WAVES AND VIBRATIONS IN INHOMOGENEOUS STRUCTURES ...

Figure 2: The desired functionality for the PP component.
Transmission
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0.28 0.29 0.30
Normalized
frequency
0.31
Left output
Right output
Total transmission
Figure 3: Left: the designed structure and the wave pattern for a single frequency, right: the transmitted
energy through the output ports relative to the input wave energy.
designated to follow the arrows and two output wave ports are specified at the lower boundary. The
desired performance is to have 50% transmitted energy in each output port measured relative to the
input wave energy.
The designed component and the wave pattern is shown in Figure 3(left) and the corresponding
performance is shown in Figure 3(right). In order to obtain a high performance in a broad frequency
range the transmission is maximized for several frequencies in the range Ω = 0.295 − 0.305 (normalized
frequencies) by using a max-min formulation. The 2D performance of the designed structure is seen
to have a high total transmission of more than 90% of the input energy and a fairly even distribution
between the two output channels.
But, even when the excess loss at various waveguide discontinuities are minimized, as in the case of
the PP component, PhC waveguides still display large propagation losses. These losses are e.g. due to
out-of-plane scattering in the air holes. It has been shown that with respect to pure propagation loss
(usually measured in dB/cm or dB/mm) PhC waveguides are inferior to the performance of photonic
wires (PhW) [3] which are simple strip or ridge waveguides that can be created from the same high
refractive dielectric as used in the PhCs.
In the following sections we show examples of the design of a basic building block for PhW waveguides:
the T-splitter.
3