... B-modes

Let $H(\theta)$ be any spin-2 field, and denote by $H^{\rm E}$ and $H^{\rm B}$ the E- and B-mode components of H. They can be obtained from H most easily in Fourier space, namely

$$\hat H^{\rm E}(\ell)={1\over 2}\left[ \hat H(\ell)+\hat H^*(-... ...hat H(\ell)-\hat H^*(-\ell)~ {\rm e}^{4{\rm i}\beta} \right] ,$$

as can be best seen by taking the shear field as a prototypical spin-2 field; here, $\beta$ is the phase of the complex wave number $\ell$.

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