Question

At 600 nm, quartz has refractive indices no =1.54421, ne =1.55333.

The beam is going through a piece of quartz 0.213 mm thick, with its fast axis along the x-axis and its slow axis along the y-axis. Find the resulting electric field Sketch the magnitude of the new x and y components after they have passed through the crystal. What is the phase difference between them?

Answer 1

Due to the difference in refractive indices, the effective path length traveled by both E-Ray and O-Ray will be different.

The phase difference which will be between them after traveling 0.213 mm = 0.213 x 10^-3 m will be:

=>

So, the O-Ray will travel along the x-axis and would obey Snell's law whereas the E-Ray will travel along y-axis. The resultant will be such that the Electric field along the fast axis (E_y) will have a phase delay of 20.342 radians after traveling the material.

From the phasor diagram, the relation between their amplitudes will be:

=> E_e = (12.8091)E_o.

therefore, the new x-component will be:

and the new y component will be:

where and .

The resulting electric field strength will be given by:

therefore, the final form of the resultant wave will be of the form: