WAVES AND VIBRATIONS IN INHOMOGENEOUS STRUCTURES ...

In our demonstrations, we have chosen a topology-optimized PhCW coarse wavelength
selective Y-splitter as shown in Fig. 2 (right). Such a device is challenging for NIL fabrication
since the frequency response of the device is highly sensitive to small variations in the
complex structures in the central part of the Y-branch. These structures also impose local
variations in the pattern density, which complicate the polymer flow during imprint.
The device optimization is illustrated in Fig. 2. The topology optimization methods
redistribute material in a given design domain in order to maximize a certain objective
function [25,26]. This method has successfully been applied within mechanical and electrical
engineering and, recently, also in fabrication of nanophotonic structures [15,16]. Figure 2
illustrates the evolution of the iterative optimization process, where the material in the design
domain (the central Y-branch) is redistributed using the simulated spectral features of the
signals transmitted in the upper and lower arms as feedback. The initial structure (Fig. 2
(leftmost)) has the same frequency response in the upper and lower output arms. The
optimization criterion was that the longer wavelengths are transmitted through the upper arm
whereas the shorter wavelengths are transmitted through the lower arm, see also Fig. 3.
Fig. 2. Leftmost: (587 kB) Movie of how the material is redistributed in the design domain
during the topology optimization procedure. The figure shows four frames from the movie of
the topology optimization process. The leftmost frame shows the initial un-optimized structure
and the rightmost frame the final topology-optimized design obtained after 760 iterations. The
two middle frames show intermediate stages (iteration steps 10 and 200, respectively) before
the optimization process has converged.
Figure 3 shows the fabrication results and optical performance of the NIL fabricated TO
PhCW wavelength selective Y-splitter.
Figure 3 (left) shows the design layout of the converged TO structure. The red and blue
arrows indicate the wavelength-selective transmission of longer (red) and shorter (blue)
wavelengths to the upper and lower arms, respectively. The circles and squares in the right
panel of the figure show the 3D FDTD simulations of a perfectly fabricated device, i.e. the
black and white structure in Fig. 3 (leftmost). The middle panel shows a SEM image of the
fabricated structure, which closely resembles the TO design. Deviations between the
fabricated and designed structures are partly caused by limitations in the resolution of the
lithography and partly caused by line broadening in the RIE. The solid red and blue lines in
the right panel show the measured optical transmission performance of the fabricated structure
for the upper and lower arms, respectively. The transmission in the upper and lower arms of
the Y-splitter is normalized to the measured transmission level of a straight PhCW of same
length. The measured spectra are seen to closely resemble to the 3D FDTD simulations both
regarding transmission levels and spectral distributions.
The optical response of the structure critically depends on the precise fabrication of small
features of sizes down below 30 nm. This was underlined by a series of 3D FDTD
calculations, where an increasing number of the ~30-50 nm sized oddly shaped holes in
succession were removed from the optimized Y-splitter region. The transmission levels
changed typically 1-2 dB in the corresponding pass band when only two features were
#76773 - $15.00 USD Received 6 November 2006; revised 18 January 2007; accepted 19 January 2007
(C) 2007 OSA 5 February 2007 / Vol. 15, No. 3 / OPTICS EXPRESS 1265