Total Angular Momentum Coherent State Fields

Abstract

Structured light fields exploit spin and orbital angular momentum for precision manipulation, advanced imaging, and high-capacity communication. Orbital angular momentum coherent state beams interpolate between Hermite- and Laguerre-Gaussian beams, enabling continuous spatial control. We introduce a symmetry-based framework for joint control of polarization and spatial structure under the shared \$su(2)\$ Lie algebra of spin and orbital angular momentum. Within this structure, we construct total angular momentum fields as superpositions of circular polarization and Laguerre-Gaussian beams, and define their \$su(2)\$ coherent states within fixed-angular-momentum subspaces. A single complex parameter controls both polarization and spatial degrees of freedom, enabling continuous, symmetry-preserving tuning.

Figures (5)

• Figure 1: Intensity and polarization distributions for TAM states with $j=1/2$. (a) Singlet state with $\left\{ J, M \right\} = \left\{ 0, 0 \right\}$. (b)-(d) Triplet states with $J=1$, $M=-1, 0, 1$. Vector field colors indicate linear (blue), right- (brown), and left-handed (green) polarizations.
• Figure 2: Intensity and polarization distributions for (a) azimuthally and (b) radially polarized TAM fields for $\left\{ J, M \right\} = \left\{ j \pm 1/2, 0 \right\}$ with $j \in \{ 3/2, 5/2, 7/2 \}$. Vector field colors follow Fig. \ref{['fig:Fig1']}.
• Figure 3: (a)-(b) Weight magnitudes $\vert c_q\vert$, (c)-(d) intensity and polarization distribution for TAMCS fields with $\{J, M\} = \{1, 0\}$ with (a),(c) $j=1/2$ and (b),(d) $j=3/2$ for $\varphi = 0$ and $\vert \alpha\vert \in \{0, \pi/8, \pi/4\}$. Vector field colors follow Fig. \ref{['fig:Fig1']}.
• Figure 4: (a) Intensity and polarization distribution, and (b) polarization mapped on the Poincaré sphere for TAMCS fields with $\{J, M, j\} = \{3, 0, 5/2\}$, $\vert \alpha\vert = \pi/8$, and $\varphi \in \{0, \pi/4, \pi/2\}$. Vector field colors follow Fig. \ref{['fig:Fig1']}
• Figure 5: Theoretical (upper line) and experimental (lower line) results of a TAMCS field with parameters $\{J, M, j\} = \{1, 0, 3/2\}$, $\vert \alpha\vert = \pi/4$, and $\varphi = \pi/2$. Intensity distributions of (a) the TAMCS field and after transmission through a linear polarizer with its transmission axis oriented at (b) $0^\circ$, (c) $45^\circ$, and (d) $90^\circ$, with respect to the horizontal.