[Meep-discuss] Electric field units

[João Luis Silva]

Hello,

I've read the web pages about meep units, but I still have questions. I'm
using a nonlinear material (silica) and I've set the nonlinear coefficient
chi3 to (4/3)*3E-8* n^2 where n is the linear refractive index and 3E-8 is
the nonlinear coefficient n2 in um^2/W as described on the web page. My
length unit is the um, so all is OK so far. My question is what are the
units of the electric field, so I know what to pass to the (amplitude A0)
of the gaussian-src. Assuming I=(1/2) epson0 c n |E|^2, the documentation
says that epson0 = c = 1 then A0=sqrt(2I/n), with I in W/um^2. Using these
values I'm not getting the results I expected (it's way off). I'm pretty
certain all the values relating to time and distance are correct in my
simulation. What are the units of the electric field in meep? Have I made
any mistake on the above reasoning?

Thanks,
João Luís Silva

[Steven G. Johnson]

Post by João Luis Silva
the nonlinear coefficient n2 in um^2/W as described on the web page. My
length unit is the um, so all is OK so far. My question is what are the
units of the electric field, so I know what to pass to the (amplitude A0)
of the gaussian-src. Assuming I=(1/2) epson0 c n |E|^2, the documentation

That's not really a useful to phrase the question, because the amount of
field you get from a given current depends on the geometry as well as on
the current amplitude.

A better way to think of it is this: the units of field and power are
arbitrary, and the units of n2 are arbitrary. The only meaningful
quantity is the product of n2 * power. So, you are free to *choose* the
units of n2 as um^2/W, and then you can choose to think of the power as
being in units of Watts.

Suppose you want to input 5W of power into a waveguide (or whatever).
What you should do is to put a source with some amplitude "A" and measure
the power P that you get in your waveguide (using one of Meep's flux
functions). Then to make the power 5, you should scale A by sqrt(5/P).

Steven

[João Luis Silva]

Post by Steven G. Johnson

Post by João Luis Silva
the nonlinear coefficient n2 in um^2/W as described on the web page. My
length unit is the um, so all is OK so far. My question is what are the
units of the electric field, so I know what to pass to the (amplitude A0)
of the gaussian-src. Assuming I=(1/2) epson0 c n |E|^2, the documentation

That's not really a useful to phrase the question, because the amount of
field you get from a given current depends on the geometry as well as on
the current amplitude.

I thought I was specifying the electric field, not the current (oops!). So I
used flux-in-box passing a plane perpendicular to the wave. However, with
real field no averaging will be done, and (flux-in-box ...) cannot be used
as a step function. So I'm trying to use (electric-energy-in-box ...) for
the whole volume, at a time point when the field is all inside the box,
which leads me to the following questions:

Assuming the same conditions described in the last post (length in microns /
n2 in um^2/W) I have two questions:

* In what units will the value returned by (electric-energy-in-box) be?
* How is it affected by a 2D vs 3D volume of the box?

Thanks,
João Luis Silva

[Steven G. Johnson]

Post by João Luis Silva
I thought I was specifying the electric field, not the current (oops!). So I
used flux-in-box passing a plane perpendicular to the wave. However, with
real field no averaging will be done, and (flux-in-box ...) cannot be used
as a step function. So I'm trying to use (electric-energy-in-box ...) for
the whole volume, at a time point when the field is all inside the box,

You can always run flux-in-box over a period and do the average.

Post by João Luis Silva
Assuming the same conditions described in the last post (length in microns /
* In what units will the value returned by (electric-energy-in-box) be?

The units are all internally consistent. So if you decide that the units
of power (flux) are Watts, then the unit of energy is Watts * (Meep time).
Meeps time units are a/c, where "a" is your unit of distance.

Post by João Luis Silva
* How is it affected by a 2D vs 3D volume of the box?

If you use a 2D volume (i.e. one dimension has zero thickness), then Meep
computes the energy density (energy/distance) in that plane. If you use a
1D volume (i.e. two dimensions have zero thickness) then it computes the
energy/area. If you use a 0d volume (a point), then it just gives you the
energy/volume at that point.

i.e. Meep takes the energy density (per unit volume) in the field and
integrates it with a d-dimensional integral for a d-dimensional box.

Steven