WAVES AND VIBRATIONS IN INHOMOGENEOUS STRUCTURES ...

Topology optimised broadband photonic
crystal Y-splitter
P.I. Borel, L.H. Frandsen, A. Harpøth, M. Kristensen,
J.S. Jensen and O. Sigmund
A planar photonic crystal waveguide Y-splitter that exhibits largebandwidth
low-loss 3 dB splitting for TE-polarised light has been
fabricated in silicon-on-insulator material. The high performance is
achieved by utilising topology optimisation to design the Y-junction
and by using topology optimised low-loss 60 bends. The average
excess loss of the entire component is found to be 0.44 0.29 dB for a
100 nm bandwidth, and the excess loss due to the Y-junction is found
to be 0.34 0.30 dB in a 175 nm bandwidth.
Introduction: A photonic crystal (PhC) is an optical material in which the
refractive index is periodically modulated [1, 2]. Planar PhC structures are
often defined as triangular arrangements of air holes in a high dielectric
material, since this configuration may give rise to a large photonic bandgap
(PBG) for the transverse-electric (TE) polarisation. Such PhC structures
have recently gained a lot of consideration as they potentially allow for the
realisation of ultra-compact photonic integrated components [3–8]. Planar
PhC waveguides (PhCWs) are typically formed by locally breaking the
periodicity along a specific direction of the PhC lattice. Most of the
research within PhCs has hitherto relied on intuitive design approaches
based on physical arguments, possibly combined with iterative trial-anderror
procedures, to improve the performance of the PhC component.
Recently, we have proposed to use a systematic inverse design strategy
called topology optimisation [9] to optimise the performance of PhCW 60
and 120 bends [10, 11]. In this Letter, we consider the important and
commonly encountered 50=50 Y-splitter and utilise topology optimisation
to design a silicon-on-insulator (SOI) based PhCW Y-splitter having a
smooth broadband spectral performance. A transmission bandwidth of
more than 100 nm with less than 1 dB excess loss is obtained for a
fabricated PhCW component with a size smaller than 10 15 mm.
initial 50 500 final
1 mm
Fig. 1 Scanning electron micrograph of fabricated structure containing
topology-optimised Y-junction and 60 bends
Top panel shows material distribution in Y-junction design domain
during optimisation procedure after 0, 50, 500 iterations, and for final
topology-optimised structure
Design and fabrication: We utilise e-beam lithography and standard
anisotropic reactive-ion etch to define the PhC structures in the top
silicon layer of a SOI material. The PhC is defined by circular air
holes arranged in a triangular lattice and the PhCWs are formed by
removing one row of holes in the G-K direction of the crystal lattice.
The lattice period is L ’ 400 nm and the diameter of the holes
D ’ 275 nm.
Several PhCW based Y-splitters have previously been reported in the
literature [4–7]. Attempts have been made to improve the performance
by adding, removing and=or resizing holes in the splitting region.
1
2
However, the useful bandwidth ( 30 –50 nm) of experimentally
realised Y-splitters has typically been almost one order of magnitude
smaller than the bandgap. The topology optimisation design method
implies that the distribution of silicon and air is freely interchanged in
the chosen design domain with no geometrically enforced restrictions.
The optimisation algorithm is based on a 2D frequency-domain finiteelement
solver. The solver is used repeatedly in an iterative scheme, in
which the material distribution is updated every iteration based on
analytical sensitivity analysis and use of a mathematical programming
tool [9]. The Y-junction is optimised by modifying the material
distribution in such a way that the transmission (power flow) through
both output ports of the splitter is maximised. The material is only
redistributed in a small design area of approximately 1.5 2.5 mm as
illustrated in the top panel of Fig. 1. During the optimisation procedure
the power flow is evaluated for six frequencies in a chosen frequency
range so that a broadband component is achieved. The optimised
splitter design was obtained after approximately 1200 iterations of the
optimisation algorithm. It is seen that the optimised splitter region has
been smoothened in both the inner and outer sides of the two waveguide
branches of the splitter region. However, the smoothening is not trivial
as the splitter region contains several separate complex structures.
Fig. 1 shows a scanning electron micrograph of the fabricated PhCW
Y-splitter containing the topology-optimised Y-junction followed by two
topology-optimised 60 bends [11]. The PhC structures have been
fabricated without applying any special proximity corrections to the
irregular shaped holes during the e-beam patterning. The designed
structure is symmetric and the minor asymmetries of the fabricated
splitter are due to fabrication tolerances.
normalised transmission, dB
0
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ELECTRONICS LETTERS 20th January 2005 Vol. 41 No. 2
l, nm
1250 1300 1350 1400 1450 1500
TO output 1
TO output 2
DUV written
0.32 0.31 0.30 0.29 0.28 0.27
normalised frequency L/ l
Fig. 2 Measured normalised transmission against normalised frequency
from two output ports for topology-optimised (TO) component shown in
Fig. 1 (solid and dashed lines, respectively) (in this case, normalised
frequency corresponds to wavelength scale at top of graph)
Also shown is measured normalised output against normalised frequency from
previously fabricated Y-junction with consecutive 60 bends (dotted lines)
[6]. For this component normalised frequency range roughly corresponds to
1350–1600 nm. Horizontal dotted line at 3 dB corresponds to zero excess
loss of component
Results: The fabricated Y-splitter has been optically characterised using a
setup described in detail in [10, 11]. Fig. 2 shows the normalised
transmission for TE polarised light from the two output ports of the
complete PhCW structure displayed in Fig. 1. The spectra have been
normalised to the transmission spectrum for a straight PhCW of same
length in order to extract the performance of the Y-junction and subsequent
60 bend. The topology-optimised splitter displays smooth, low-loss, and
nearly indistinguishable transmission spectra for the two output ports. The
complete component is experimentally found to have a 100 nm bandwidth
with an average loss of 0.44 0.29 dB. This value includes excess losses
due to both the Y-junction and the subsequent 60 bend. Also shown in
Fig. 2 is the performance of a previously reported low-loss Y-splitter [4]
designed using intuitive design ideas and fabricated using deep UV (DUV)
lithography. In contrast to the topology-optimised splitter, the spectrum for
the DUV written Y-splitter is seen to be rather spiky, indicating resonant
and high-loss behaviour often observed for PhCW components.
Fig. 3 displays the normalised transmission of the topologyoptimised
Y-splitter corrected for the loss introduced by the 60 bend
[11]. Hence, this graph presents the excess loss due to the Y-junction
itself. The excess loss is found to be 0.18 0.20 and 0.34 0.30 dB for
100 and 175 nm bandwidths, respectively. Hence, the topology optimised
design opens up for a practical implementation of the Y-splitter
without the need for delicately matching a narrow operational