How to make a long waveguide simulated as a short waveguide

[lmeng9]

Hi, all.
I am trying to simulate a long rectangular hollow waveguide with PEC surfaces.
A point source is put at the center.
Besides, a time monitor is put at the center too.
This simulation is just to get the spectrum of the point source within the waveguide.
The waveguide has two open boundaries with surfaces on x-y plane (i.e., the wave travels along z direction).
Originally, this is a very simple simulation. PML can be put on both open boundaries.
However, to save the simulation time and memories, I hope I can model a shorter waveguide with other boundary conditions thus the spectrum from the time monitor can still be the same as the original waveguide.
It seems that the periodic boundary condition is not correct.
Is it possible for a short waveguide with some special boundary condition that can achieve the same response as the long waveguide (maybe we can just think this long waveguide has infinite length) ?

Many thanks!

[konslekk]

Hi @lmeng9
I would recommend you to upload the simulation file. Also, i would like to inform you that if you do not change the size of the waveguide, the propagation coefficient β of the waveguide remains the same. I suppose that width and height remain the same so β cannot change. So i think that the response will be the same.

[aya_zaki]

Hello,
I suggest you can use the bidirectional eigenmode expansion (EME) solver which is ideal for simulating light propagation over long distances.
Since your case considers a constant cross section, it would be even easier than this example:
https://kb.lumerical.com/en/pic_passive_spot_size_converter.html

What do you mean by Open boundaries? * Infinite Waveguide OR *Open circuit transmission line termination

You are welcome to upload the example or theory you are trying to simulate. I’ll be happy to further help with this topic.

[lmeng9]

Hi, many thanks to your reply.
I will think about your point of the same propagation constant and to see whether they have the same response.

Best,
Lingling.

[lmeng9]

Hi, many thanks to your suggestions.
Now I only have FDTD solutions.
Yes, the cross section is constant (the width and height in x and y direction keep constant).
Sorry for the confusion of open boundaries. I just want to say the two ends are open to the air, a normal hollow waveguide.
But the length of the waveguide is large compared to the width and the height of the cross section.
Thank you for your attention again!

Best,
Lingling.

[aya_zaki]

Hello,
You are welcome.
The point here is that the PML boundaries are not the right way to simulate open boundaries. PML are like using a good absorber which is not the case. Actually, you should have strong reflections at the ends of the waveguide, I presume. What do you think?

[lmeng9]

Hi, thank you for your suggestions again.
This is a hollow waveguide and it hasn’t been connected to any other devices. The material inside the waveguide and outside the waveguide is only the air (or vacuum).
That’s the reason why I assume the waves propagating out can be taken as absorbed since there is no reflector (since both sides of the interface are just the air).
Did I make a wrong point?

[aya_zaki]

Hi,
Well, I suppose there’s something wrong with this assumption.
To assume the waves will be absorbed you should have a matching impedance terminating the waveguide. But the “air medium” is not a matching impedance. The waves propagate from a guide mode to free space so there is certainly a mismatch in the impedance; which results in reflections at the ends of the waveguide.

This paper is relevant to this point: http://www.jpier.org/PIERM/pierm12/12.10033104.pdf
This figure shows there is a considerable reflection coefficient:

[lmeng9]

Hi, I see.
Thank you for pointing out my mistake.
I will take a look at that paper.
Many thanks again for your help!