Simulations Based on Paper Nanophotonics, 2014 Review Simulation with different waveguide geometry Simulation with different junction location Simulation of interleaved junction modulator Conclusion

Carrier Depletion Based Modulator <Carrier depletion modulator> <Refractive index vs Carrier concentration> Plasma dispersion effect -Change in carrier concentration change in refractive index, absorption coefficient change in phase & intensity ∆𝑛=−[8.8× 10 −22 ∆ 𝑁 𝑒 +8.5× 10 −18 ∆ 𝑁 ℎ 0.8 ] ∆𝛼=6× 10 −18 ∆ 𝑁 𝑒 +4× 10 −18 ∆ 𝑁 ℎ ] <Loss vs Carrier concentration> Ref. “Electrooptical Effects in Silicon”, Soref and Bennett, IEEE J. of Quantum Electronics, 1987

Categories Of Modulators Three types of modulator -Vertical junction -Horizontal junction -Interleaved junction <Vertical Junction> <Horizontal Junction> <Interleaved Junction>

Waveguide Geometry(Height) 500 nm 500 nm 220 nm 450 nm 90 nm <220nm Height> <450nm Height> Different height of waveguide -Rib waveguide -Doping: p(1× 10 18 ), n(2× 10 18 ) -Same waveguide width(500nm) -1cm length

Simulation Results 500 nm 500 nm 220 nm 90 nm 450 nm <220nm Height> <450nm Height> Smaller effective index changes for larger height -Effective index without bias is larger  Smaller effective index changes Smaller loss for larger height -Large confinement factor  Smaller loss

Transmission Curves <220nm Height> <450nm Height> Smaller effective index changes for larger height Larger efficiency Smaller loss for larger height Smaller insertion loss

Position of PN Junction Offset of junction location -P-type has larger refractive index change (Soref & Bennett equation) -Large portion of P-type Increased efficiency <Cross section of modulator>

Junction Location 500 nm 500 nm 100 nm <Junction located on middle of waveguide> <Junction located with offset from middle> Different junction location -Rib waveguide -Doping: p(1× 10 18 ), n(2× 10 18 ) -Same waveguide width(500nm) -1cm length

Simulation Results 500 nm 500 nm 100 nm <No offset> <100nm offset> Larger effective index changes with offset -P doping has larger effect on effective index changes  Larger effective index change Smaller loss with offset -N doping has larger effect on loss(doping concentration)  Smaller loss

Transmission Curve <No offset> <100nm offset> Larger effective index changes with offset Smaller efficiency Smaller loss with offset Smaller insertion loss

Interleaved Type Modulator Density of depletion increase -Period of p,n region should be small -Increase in capacitance Lower BW, more power -Tolerant to alignment errors MZM -44-Gbps, 1.7V.cm efficiency 1dB/mm loss is reported <Interleaved Junction> <MZM with interleaved junction>

Simulation Setup & Results <Interleaved junction> Ref. “A 25Gbps silicon microring modulator based on an interleaved junction”, J. C. Rosenberg, et al., Optics Express, 2012 -Rib waveguide(220nm height) -Doping: p(2× 10 18 ), n(2× 10 18 ) -Junction period: 560nm -Field profile in one period  Extract phase information  Calculate Vπ <Simulation Result>

Conclusion Waveguide Geometry Larger height has small loss, but larger efficiency Junction Location Large portion of p-doping has small loss & small efficiency Interleaved Junction Small efficiency achieved