Question

Suppose we have two light beams, described by the Stokes vectors (1,0,1,0) and (4,0,0,−4). What is the Stokes vector of a beam formed by incoherent superposition of these two? What is its degree of polarization?

Answer 1

The Stokes vector of the beam formed by incoherent superposition of (1,0,1,0) and (4,0,0,-4) is (5,0,1,-4). The degree of polarization of this combined beam is approximately 0.83 or 83%.

Step-by-step explanation:

To find the Stokes vector for a beam formed by the incoherent superposition of the two given beams, we simply add the corresponding elements of each vector. The first vector is (1,0,1,0), and the second vector is (4,0,0,-4). Adding these component-wise gives us the Stokes vector of the combined beam: (5,0,1,-4).

The degree of polarization (P) is given by the formula:

P = sqrt(Q^2 + U^2 + V^2)/I

Where I, Q, U, and V are the elements of the Stokes vector. Substituting the values from our combined Stokes vector:

P = sqrt(0^2 + 1^2 + (-4)^2) / 5 = sqrt(1 + 16)/5 = sqrt(17)/5

Thus, the degree of polarization of the beam formed by the incoherent superposition is sqrt(17)/5, which is equal to approximately 0.83 or 83%.