We experimentally demonstrated a fast optimization algorithm based on the method of gradient descent for achieving optimum spectral response of high-order silicon microring optical filters. The filter optimization was performed on a 4th-order serially-coupled silicon microring filter by thermo-optically tuning the microring resonances using Ti/W heaters. Three different optimization objective functions were used to obtain the optimum filter shape, namely, the single-wavelength method, the dual-wavelength method, and the total transmitted power method. The efficacy of each optimization method was evaluated and compared based on the number of required iterations, the ideality of optimized response, and the wavelength tuning accuracy.

1. Fast Thermo-Optic Optimization of
High-Order SOI Microring Optical Filters
by Method of Gradient Descent
Tyler J. Zimmerling, Yang Ren, Huynh Ngo, Vien Van
University of Alberta, Edmonton, Alberta, Canada

2. Silicon Microring Optical Filters
Photonic Integrated Circuits (PICs)
Wavelength Division Multiplexing
Inherent fabrication errors and defects
Post-fabrication optimization
Thermo-optic tuning
Metallic resistors
Doped silicon
Electro-optic tuning
Free carrier injection
1

3. Motivation 2
2nd Order Systems
Tune 1 resonance to the other
Higher Order Systems
Complex, co-ordinate descent, Nelder-Mead algorithm
Filter shape, in-band ripple
Investigate and compare 3 different optimization objective
functions:
Single-Wavelength
Dual-Wavelength
Total Transmitted Power

4. Microring Filter Design 3
4th Order Vernier microring filter
3 dB Bandwidth: 25 GHz, FSR: 158 nm
450 nm x 220 nm silicon strip waveguides
R1 = 11.272 μm, R2 = 14.090 μm
𝑔1=157 nm, κ1=0.61, 𝑔2=312 nm, κ2=0.12, 𝑔3=358 nm,
κ3=0.09, 𝑔4=298 nm, κ4=0.15, 𝑔5=157 nm, κ5=0.68

5. Method of Gradient Descent 4
Line-search optimization
𝑇′
𝐼 =
−𝑇 𝐼+2𝑎 +8𝑇 𝐼+𝑎 −8𝑇 𝐼−𝑎 +𝑇(𝐼−2𝑎)
12𝑎
Φ 𝑠𝑖𝑛𝑔𝑙𝑒 = 𝑇 𝜆 𝑐
Φ 𝑑𝑢𝑎𝑙 =
𝑇 𝜆3𝑑𝐵− + 𝑇 𝜆3𝑑𝐵+
2
Φ 𝑇𝑇𝑃 =
𝜆3𝑑𝐵−
𝜆3𝑑𝐵+
𝑇 𝜆
𝑁
𝜙 𝑒𝑟𝑟 𝑖
𝑚
=
Φ𝑖
𝑚
− Φ𝑖
𝑚−1
Φ𝑖
𝑚−1
𝑇 𝜆 : Transmission at
Wavelength 𝜆
𝜆 𝑐 : Target Center Wavelength
𝜆3𝑑𝐵± : Long/Short-Wavelength
3 dB passband edges
N : Number of Samples
m : Iteration Number
i : Optimization Method

6. Experimental Setup 5
Tunable Semiconductor Laser and polarization controller
Lensed fibres butt-coupled in/out of silicon chip facets
Measured using a photodetector: 10 pm resolution
Computer-connected microcontroller and DAC
Resistance of each circuit ~200 Ω
Max voltage: 3 V, Max current: ~15 mA,
Max power: 45 mW.
Tuning efficiency ~80 pm/mW
Heater setup uncertainty: ± 0.1 mW.
Thermal tuning uncertainty: ± 8 pm.

7. Single-Wavelength Method 6
12345678910
Φ 𝑠𝑖𝑛𝑔𝑙𝑒 = 𝑇 𝜆 𝑐
Trials 1-10
Black line: optimization
wavelength, 1547.05 nm.
Dashed cyan spectrum: initial
response after coordinate
descent.

8. Dual-Wavelength Method 7
12345678910
Φ 𝑑𝑢𝑎𝑙 =
𝑇 𝜆3𝑑𝐵− + 𝑇 𝜆3𝑑𝐵+
2
Trials 1-10
Black lines: optimization
wavelengths, 1546.95 and
1547.15 nm.
Dashed cyan spectrum: initial
response after coordinate
descent.

9. Total Transmitted Power Method 8
12345678910
Φ 𝑇𝑇𝑃 =
𝜆3𝑑𝐵−
𝜆3𝑑𝐵+
𝑇 𝜆
𝑁
Trials 1-10
Black lines: optimization region,
1546.95 to 1547.15 nm.
Dashed cyan spectrum: initial
response after coordinate
descent.

10. Results I 9
Single-λ and TTP converge ~5 iterations
Dual-λ fluctuates around optimized result
TTP: 20% decrease in 3 dB bandwidth
Dual-λ: Outperforms in center wavelength accuracy with ∆λ = 10𝑝𝑚
Single-λ: Least in-band ripple at 0.53 dB

11. 10Results II

12. Conclusions and Future Work 11
Optimization Method Bandwidth (GHz) Δλ (pm) In-Band Ripple (dB) Iterations
Single-Wavelength 25.1 30 0.53 5
Dual-Wavelength 25.1 10 2.36 9
TTP 20.0 50 2.56 5
Single-Wavelength: Worst center λ accuracy, best in-band ripple
Dual-Wavelength: Best center λ accuracy, significant in-band ripple
TTP: Most stable, worst filter shape and in-band ripple
 Focus on In-Band Ripple
Order of Optimization
Weighted Objective Functions