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Electric field of plane wave

  1. Jun 12, 2008 #1
    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
  2. jcsd
  3. Jun 12, 2008 #2


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    Science Advisor
    Homework Helper

    Well really E(s) = Re{Eo * exp(-jks)} (ie the real part)... so in short you're supposed to ignore the sin term.
  4. Jun 12, 2008 #3
    I think that equation was somewhat wrong. I think the EM field can be represented as a complex vector:

    A complex vector as in a 3d vector whose components are complex
    numbers :
    (a1 + i * b1) xhat + (a2 + i * b2) yhat + (a3 + i * b3) zhat

    where xhat, yhat, zhat are unit vectors along x, y, z respectively.

    one can rearrange it to get real part as the electric field vector and
    imaginary part as the magnetic field vector, both at right angles to
    each other :
    real + i * imag

    electric field: (a1 * xhat + a2 * yhat + a3 * zhat)

    magnetic field: (b1 * xhat + b2 * yhat + b3 * zhat)

    instantaneous electric field: Re( EM(0) * exp( -jks ) )
    instantaneous magnetic field: Imag( EM(0) * exp(-jks) )

    where k (wave number ) = 2 * pi / wavelength
    s = distance travelled in the direction of the plane wave
    EM(0) is the EM field at reference point.

    Here it seems the problem wont arise while multiplying EM(0) and exp(-jks) as both are complex numbers.

    Is this correct ??
    Last edited: Jun 12, 2008
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