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 Page 2 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 Page 3 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 Page 4 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 Page 5 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 Page 6 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: Page 7 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) Page 8 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 1015 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] Page 9 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] Page 10 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 !!! Page 11 COMSOL Conference Stuttgart 2011 C. Kraeh © Siemens AG, Corporate Technology
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