A usage of the mode area in FDTD Solutions

If the nanoparticle is irradiated with a plane-wave source moving in the downward direction of the y-axis as shown below, I can calculate the mode area using the profile monitor and index monitor by referring to this KB web page.

In the KB example the mode source is implemented on the device (instead of the plane-wave source), to calculate the mode area on the plane (xz-plane) perpendicular to the source direction (x axis). Can I apply the same mode area equation to a plane perpendicular to the source direction (xz-plane) as well as planes parallel to it (xy-,yz-planes) for this example in FDTD Solutions? I want to evaluate the field localization (such as Anderson localization) area for this system by using the mode area approach.

Could you give me some guide line for this mode area calculation with repsect to planes and a source?

Dear @isawjsy

In waveguides, such as the example in the KB page, light is confined in the yz-plane by total internal reflection. Effective mode area is the measure of this confinement and for highly confined light, it will be less sensitive to any perturbation outside the waveguide.

Since your light is propagated along the x-direction and its not confined on the xy and xz plane, effective mode area will not be a useful measure in these planes (at least I haven’t seen people to use it). This is being said that as long as you have field and index profile, you can calculate the effective mode area but interpreting the results in the planes where light propagates will not be a useful term.

With a similar analogy, for 3D confinement we use effective mode volume, which is a measure of how much light is confined in 3D objects such as in cavities (microring, microsphere, photonic crystal and etc). For example, for light matter interaction you want to have a cavity that has a high Q and smaller mode volume.

Some additional notes:

Mode area and mode volume are the properties of geometry and is independent of the type of the source. Also, they are normalized and as a result are independent of the injected light intensity.

For Anderson localization, if your field (Ψ) is in defined in 3D, it makes sense to use effective mode volume.

Please let me know if I could answer your question.