Folie 1 - COMSOL.pt

FEM Simulations of Rod-Type Photonic Crystal
Slabs as Resonant Microsystems for Optical Gas
Sensors
M.Sc. Christian Kraeh and Dr. Harry Hedler
Siemens AG, Corporate Technology
Excerpt from the Proceedings of the 2011 COMSOL Conference in Stuttgart
© Siemens AG, Corporate Technology
Motivation: From a conventional gas sensor to a
small integrated gas sensor
Gas detection with IR spectroscopy
Conventional spectroscopic gas sensor:
Interaction
path
Detector with Lens
Diffuse reflector
Electronics
Cable
Reflector
Gas
Lightsource
Detector with lens
laser diode
Light
Source
Size:
10 – 100 cm
Detector
Mirror
Conventional design
Gas molecules
Photonic Crystal based gas sensor:
Size:
0.1 – 1 cm
Lightsource
Detector
Photonic crystal
structure
Small integrated sensor
We used COMSOL Multiphysics to simulate light propagation in the photonic crystal
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COMSOL Conference Stuttgart 2011
C. Kraeh
© Siemens AG, Corporate Technology
Outline
Photonic crystal structures
Simulations with COMSOL Multiphysics
 Optical properties of a photonic crystal
 Photonic crystal waveguides
- Slow light for gas detection
- Coupling into photonic crystal waveguides
 Simulation of the gas detection
Conclusion
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COMSOL Conference Stuttgart 2011
C. Kraeh
© Siemens AG, Corporate Technology
Photonic crystal structures
5 µm
5 µm
 Experimental realization of photonic crystal
structures by a special etching technique
20 µm
 To have a broad application window for IRgas analysis by photonic interaction the
structure dimensions (pitch and roddiameter) are in the lower µm-range
(0.3…0.6 λGas)
Pictures: Markus Schieber
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COMSOL Conference Stuttgart 2011
C. Kraeh
© Siemens AG, Corporate Technology
Optical properties of a photonic crystal
 Photonic crystals are composed of periodic dielectric structures that affect
the propagation of EM waves
 The propagation of EM waves through a photonic crystal depends on the
wavelength; for certain wavelengths the propagation in the photonic crystal
is forbidden (Photonic Band Gap)
 In case of very high structures (z-direction), the photonic crystal can be
approximated as two-dimensional
 The COMSOL Multiphysics RF Module (2D, TE waves) is used to
simulate light propagation through our photonic crystal structures
z
x
Frequency (ωa/2πc)
TM Bands of a rod-type Si photonic crystal:
above
BG
BG
Bandgap
Г
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y
X
below
BG
M
Г
COMSOL Conference Stuttgart 2011
Plane Wave,
Ez component
C. Kraeh
Photonic Crystal
© Siemens AG, Corporate Technology
Photonic crystal waveguides for gas detection
 A waveguide is created by removing a row of rods (line
defect). It guides light, which's frequency lies in the
bandgap of the photonic crystal
 The length of the waveguide can be increased by several
bends:
This increases the absorption length
 At certain frequencies the light propagates with an
extremely slow group velocity (slow light):

k
Frequency (ωa/2πc)
vG 
k (2π/a) Γ → X
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COMSOL Conference Stuttgart 2011
C. Kraeh
© Siemens AG, Corporate Technology
Simulation of light propagation through a photonic
crystal waveguide
Calculation of the transmission spectrum:
1. Light propagation and coupling into a photonic crystal waveguide
Plane Wave
(Amplitude Ez = 1)
is applied to the
left boundary
Power Outflow
(Pout) through the
right boundary is
calculated for each
wavelength
Wavelength scan
Scattering boundary condition
2. Light propagation in an empty air box of equal size
Plane Wave
is applied to the
left boundary
Power Outflow
(Pout) is calculated
same wavelengths
The Transmission through the waveguide is:
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COMSOL Conference Stuttgart 2011
T
C. Kraeh
Pout,WG
Pout, Airbox
© Siemens AG, Corporate Technology
Coupling into photonic crystal waveguides
 Light is produced by an external light source
 Coupling of light into the waveguide from “outside”
Transmission - Cubic Lattic e
0.4
no Tap er
Tap er 1
 Strong Fabry-Pérot Interferences can be observed in
the transmission spectrum (wavelength in units of the
lattice pitch a)
 The Transmission can be increased strongly by taperlike coupling geometries
0.4
Transmission
no Taper
no
noTaper
Taper
0.3
0.4
0.2
Slow light
regime
no Tap er
Tap
er er
no
Tap
Tap er
0.1
0.3
Transmission
Transmission
0.3
Taper
Taper 1
Taper
0
3.5
3.6
3.7
3.8
Wavelength (a)
0.2
Transmission - Cubic Lattic e
0.2
0.4
no Tap er
Tap er 2
0.1
0.1
Taper 2
Transmission
0
3.5
0
3.5
0.3
0.2 3.6
3.7
3.6
3.8
3.7
3.8
Wavelengt h (a)
Wavelengt h (a)
0.1
0
3.5
3.6
3.7
3.8
Wavelength (a)
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COMSOL Conference Stuttgart 2011
C. Kraeh
© Siemens AG, Corporate Technology
Simulation of the gas detection
with methane (700 ppm) at 7.625 µm
To simulate the influence of a test gas (methane) on an
optical gas sensor, two things are needed:
 Absorption cross section of methane at 7.625 µm,
obtained from literature (HITRAN database):
The fit-function and the absorption cross section are used to
calculate an expression for the light extinction (κ) as a
function of the wavelength:
 Methane( ) 
 Methane  4.375 1015 mm2
 The shape of the absorption line at RT (obtained from a
previous experiment with a conventional gas sensor)
0.4
Experiment
Lorentzian fit
with: b = 3.5055 10-10
kα = 1.1056 107
Subsequently the complex refractive index n of air containing
700 ppm methane is:
n( )  1  i   Methane( )
This function is used in COMSOL to describe the material
property of the air-subdomain:
0.3
Absorption
7.625µm
b
 2
2
4    k b  (  7.625µm) 2
0.2
0.1
0
7.62
7.623
7.625
7.627
7.63
Wavelength [µm]
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COMSOL Conference Stuttgart 2011
C. Kraeh
© Siemens AG, Corporate Technology
Simulation of the gas detection
with methane (700 ppm) at 7.625 µm
The absorption due to methane is calculated by comparing the Power Outflow (P out) of a structure containing
methane to a structure containing only air (n = 1):
Absorption  1
Pout, Methane
Pout, Air
Comparing the absorption of a 1 mm long waveguide in slow light condition with an air box of the same length:
1 mm absorption length
0.6
no Waveguide:
Waveguide (slow light):
Absorption
Waveguide
no Waveguide
0.4
0.2
0
7.615
1 mm length
Strong
increase of the
absorption due
to the reduced
group velocity
of the light in
the waveguide
7.62
7.625
7.63
7.635
Wavelength [µm]
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COMSOL Conference Stuttgart 2011
C. Kraeh
© Siemens AG, Corporate Technology
Conclusion
COMSOL Multiphysics (RF module) was successfully used to simulate:
 Light propagation though a bulk photonic crystal / photonic crystal waveguide
 Transmission spectra of photonic crystal waveguides to identify optimal coupling
geometries
 Increased gas absorption in a photonic crystal waveguide due to slow light effects
Thank you for your attention !!!
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COMSOL Conference Stuttgart 2011
C. Kraeh
© Siemens AG, Corporate Technology