Guilin Sun
Ansys Employee

"However, for the case “theta=15 and phi=45”, the polarization plot of the linearly polarized light without the structure is in 45 degrees while the circularly polarized light is transformed to vertical direction after passing through the waveplate. I know the function of the quarter waveplate is correct, I just wonder why the case “theta=15 and phi=45” is different from the others."

I guess the confusion is from phi. When phi is not zero, the polarization actually changes. Please check! When phi=0 but theta is non zero, the polarization is still in the plane, say xz. However if phi is not zero (theta is also not zero), then the polarization is not only in xz plane, but also in yz plane. 

If phi=0, the polarization is at 45 deg after the waveplate with circular polarization. When phi is 45, the result changed to 90 deg, which is correct. It will not be 45 deg. 

Please check the polarization state:

1: linear polarization of theta 15deg, phi=0;

2: linear polarization of theta 15 deg but phi=45.

The textbook gives simple case for illustation. Now you are working on a complicated case so you may need to follow the first principle and see where the polarization should be when phi is not zero. 

I believe your simulaiton results are correct.