COMSOL Design Tool: Simulations of Optical Components Week 6: Waveguides and propagation S matrix

Transcription

1 COMSOL Design Tool: Simulations of Optical Components Week 6: Waveguides and propagation S matrix Nikola Dordevic and Yannick Salamin

2 Content Revision Wave Propagation Losses Wave Propagation Examples Dielectric Slab Quantitative analysis of photonics system S matrix Transmission Reflection Scattering losses Example Bending radius of a waveguide

3 Homework - Mode solver For a confined mode, no energy flow in the radial direction: n n eff Wave cannot be evanescent in the core region: n n n 2 1 eff 2 Core r = 8um n = Cladding r = 40um n = n 2 n

4 Step Fiber Mode - solution LP01 LP11 HE11 TE01 TM

5 Waveguide Out-of-plane In-plane

6 Revision Propagation Out-of-plane : Port aren t defined (eigenvalue solution to whole geometry) In-plane: Port need to be defined (eigenvalue solution to defined port) Out of plane Excitation from surface plane Electromagnetics node: NO PORT In plane Port Excitation from boundary Electromagnetics node: TE or TM

7 Revision Effective index n eff n 2 n 1 n 2 Cladding Core Cladding n 2 < n eff < n 1 (1) Only 1 material More materials n mode == n material Maxwell s Laws (Field Continuity) n eff close n 1 Most power in core (confinement) n eff close n 2 Most power in substrate/superstrate Field must have a continuous profile across interface

8 Revision Types of modes (z-propagation) Planar (infinite parallel plates) TE No E z. Only E y (or E x ), H x (or H y ) and H z TM No H z. Only E y (or E x ), H x (or H y ) and E z Dielectric Waveguides TE TM Mix of TE & TM All components Fundamental In reality modes are quasi-te or quasi-tm

9 Wave Propagation - revision Dielectric Slab What we want Propagation in core Decay (exponential) in sub/superstrate High confinement What we don t want Propagation in sub/superstrate Low confinement (except in certain application - e.g Couplers) But how does a propagating wave look in Comsol??

10 Dielectric Slab Waveguide 2D n core = 1.5 n cladding = 1 λ = 1550nm 2 2d 2 2 M n1 n2 d n n n n d = 1um

11 Wave Propagation Examples Dielectric slab waveguide

12 Wave propagation quiz We have 1W at the input of our waveguide It s straight We have lossless material Now, the output P out will be a) W b) 0.5 W c) 1 W d) Nah, who cares! P in = 1W

13 Wave propagation Many inputs What happens with system when we have MIMO? Examples How do we calculate those things?

14 S Matrix for photonics How to characterize our photonics system as whole? Scattering matrix (so called S-matrix) output input Superposition: b i = S ij a j j=1..n b 1 b 2 b n = S 11 S 1n S n1 S nn a 1 a 2 a n

15 S parameters for photonics How to characterize our photonics system as whole? S matrix Unitary in lossless systems Diagonal S ii terms are complex valued amplitude reflection coefficients Superposition: b i = j=1..n S ij a j b 1 b 2 b n = S 11 S 1n S n1 S nn a 1 a 2 a n

16 S parameters for photonics How to characterize our photonics system as whole? S matrix Unitary in lossless systems Diagonal S ii terms are complex valued amplitude reflection coefficients Two input/output ports: a 1 b 1 = S 11 S 12 a 1 a 2 b 2 S 21 S 22 a 2 T T = R = b 1 R b

17 S parameters for photonics How to characterize our photonics system as whole? S matrix Unitary in lossless systems Diagonal S ii terms are complex valued amplitude reflection coefficients Two input/output ports: a 1 b 1 = S 11 S 12 a 1 a 2 b 2 S 21 S 22 a 2 T T = S 21 2 R = S 11 2 b 1 R b

18 S parameters for photonics: COMSOL Can COMSOL help? S matrix Luckily, COMSOL has built in calculation of these! Two input/output ports: These are the ports we define in COMSOL! a 1 b 1 = S 11 S 12 a 1 a 2 b 2 S 21 S 22 a 2 T T = S 21 2 R = S 11 2 b 1 R b 2 COMSOL calculates this!

19 Example Tapering Sometimes, photonics design requires that waveguide also changes its width Example is Multi Mode Interference coupler (one of the projects)

20 Homework - Tapering Tasks: Plot transmission curve for different taper lengths (Note: you can add trapezoid in COMSOL) L taper greater then 100 nm SiO 2 L 2 L taper w 1 w 2 L 1 Si

21 Tapering What do you expect to happen?

22 Tapering

23 Tapering What do you expect to happen?

24 Port 2 COMSOL Homework Now, let s see how it works SiO 2 Port 1 Si We will launch 1W at the port 1 We add circular segment with a radius r We collect the power at the port 2 We calculate the transmission Bending radius r

25 COMSOL Homework Parameters (in_x,dy/2) Si_w dy Si_l (-dx/2,out_y) dx

26 Geometry section

27 Geometry

28 Geometry

29 Geometry

30 Geometry

31 Geometry

32 Geometry

33 Materials

34 Frequency domain We have to initialize ports We want to inject a mode and measure the transmission We want to prevent scattered waves to reflect back into the domain

35 Frequency domain Port

36 Frequency domain Port

37 Mesh definition We want to customize the mesh size!

38 Mesh definition We want to customize the mesh size! We want high resolution inside the curvature!

39 Mesh definition We want to customize the mesh size! We want the remaining part of geometry to be meshed using the regular size

40 Mesh - result

41 Study Parametric sweep we want to change the radius of curvature Boundary of the ports are analyzed and fundamental mode injected (Port 1) and power at the Port 2 is received Propagation at single frequency (wavelength) is analyzed using the Frequency domain

42 Study

43 Study

44 Study

45 Results Transmission for different bending radius