Learning Forum

[stefan.appel]

Hi,

I do face the following problem in 3D FDTD:

In a layered/stratified substrate, infinitely extended in the x-y-plane, with layer/interface normals along the z-axis (easiest case: a single film/slab/layer of refractive material in air), I want to excite a specific mode propagating in the xy-plane.

For a mode propagating only in one direction, say in the positive x-direction, I know I can achieve this using a mode source extended over the whole y-z-plane of the simulation space.

However, I do want to excite the mode at a single point x0,y0 and to propagate it outwards from there in all directions within the x-y-plane. This "line source" would therefore extend over the complete z-axis, but only cover a single point x0,y0 in the x-y-plane.

I am thinking of dipole-like emission patterns: For a TM/TE mode with Ez/Hz polarization, the emission would either be isotropic within the x-y-plane, similar to an electrical/magnetical dipole with vertical (z) orientation. Alternatively, the emission pattern could also behave similar to a horizontal magnetical/electrical dipole, forming dipole-lobes in the x-y-plane.

However, in contrast to a single dipole source, this line source should only excite one single, distinctive, guided mode propagating in the substrate, and should not excite any other guided or unguided modes, like emission from the substrate. This source in fact would be equal to the varFDTD dipole source, but implemented in FDTD.

To achieve this, I thought of calculating the mode profile using a mode monitor. Then, I would place lots of dipoles along the z-axis at point x0,y0 with their amplitudes (and possibly phases) adjusted to represent the mode profile along the z-axis.

However, this would include retreiving the mesh structure to find the z-coordinates for all dipoles, discretizing the mode profile onto the dipoles and then placing lots of dipoles very close to each other, such that they may influence each other.

Is there any easier, and possibly more accurate way to do this?

Thank you for your help!

[Guilin Sun]

"to propagate it outwards from there in all directions within the x-y-plane"

This can only be done with a dipole source. All other sources have surpressed their back propagation. and they must travel according to the defined direction of theta and phi.

"this line source should only excite one single, distinctive, guided mode propagating in the substrate, and should not excite any other guided or unguided modes, like emission from the substrate. This source in fact would be equal to the varFDTD dipole source, but implemented in FDTD."

Unfortunately we do not have such a source, and there is no such description on physics.

 

"To achieve this, I thought of calculating the mode profile using a mode monitor. Then, I would place lots of dipoles along the z-axis at point x0,y0 with their amplitudes (and possibly phases) adjusted to represent the mode profile along the z-axis."

This idea is creative and you could use a array of dipoles to create radiation only in a plane but in the 3rd dimension all the radiations cancel each other. This will need a theoretical analysis and guide.

I have not found any other easier, yet accurate way to do this. The 3rd dimension can only cancell the fields from interference, but not by material/geometry confinement.

 

VarFDTD compresses the 3rd dimension so to be 2D.  you could try. Other than this way I do not see any other way to create a 360deg radiation in a plane without radiation in the 3D dimension. 2D FDTD assumes that any cut along z is the same, meaning the structure is alos infinite in z, which is not what you expect.

 

You may also need to think if this is physically possible, experimentally doable. 

 

 

 

[stefan.appel]

I wrote a little function to create such a source, and it does work reasonable well in a refractive slab (2TE, 2 TM modes). There is no emission into guided modes other than the one selected (suppression around 10^7), and also fairly low emission into radiative/lossy/freespace modes (about 1-5%). Either magnetic or electric dipole injection is possible, with the dipoles oriented along x,y, or z and the line oriented along x,y,z as well.

The amplitudes of the dipoles just follow the mode amplitudes, without any rescaling based on discretization or material.

There are some issues with convergence, but this may well be due to suboptimal PML configuration.

Unfortunately, it is not possible to implement this into a self-updating analysis group, since the setup script of the analysis group is not able to retrieve mode profile information. So for any change, you have to delete the source completely and recreate it with the script function.

The script is appended as the following corrupted jpg file - rename it to .lsf to retrieve the script.

[stefan.appel]

Regarding the physical possibility: No physical implementation is planned. This is just for theory, to better understand radial propagation of guided modes.

[Guilin Sun]

We are not allowed to download files here and your file is not downlable also. Please send me your file to support and mention this post, and I will see if I can help you further.

[sagar]

Can I use dipole as a mode source in FDTD for mode analysis? 

[stefan.appel]

In reply to sagar:

Yes you can definetly use this script-generated line of dipoles as a mode source for mode analysis. However, be aware that the mode is travelling outward radially, so you either need a curved mode monitor (does not exist yet, bu may be implemented in a similar fashion like the line mode source) or a very slim monitor at large distance (where the curvature is negligable and therefore a small flat monitor is a good approximation).

Also, take care to check the radiated power. As all dipoles interact and purcell-enhance each other, you can not rely on the dipolepower or sourcepower functions, but instead have to but a monitor box and record the total transmission for power normalization.

[sagar]

Actually, I had used dipole as a source inside a cylindrical waveguide and placed a mode monitor to select a particular mode, and tracked the T_forward of a power monitor placed at the edge of the cylinder to compare with the total power emitted through the monitor, to get an idea out of the total power the contribution of the selected mode. But getting very wired results. As for a particular diameter of the cylindrical waveguide, there would be only fundamental mode, so T_forward of the fundamental mode should be equal to the total T, transmitted through the power monitor.  But for the diameter sweep of the cylinder the T_forward value is fluctuating in between 0.0001 to 0.4, and at lower diameter the T_forward value is very less. 

[Guilin Sun]

T_forward of the fundamental mode is not the total T, since total T is for all radiation including propagating modes and non-propagating modes such as radiating modes etc.

T_forward is only the mode you choose.

[sagar]

Yes.  But at some dimensions of the waveguide, it only supports the fundamental mode. As with the FDE solver, I found that the only supported mode below 230nm diameter of the waveguide is the fundamental mode. Higher order modes appear after that.

So, the dipole should radiate in the fundamental mode only for a diameter below 230 nm. So, the transmission corresponds to the power monitor which basically gives T_total should be equal to the T_forward which is basically the power radiated only by the fundamental mode. But I am getting minimum transmission corresponding to the fundamental mode in these regions. Also, the data set is not consistent. It's like it is picking some random number between 0.01 to 0.4. 

[stefan.appel]

Lets just clarify: sagar's problem is about axial transmission/propagation in a cylindrical waveguide. Regarding the described results: The dipole will not only emit into the single existing mode, the fundamental mode. It will also emit into the infinite number of freespace/lossy modes around the waveguide. With your simulation, you are measuring the coupling of a single dipole to the fundamental waveguide mode. This will change with the diameter of your waveguide, thats where the strongly random (actually I would guess oscillating) results come from.
If you want to study the axial propagation of a single mode, I suggest using the standard mode expansion source to excite this mode of interest.

My problem is about radial transimission/propagation in a planar waveguide. So instead of a planar mode front in a circular guide, I am interested in a circular mode in a planar guide.

So I guess there was a mix-up...

[Guilin Sun]

Totally agree with Stefan! The waveguide can support only one fundamental mode, but it does not forbid the dipole to radiate power to other radiation modes. If you have lab experience in lauching fiber modes, you will know that the initial section of the fiber will be bent to get ride of all other non-fundamental modes.

Regarding to Stephan's radial propagation source in a plane, it can only happen if the radiation cancells each other. I think it is difficult, ecept a cylindrical line source, which has the same radial property at each plane in the 3rd dimension, and therefore it is a 2D problem. But if you need to interact with the sources from intermittent simulation result, you may need to do iterated simulations, somehow.