Maria Bayard Dühring - Solid Mechanics

30 Chapter 5 Design of photonic-crystal fibers by topology optimization [P2]
Figure 5.3 The geometry of the center region of the holey fiber where black is silica and
white is air. The contour lines indicate the normalized absolute value of the magnetic field
|H1|/|H1,max|. (a): Initial design. (b): Optimized design.
and the peak value in the center has increased compared to the initial design. The
magnetic field of the optical mode is mainly polarized in the horizontal direction and
the distribution of the normalized field |H1|/|H1,max| is plotted with contour lines
for the initial and the optimized design in figure 5.3(a) and 5.3(b), respectively.
|H1,max| is the maximum value of |H1| for the initial design. The field distribution
is symmetric around the vertical axis for both the initial and optimized design and
like the distribution of the objective function, |H1| is confined by the vertical walls
to the sides and is elongated in the vertical direction after the optimization. For the
initial design, concentrations of |H1| are found where the three fingers are pointing
towards the center, but for the optimized design the two field concentrations at the
sides has disappeared caused by the forming of the vertical walls. This means that a
smaller part of the total field is in the lossy silica material and therefore less energy
is absorbed. Thus, the energy flow in the core region can increase. This example
shows that the presented method can be employed to improve the energy flow in a
holey fiber by reducing the overlap between the optical mode and the lossy cladding.
The optimized design has many small details and will therefore be difficult to
fabricate by a drawing process that tends to smoothen the geometry. In order to
examine how important the details are for the performance of the fiber and to get
designs that are simpler to fabricate, two simplified geometries are constructed and
shown in figure 5.4(a) and 5.4(b). The distribution of Φ/Φmax is indicated by the
contour lines. Design (a) imitates the optimized design well with tilted side walls and
a detailed upper part above the optical wave. The objective function for this case is
increased 2.95 times compared to the initial design. The increase is not as big as for
the optimized design, but the improvement is still significant. Design (b) is further
simplified with vertical side walls and rounded upper part, and Φ is correspondingly
smaller and has increased 2.62 times. Thus, these examples show that it is possible