# Linear Polarization # Circular Polarization Given that the [[polarization operator]] in the circularly polarized case is simply the 2nd [Pauli Matrix](Pauli%20Matrices.md), $\hat{\sigma}_2$, it generates rotations in [[SU(2)]] of the form $\hat{R}(\theta)=e^{i\mathbf{\sigma}\cdot\mathbf{a}}=\cos{(\theta)}+i\hat{\sigma}_2\sin{(\theta)}$ which follows from the form of the Pauli matrix [Complex Matrix Exponential](Pauli%20Matrices.md#Complex%20Matrix%20Exponential) where here, $\mathbf{\sigma}$ is a [vector of Pauli matrices.](Pauli%20Matrices.md#Vector%20of%20Pauli%20Matrices) %%This note is describes a category of unitary transformations and the concepts here should be inherited from an eventual note on the dynamics of two level systems that will decouple this note from directly connecting to the general note on Pauli matrices.%% #QuantumMechanics/QuantumOptics #QuantumMechanics/QuantumDynamics