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Hamburg University of Technology Institute of Optical and Electronic Materials1
Institute of Optical and Electronic Materials, Hamburg University of Technology
Optimization of silicon-on-insulator
omnidirectional photonic crystal mirrors
Hendrik Preuss
Hamburg University of Technology Institute of Optical and Electronic Materials2
Gases have strong absorption peaks in mid infrared
ABSORPTION OF GASES
CO2: 4.2 − 4.35 μm
CH4: 3.15 − 3.45 μm
J. Hodgkinson and R. P. Tatam, Measurement Science and Technology, 24, 012004 (2013)
Hamburg University of Technology Institute of Optical and Electronic Materials3
A 2D integrating cell can be envisaged to create a long
optical path in a small area of a silicon slab
2D INTEGRATING CELL
2D photonic crystal with
omnidirectional 2D bandgap
The evanescent optical
field is used to sense the
surrounding medium
Hamburg University of Technology Institute of Optical and Electronic Materials4
EIGENMODE SOLVER BAND DIAGRAM
Band diagram of triangular lattice of holes in a silicon
slab shows a large bandgap for TE modes
Fre
quency (
TH
z)
Wavevector
𝑎 = 420 nm
𝑟 = 126 nm
ℎ = 220 nm
𝑛𝑆𝑖 = 3.48
𝑛𝑆𝑖𝑂2 = 1.45
TE
Hamburg University of Technology Institute of Optical and Electronic Materials5
The losses of a PhC cell are determined by vertical
scattering at the PhC mirrors
SCATTERING LOSS OF THE 2D INTEGRATING CELL
Reflection at the PhC mirrors
Vertical scattering
Vertical mismatch
between slab mode and
evanescent PhC mode
𝛼𝑠𝑐𝑎𝑡 = 1 − 𝑅
𝛼𝑠𝑐𝑎𝑡: Scattering loss
𝑅: Reflectivity
Hamburg University of Technology Institute of Optical and Electronic Materials6
A hexagonal cell with 4µm side length was designed to
estimate the reflectivity from FDTD simulations
2D CELL MODEL FOR TIME DOMAIN SIMULATION
bar: 2 µm
Uniform Taper1 Taper2
Smallest hole radius 126 nm 90 nm 65 nm
Taper length - 5 holes 7 holes
Side length of cell:
Effective path length
between 2 reflections:
Photonic bandgap:
𝑎 = 0.42 μm
𝑟 = 9𝑎 = 3.78 μm
𝐿𝑒𝑓𝑓 ≈ 4.8 μm
1.26 − 1.60 μm
1.27 − 1.60 μm
Lattice constant:
Discrete
Port
Photonic
Crystal
𝑟
Excitation spectral
range:
Hamburg University of Technology Institute of Optical and Electronic Materials7
The calculated PhC reflectivity will be the average over
the excited frequency range
FIELD PATTERN IN CELL
𝑓 = 200THz
𝜆 = 1.50 μm
𝐸(𝑡)
Hamburg University of Technology Institute of Optical and Electronic Materials8
Monitoring the energy decay within the simulated 2D cell
gives an upper and lower estimate of the reflectivity
CST SIMULATION OF ENERGY IN 2D CELL
Energ
y (
dB
)
Time (ps)
Energy in 2D cell with uniform holes
Lower estimate: 𝑅 = 95.8% Upper estimate: 𝑅 = 98.4%
𝑑𝑊 𝑡
𝑑𝑡= −𝑊 𝑡
𝛼𝑠𝑐𝑎𝑡ҧ𝑡
𝑅 = 1 + ҧ𝑡ln(10)
10
𝑑𝑊𝑑𝐵(𝑡)
𝑑𝑡
ҧ𝑡 =𝐿𝑒𝑓𝑓
𝑣𝑔𝛼𝑠𝑐𝑎𝑡 = 1 − 𝑅
Hamburg University of Technology Institute of Optical and Electronic Materials9
The reflectivity is calculated from the transmission
through cells with various propagation lengths
EXPERIMENT
Fohrmann et al., APL Photonics 2(9), 96102 (2017)
Uniform: 𝑅 = 98.1%
Taper 2: 𝑅 = 99.1%
𝑟 = 𝑎𝑁
𝑁: Number of holes per cell side
Hamburg University of Technology Institute of Optical and Electronic Materials10
The measured reflectivities lie within the simulated
reflectivity ranges for all PhC designs
SIMULATION / EXPERIMENT COMPARISON
Uniform
Taper 1
Taper 2
bar: 2 µm
Reflectivity (%)
CST Simulations
Experiments
An total propagation
path of 𝐿𝑡𝑜𝑡𝑎𝑙 = 25 cmwas achieved with the
largest Taper 2 cell with
𝑟 = 1.8mm.
Hamburg University of Technology Institute of Optical and Electronic Materials11
With decreasing radius the photonic crystal bandgap
vanishes
EIGENMODE SOLVER SWEEP OVER RADIUS
Hole radius 𝑟 (nm)
Fre
quency (
TH
z)
𝑎 = 420 nm
ℎ = 220 nm
𝑛𝑆𝑖 = 3.48
𝑛𝑆𝑖𝑂2 = 1.45
Hamburg University of Technology Institute of Optical and Electronic Materials12
Acknowledgments
We acknowledge the cooperation with Dassault Systemes and the support
with their CST Studio Suite software.
https://www.3ds.com/de/produkte-und-services/simulia/produkte/cst-studio-suite/
