Modeling of a 2D Integrating Cell using CST Microwave Studio

Transcription

1 Modeling of a 2D Integrating Cell using CST Microwave Studio Lena Simone Fohrmann, Gerrit Sommer, Alexander Yu. Petrov, Manfred Eich, CST European User Conference

2 Many gases exhibit absorption lines in the mid infrared OPTICAL GAS SENSING Carbon dioxide: absorption coefficient: α = 34.7 db/cm possible applications: air conditioning, CO 2 control in automobiles J. Hodgkinson and R. P. Tatam, Meas. Sci. Technol. 24, (2013) 2

3 For a gas cell a long optical pathlength is required 3D INTEGRATING SPHERE 3D Integrating spheres exist that use diffuse reflectors in order to increase the beam pathlength Can this approach be adapted for sensors integrated on a chip? J. Hodgkinson and R. P. Tatam, Meas. Sci. Technol. 24, (2013) 3

4 A 2D integrating cell can be used to create a long optical path in a small area of a silicon slab 2D INTEGRATING CELL 2D photonic crystal or quasi crystal with omnidirectional 2D bandgap Multimode emitter (100 µm) Multimode detector (100 µm) Use CST Microwave Studio to simulate the field energy decay per time in order to calculate the average optical pathlength 4

5 The losses of a PhC cavity are determined by vertical scattering at the PhC mirrors SCATTERING LOSS OF THE 2D CELL vertical mismatch between slab mode and evanescent PhC mode vertical scattering reflection at the PhC mirrors 5

6 A discrete port is used to excite a TE mode in a periodic cavity inside of a PhC slab MODELING OF A PERIODIC CAVITY USING CST MICROWAVE STUDIO L a r periodic boundaries discrete port TE modes are excited Use analysis of Q-factor in order to determine the reflectivity of the PhC mirrors 6

7 The reflectivity of the PhC mirrors can be calculated from the energy decay inside of the cavity CALCULATION OF THE REFLECTIVITY L a r periodic boundaries discrete port approximation for a large number of reflectors: R 1 mπ Q Q = 2π 10 ln 10 [1] ν [THz] de db dt ps R: Q: m: ν: de/dt: reflectivity quality factor mode number resonance frequency energy decay per time [1] Ph. Lalanne, Optics Express 12, (2004) 7

8 The field energy inside of a periodic PhC cavity decays nearly exponentially ENERGY DECAY INSIDE OF AN EXEMPLARY PHC CAVITY de/dt = 8.33 db/ps mode number: frequency: Q-factor: reflectivity: m = 7 ν = THz Q = 2π 10 ln 10 R 1 mπ Q ν THz de dt db ps = 741 = 0.13 db 8

9 Reflectivities for both orientations are in the same order of magnitude PERIODIC CAVITIES WITH DIFFERENT ORIENTATIONS ΓK L ΓM L r a a r r = µm a = 0.42 µm Γ L = 2.9 µm m = 12 mode number m = 7 Μ Κ Q = 536 quality factor Q = 741 R = db reflectivity R = db 9

10 The average loss per reflection can be determined from the simulation of the field energy decay SIMULATION OF A 2D INTEGRATING CELL L = 6 µm r = µm a = 0.42 µm energy decay after an excitation with a discrete port de/dt = 2 db/ps 0.06 db per reflection 10

11 A waveguide port can be implemented in order to excite a signal in the integrating cell MODEL OF A 2D INTEGRATING CELL WITH WAVEGUIDE PORT L = 6 µm r = µm a = 0.42 µm TE mode 11

12 2 models are considered to distinguish between the losses by vertical scattering and the waveguide port DIFFERENT CST MODELS TO DETERMINE THE LOSSES INSIDE OF THE 2D INTEGRATING CELL A TE mode is excited using a waveguide port 1) consider only losses given by the waveguide port magnetic boundary conditions (Ht = 0) above and below the PhC slab 2) consider losses from vertical scattering and waveguide port simulate a 220 nm PhC slab with air surrounding and open boundary conditions 12

13 Assuming uniform illumination the energy decay can be estimated APPROXIMATION OF THE ENERGY DECAY IN A CAVITY WITH WAVEGUIDE PORT LOSSES 1) consider only losses given by the waveguide port perimeter of the 2D cell: S 0 = 40 µm width of the waveguide port: S p = 0.73 µm effective refractive index: n eff = 3.5 average pathlength between two reflections: L 0 = 7 µm average number of reflections: n = S 0 /S p = 55 average optical path inside of the cavity: L = n L 0 = 385 µm average photon lifetime: average energy decay per time: τ = L n eff = 4.5 ps c de = 0.97 db/ps dt 13

14 Energy decay from simulation is very close to estimation SIMULATION OF ENERGY DECAY IN CAVITY WITH WAVEGUIDE PORT LOSSES 1) consider only losses given by the waveguide port de/dt = 1.3 db/ps 14

15 Energy decay is in the same order of magnitude as in the lossless case ENERGY DECAY IN CAVITY WITH SCATTERING AND PORT LOSSES 2) consider losses from vertical scattering and waveguide port de/dt = 3.57 db/ps 15

16 The 2D Integrating Cell is suitable for optical gas sensing EXAMPLE OF A 2D INTEGRATING CELL FOR SENSING APPLICATIONS length: average pathlength inside of the cavity: average loss per reflection: average loss due to waveguide port: L 0 = 2 mm average number of reflections: n = 55 L = 7.8 cm ΔE r = 0.06 db ΔE p = 4.37 db total loss: ΔE total = n ΔE r + ΔE p = 7.67 db 0.98 db/cm absorption coefficient of CO 2 : α = 34.7 db/cm 16

17 Implementing an adiabatic transition in ΓK-direction improves the reflectivity by a factor of 3 CAVITY WITH LINEAR ADIABATIC TRANSITION IN ΓK-DIRECTION midgap-mode: m = 12 r = r = r = r = r = r = Q = 536 R = db Q = 1444 R = db 17

18 Implementing an adiabatic transition in ΓM-direction improves the reflectivity by a factor of 18 CAVITY WITH LINEAR ADIABATIC TRANSITION IN ΓM-DIRECTION midgap-mode: m = 7 r = r = r = r = r = r = Q = 757 R = db Q = R = db 18

19 SUMMARY CST Microwave Studio is used to simulate the energy decay inside of a periodic photonic crystal cavity in order to calculate the reflectivity of the PhC mirrors A 2D Integrating Cell was modeled and excited with a discrete port to get information about vertical scattering losses at the PhC mirrors A waveguide port was implemented into the PhC cell and two models were used to simulate both the losses caused by the waveguide port and the total loss of the 2D Integrating Cell The simulation results show that our 2D cell can exhibit losses smaller than 1 db/cm and therefore can be used for optical sensing applications The reflectivities can be further improved by adiabatic transitions between the waveguide slab and the photonic crystal 19