- #1
broli86
- 4
- 0
Hi I've working on a computer program where I need to calculate some
electric fields. I am referring to a thesis which provides these
formulas. For eg:
The electric field for a ray(plane wave actually) at a distance s from
the reference point:
E(s) = E(0) * exp(-jks)
where E(s) = electric field at a distance s from the reference point.
E(0) = electric field at reference point.
s = distance travelled.
k = wave number = 2 * PI / wavelength
exp(-jks) as per my thesis, represents the phase variation of the
electric field along the ray.
now, electric field is always a vector(3d in my case). so the user
will input a magnitude for the electric field at the reference point
and i can calculate the reference electric field vector[ E(0) ] easily
by multiplying it with the unit direction vector the wave.
exp(-jks) expands as
cos(ks) - j sin(ks)
^ ^ ^
if E(0) is a vector of the form a x + b y + c z,
^ ^ ^
Then E(s) = (a x + b y + c z) * ( cos(ks) - j sin(ks) )
I'm really confounded at this expression because how does one multiply
a complex number and a vector ? And even if it is possible then what
about E(s) ? If E(0) was defined to be a 3d vector then E(s) must also
be a 3d vector. What does it actually mean ? If there are some EE/
physics experts who can probably figure it out then it would be really
great.
electric fields. I am referring to a thesis which provides these
formulas. For eg:
The electric field for a ray(plane wave actually) at a distance s from
the reference point:
E(s) = E(0) * exp(-jks)
where E(s) = electric field at a distance s from the reference point.
E(0) = electric field at reference point.
s = distance travelled.
k = wave number = 2 * PI / wavelength
exp(-jks) as per my thesis, represents the phase variation of the
electric field along the ray.
now, electric field is always a vector(3d in my case). so the user
will input a magnitude for the electric field at the reference point
and i can calculate the reference electric field vector[ E(0) ] easily
by multiplying it with the unit direction vector the wave.
exp(-jks) expands as
cos(ks) - j sin(ks)
^ ^ ^
if E(0) is a vector of the form a x + b y + c z,
^ ^ ^
Then E(s) = (a x + b y + c z) * ( cos(ks) - j sin(ks) )
I'm really confounded at this expression because how does one multiply
a complex number and a vector ? And even if it is possible then what
about E(s) ? If E(0) was defined to be a 3d vector then E(s) must also
be a 3d vector. What does it actually mean ? If there are some EE/
physics experts who can probably figure it out then it would be really
great.