The three dimension form of farfieldexact2d. This function projects complete complex vector fields to specific locations. It is expected to be correct down to distances on the order of one wavelength. The projections from multiple monitors can be added to create a total far field projection  see Projections from a monitor box .
farfieldexact3d projects any surface to the grid points defined by the vectors x,y and z. If only E field is returned as the result, the data is returned in a matrix of dimension NxMxKx3 if one frequency point is projected, and NxMxKx3xP if more than one frequency point is projected where N is the length of the vector x, M the length of the vector y, K is the length of the vector z, P is the number of frequency points, and the fourth index represents Ex, Ey, and Ez. Note that N, M and K can be 1, and when they are all 1, the function is the same as farfieldexact. If both E and H fileds are returned, the data is returned as a dataset with the E and H fields packaged with the corresponding x,y,z and frequency/wavelength.
Syntax 
Description 

out = farfieldexact3d( "mname", x, y, z, f, index); 
Projects a given power or field profile monitor to the far field at grid points specified by the vectors x,y,z. Returns E field only. 
out = farfieldexact3d( dataset, x, y, z, f, index); 
Projects a given rectilinear dataset to the far field at grid points specified by the vectors x,y,z. Returns E field only. 
out = farfieldexact3d( "mname", x, y, z, opt); 
Projects a given power or field profile monitor to the far field at grid points specified by the vectors x,y,z. Returns E field or E and H fields. Refer to the table below for the options. 
out = farfieldexact3d( dataset, x, y, z, opt); 
Projects a given rectilinear dataset to the far field at grid points specified by the vectors x,y,z. Returns E field or E and H fields. Refer to the table below for the options. 
Parameter 
Default value 
Type 
Description 


mname 
required 
string 
name of the monitor from which far field is calculated 

x 
required 
vector 
x coordinates of the grid points where far field is calculated 

y 
required 
vector 
y coordinates of the grid points where far field is calculated 

z 
required 
vector 
z coordinates of the grid points where far field is calculated 

f 
optional 
1 
vector 
Index of the desired frequency point. This can be a single number or a vector. Multithreaded projection was introduced since R2016b. 
index 
optional 
value at monitor centre 
number 
The index of the material to use for the projection. 
opt 
optional 
struct 
the 'opt' parameter includes the following options: "field": This parameter is optional. It defines the return field, can either be "E" or "E and H". "f": This parameter is optional. It defines the index of the desired frequency point. This can be a single number or a vector. Multithreaded projection was introduced since R2016b. "index": This parameter is optional. It defines the index of the material to use for the projection. 
[[Note:]] When using a dataset, the default value of the refractive index is 1.
Example
This 3D example calculates the far field electric field intensity on a 2mm x 2mm image plane located a distance of z=+1.5mm from the simulation region. For the example of far field projection of a rectilinear dataset see farfield3d.
mname="trans"; # Monitor name num=25; # resolution # define far field plane to image fields x=linspace(1e3,1e3,num); y=x; z=1.5e3; # compute far field E=farfieldexact3d(mname,x,y,z,{"field":"E"}); # select component Ex=pinch(E,4,1); Ey=pinch(E,4,2); Ez=pinch(E,4,3); # image intensity E2= abs(Ex)^2 + abs(Ey)^2 + abs(Ez)^2; image(x*1e3,y*1e3,E2,"x (mm)","y (mm)","Electric field at z=1.5mm from source");
The following example shows how farfieldexact and farfieldexact3d output data differently.
When x=[1 2], y=[1 2], z=[0],
farfieldexact: The result is a 2*3 matrix. First dimension is position;second is field component. This calculates the far field at the positions [1,1,0] and [2,2,0] .
farfielexact3d: The result is a 2*2*1*3 matrix. First three dimensions are positions; the fourth dimension is field component. This calculates the far field at the positions [x,y,z] = [1,1,0], [1,2,0], [2,1,0], [2,2,0].
x=1:2; y=1:2; z=0; m="monitor"; E_far=farfieldexact3d(m,x,y,z,{"field":"E"}); ?size(E_far); result: 2 2 1 3
See Also
List of commands , farfield3d , farfieldexact2d , farfieldexact