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Sample I-2 exhibited clear type I growth characteristics and strong transmission dips at both λB and 2/3 λB as will be shown in Figure 4-8(e) and

(f), respectively. The images in Figure 3-18(a) and (b) were recorded at orthogonal fibre orientations and were identified as having been recorded in the planes corresponding to perpendicular (0°) and parallel (90°) to the writing beam, respectively, using the reasoning described in section 3.2.3. The image in Figure 3-18(a), clearly exhibits a grating which is written uniformly across the core as expected for the image plane perpendicular to the writing beam. The image in Figure 3-18(b) shows evidence of a Talbot diffraction pattern which is consistent with the image plane parallel to the writing beam. The non-exposed fibre image in Figure 3-18(c) was subtracted from cropped regions of each of the images in Figure 3-18(a) and (b); the resulting images are shown in Figure 3-18(d) and (e), respectively.

The refractive index variations in the DIC image in Figure 3-18(a) and the corresponding processed image in Figure 3-18(d) are distributed uniformly across the core with evidence of a slight tilt in the grating planes. The apparent non-uniformity of the grating planes at the edges of the core in Figure 3-18(d) is likely to be the result of misalignment during image subtraction. As discussed in section 3.2.3, the imaged structure is consistent with a fibre orientation corresponding to perpendicular to direction of the UV beam during fabrication. The refractive index structure in the images in Figure

3-18(b) and (e), however, reveals a complex refractive index structure that is expected for an image recorded at a fibre orientation corresponding to parallel to direction of the UV beam during fabrication. The images in Figure 3-18 provide clear evidence of an orthogonally distinguishable refractive index structure, as expected for gratings written with a phase mask.

Figure 3-18. DIC images of a type I FBG written with a standard phase mask in small-core fibre: sample I-2 recorded at fibre orientations (a) Image 1: 0° and (b) Image 2: 90°. The

dimensions of each image are approximately 47 × 47 µm. (c) DIC image of sample I-2 recorded in a non-exposed region of fibre. (d) Result of Image 1 after subtraction of non- exposed fibre image in (c); (e) result of Image 2 after subtraction of non-exposed fibre image

in (c). The images in (c) to (e) are approximately 47 × 14 µm.

(b) (a)

(d)

Refractive index perturbations are evident in the depressed cladding on either side of the central core region in Figure 3-18(b) and more clearly in Figure 3-18(e). As discussed in section 3.2.3, the depressed cladding region either side of the core of fibre F-3 was most likely formed by introducing fluorine or boron during fabrication to lower the refractive index. The weak perturbations evident either side of the core of sample I-2 are expected to be due to UV- induced refractive index changes as a result of low concentrations of germanium or the presence of fluorine/boron in the depressed cladding region [85]. Photosensitivity in depressed claddings has been previously reported to lower cladding mode losses [85, 114, 115]. Whatever the dopants are in the depressed cladding region of fibre F-3, the core region must be more photosensitive; giving rise to higher refractive index changes which are apparent from the larger intensity perturbations measured in the core region of the DIC images than in the depressed cladding.

The linescans in Figure 3-19(a) and (b) were taken along the fibre axis from the perpendicular image in Figure 3-18(d) and averaged over the two adjacent 30 × 1 µm regions illustrated on the right of the figure. It can be seen that the periodic features on either side of the core are in phase, which was verified with a negligible phase shift of 0.04π radians, as determined by fitting the data with the function in Equation 3-6.

The linescans in Figure 3-20(a) and (b) were taken along the fibre axis from the parallel image in Figure 3-18(e) and averaged over the two adjacent 30 × 1 µm regions illustrated on the right of the figure. It can be seen that the periodic features in both regions are out of phase by approximately half a

period, i.e. π radians. The phase shift was determined as (1.0 ± 0.1)π radians

by fitting the data with the function in Equation 3-6. The periods of the four linescans in Figure 3-19 and Figure 3-20(a) to (b) were determined to be 1.09 ± 0.05 µm, which is in excellent agreement with the period of the phase mask used in fabrication, 1.0668 µm.

0 1 0 5 10 15 20 25 30 0 1 0 5 10 15 20 25 30

Figure 3-19. Analysis of perpendicular image features of a type I FBG: normalised average of linescans along the fibre axis from the DIC image of sample I-2 in Figure 3-18(d), taken from

two adjacent regions as illustrated: (a) the left side of the core and (b) the right side of the core.

Fibre F-3 has a core diameter of 3.6 µm, which prevents the measurement of a full period of the expected Talbot length of 4.56 µm. Consequently, linescans were averaged over the ten regions illustrated in Figure 3-20(d), which each cover approximately 0.4 × 12 µm to include the core and depressed cladding regions. The linescans were then averaged and normalised to provide the profile (blue) in Figure 3-20(c). The large differences in measured intensities due to the index perturbations in the core and depressed cladding regions also make it difficult to measure the Talbot length. The maximum and minimum intensities occurring at approximately 4.5 µm and 7 µm, respectively, in the blue plot in Figure 3-20(c) are very different to the intensity levels observed in the cladding due to the higher UV-induced refractive index perturbations in the more photosensitive core. The intensity dip at approximately 8.6 µm is due to the ridge running down the right hand side of the core in Figure 3-18(e) which is likely to be the result of a misalignment during the subtraction of the non-exposed fibre image. The subtraction process involves a pixel by pixel subtraction of the intensity values and consequently small deviations from parallel alignment between the fibres in the two images can have a significant impact on the resulting image.

(a) (b) N or m al is ed int ens it y ( a. u. )

Distance along the fibre z (µm)

Figure 3-18(d) in phase

0 1 0 5 10 15 20 25 30 0 1 0 5 10 15 20 25 30 0 1 0 1 2 3 4 5 6 7 8 9 10 11 12 measured expected

Figure 3-20. Analysis of parallel image features of a type I FBG: normalised average of linescans along the fibre axis from the DIC image of sample I-2 in Figure 3-18(e), taken from two adjacent positions as illustrated: (a) the left side of the core and (b) the right side of the

core. (c) Comparison between the expected and measured Talbot profiles from linescans averaged over the ten regions in Figure 3-18(e) as illustrated in (d).

Despite the large differences between the detected intensity levels of the refractive index perturbations in the core compared with those in the depressed cladding regions, the interleaving fringes of bright and dark regions can be seen to extend across the fibre in Figure 3-18(e). The sinusoidal function with a period equal to the expected Talbot length of 4.56 µm (shown in red) compares well with the period of the data in Figure 3-20(c). The observed Talbot length is estimated as 4.6 ± 0.5 µm indicating that the observed refractive index patterns are likely to have formed as a result of

N or m al is ed int ens it y ( a. u. )

Distance across the fibre x (µm)

(c) (d) (a) (b) N or m al is ed int ens it y ( a. u. )

Distance along the fibre z (µm)

Figure 3-18(e) out of phase

beating between the ± 1st _{and ± 2}nd _{orders of the SM-2 phase mask, as detailed}

in Table 3-2.