## Photonics

#### 1D waveguide simulation

• Anja T
Subscriber

I want to find the modes in a 1D waveguide (e.g. air - semiconductor - air) for a range of different frequencies, by using Lumerical FDE.

When I try to solve analytically using the refractive index at a given frequency, my result vary significantly from the result I get in my simulation. Analytically, the number of modes in a symmetric waveguide can be inferred from the cuf-off frequency $$V=2πdλn12−n22">V=2πdλ \sqrt(n1^2-n2^2)$$ by using $$#(modes)=2∗[Vπ]int">#(modes)=2∗cel([V/π])$$. When running my Lumerical project, I get significantly more modes. Also, the effective index for e.g. TE0 mode is different using both approaches. I increased the number of trial modes until the Lumerical solver did not find any more constrained modes (n_air < n_eff < n_waveguide). But I also notice that - obviously - increasing the number of trial modes changes the number of modes the solver finds.

How can know which number of trial modes is physically correct? Also, when I run a frequency sweep, the n_eff plotted in the sweep window does not correspond with the n_eff I get when solving Mode Analysis for the same wavelength. Why is this different and which one is then corrrect?

• Guilin Sun
Ansys Employee

"How can know which number of trial modes is physically correct? "

As long as you can find the desired modes.

"when I run a frequency sweep, the n_eff plotted in the sweep window does not correspond with the n_eff I get when solving Mode Analysis for the same wavelength."

If it is for the same mode, it is unlikely. The most possible explanation is, it tracks the wrong mode in sweep or independently. Please make sure the modes are the same.

if you use metal BCs, there are many no physical modes since the metals form a cavity, leading to cavity modes, or "box modes".