Si Micro-Ring Resonator. Yoojin Ban

Transcription

1 Si Micro-Ring Resonator Yoojin Ban

2 Why Photonics? Copper wires reaching physical limits ~10 Gbps or higher becoming challenging Distance/speed tradeoff shortens lengths Alternative: Transmit data over optical fiber Much further reach at any given speed Multiple signals can travel on one fiber Thin & light =easy cable management 2 / 18

3 Bringing Si Manufacturing to Optical Comms Si Manufacturing Optical Communications High volume, low cost Highly Integrated Scalable Very high bandwidth Log distances Immunity to electrical noise 3 / 18

4 Si Photonics Optical Anywhere Incredible Potential 4 / 18

5 Silicon Photonics Link intel Demonstrated 50 Gbps Silicon Photonics Link 5 / 18

6 Lumerical Solutions 3D FDTD Finite difference time domain method Exact numerical calculation of 3D Maxwell equation in time domain Accurately simulation of material dispersion or device response over wide wavelength range Short pulse of light wide optical bandwidth (mesh size accuracy ) Computationally intensive 2D FDTD Dramatically improved simulation speed Only for 2 dimensional structure 6 / 18

7 Lumerical Solutions 2D FDTD with Effective Index Method 2.5D FDTD Lumerical MODE Solutions Collapsing a 3D geometry into a 2D set of effective indices Solving slab waveguide using 2D FDTD Excellent assumption : less than 240 nm thickness of 1550 nm wavelength Calculation step Identification of the vertical slab modes of the core waveguide structure Meshing the structure and collapsing of the 3D material in to effective 2D indices (Dispersive characteristics) 2D FDTD simulation with new effective materials 7 / 18

8 Lumerical Solutions 2.5D FDTD vs. 3D FDTD Faster simulation speed 2.7% group index error in FSR in ring resonator Only for similar vertical profile with original slab mode (small bend radius X) Eigenmode Solver Solving optical modes in a cross section of an arbitrary waveguide geometry Solving Maxwell s equation using finite difference algorithm Formulated into a matrix eigenvalue problem Effective indices and mode profiles 8 / 18

9 Si Micro-Ring Resonator jκ γ α Input & through port matrix relation: Et1 γ jκ Ei1 = E jκ γ E t2 i2 E = αe E γ j θ i2 t κ = 1 γ: Through coefficient κ: Coupling coefficient α: Round-trip loss factor θ: Round-trip phase shift 9 / 18

10 Si Micro-Ring Resonator jκ γ α Propagation constant: β = k n = eff 2π neff λ Round-trip phase shift: θ = βl = 2π neff λ L k: Wave number λ: Wavelength n eff : Effective index of ring L: Ring circumference 10 / 18

11 Si Micro-Ring Resonator γ jκ α Input & through port matrix relation: Et1 γ jκ Ei1 = E jκ γ E t2 i2 E = αe E j θ i2 t2 ( ) = γ κα 2 exp( θ) καγ 2 2 exp( 2θ) καγ exp( 3θ) ( ) E1 t t j j j E1i t = n= 1 2 n n 1 γ κ αγ exp θ ( jn ) E ( t) 1i 11 / 18

12 Si Micro-Ring Resonator E E 1t 1i = n= 1 2 n n 1 γ κ αγ exp θ ( ) ( ) ( jn ) ( ) ( ) ( ) ( ) ( ) κ aexp jθ γ aγ exp jθ aκ exp jθ γ aexp jθ = γ = = 1 aγ exp jθ 1 aγ exp jθ 1 aγ exp jθ 2 E 1 1t γ aexp t = = 2 1i E 1 γ exp 1i 2 2 α + γ 2αγ cos( θ ) α γ 2αγ cos( θ ) ( jθ) ( θ) P P a j = / 18

13 Coupling Type of Micro-Ring Resonator α < γ α > γ α γ At resonance: P P 1t 1i α + γ 2 αγ ( α γ ) = = 1+ α γ 2 αγ (1 αγ ) / 18

14 Resonator Parameters: FSR FSR β = 2π neff λ β β n k eff β = + λ λ λ λ 1 2 2π β λ FSR = λ = L λ n L eff Wavelength dependency: eff ng = neff λ λ β β = λ λ FSR n g = λ = n 2 λ nl g 14 / 18

15 Si Micro-Ring Resonator Design κ 1 Critical coupling: γ = γα 1 2 κ 2 P through P input γ α + γ 2αγ γ cos( θ) = 1 + ( αγ γ ) 2αγ γ cos( θ) P P drop input α(1 γ )(1 γ ) = 1 + ( αγ γ ) 2αγ γ cos( θ) / 18

16 Si Micro-Ring Resonator Design 2.5 FDTD simulation 16 / 18

17 Si Micro-Ring Resonator Design FSR Calculation (n g ) 17 / 18

18 Si Micro-Ring Resonator Design Resonance Characteristic 18 / 18