Biomedical Engineering Reference
In-Depth Information
Figure 7.10
Field amplitudes obtained along circular paths. The radii of
contours for (a)and (b) are 0.8
μ
mand3
μ
m, respectively.
dark region. However, such a ring pattern is not observable in
Fig. 7.9(f). To examine the reason for this difference, we present
snapshots of the field distributions for a fixed time for these two
responses in Fig. 7.10.
To represent the rotational properties that cannot be identified
from snapshots of the field distributions, we added arrows in the
figures. In Fig. 7.10(a), the field near the center region rotates in
an opposite direction (CCW) to the field in the outer region (CW).
However, in the field distribution in Fig. 7.10(b), the directions
of rotation are approximately in the same direction (CW) for all
regions. As the outer region of the pattern in Fig. 7.8(c) has 10
wings of which directions are LH, from Eq. (7.1), the topological
charge numbers for Fig. 7.10(a) and (b) are found to be -9 and
-11,respectively.AsonecaneasilyseefromFig.7.10,thesenumbers
coincidewiththenumbersidentifiedbydirectcountingthepeaksin
the field distributions for the results shown in Fig. 7.10(a) and (b).
To show a more clear view to the topological charges in
these cases, we present field amplitude plots in Fig. 7.11 that are
measured along two different circular contours obtained from the
field distributions in Fig. 7.10. The radii of the contours for Fig.
7.11(a)and(b)are0.5
μ
m(centralregion)and3
μ
m(outerregion),
respectively. Therefore, from Fig. 7.11(a) and (b), the topological
charge numbers can be found more readily. From the geometry in
Fig. 7.8(c), the helical directionality at the outer region corresponds
to 10 wings in LH directions. However, at the central region, the
