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Calculating the amplitude of the oscillating magnetic field in a laser beam?
If I have the cross sectional area of a laser beam (mm2) and the total power (mW) how do I go about working out the above? Is it similar to working out electric field? The answer should be in T and that's whats thrown me!
Thanks in advance
The power crossing per unit area is Poynting's vector;
p = (1/u(o))(E X B)
for a plane wave E & B are perpendicular and also the magnitudes are related as IEI = cIBI
So the Poynting vector can be written;
p = [(c/u(o))IBI^2]n
where "n" is a unit vector in the direction of wave propagation, which is parallel to the beam and perpendicular to the area "A" it is crossing.
To get the total power crossing "A" you Dot vector "A" into p to get;
P = p Dot A = [(c/u(o))IBI^2A
Now this is the power at any time "t" which has the basic time dependence from IBI as IBI = IB(o)ISin(wt)
P = [(c/u(o))IAB(o)I^2Sin^2(wt)
Where B(o) is the amplitude.
Now if you are given the "maximum" power then you can write;
P(max) = (c/u(o))AB(o)^2
and solve for B(o).
However you are probably given the "time average" power. Which is the average power crossing in one cycle. Then you average the Power over one cycle which gives (1/2) for the time average of Sin^2(wt) and;
P(avg) = (1/2)(c/u(o))AB(o)^2
and you solve this for B(o).
So depending on which "power" you are given will determine which of the two formulas to use.
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