Learning Forum

[schinta3]

Hello,

In the rectangular bandstructure example (https://support.lumerical.com/hc/en-us/articles/360041566614-Rectangular-Photonic-Crystal-Bandstructure)

The k vectors are swept to values of 0.5 along the edges of the square brillouin zone. In general, since k vectors are represented by numbers, and ax,ay are equal to 0.5 microns

Let us say I have a similar rectangular lattice, with a lattice constant ax=ay=350nm.

Should the k vectors be swept to 350, represented as a number?

[Guilin Sun]

Good question! The online examples did not mention this.
Actually the true value of k vectors are calculated inside "model" script:
This means the FDTD object pass the absolute values to the simulation, whereas in the sweep it uses normalized k values, which are represented as points.

[schinta3]

Hello Thanks. I did notice this, however does this mean that the actual sweep ranges should extend all the way to 'a' with the correct units.
For example, if a=250nm, should the k values in the sweep be from 0 to 250
Or if a=0.250um should the k values in the sweep range from -0 to 0.25, sue to usage of SI units?

Best Sreyas

[Guilin Sun]

In SI unit yes the wave vector should be 2pi/a. but in the sweep, it samples it (0~0.5)*(2pi/a) and the result only uses (0~0.5). As mentioned previously, the absolute values of the wave vectors are applied. Maybe the file should not use "k", but use n_k to represent wave vector sampling n_k*k_max where k_max=2pi/a. The sweep kx, ky actually are the normalized values.
As you can see:

FDTD applies the correct wave vector whereas "dipole_cloud" is the normalized, sampling point. Do not be confused with the symbols.

[schinta3]

Hello One more question. In the above comment, the dipole_cloud object has kx and ky variables set, by whichever the sweep kx/ky pass. However, this screenshot is from the hex packed slab (https://support.lumerical.com/hc/en-us/articles/360041567454-Bandstructure-of-planar-photonic-crystal-with-a-hexagonal-lattice
However, the rectangular packed slab does not include this. Should it?
https://support.lumerical.com/hc/en-us/articles/360042038213-Bandstructure-of-planar-photonic-crystal-with-a-square-lattice

[Guilin Sun]

They have different purpose.
The Bloch vectors are enforced in FDTD, in all the cases.
For hexagonal lattice, since its unit cell is not rectangular, but FDTD must be rectangle, so FDTD simulation has to simulate more than one unit cell. Therefor it needs phase compensation in the second unit cell, which needs the k values.
phase_offset = kx * dipole_offset_x * ((x>x(1))*2-1)/a*2*pi +
ky * dipole_offset_y * ((y>y(1))*2-1)/a*2*pi ;
phase_offset = phase_offset *180/pi;
AS you can see it has used the actual wave vector 2pi/a.

[schinta3]

Hello That makes sense regarding the phase compensation. One final question:
Again in the rectangular example, the bandstructure object is set with an offset z-axis:
For a 200nm slab. I understand why the dipole cloud is all set to be randomly within the crystal slab, to excite all modes.
However, due to using relative coordinates, the time monitors may end up above the slab:
As we are trying to calculate the in-plane band structure, shouldn't all time onitors be within the slab?

[Guilin Sun]

Time monitors in the background or uniform material can give you the light line. But since we know it, you can modify the group span (x,y, or z spans depending on simulation settings) to limit the locations of the monitors inside the slab.

[Saraah]

This was a great conversation: I am facing the same issue, so from what i get that:
If we have a square lattice where ax=ay= 600 nm, then we don't change the k value of k vectors (kx, ky) inside "model" variables, because there are calculated in teh script correctly, but we should change teh sweep values to match the period ? let's say if a= 600 nm, then the sweep should go to 0.6 ?

Is what I understood correct?

[Guilin Sun]

Hi, it depends on where the period ax ay are defined. If they are defined in "model" (and most of Lumerical examples are done so) when you do sweep using the built-in feature, you will choose the parameters which have unit there. it should be either 600nm or 0.6um:
If you use your own separate script, it should be assigned as
period=linspace(0.5,0.6,11)*1e-6;
for (n=1:11){
setnamed("model","a",period(n));
run;
....
}
this is because in script everything is in SI, the International Units.

If you are not sure, just try to sweep 2 or 3 values, and then check the swept files and make sure the parameters are correctly set.

[Saraah]

Thanks for teh explanation, I define my ax ay in the defined in "model". I understand setting the correct parameters and type part, but i am a little confused about what to start and stop? should I change the start and stop points, so that will include my period just like in your picture, from 0.5 to 0.7, so that 0.6 is in the middle?

[Guilin Sun]

In my screenshot, 0.5 to 0.7 has the unit of um, which is defined in "Type". You would do the same thing with proper type and value corresponding to the physical parameters, with unit. Just try 2 values and see if they can pass to the sweep file correctly.