1
$\begingroup$

While studying concept of slab waveguide mode, I got stuck on some problems.
In textbook(Yariv chapter 3 pg 112), for guided TE modes it tells that the mode function is taken as enter image description here

which means that the y component of electric field's amplitude is determined by Em(x). And also, (3.1-8) is plotted like this. enter image description here

But if I plot slab modes using with ansys lumerical, I got some different results. enter image description here

enter image description here enter image description here

These are mode profiles which I obtained from the simulation. And my question is come from this. In text book(Yariv), it tells that the spatial confinement is done along the slab thickness(d).

So, what I thought is that the mode profile should have peak along the y axis like figure 3.3(which is contrary to the simulation result). Also, the simulation result tells there are x dependence (simulation axis) but in yariv book I can not see those of it. Is there any reason why the simulation slab mode peak occurs along the x axis? Can somebody help me please?

(Sorry for different notations, yariv book -> x axis for slab thickness / simulation -> y axis for slab thickness)

Improve this question
$\endgroup$

1 Answer 1

Reset to default
0
$\begingroup$

I understand the problem in the following way (please comment if it is not what you want): you have a infinite slub - a sandwiched layer inside a dielectric. One dimension is infinite in the model proposed in the book. It is written in the book that you should have a wave nodes along the axis perpendicular to a slub.

In order to show that you are realizing the ANSYS simulations and you see that yo have nodes along other direction. The problem is that you are limiting the wave in the x dimension according to your pictures, and you have a rectangular waveguide. It is known that in this structures the waves modes are no longer $TE_m$ but $TE_{mn}$ (by the way do not forget also TM modes that can exist in both structures).

What you see is are modes $TE_{10}, TE_{20}, TE_{30}$, but you want to see $TE_{01}, TE_{02}, TE_{03}$. It might be that the desired wave cutoff is higher that the drown ones. It can be illustrated with a cutoff $k_c = \sqrt{ (\frac{m \pi}{a})^2 + (\frac{n \pi}{b})^2} $ according to directions. It means that for lower distance the cutoff will be higher.

I would suggest to increase the x guide dimension in order to have a good slub guide instead of rectangular guide

Improve this answer
$\endgroup$
7
  • $\begingroup$ Thank you for your reply. Then you are meaning that the above simulation results tell us the confinement along the x axis(not along the y axis - slab thickness)? $\endgroup$
    – photonics2024
    Commented May 17 at 8:02
  • $\begingroup$ yes I do, this is what I mean $\endgroup$
    – Pierre Polovodov
    Commented May 17 at 8:04
  • $\begingroup$ Also I'm confusing with TE(mn) mode. Can I interpret it as that the mode function (3.1-8) should consist of not only x parameter but also with y? (like E(x,y)) $\endgroup$
    – photonics2024
    Commented May 17 at 8:07
  • $\begingroup$ Yes there is another dimension where nodes appear, there is another cos or sin function along this dimension (depends on the boundary condition mathematically, or multiple reflection of waves from a physical point of view). Check the book [Pozar "Microwave engineering" 2012], there is a chapter on the parallel plate and rectangular waveguide for the equations. Also any other book treating waveguide might be useful. Usually the subject is well studied in microwave books, since a bulk rectangular guides is an older technology then optic guides. $\endgroup$
    – Pierre Polovodov
    Commented May 17 at 8:13
  • $\begingroup$ There might be a chapter in your book (I do not know it , unfortunately) $\endgroup$
    – Pierre Polovodov
    Commented May 17 at 8:15

Not the answer you're looking for? Browse other questions tagged or ask your own question.