flattened due to diffusion and becomes lower than the detection limit.
The same measurements were performed with a taper drawn from fiber 2. The results are shown in Figure 5.
Even for large cladding diameters, the core was more difficult to observe than for fiber 1, which we attribute to a smaller initial step index. The step index for the untapered fiber 2 being known( Dn ¼ 5:2 10 �3), we deduce that the step index of untapered fiber 1 should be higher. Determining its exact value would require a calibration of theLC-OCTsystem, whichwewerenotabletodoforpractical reasons. As for fiber 1, the vanishing of the core corresponds to the limit of detection of the LC-OCT device. We conclude that the range of variation of the step index we were able to measure for fiber 2 extends from 5:2 10 �3 to 10 �4. InFigure 5a, the core vanishes for a cladding diameter of 91 lm, and the smallest core diameter that could be measured is 2.7 lm. The smallest cladding diameter measured is 1.8 lm, in good agreement with the targeted diameter of 1.71 lm. In Figure 5b, wereportthe ratio of the core and cladding diameters. As for fiber 1, this ratio decreases, from 0.072 to 0.023. The decrease appears more monotonic than for fiber 1, with a two step behavior without any increase of the ratio R, suggesting that the diffusion of Ge does not counter balance the effect of the geometrical reduction of the core size. Further investigations