A monochromatic laser beam of intensity I o = 297 W/m 2 is polarized in the y-di

Question

A monochromatic laser beam of intensity Io = 297 W/m2 is polarized in the y-direction and propagates in the positive z-direction. This beam is incident upon a quarter-wave plate whose fast axis makes an angle of 45 degrees with the x-axis as shown. Following the quarter-wave plate are two polarizers; the transmission axis of the first polarizer is aligned with the x-axis, while the transmission axis of the second polarizer makes an angle of 1 = 70 degrees with the positive x axis.

1)What is Imid, the intensity of the beam immediately following the polarizer whose transmission axis is aligned with the x-axis?

2)What is Ifinal, the intensity of the beam immediately following the last polarizer?

3)What is the ratio of Ey,final, the maximum value of the y-component of the electric field immediately following the last polarizer, to Eo, the amplitude of the electric field oscillations in the incident polarized beam?

4)The positions of the quarter-waveplate and the last polarizer are now interchanged. What is Ifinal,new, the intensity of the beam after passing through the new arrangement of the two polarizers and the quarter-wave plate?

5)What is the polarization of the beam immediately following the quarter-wave plate?

Right Circularly Polarized

Left Circularly Polarized

Linearly polarized at 45 degrees to the positive x-axis.

Linearly polarized at 135 degrees to the positive x-axis.

6)Suppose you are free to rotate 1, the transmisison axis of the initial polarizer. How many values of 1, 0 1 < 180o, will produce a final intensity of zero after the quarter-wave plate?

None

One

Two

Explanation / Answer

1) I mid = I0 cos^2 theta

I mid = 207 cos ^2 45

I mid = 103.5 W/m2

2)

I final = 103.5 * cos^2 70

I final = 12.107 W/m2

3)

Ratio = sqrt ( 12.107/297)

Ratio = 0.2

4)

I mid = I0 cos^2 theta

I mid = 207 cos ^2( 45+70)

I mid = 53.04 W/m2

I final = 53.04* cos^2 225

I final = 26.52W/m2

5)

Linearly polarized at 135 degrees to the positive x-axis

6)

one

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