# Different grating coupler efficiencies when using Ports versus DFTMonitor with mode expansion

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When performing 2D FDTD simulations of grating couplers I have noticed there is a difference in the estimate coupling efficiency when using a Ports versus using a DFTMonitor coupled with a Mode Expansion monitor. The calculated transmission of the Port is generally around 3-5% higher compared to the mode expansion, even if both have the same position and span. What are the fundamental difference between the two and which is better to use?

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Thanks for the clarification, @dpeace. The results you got actually make sense: the quantity, T, you extract from the port, is the transmission or fraction of power going through the port, while T_backward from the mode expansion monitor is the fraction of power that will couple to the mode you selected in the mode expansion monitor. The difference between the 2 is the fraction that is lost as it won't couple in the waveguide.

To compare the port and mode expansion, you can either look at the S parameter or at the "expansion for port monitor" result from the port. abs(S)^2 will give the fraction of power coupling to the mode while S is the complex transmission coefficient.

• Hi @dpeace,

Thank you for posting your question on the forum. Could you eventually specify what quantities you are comparing and give further information about the simulation settings? Ports and mode expansion monitor should give the same results, as far as I know.

• I am calculating the amount of power coupled into a waveguide mode, when placing an optical fibre as the source above a uniform grating. In both cases I am using a port on the input fibre as the source. My figure of merit is to measure the transmission from the source to the waveguide mode as calculated by an FDTD Analysis script which are as below for each scenario. For the 2D FDTD settings of mesh accuracy of 3 with precise volume average set to 10 and simulation time of 5000 fs, I measured 0.88481 using ports and 0.860574 using mode expansion. Note my simulation includes a birefringent material and a metal layer. Currently for these simulation I am only recording the fields and calculating T for a single wavelength point.

Using the ports my FOM is as follows:

T_data = getresult("::model::FDTD::ports::port 2","T");

T = abs(T_data.T);

For Mode Expansion my FOM is:

temp = getresult("fom_exp", "expansion for fom");

T = -temp.T_backward;

Thanks for help!

• Ah, I see! The Abs(S)^2 and mode expansion match perfectly now. Thanks for the help, much appreciated.

• You're very welcome! :)