Trial modes and TE/TM fraction


Hello dear all,
I am looking for the answer of following basic issues that I encountered (could not understand) while trying to simulate strip-slot waveguide converter.

  1. why is the number of trial modes shown by mode expansion monitor and Eigensolver analysis are different for the same structure? (can check for strip and slot waveguide here coupler3.fsp (4.2 MB) and strip slot strip coupler.lms (338.4 KB) ).

  2. If I launch a fundamental mode in a uniform waveguide which supports multimodes, will power be preserved in fundamental mode or fraction of power be transferred to higher order modes?

  3. If the mode is TE of TM is indicated by the TE/TM fraction. But sometimes mode looks like TE though TM fraction is greater than TE fraction

    . So, how can I distinguish TE or TM mode just by looking at TE/TM fraction.

Thanks in advance.



So, you get different modes in MODE solutions other than those of FDTD. This usually happens due to the difference in the meshing between both. While FDTD chooses an adaptive mesh, MODE uses a mesh of constant cell size for it FEM solver. That means you need to decrease the mesh size to reach more accurate results or you can also use an overgrid mesh over the smaller features, like here you can use a mesh for the slot, for example.

Yes, it should be preserved in the fundamental mode.

The TE polarization fraction (Ey) indicates if Ey is the major component or not. So, you can quickly tell if this is TE or TM by checking this column.

For the exact definitions of TE/TM fraction and TE polarization fraction, check this post:

I have worked before on the design of a slot-strip converter, so I will be happy to further discuss this.

Hope this helps!


Dear @aya_zaki,
Thank you very much for clarification.
Regarding 3 issue, my question was not about TE polarization fraction (Ey). It was about “waveguide TE/TM fraction (%)”. In Ring resonator and TM mode propagation post, it has mentioned that 'If the mode is TE or TM is indicated by the TE/TM fraction. 100% TM fraction indicates TM mode.

’ But if “waveguide TE/TM fraction (%)” is 76.29/81.9 (shown in previous post), is this TE or TM mode?
thank you very much for asking me to discuss on slot strip converter.
when i did the 3D FDTD simulation (coupler3.fsp), i got 0.94-0.95 output transmittance at fundamental mode. how can i improve the output transmittance? (do i need to increase the mode converter length?)

i have one another question not related to mode converter.
Will group index ng calculated from ring resonator by ng = lambda^2/(FSR * del L) expression and ng of straight waveguide with identical dimension as ring calculated by mode solver be equivalent or not?


Hi @Ktwayana,
The “TE/TM fraction (%)” indicates if the mode is TE or TM because it calculates how much longitudinal component of E or H is there compared to the total field. For example, in the 1D mode analysis of a slab waveguide, TE mode by definition is the one whose E_longitudinal = 0. Hence, “Transverse Electric”.

However, back to the real 2D profile, you will find there are no pure TE or TM modes. Those modes, we conventionally call TE or TM, are rather Quazi-TE or Quazi-TM. Their longitudinal components never vanish.

In view of the above, the higher the TE fraction, the more the mode is TE. But I think the comparison between the TE and TM fractions has little to do with determining TE or TM especially when the fraction values are close like in your case.


Dear @aya_zaki,
thank you very much.
i am sorry, i don’t get "the TE and TM fractions has little to do with determining TE or TM especially when the fraction values are close like in your case."
In my case, what should i do, so that i can say that the first mode with “waveguide TE/TM fraction (%)” 76.29/81.9 is TE or TM mdoe.


I mean in integrated optics, “TE polarization fraction” definition is typically used.
The first mode in your analysis has Ey = 98% of the total E. So, Ey is the major component which indicates this mode must be a TE mode. From the TE/TM fraction, you can only deduce that 76.29% of the Electric field is really transverse (Quazi-TE).

This is mentioned in this page:

Let me know if you have further questions.


Yes, they should be almost the same. Well, except for the small change in the effective index of the bent waveguide in the ring structure. But as long as the radius is large enough, the two results will be the same.


Dear @aya_zaki,
why we don’t care about H field? For the same case, if Hz = 100% and x- axis is direction of wave propagation, is it still consider as TE mode?
thank you.


Dear @aya_zaki,
Thank you very much.
Can I calculate the required refractive index value of the waveguide for a given ng and fixed waveguide dimension? i am wondering to change the refractive index of that waveguide till it generates a given value of ng at a specific wavelength by using Eignemode Analysis Frequency Sweep option.


Actually if Ey is the major E component, then Hz would be the major H component when the propagation is along the x-axis. So, it is quite the same thing.


No, I think this is not possible since ng basically depends on the dispersion in the refractive index, (dn/dlambda), not on the absolute value of n_eff.


Dear @aya_zaki,
thank you very much for clarification.


Dear @aya_zaki,
thank you.
Actually, i am trying to find out an equivalent slot waveguide of sub-wavelength grating with slot. i could not find any way to calculate the effective index and its equivalent slot waveguide of sub-wavelength grating with slot waveguide . there is a way to calculate equivalent strip waveguide of SWG structure without slot.
i thought that i could calculate equivalent refractive index of slot waveguide form group index, but it is possible (as you mentioned in previous post ).
please suggest me is there any way to calculate equivelent refractive index of my sturcture in terms of duty cycle.