Discussion Forum

Hi,

I am trying to compute the optical forces acting on a slot waveguide composed of two suspended silicon beams separated by a gap of width g. This calculation is a departure point to more complex optical force calculations. Since the waveguide is translationally invariant, I use a 2D Mode analysis simulation and I integrate the upward component of Maxwell's stress tensor in the direction between the two waveguides over the boundary of one of the two silicon beams. This value is then divided by the power carried by the mode to get a force/length/power.

The exact calculation is Vslotbound(ewfd.unTx)/Vall(ewfd.Poavz)

with Vslotbound the surface integral over the boundary of one of the beams and Vall an integration over the full 2D domain (z is the direction along the waveguide, which is not included in the 2D simulation).

That same force can also be calculated from energy arguments by means of the derivative of the effective refractive index, n_eff , with respect to the gap distance, g (see e.g. https://ieeexplore.ieee.org/document/7355298). The problem is that the two methods give me different results, with the integration leading to a stronger force by a factor of two (for all gap distances). I have checked for all possible source of errors due to symmetries used in the simulation by also running the simulations without symmetries.

In order to check if the method involving integration is giving a force twice of what it should or if the other method gives a force half of what it should, I have done a 3D eigenfrequency simulation over a slot waveguide of length 200 nm (this length is arbitrary and the force in the end is normalized to the length). I use Floquet periodic boundary conditions and the right propagation constant as obtained from the 2D simulation. The 3D simulation agrees with the calculation using the derivative of the refractive index (see the image attached).

The question is then where is this factor of 2 coming from and whether there is something intrinsic to the 2D mode analysis simulation that is leading to the factor and that I am completeley missing. Any help with this would be really appreciated.

Thanks for any help in advance. I have attached an .mph model for the 2D simulation.

Guillermo