# Photonic Crystal Power Divider

Java applet by Jasmin Smajic.

### Short description

Light is incoming from the left hand side. Half of the energy should be
transmitted to each of the two output ports and the reflection coefficient R
should be as small as possible. Obviously, the design must be symmetric. The
posts in the center area of this structure have a strong influence on the
characteristic data. For a center area of 4 times 5 cells, one has 4096 possible
symmetric structures. Most of them are rather bad, i.e., the corresponding
reflection coefficient is big.

Assume that you want to operate the structure at the center frequency of the
first band gap. A accurate MaX-1 solution takes about 400 seconds on a PC. We
have computed all 4096 possible designs and saved the results in a table. The
Java applet displays the values from this table when you press the Calculate
button.

### Things to do and questions

Try to minimize the the reflection coefficient R (at the center frequency of
the first bandgap) by defining the locations of the posts in the center area of
the structure!

We have designed a smart search algorithm takes around 400 evaluations to
find the best solution, that has R=0.14%.

Can you outperform our smart search algorithm? Is your intuition good enough?
Do you have a successful search strategy? How many sub-optimal designs with
R<1% can you find? Can you imagine how the frequency dependences of good
designs look like? Which of the good designs has a small reflection coefficient
over a wide frequency range? Can you explain how these structures work?