## Photonics

#### “import source ” on FDTD-lumerical introduces a phase shift of pi/2?

• Iago Diez
Subscriber

I have a question regarding the  simulation object “import source” that allows the user to specify a custom spatial field profile for the source injection plane (link), in FDTD Lumerical.

I would like to know how the specified field profile E(x,y,z,f) is put into Maxwell’s equations: is E(x,y,z,f)  consider a source term in the equations or a field term? In particular, I would like to know if by any reason the way the equations are solved introduces a phase term exp{i*pi/2}, i.e. a phase of pi/2, to the specified profile E(x,y,z,f). (i is the imaginary number). Because I am finding a mismatch of pi/2 in the phase of the field I am supposed to get analytically

Thanks,

Iago

• Guilin Sun
Ansys Employee

For details of source implementation you can refer a FDTD book, or Shineider's online book.

where did you get the simulated result? from source its self or from a monitor? where the monitor is located? I did not find more information how did you import and how did you measure it.

I tested a plane wave import without noticing any additional phase from the source.

simply modify this examle https://optics.ansys.com/hc/en-us/articles/360034383054-Using-an-equation-to-define-the-spatial-field-profile-of-a-source-in-FDTD

Ex=envelope/envelope;

Ey=Ex*0;

Ez=Ex*0;

and set the xy boundary conditions as periodic. Please test your own and compare with your original simulation.

• Iago Diez
Subscriber

What I would like to know is:

1) Is the field " E " specified by the user in the "imported source" taken as a current density " J " in the equations? Because the electric field of a current density is given by:  E = i ω µ ∫ G(x,x') J(x') dx' ,    where ∫ is the integral symbol, G is the green's function.

2) What convention does lumerical use for monochromatic fields: exp(- i ω t ) or exp( i ω t)  ?

• Guilin Sun
Ansys Employee

A1: The imported source only accepts the electric and magnetic fields spedicifed by the users, from whatever the origins.

A2: Lumerical uses exp(- i ω t ).

• Iago Diez
Subscriber

But this imported electric E and magnetic H fields how are they introduced in the equations?
For example, is the specified E field implemented as a displacement current J = D/t = - iωε E or as a current J = E directly?

• Iago Diez
Subscriber

Also, Guilin Sun, I have another doubt about "import source":

I import an specified " E " and " H " field, and change the injection propagation to be backwards (towards negative z). I compare the phase of the fields and is the same regardless the source is being injected forward or backward.

Let's assume the Poynting vector S = E x H > 0 is positive towards positive values of z, when the source is injected forward. Then when is injected backwards the phase of the fields should change so that the Poynting vector is now negative (towards negative values of z). For example, if the " H " field changes to "-H" this would make S be negative S = E x - H <0. However, the phase of the fields remained the same when I check fields in teh visualiser of the "import source" simulation object.

Could you clarify what is happening? Thanks

• Guilin Sun
Ansys Employee

NO, the specified E field is not implemented as a displacement current. It is simply the E fields according to Maxwell's equations.

As for "then when is injected backwards the phase of the fields should change so that the Poynting vector is now negative (towards negative values of z). ", we can discuss more:

The source will propagate along the direction as it is specified. Internally it suppresses the propagation opposite to what you define (if it has no suppression it will propagate along both directions). For example, when you specify this source is propagating along -z, it supresses the propagation along +z. This is why the grey region in the source is designed for. If your imported fields are designed to propagate along +z, but you specify it to propagate along -z, please check that the H field phase is negative.E field does not change phase.

One more side note: when you use transmission to get the relative power, the monitor surface normal is always possitive , but the Poynting vector is positive when along + axis and negative when along - axis. Thus you get + or - transmission. In physics it is always positive. You can extract monitor surface normal:

?getdata("monitor","surface_normal"); it can be 1,2,3 for xyz, but all positive.

I hope this clarifies.

• Iago Diez
Subscriber

Yes, thanks Guilin, it clarifies.

Related to your comment: "If your imported fields are designed to propagate along +z, but you specify it to propagate along -z, please check that the H field phase is negative.E field does not change phase."

What happens if I don't manually change the field of H?

• Guilin Sun
Ansys Employee

You do not need to manually change the H field. The solver automatically corrects it from your specified propagation direction. You can even not specify H and let the solver calculate H. If you have H, please import it as it is usually more accurate than the solver does with coarse mesh.