Si-EPIC Workshop: Silicon Nanophotonics Fabrication Directional Couplers

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1 Si-EPIC Workshop: Silicon Nanophotonics Fabrication Directional Couplers June 26, 2012 Dr. Lukas Chrostowski

2 Directional Couplers Eigenmode solver approach

3 Objectives Model the power coupling in a directional waveguide coupler gap, g Coupler Length, L For g = 200 nm What is the cross-over length of the coupler? Plot coupling vs. length What is the power coupling for L = 10 µm? y W Si x Air, n=1 G W s Si Si02, n= nm 220nm 1000nm 3

4 Fabricated Coupler 4

5 Two Methods: 1) Coupled-mode theory Find supermode effective indices, using: Lumerical mode solver calculate coupling 2) FDTD propagate a pulse down a coupler and observe power coupling 2D FDTD Effective Index Method 3D FDTD 5

6 Supermode Effective Index + Analytic Expression Find neff for the two supermodes (symmetric, anti-symmetric) Use coupler expressions to predict response Symmetric Anti-Symmetric Note: original single waveguide mode does not exist! It is only available via a superposition of the above two supermodes. 6

7 What is a supermode? A supermode is a mode of a super-structure, in this case, two waveguides. It is really an ordinary mode, and propagates just like any other mode: However, we can excite simultaneously 2 supermodes and observe interference (beating) 7

8 Directional Coupler Theory Cross-over length: L = 1sym 1asym = 0 2(n e 1sym n e 1asym ) Coupling coefficient (field), for a coupler with length Lc: r Pc apple = P 0 = sin 2 Lc L Assuming lossless coupling, the straight-through transmission amplitude coe cient is t = p 1 apple 2. However, if the couplers are lossy, then t 2 =1 apple 2 2, where 2 is a coe cient representing the existence of coupling losses.. 8

9 2D & 3D FDTD Mode Solver 9

10 Coupler calculations Question: Plot the mode profiles of the 2 guided modes. What are the effective indices? What is the cross-over coupler length? Cross-over length = distance after which the two super-modes are π shifted, 180º out of phase, i.e., ß1L-ß2L=π e.g. neff1 = , neff2 = Coupler cross-over length =1550e-9 / 2 / (neff1-neff2) = e-06 10

11 Mode profiles y Position [µm] x Position [µm] y Position [µm] x Position [µm]

12 Kappa vs. L apple = r Pc P 0 = sin 2 Lc L. Coupling power ratio Cross port (κ 2 ) Through port (t 2 ) Coupler Length [µm] 12

13 Cross-over length vs. Gap 3.5 x Cross over length [µm] Cross over length [µm] Coupler Gap [nm] Coupler Gap [nm] 13

14 Kappa vs. Gap (given L) apple = r Pc P 0 = sin 2 Lc L Field coupling, κ µm long coupler 15 µm long coupler Field coupling, κ Coupler Gap [nm] µm long coupler 15 µm long coupler Coupler Gap [nm] 14

15 Wavelength dependance Cross-over length Symmetric mode Antisymmetric mode Effective Index Cross over Length [µm] Wavelength [µm] Wavelength [µm] 15

16 Wavelength dependance Kappa µm long coupler 2 µm long coupler 5 µm long coupler Field coupling, κ Wavelength [µm] 16

17 Parasitic coupling 10 5 Coupler length [m] db coupling 30 db coupling 50 db coupling -50 db coupling for a 2 µm gap after 1 m! Coupler gap [µm] 17

18 Finite Difference Time Domain (FDTD) Modelling

19 What is FDTD? Exact numerical calculation of Maxwell s equations in the time domain Simulates pulses of light inside arbitrary geometries and materials Pulses of light contain many optical wavelength (short pulse = wide optical bandwidth, via Fourier Transform) A single pulse simulation provides response of the optical system for multiple wavelengths at once 19

20 FDTD Manuals FDTD_getting_started.pdf FDTD_reference_guide.pdf 20

21 FDTD Tutorial Waveguides

22 Lumerical MODE Propagator Uses Effective Index Method to collapse a 3D simulation into a 2D simulation Then performs a 2D FDTD simulation 22

23 Geometry 220x500 WG on oxide centred at y=0 Use Si-Palik 23

24 Simulation Volume 24

25 Mesh Settings Automatic mesh generation, with accurate conformal mesh. Auto non-uniform mesh Mesh Accuracy = 1 start with a very fast simulation to verify Mesh refinement conformal 25

26 3D Simulation Volume Ensure that Si & SiO2 extend through PML. Leave 0.5 to 1 um around the waveguide. 26

27 MODE Propagator Effective Index Method 27

28 Mode Source Used to launch light into a waveguide. FDTD calculates the field distribution to match the guided optical mode of the waveguide. Calculation provides effective index of the optical mode. 28

29 Mode Source 29

30 Mode Source 3D FDTD Choose geometry, ensuring that mode source surrounds the waveguide. Choose injection axis, i.e. propagation direction Select Mode FDTD will calculate mode profile (with the mesh defined in FDTD simulation parameters). 30

31 3D Mode Source 3D FDTD Calculate Modes 31

32 Mode Profile, Effective Index 32

Mode Source PROP Choose geometry, ensuring

33 Mode Source PROP Choose geometry, ensuring that mode source surrounds the waveguide. Choose injection axis, i.e. propagation direction Select Mode PROP will calculate mode profile (with the mesh defined in FDTD simulation parameters). Or use Fundamental mode 33

34 Movie monitor Speed up the movie: 34

35 Simulation Plot E vs. x in waveguide Plot transmission vs. wavelength at output of waveguide Watch movie 35

36 Simulation Transmission 36

37 Movie 37

38 Directional Couplers FDTD approach

39 FDTD Model Launch a pulse in one waveguide, model the pulse propagation Observe the power in each waveguide to determine the coupling coefficient study: wavelength dependance, gap dependance... Field profile, movie... 2D: use effective index method 3D: more time consuming, but more accurate includes bend regions 39

40 Coupling Lx=20.7;? sin(pi/2*l/lx)^2; 40

41 Effect of the bend region vs. 41

$2D FDTD Structures Geometry Material index of refraction found from Mode Solver$

42 2D FDTD Structures Geometry Material index of refraction found from Mode Solver calculation for the SOI wafer slab, i.e. neff~ nm wide waveguides, 100 nm gap Bend regions: 42

43 2D FDTD Simulation Simulation region, x: PML, y: periodic dx=dy=40nm Mesh override in the two waveguides, dy=20 nm 43

44 2D FDTD Source Mode source Ensure that E-field is in y direction (i.e. TE-like) 44

45 2D FDTD Monitors Linear X Power Monitor 45

46 2D FDTD Results Plot monitor1, monitor2: Intensity vs. x Chose lambda ~ 1550 nm (closest for 5 freq. points is 1535 nm) x=getdata("monitor1","x"); y1=getdata("monitor1","ey"); y2=getdata("monitor2","ey"); plot (x,abs(y1(1:length(x),3))^2, abs(y2(1:length(x),3))^2, "x (um)"," E ^2"); Cross-over length: 20 um 46

47 2D FDTD Monitors Movie, 2D Power Monitor Movie & 2D Power Monitor of the entire structure Increases the simulation from ~10 s to ~1 minutes. 47

48 2D Power monitor at um What about other wavelengths? 48

49 2D Power monitor at 1.4 um: at 1.7 um: 49

50 Narrow band source Coupler is wavelength dependant Narrow-band source: 7 nm wide 1.55 um ~ THz 50

51 Coupler without bend region 51

52 Coupler without bend region Slight loss due to radiation 52

53 coupler2d_movie.fsp 2D FDTD Movies Note: large field in the gap 53

54 coupler2d_3db_v3.fsp Effect of the bend radius Sharp radius introduces losses by coupling the light into higher order modes of the waveguides. These modes have high losses (surface roughness). Increased bend radius reduces the coupler s losses. 54

55 Directional Coupler 3D FDTD Use a curved region (i.e. 2 nd waveguide comes in gradually ) Allow the input waveguide mode to gradually decompose into the two supermodes. Use silicon (3.48, or dispersive model) 55

56 3D FDTD Large field component in gap Coupling length ~ 30 um for wavelength = 1.54 um 56

57 Conclusions 2D FDTD 3D FDTD 2D MODE 3D MODE 2.5D MODE Propagator reasonably fast, good for tutorial example reasonably accurate, fast reasonably fast, reasonably accurate inaccurate slow inaccurate misses bend region effect EIM approximation 57

58 Directional coupler 200 nm gap, Ridge WG 58

Experimental data 1 0.9 Power Coupling 0.8 0.7 0.6 0.5 0.4 0.

59 Experimental data Power Coupling apple 2 =sin [z + z bend ] 2L x t 2 =cos [z + z bend ] 2L x Cross port (κ 2 ) Through port (t 2 ) L x = 16.8 µm Z bend = 2.3 µm Coupler length [µm] 59

60 3D FDTD simulation Import GDS layout Setup FDTD simulation Vary structure parameter (e.g., length) Simulate each one Determine the through and cross coupling Plot coupling vs. Length Compare with experiments 60

61 DC_MODEprop.zip scripts to simulate coupler 61

62 Experiment vs. 3D FDTD Power Coupling apple 2 =sin [z + z bend ] 2L x t 2 =cos [z + z bend ] 2L x Through port (t 2 ) Cross port (κ 2 ) L x = 15.4 µm Z bend = 2.8 µm Coupler length [µm] 62

63 MODE vs. FDTD Field coupling, κ κ 2, 7.7 µm long coupler t 2, 7.7 µm long coupler κ 2, 5 µm long coupler, 3D FDTD t 2, 5 µm long coupler, 3D FDTD Coupler Gap [nm] 63

64 MODE vs. FDTD 10 1 Power coupling, κ 2, t κ 2, 5 µm long coupler, MODE κ 2, 7.7 µm long coupler, MODE t 2, 5 µm long coupler, MODE t 2, 7.7 µm long coupler, MODE κ 2, 5 µm long coupler, 3D FDTD t 2, 5 µm long coupler, 3D FDTD Coupler Gap [nm] 64

65 FDTD Tutorial Y-Branch Couplers

66 66

67 Fabricated Y-Branch splitter / coupler SEM image 6 between branches 67

68 Fabricated Y-Branch splitter / coupler FDTD can import SEM images; draw in black in the region of the coupler from SEM scale: 0.35 um um 44 nm 68

69 2D FDTD Import structure 69

70 2D FDTD Simulation Add input & output waveguides to match image data Effective index material (~2.8) Auto mesh 6; PMLs (to absorb scattered light) Mode source, 1550 nm Monitors: Linear Y ( L, R ) and 2D Power Monitors 70

71 2D FDTD Results at 1535 nm: L=getdata("monitorL","Px"); R=getdata("monitorR","Px"); y=getdata("monitorl","y"); plot(y,l(1:length(y),3),r(1:length(y),3),"position, y","power" ); legend("left side","right side"); Almost a 50-50% splitter. 71

72 FDTD Model Ideal layout Layout: 500 nm wide waveguides Each waveguide is rotated by 3 Separation of output waveguides is 500 nm In, Out1, Out2: Point Power Monitors, 200 frequency points. 72

73 Y-Branch Output Spectrum out1=pinch(getdata("out1","px"));out2=pinch(getdata("out2","px")); in=pinch(getdata("in","px")); f=getdata("out1","f"); plot(c/f,out1/in,out2/in,"wavelength","power" ); legend("output: Top","Output: Bottom"); 20 nm Mesh 10 nm Mesh 73

74 Y-Branch Movie 74

75 Y-Branch Combiner Reverse operation of a 50%-50% splitter In-phase sources (Gaussian, beam waist of 0.3 µm) constructive interference 180º out-of-phase sources (Gaussian, beam waist of 0.3 µm) destructive interference where does the power go? 75

Si-EPIC Workshop: Silicon Nanophotonics Fabrication Fibre Grating Couplers

Si-EPIC Workshop: Silicon Nanophotonics Fabrication Fibre Grating Couplers June 30, 2012 Dr. Lukas Chrostowski Outline Coupling light to chips using Fibre Grating Couplers (FGC, or GC). Grating coupler