Maria Bayard Dühring - Solid Mechanics

performance will decrease and some details, as the layout of the top part, are crucial.
4 Conclusion
A method to optimize the energy flow trough the core of a holey photonic-crystal fiber based on
topology optimization has been presented. As the cladding material is lossy, the aim is to design the
cross section of the fiber such that the mode shape is overlapping the cladding as little as possible.
The optical model is based on the time-harmonic wave equation for the magnetic field. Matching
values for the propagation constant and the optical wavelength are employed in order to solve the
wave equation in a time-harmonic way where the wave is exited by a magnetic force in the center of
the fiber. The topology optimization is based on linear interpolation functions between the refractive
indices and the objective function is the sum of the squared absolute value of the magnetic fields
in the plane. A close type morphology filter and a continuation method based on the damping are
applied to obtain appropriate designs.
The performance of the method is illustrated by an example where a 0-1 design is obtained,
which is symmetric about a vertical axis in contrast to the 60 degree symmetry of the initial design.
The objective function is increased 375% because the optimized design changes the distribution of
the magnetic field such that its overlap with the lossy cladding material is decreased. It is shown,
that by maximizing the objective function the time-average power flow in the propagation direction
is increased 378% times, and its distribution in the initial and the optimized design is similar to
the distribution of the energy measure form the objective function. Thus, the same improvement is
obtained for power flow and the objective function. It is furthermore shown that simplified designs
with the main features from the optimized design can be created, which are simpler to fabricate.
The improvement is decreasing when the simplified designs deviate more from the optimized design.
Further work encompasses the inclusion of a symmetry constraint around the vertical axis and
a study of other types of filters to further eliminate small details and the gray transition zones at
the air/cladding interfaces. Methods to optimize for tolerant designs are relevant to apply, see [32],
as the drawing process tends to smooth out the details in the design. Optimization of wavelength
intervals to obtain broadband solutions can be performed by the method described in [18]. Finally,
the method can be extended to other types of photonic-crystal fibers, as fibers where the light is
confined by index guiding, and to other objective functions where dispersion properties and nonlinear
effects are optimized.
5 Acknowledgements
This work received support from the Eurohorcs/ESF European Young Investigator Award (EURYI,
www.esf.org/euryi) through the grant ”Synthesis and topology optimization of optomechanical systems”
and from the Danish Center for Scientific Computing (DCSC). Also support from the EU
Network of Excellence ePIXnet is gratefully acknowledged. The authors are thankful to Jakob S.
Jensen from the Department of Mechanical Engineering, Technical University of Denmark, for helpful
discussions related to the presented work.
References
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