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## Main Question or Discussion Point

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.