Maria Bayard Dühring - Solid Mechanics

Figure 4: 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.
three fingers are pointing towards the center. In the optimized design the two field concentrations
at the sides has disappeared because of 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 and the
energy flow in the core region is increased. Similar tendencies are found for |H2|, but as its values
are an order of magnitude lower than for |H1|, the plots are not included here.
When the outer radius of the design domain is increased to 1.65R the optimized design is
essentially not changed and the objective function is also increased 375% as with the original radius.
This indicates that the optimized design is not so sensitive to the outer radius of the design domain
in this range.
3.2 Study of simplified designs
The previous example shows that the presented method can be employed to design holey fibers such
that the overlap between the magnetic field and the lossy material is deceased and the energy flow
in the core region is increased. The optimized design, however, has many small details that will be
difficult to fabricate as the drawing process tends to smoothen the interface between air and silica.
Especially the walls pointing away from the center have small details and spikes that appear due
to the filter radius r. When a bigger value of r is used these walls get more smooth, but a gray
transition zone of intermediate materials has a tendency to appear between the silica and the air.
In order to examine how important the details are for the performance and to get designs that are
simpler to fabricate, four simplified geometries with the main features of the optimized design are
constructed. The wave equation (2) is solved as an eigenvalue problem for each of the designs and
the propagating constant β1 for the guided mode is found. The model is then solved with the forcing
term and αs equal to zero. The simplified designs denoted (a) to (d) are seen in figure 5(a) to 5(d)
and the distribution of Φ/Φmax is indicated by the contour lines with the same scale as for the initial
and optimized design in figure 3(a) and 3(b). The level of details imitating the optimized design
is decreasing for the four designs and the improvement of the objective function Φ and the average
power flow P compared to the initial design is decreasing accordingly, see table 1. Design (a) has
tilted walls to the sides and a detailed layout at the top part above the mode, which represent the
details of the optimized design well. The objective function is improved almost 300% compared to
the initial design, which is not as much as for the optimized design, so the smaller details do have
an influence on the performance. Design (b) has been further modified by simplifying the geometry
above the optical mode and by vertically cutting off the structures behind the side walls. The side
8