Reflection from a waveguide bend




I am interested in determining the reflection from a straight waveguide to bent waveguide interface. e.g., 500x220 nm straight strip waveguide connected to a 90º bend with a radius of 1 µm. I know such an interface has a large mode-mismatch loss (0.5 dB for a 90º bend with two interfaces). Most of the power scatters away (See Fig 3.26 in my book)

How much is reflected back into the fundamental mode of the source waveguide?

I looked through your manual,, which calculates the S11. Can this be interpreted as S11 = reflection coefficient when going from mode 1 to mode 2?

I wrote a script that does this calculation, and it gives numbers of about -30 to -40 dB for ranges of 1-3 µm bends. Seems small, but not unreasonable.

I also did this using 3D-FDTD, using mode expansion monitors. I get values between -40 and -65 dB for a 1 µm bend, depending on the mesh accuracy (between 1 and 5). I suspect that in FDTD it will be challenging to eliminate all the reflections from the PML boundaries, and I haven’t been able to get a converged result where I can be sure I have the actual reflection coefficient.

So I am wondering what is the best method to determine the reflection for this case?

thank you


Do you mean mode 1 is the straight waveguide mode and mode 2 is the bent one? In this case, yes, S11 is interpreted as you said. But I have a question; should S11 = b or S11 = b/a??

Regarding the PML reflections, I once had a similar problem to calculating the bend loss – but for a different waveguide-- and increasing the input and output excess length is useful. The S-parameters converged to some final value. Although I wasn’t interested in the S11 (the reflection), the S21 also depended on the excess length before convergence because the interface between the straight and bend parts was lossy and the value of S11 was significant.

Thank you for starting this discussion


S11 = b or b/a? The KB says “b”,
This is different from FDTD Sparameters where you divide the two port expansion monitors.
But I did want to check since I’m not sure.

Also, perhaps not surprisingly, M = expand(’::radius0’,’::radius’+num2str(radii(i)),0,0,0);
M = expand(’::radius’+num2str(radii(i)), ‘::radius0’,0,0,0);
give different results (i.e., mode 1 into 2, versus 2 into 1).

Regarding PML reflections, I found converging the simulation for S21 was pretty easy. The backreflections are reasonably small that they don’t contribute much to the error in S21… But get S11 seems much more challenging.

Other devices which have larger reflections (e.g,. grating couplers, ybranch) are much easier to get accurate S11 data for.


For the 3D FDTD simulation, S11 = b/a is correct - I think the example code from assumes that the “a” term is 1.

For the FDTD simulation you may want to try out the new port object in the 2017a release:

It should make the extraction of S parameters easier since the port object returns a result “S” directly, so it avoids having to calculate S from the a and b terms from the expansion result. It also acts as both source and monitor so the setup is also simpler.

However, to get the S11 result for a bend I think it’s easier to use the method which uses the FDE simulation in MODE Solutions since it avoids any errors from propagating the fields, and as you mentioned, since the reflection to the fundamental mode is small, the numerical error will be large relative to the S11 result making it more difficult to converge.

Hopefully this helps.


Hi Nancy,

Thanks for the response. I was specifically wondering if the b/c approach works correctly for MODE? And second, the results from FDTD are quite different than from MODE – the MODE results show larger reflections than FDTD.


Sorry for misunderstanding the previous question.

After consulting a colleague about using the “expand” script function calculation to calculate the S parameters, I think it’s possible that this method doesn’t work since the expansion calculation is meant to expand a given field profile onto basis modes. In the 3D FDTD simulation, the basis modes are the calculated eigenmodes of the straight waveguide, but in the MODE Solutions case, the straight waveguide mode is being expanded onto the bent waveguide mode, but the bent waveguide mode is not a basis mode of the straight waveguide. It should be possible to get the overlap result, but the expansion may not make sense here. Please let me know what you think.


Thanks Nancy. I agree with your statement that straight waveguide mode is not the same as the bent. This is where the mode-mismatch loss comes from which is calculated by the overlap intergrals. But what about the light being reflected back into the 1st mode, as a result of this mode-mismatch? How does one calculate this?



I’m sure there is a way to calculate this since the EME solver of MODE Solutions is able to calculate the S11 result from the eigenmodes of the different sections of the device. I guess that one difference is that the S11 result from the EME solver will take into account the reflection coefficient back to the fundamental mode from all of the modes for expansion in the neighboring cell. I’m not sure if there is some additional normalization which needs to be done. I’m consulting a colleague about the method and I’ll get back to you again with further details once I have them.

In the meantime, it could be interesting to try to get the same result by using the EME solver. You can set the eigensolver settings of an individual cell group to use the “bent waveguide” solving method to represent the bent portion of the waveguide.


Hi Lukas,

I spoke to one of our R&D scientists and their idea is that expanding the straight waveguide mode onto the bent waveguide mode will always overestimate the reflection since it assumes that the field profile changes abruptly between the straight and bent waveguide segments, so an FDTD simulation would be more accurate. Let me know if this makes sense.