Bloch-type photonic skyrmions in optical chiral multilayers

1. Problem Statement

• Context: Magnetic skyrmions are topologically stable spin textures with potential applications in spintronics and data storage. Their photonic counterparts, photonic skyrmions, have recently been discovered in surface plasmon polaritons (SPPs).
• Limitation: To date, only Néel-type photonic skyrmions (where the spin vector is radial) have been theoretically predicted and experimentally observed.
• The Gap: The Bloch-type photonic skyrmion (where the spin vector is azimuthal) and the twisted Néel-type (a hybrid state) have remained unexplored in the photonic domain. This is largely because in standard isotropic, non-chiral materials, SPPs exist only for Transverse Magnetic (TM) polarization, resulting in a transverse spin component ($S_r$) that never vanishes, preventing the formation of a pure Bloch-type structure ($S_r=0$).
• Objective: The authors aim to theoretically predict and demonstrate the existence of Bloch-type and twisted Néel-type photonic skyrmions by exploiting the properties of chiral materials and plasmonic vortices.

2. Methodology

The authors employed a rigorous theoretical framework based on electromagnetic theory and topology:

• System Design:
  • Single Interface: A chiral material-metal interface supporting a plasmonic optical vortex (OV) beam.
  • Tri-layered Structure: A Metal-Insulator-Metal (MIM) structure where the insulator is a chiral material.
• Theoretical Modeling:
  • Constitutive Relations: Used the constitutive equations for chiral media ($D = \epsilon_c E + i\xi\sqrt{\mu_0\epsilon_0}H$, etc.), where $\xi$ is the chirality parameter.
  • Bohren Decomposition: Decomposed the electromagnetic fields into Right-Handed Circularly Polarized (RCP) and Left-Handed Circularly Polarized (LCP) eigenmodes ($F_{\pm}$) to solve Maxwell's equations in the chiral medium.
  • Field Solutions: Derived analytical solutions for the field components ($f_{\pm z}$) using Bessel functions ($J_l$) for a vortex beam with topological charge $l$.
  • Spin Angular Momentum (SAM) Calculation: Calculated the local photon spin vector $\mathbf{S} = \frac{1}{4\omega}\text{Im}[\epsilon_c \mathbf{E}^* \times \mathbf{E} + \mu_0 \mathbf{H}^* \times \mathbf{H}]$ in cylindrical coordinates $(S_r, S_\phi, S_z)$.
  • Topological Analysis: Computed the Skyrmion number ($n$) to verify the topological stability of the structures.
  • Energy Flux: Analyzed the Poynting vector ($\mathbf{P}$) to understand the relationship between energy flow and spin texture ($\mathbf{S} \propto \nabla \times \mathbf{P}$).

3. Key Contributions

1. Prediction of Twisted Néel-Type Skyrmions: The paper theoretically demonstrates that introducing chirality ($\xi \neq 0$) to a plasmonic OV at a single interface generates a twisted Néel-type skyrmion. This is a state where the spin vector has both radial ($S_r$) and azimuthal ($S_\phi$) components, a state previously unreported in photonics.
2. Realization of Bloch-Type Skyrmions: The authors propose a MIM (Metal-Chiral-Metal) structure. By engineering the counter-propagating transverse spins on the top and bottom interfaces of the chiral film, they achieve a cancellation of the radial spin component ($S_r = 0$) at the center of the film. This allows for the formation of a pure Bloch-type photonic skyrmion ($S_\phi \neq 0, S_r = 0$).
3. Chirality Control: The study establishes that the handedness (swirl direction) of the skyrmion is directly controlled by the sign and magnitude of the material's chirality parameter ($\xi$).
4. Subwavelength Confinement: The MIM structure significantly compresses the effective wavelength, resulting in a skyrmion size ($r \sim 90$ nm) that is much smaller than that of single-interface structures ($r \sim 220$ nm).

4. Key Results

• Spin Texture Evolution:
  • In a non-chiral system ($\xi=0$), the spin texture is purely Néel-type ($S_\phi = 0$).
  • In a chiral single interface, the texture becomes twisted Néel-type. The helicity angle $\chi$ (defined by $\tan \chi = S_\phi/S_r$) evolves but never reaches $90^\circ$ because $S_r$ never vanishes due to the intrinsic spin-momentum locking of SPPs.
  • In the MIM chiral structure, the interference of SPPs from both surfaces creates a region in the center of the film where $S_r = 0$. Here, the spin texture transitions to a Bloch-type ($\chi = \pm 90^\circ$).
• Topological Stability: The calculated skyrmion number is $n = 1$, confirming the topological stability of these photonic structures.
• Chirality Dependence:
  • The sign of the azimuthal spin component ($S_\phi$) flips when the sign of the chirality parameter ($\xi$) is reversed.
  • In the MIM structure, the strong coupling between the top and bottom surfaces in thin films (e.g., 10 nm) reverses the handedness of the Bloch skyrmion compared to the single-interface twisted Néel case for the same chirality sign.
• Energy Flux: The analysis of the Poynting vector reveals a non-zero axial energy flux ($P_z$) inside the chiral film, which is distinct from standard plasmonic vortices and correlates with the emergence of the azimuthal spin component.

5. Significance

• Enriching Photonic Skyrmion Family: This work expands the classification of photonic skyrmions beyond the Néel-type, introducing twisted Néel and Bloch types, thereby bridging a gap between magnetic and photonic topological quasiparticles.
• Chiral Sensing and Information Processing: The dependence of the skyrmion's swirl handedness on the material's chirality offers a new degree of freedom for chiral sensing technologies. It suggests a mechanism to encode information in the topological state of light based on material properties.
• Ultra-Compact Devices: The ability to generate Bloch-type skyrmions with deep-subwavelength sizes ($\sim 1/6 \lambda$) in MIM structures paves the way for ultra-compact nanophotonic devices for data storage and quantum information processing.
• Fundamental Physics: The study reveals a remarkable resemblance between the behavior of photonic skyrmions in chiral multilayers and magnetic skyrmions in chiral bulk magnets, validating the analogy between spintronics and nanophotonics.

In conclusion, the paper provides a theoretical blueprint for generating and controlling Bloch-type photonic skyrmions, overcoming the limitations of standard isotropic materials through the strategic use of chiral multilayer structures and plasmonic vortices.