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Published byKaylee Coffey Modified over 3 years ago

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Polarization of EM waves The polarization of a uniform plane wave refers to the time-varying behaviour of the electric field vector at fixed point in space. Consider, for example, a uniform plane wave travelling in the z-direction. With the E and H vectors lying in the x-y plane. If E y =0, and only E x is present: The wave is said to be polarized in the x direction. If E x =0, and only E y is present: The wave is said to be polarized in the y direction. Case 1:

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If both E x and E y are present, and are in phase ( =0, 2, 4....) the resultant electric vector has a direction, dependent on the relative magnitude of E x and E y. The resultant vector will make the angle tan -1 (E y /E x ). In all the above cases the wave is said to be linearly polarized because the resultant vector is constant with time. Case 2: If both E x and E y are not in phase ( =(2n+1) /2, n=0, 1, 2.....), i.e. their maximum values (of amplitude) reach at different time, the direction of resultant electric vector will vary.

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The locus of the end point of the resultant E will be an ellipse and the wave is said to be elliptically polarized. Case: 3 When E x and E y have equal magnitudes and not in phase i.e.( =(2n+1) /2, n=0, 1, 2.....), the locus of the resultant E will be an circle and the wave is said to be circularly polarized.

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Let the two plane polarized EM waves may superimpose. One has Electric vector, E x in X direction and other has electric vector, E y in Y direction, and both are propagating in Z direction. Where a and b are the amplitude of the waves and is the phase difference between them. Equation (1) can be written as:

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From 2 nd equation: From above equation we can find: Put these values in equation 3: or

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This equation in general represents an ellipse. Therefore in this case the resultant will be elliptically polarised light. But actual nature of resultant wave can be given by following cases: Case I: n: integer then

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So equation 4 will be: or Which is the equation of a straight line. Thus emergent ray in this case will be plane polarised light.

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Case II: then So equation 4 will be: Which is the equation of an ellipse. Thus emergent ray in this case will be elliptically polarised light.

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Case III: with a=b So equation 4 will be: Which is the equation of a circle of radius a. Thus emergent ray in this case will be circularly polarised light.

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