## Photonics

#### Calculation of Greens function in periodic array

• June Yim
Subscriber

Hello,

I'm struggling with calculating the 'local density of optical states' in periodic structures.

I have the following questions.

1. Can I use a dipole source in periodic boundaries (in x, and y, while z is PML)? To my understanding, periodic boundaries will also copy and superimpose the field and the source, so I should use PML boundaries for every boundary.
2. I followed this demonstration (Greens function and local density of states of a dipole source – Ansys Optics) to obtain the partial local density of states (PLDOS) and radiated power enhancement. As far as I know (correct me if I'm wrong) the ratio PLDOS calculated over PLDOS of the free space should be equal to the radiated power enhancement, which is the Purcell factor. However, even using the demo fsp file, two values came out to be different. I just normalized PLDOS calculated using the file with w^2/3/pi^2/c^3. Is there something wrong with my understanding?
3. In my own simulation, the PLDOS or radiated power enhancement value calculated from the dipolepower function, transmission box, and the Greens function are different though Greens function is the one that deviates from the two the most. Is it indicating that my simulation is incorrect? I have changed the number of unit cells in the FDTD region (PML for all boundaries) and the PLDOS value calculated from the dipole power function and transmission box seems to stay the same after a certain number.

I would really appreciate anyone's comment, and I will provide more info if that's needed during the discussion.

• Guilin Sun
Ansys Employee

A1: you are right that,using periodic BCs will force the dipole to duplicate, which might not be what you want.

You can use PML, provided that the simulation region is large enough that you can see the contributions from the periodicity. You can use monitors inside the periodic structure and make sure the fields at the edges are very small.

A2: Please note that there are two definitions of the Purcell factors and they do not necessarily give the same result. The Purcell factor calculated inside the dipole is dipowerpower/sourcepower, where the sourcepower is calculated assuming the dipole is in that homogeneous material.

In addition, the dipolepower can diverge if the mesh is very small. However we do not know exactly how small it can be before diverging: dipolepower - Script command

Greens function and local density of states of a dipole source

A3: the two methods may not lead to the same result. Maybe you can choose one of the two. It is good to know that the dipolepower gives the same as the box method.  You mat test if the online exmples give the same results with the two methods.