# Supported mode in hollow core cylindrical waveguide

I’m trying to calculate the supported mode in a hollow core waveguide made from AL2O3. There is an error with simulation indicating “No physical mode were found”, even when I adjust the mode calculation in n=1 ( to search the modes in the core (air) and not in the cladding (Al2O3)). Any suggestion would be great!
The modeling file is attached.

I’m also interested to see how to calculate the modes when they coupled to the free space, and then how to use these data (calculated modes coupled to free space) in connection with Zemax for mode propagation through lenses/mirrors

Ceramic hollow core WG.lms (2.3 MB)

Thank you.

I took a look at your simulation and I have a few suggestions.

• The cc-fiber Structure Group, was using a dialectric material in the core which was close to 1.4. Since the ring structure is much bigger than the wavelength the effective index of all the modes will essentially be that of the core material. You can double check your indices and meshing in FDE solver (See Below).

• The material model that you were using was fitting the $Al_2O_3$ near telecom wavelength (see below). The material properties at 1550nm are a transparent dielectric, but aluminum oxide has strong absorption at 10 $\mu m$ which significantly effect the solutions.

Try to improve the fit by adjusting fit parameters like bandwidth, fit tolerance and imaginary weight.

• Finally the FDE region is a bit too close to the waveguide, and so you have some unphysical modes due to coupling with the boundary conditions.

Single mode wave-guides are not good at coupling to free space, but in FDTD you could terminate the waveguide and place monitors after to see the divergence. Since your waveguide is multi-mode you may find the modes couple to a Gaussian beam efficiently. You could look at how efficiently using FDE in MODE. Maybe consider a horn antenna to improve gain and analyze it with the EME solver. If you would like simulate a complete optical set-up we recommend the Zemax interoperabillity.