Maria Bayard Dühring - Solid Mechanics

Chapter 5
Design of photonic-crystal fibers by topology
optimization [P2]
The second type of wave problem is studied in this chapter and is about optical
waves propagating in hollow core photonic-crystal fibers. The method of topology
optimization is used to maximize the energy flow by redistributing air and silica
material around the core, such that the overlap of the magnetic field in the lossy
silica cladding is decreased. The chapter is a summary of publication [P2].
One- or two-dimensional photonic crystals are employed to confine optical waves
in the core region of photonic-crystal fibers, which were first studied in the 1990s
[75, 76]. A holey fiber consists of a hollow core, which is surrounded by a two
dimensional periodic pattern of air holes that confine the wave by the band-gap
effect [17]. Thus, a part of the optical wave propagates in air for this type of fiber,
and therefore losses as well as unwanted dispersion and nonlinear effects from the
cladding material can be reduced. Another part of the wave propagates in the
cladding, which is usually silica. For optical wavelengths in general, silica is a lossy
material and will absorb a part of the energy. For most wavelengths holey fibers
will therefore not be convenient for long fiber links, but rather for short distance
applications as for instance in laser surgery. Compared to conventional laser surgery
with reflecting mirrors fibers gives the possibility to do operations inside the body
without the need to open it. A first application of photonic-crystal fibers for medical
purposes is found in [77] where a fiber is employed successfully in laryngeal and
airway surgery. In order to get a high energy flow in the fiber it is important to
design the cross section such that the overlap between the optical mode and the
cladding is as small as possible. This problem is considered in a number of papers
[78, 79, 80], where geometry parameters such as the core size, the thickness and the
shape of a solid core boundary as well as the size of the fingers pointing towards
the core have been varied. In this chapter topology optimization, which has already
been applied to design photonic crystals [50, 53, 54, 56], is employed to increase the
energy flow in a holey fiber. First the method is presented and then an example of
its performance is shown for an optical wavelength relevant for medical purposes.
5.1 Method
The purpose of the presented method is to distribute air and silica material in the
design domain Ωd around the fiber core such that the energy flow in the core region
Ωc is maximized. The initial design of the holey fiber is given in figure 5.1. The
pitch is Λ = 3.1 µm, the hole diameter over the pitch ratio is d/Λ = 0.92 and the
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