Question

1. The indices of refraction for the fast and slow axes of quartz with 589 nm light are 1.5462 and 1.5553, respectively.

   1. (a) By what fraction of a wavelength is the e-ray retarded, relative to the o-ray, for every

      wavelength of travel in quartz?

   2. (b) What is the minimum thickness of quartz needed to manufacture a quarter-wave plate

      (QWP)?

   3. (c) Imagine that the thickness found in part (b) turned out to be too thin for the QWP to be

      durable and you want to manufacture a QWP with a thickness of at least 0.725 mm. What will be the thickness of the thinnest possible QWP that will be larger than 0.725 mm?

Answer 1

(a)

difference in indices

n = 1.5553 - 1.5462

n = 9.1e-3

so, for one wavelength, retardation will be

d/ = n

d/ = 9.1e-3

or

d/ = 0.0091

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(b)

for multiple order QWP, we have

(m + 1/4) = tn

for minimum thickness, set m = 0

so,

/4 = tn

t = /4n

t = 589 / 4 * 0.0091

t = 16181.32 nm ( mind the units , please !!!)

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(c)

we want t = 0.725 mm

so,

( m + 1/4) 589 = 0.725e-3 * 0.0091

m = 10

we need thickness to be just more than 0.725 mm

so, we will use m = 11

so,

we get

t = 0.728 mm