High-Speed Circuits & Systems Lab.Dept. of Electrical and Electronic Engineering

Yonsei University

Directional coupler

Byung-Min Yu

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Silicon photonics

EIC + OIC = EOIC

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Silicon photonics

http://www.trendguardian.com/2010/08/silicon-photonics-1terabyte-of-data-in.html

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Simulation tool

MODE Solutions

- Eigen mode solver for waveguide

- 2.5D FDTD propagation method(Analyzing how optical fields propagate within waveguiding structures)

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What is directional coupler (DC)

PthroughPin

Pcoupled

- Directional coupler: relation between nearby two waveguide

- Light field in waveguide affect another waveguide

Directional coupler overview Field in directional coupler

Coupling gap

Coupling length

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What is directional coupler

Even-mode of Ey field Odd-mode of Ey field

- Even-mode: phases of E-fields are same direction in two waveguides

- Odd-mode: phases of E-fields are opposite direction in two waveguides

Effective indexes of two modes are different (group velocity is also different)coupled power of light affects effective index difference between two modes

Even-mode of |Ey|2 field Odd-mode of |Ey|2 field

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E-field modes in DC

Power transformation in directional coupler

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E-field modes in DC

• Through power: = = where is through coefficient

• Coupling power: = = where is through coefficient= ∆ / (∆ : effective index difference between even and odd modes)

Coupling power and through power in directional coupler

Cross-over length

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Key parameters of DC

PthroughPin

Pcoupled

Coupling gap

Coupling length

- Coupling gap: effective index difference of even and odd modes (C)

- Coupling length: coupled power and through power

- Wavelength: directional coupler have wavelength dependency

Coupling power: = = , ( = ∆ / )

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Coupling gap variation

Cross-over length as various coupling gapCoupling coefficient at particular wavelength

as various coupling gap

- Cross-over length increased as coupling gap is increased coupling gap affects effective index difference

- Coupling coefficient

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Coupling length variation

Coupling power and through power in directional coupler

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Wavelength variation

Coupling coefficient as various wavelengthEffective index of two modes

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Simulation

Simulation using propagatorSimulation using mode solver

- Mode solver simulation: find effective indexes even and odd mode

- Propagator simulation: light input and find light power directly

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Mode solver vs propagator

- Easy to simulation

- Simulation time is fast

- Simulation accuracy is relatively bad

Mode solver

- Simulation accuracy is relatively good

- Simulation time is slow

- Simulation is complicated

Propagator

Coupling length

Coupling power exist !

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Mode solver

Material setting

material_BOX = "SiO2 (Glass) - Palik";

material_Si = "Si (Silicon) - Palik";

draw box

addrect; set("name","Clad"); set("material", material_Clad);

set("y", 0); set("y span", Y_span+1e-6);

set("z min", 0); set("z max", thick_Clad);

set("x min", Xmin); set("x max", Xmax);

set("override mesh order from material database",1);

set("mesh order", 3);

set("alpha", 0.05);

Make structure

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# define simulation parameters

wavelength = 1.55e-6;

meshsize = 10e-9; # maximum mesh size

# add 2D mode solver (waveguide cross-section)

addmode; set("solver type", "2D X normal"); set("x", 0);

set("y", 0); set("y span", Y_span);

set("z max", Zmax); set("z min", Zmin);

set("wavelength", wavelength); set("solver type","2D X

normal");

set("define y mesh by","maximum mesh step");

set("dy",meshsize);

set("define z mesh by","maximum mesh step");

set("dz",meshsize);

N_modes=2; # modes to output

set("number of trial modes",10);

Mode solverMake mode solver

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Mode solver

for(jj=1:length(gap_list)) {

switchtolayout;

setnamed("waveguide2","y", -width_ridge/2-gap_list(jj)/2);

setnamed("waveguide1","y", width_ridge/2+gap_list(jj)/2);

n=findmodes;

for (m=1:N_modes) { # extract mode data

neff (jj,m) =abs( getdata("MODE::data::mode"+num2str(m),"neff") );

}

L_cross(jj) = wavelength / 2 / abs( neff (jj,1)-neff (jj,2));

}

Coupling gap sweep using mode solver

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PropagatorMake structure

addring;

set('name',"circle1_right2");

set("material",material_Si);

set('x', lc/2 + 2*rad);

set('y',rad + gap/2 + width_ridge/2);

set('z min',0);

set('z max',0.22e-6);

set("inner radius",rad - width_ridge/2);

set("outer radius",rad + width_ridge/2);

set('theta start',90);

set('theta stop',180);

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PropagatorSimulation

addpropagator;

set("background index", 1.44);

set("simulation time", 2000e-15);

set("x", 0);

set("x span", 2*(lc/2 + sqrt(2)*rad + 4.6e-6));

set("y", 0);

set("y span", 2*(gap + 2*width_ridge + rad));

set("z min", -0.5e-6 + thick_Si/2);

set("z max", 0.5e-6 + thick_Si/2);

set("x0", 0);

set("y0", -width_ridge/2);

set("bandwidth", "broadband");

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PropagatorSimulation

addmodesource;

set("injection axis", "x-axis");

set("direction", "Forward");

set("x", -lc/2-sqrt(2)*rad-3e-6);

set("y", -gap/2-width_ridge/2-(2-sqrt(2))*rad );

set("y span", 1e-6);

set("wavelength start", 1.5e-6);

set("wavelength stop", 1.6e-6);

addpower;

set("name", "through");

set("monitor type", "Linear Y");

set("x", lc/2+sqrt(2)*rad+3e-6);

set("y", -gap/2-width_ridge/2-(2-sqrt(2))*rad);

set("y span",1e-6);

set("z", 0.11e-6);