# Vertical and horizontal mode confinent in a waveguide

1. What device are you trying to simulate? Include diagrams if available.
Optical waveguide rib/strip

2. What results are you trying to obtain? Be as specific as possible.
Horizontal and vertical mode confinement in rib/strip waveguide

3. Description of the problem or issue.
Is there a simple way to calculate optical mode confinement separately in the horizontal and vertical direction using 2D- FDE solver?

Power and impedance integration gives confinement in 2D. I can calculate 1D mode confinement by doing some calculations on the mode field but I will appreciate it if there is any simple way to achieve that.

4. Lumerical product and software version.
2021, FDE

Hello @nouman.zia1 ,

I don’t think that there is any built-in method for doing this, so some scripting will be required. You would have to create an integration filter then multiply the E field intensity matrix by the filter to get only the field intensity inside the waveguide. Then you integrate the fields inside the waveguide, and normalize with respect to the integral of the original fields without the integration mask. For example:

E = getresult("::model::FDE::data::mode1", "E");

E2 = pinch(E.E2);
x = E.x;
y = E.y;

# create integration filter
wg_xmax = 1e-6;
wg_xmin = -1e-6;
wg_ymax = 0.5e-6;
wg_ymin = -0.5e-6;

X=meshgridx(x,y);
Y=meshgridy(x,y);

wg_filter = (X<wg_xmax) & (X>wg_xmin) & (Y<wg_ymax) & (Y>wg_ymin);

confinement_x = integrate(wg_filter*E2_wg, 1, x)/integrate(E2, 1, x)
confinement_y = integrate(wg_filter*E2_wg, 2, y)/integrate(E2, 2, y);

plot(x,confinement_x);
plot(y,confinement_y);


I hope this helps. Let me know if you have any questions.

Hi @kjohnson
Thank you for the script!

To get a unique figure of merit I further take the average of non-zero elements of confinement_x. The direct average of confinement_x also takes into account the full z-axis range which lowers the confinement factor.

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