Table 1.

The expressions of the synthetic SU(2) and U(1) gauge potentials in terms of the constitutive parameters of the non-Abelian media

SU(2)	Vector potential $\widehat{\mathcal{A}}={\mathcal{A}}^a{\widehat{\sigma }}_a$	${\mathcal{A}}^1=k_0\mathrm{Re}\left({\mathbf{g}}_{-}\right)\times {\mathbf{e}}_z$ a
		${\mathcal{A}}^2=k_0\mathrm{Im}\left({\mathbf{g}}_{-}\right)\times {\mathbf{e}}_z$
		${\mathcal{A}}^3=0$
	Scalar potential ${\widehat{\mathcal{A}}}_0={\mathcal{A}}_0^a{\widehat{\sigma }}_a$	${\mathcal{A}}_0^1=k_0{\mathbf{e}}_z\cdot \left[\nabla \times \left({\mathrm{\leftrightarrow \epsilon }}_T^{-1}\cdot \mathrm{Im}\left({\mathbf{g}}_{+}\right)\right)\right]$
		${\mathcal{A}}_0^2=-k_0{\mathbf{e}}_z\cdot \left[\nabla \times \left({\mathrm{\leftrightarrow \epsilon }}_T^{-1}\cdot \mathrm{Re}\left({\mathbf{g}}_{+}\right)\right)\right]$
		${\mathcal{A}}_0^3=k_0^2\left[\frac{{\epsilon }_z-{\mu }_z}{2}-2\mathrm{Re}\left({\mathbf{g}}_{-}^{†}\cdot {\mathrm{\leftrightarrow \epsilon }}_T^{-1}\cdot {\mathbf{g}}_{+}\right)\right]$
U(1)	Scalar potential	$V_0=k_0^2\left[\left({\mathbf{g}}_{+}^{†}\cdot {\mathrm{\leftrightarrow \epsilon }}_T^{-1}\cdot {\mathbf{g}}_{+}\right)-\frac{{\epsilon }_z+{\mu }_z}{2}\right]$

^aHere $k_0=\omega ∕c$ is the vacuum wave number, and ${\mathbf{g}}_{\pm }=\left({\mathbf{g}}_1\pm {\mathbf{g}}_2^{*}\right)∕2$.