(a) Find the allowable thicknesses for a half-wave plate operating at 589.3 nm wavelength. Use the natural birefringence of quartz as in the table below. Recall that the phase difference must be an odd multiple of half wavelength.

b) Which is the smallest possible thickness?

c) What is a zero-order waveplate? Discuss briefly with a sketch.

d) Design a zero-order quartz half-wave plate at this wavelength. Make a sketch and denote the orientation of the optic axis clearly in each section.

e) Name three advantages of zero-order waveplates over multiple order waveplates.

Crystal	n o	n c
Tourmaline	1.669	1.638
Calcite	1.6584	1.4864
Quartz	1.5443	1.5534
Sodium Nitrate	1.5854	1.3369
Ice	1.309	1.313
Rutile (TiO 2 )	2.616	2.903

The table above is Table 8.1 Refractive indices of some uniaxial birefringent crystals (λ = 589.3 nm)