Fiber Bragg Grating with cylindrical holes

I am struggling to simulate light propagation through a 3D fiber containing couple of cylinders perpendicular to its axis which form a kind of FBG in 1550nm, as shown in the picture:


the fsp file is attached here:
KMA_FBG100_3D.fsp (2.5 MB)
I used a fundamental mode source and detectors in order to measure reflection and transmission. Simulation is performed in 3D. I set the boundary condition as PML by taking advantage of symmetry in Y and Z axis to reduce calculation. The mesh accuracy is set to 3 for faster calculation.
The autoshutoff level seems set right because it reduces down to 0.001 finally.
But there is some problems here
1- when the number of cylinder is low (eg. 100) the peak in reflection seems reasonable (R~0.5). But when I increase it up to 500 cylinder, R goes beyond the unit!!! this happen even in 2D version.
2- the spectrum should has one peak at reflection, but the simulation contains two peaks!
3- Is there another method like Eigenmode Expansion method using “Mode” software or considering one unit cell like the one in example:
https://apps.lumerical.com/pic_passive_bragg_initial_design_with_fdtd.html
Thank for kind help
Keivan

Hello @k.aghdami,

Thank you for the question, and sorry for the slow reply. I’ll begin with question 3. Yes, I believe the Eigenmode Expansion solver in MODE Solutions would be very well suited for this example. It is often used for gratings like this, and should be much more efficient than the FDTD solver. It is quite a bit different than the FDTD solver, so if you have not used it before I would recommend taking the FDE and EME solver courses first. You could also take a look at our Application Gallery examples that use the EME solver:

As for your other questions:

  1. The results of a power monitor can become greater than one for a few reasons, often because of reflections from the PML boundaries. You could try a few different things to fix this issue, but I would recommend just using the EME solver instead of spending your time on this.
  2. I noticed that the mesh is not refined enough to properly resolve the holes:
    image
    This may be why you are not seeing the results you expect. You could add a mesh override region to increase the mesh density around the holes but this would dramatically increase your simulation time. Again, I would recommend just using the EME solver instead.

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

Hi Thank you @kjohnson for your kind and comprehensive reply.
As you suggest I will try EME then, but according to increasing mesh size I tried it with non uniform meshing by checking the “Based on structure” in Mesh>Geometry tab in order to refine mesh grids inside the holes as in following picture.


But the result shows an unwanted peak because of mesh periodicity in 1550! It also does not disappear even when hole matches with fiber in refractive index!
Is there any way to resolve this?
Regards
Keivan

Hi dear @kjohnson
According to your suggestion I move to EME and perform a setup for a period of my structure which is a fiber core(Diameter=8um) where a air cylindrical hole drilled across the core with diameter 200nm. The background is taken with n=1.4 representing cladding medium.
the period for it is 1.072um. As follow:
FBG_Hole_EME1.lms (632.6 KB)
but I have this problems:
1- The Z-normal refractive index monitor doesn’t show the cross section of hole at the center.
2- Is the override mesh order right for core and Hole?
3- the X-normal monitors do not show any change in field intensity?
Your kind reply is highly appreciated.
regards
keivan

Hi,
I stuck on a problem of FBG where we have array of holes (Diameter=200nm) across the SMF-28 fiber in 1.072um inter-distance. consider holes are etched and their ref. index is 1.
The final goal is calculation of transmission/Reflection spectrum.


I tried it first with Lumerical-FDTD but in the spectrum I found some incorrect results. Then I switched to EME method in MODE.
You may find my setup at the following file:
FBG_Hole_EME.lms (671.7 KB)
-The core is a cylinder (R=4um) along X direction(length=1.072um) (n=1.444)
-Background refractive index is taken 1.4 as the refractive index of cladding.
-Hole is place at center along Z, a cylinder (length=8um , R=0.1um , n=1)
Now I have this problems:
1: the refractive index monitor does not show the hole which is a cylinder across the core!
2. There is no evidence of hole in profile !
Thank you
Keivan

Hi @k.aghdami,

I merged your topics because they were regarding similar issues.

Yes, to make sure the hole is included in the simulation you need to make sure its mesh order is lower than that of the core (see this page for more information: https://support.lumerical.com/hc/en-us/articles/360034915233-Understanding-mesh-order-for-overlapping-objects). You can do this automatically by using the “etch” material, which by default has a mesh order of 1 and a refractive index of 1.

A few more recommendations for your simulation:

  1. Remove the third port object, you should only have one port on each end of the waveguide.
  2. Extend your simulation y and z spans to 20 um, and make sure the ports use the full simulation span.
  3. Use a mode convergence sweep to make sure you are using enough modes.

Let me know if you have any questions.