$${E_\varphi = E_0 \exp\bigg[ i \bigg(\omega t - \frac{kb}{2} \sin \varphi \bigg) \bigg] \frac{1}{\frac{kb}{2} \sin \varphi} \frac{1}{2i} \bigg[ \exp\bigg( i \frac{kb}{2} \sin \varphi\bigg) - \exp\bigg( -i \frac{kb}{2} \sin \varphi \bigg) \bigg]}$$