We demonstrate that light propagation in reciprocal chiral photonic media admits a unified description in terms of an emergent Dirac structure in helicity space. Starting from Maxwell's equations, we reformulate the electromagnetic field as a four-component spinor governed by an effective non-Hermitian optical Dirac equation. In this representation, the magnetoelectric response of the chiral medium appears as a helicity-dependent background that modifies the spectrum and eigenmodes, while the breaking of the spin-degenerate condition generates the intrinsic spin-orbit coupling between helicity and orbital degrees of freedom. After projection onto the positive-frequency sector, the theory reduces to an exact two-level helicity-orbital model. This model is found to have an analytical solution and describes coherent Rabi-like oscillations between spin-orbit-coupled vector modes. Chirality controls the helicity splitting and detuning, whereas the electromagnetic mismatch of the medium determines the coupling strength responsible for oscillatory spin-orbit conversion. The resulting dynamics is constrained by exact conservation of the total angular momentum, leading to reversible conversion between spin and orbital angular momentum with well-defined selection rules. Our work establishes an optical Dirac framework for structured light in chiral media, and provides experimentally accessible predictions for chirality-controlled oscillations, polarization dynamics, and orbital angular momentum conversion in structured optical fields.
We demonstrate that light propagation in reciprocal chiral photonic media admits a unified description in terms of an emergent Dirac structure in helicity space. Starting from Maxwell's equations, we reformulate the electromagnetic field as a four-component spinor governed by an effective non-Hermitian optical Dirac equation. In this representation, the magnetoelectric response of the chiral medium appears as a helicity-dependent background that modifies the spectrum and eigenmodes, while the breaking of the spin-degenerate condition generates the intrinsic spin-orbit coupling between helicity and orbital degrees of freedom. After projection onto the positive-frequency sector, the theory reduces to an exact two-level helicity-orbital model. This model is found to have an analytical solution and describes coherent Rabi-like oscillations between spin-orbit-coupled vector modes. Chirality controls the helicity splitting and detuning, whereas the electromagnetic mismatch of the medium determines the coupling strength responsible for oscillatory spin-orbit conversion. The resulting dynamics is constrained by exact conservation of the total angular momentum, leading to reversible conversion between spin and orbital angular momentum with well-defined selection rules. Our work establishes an optical Dirac framework for structured light in chiral media, and provides experimentally accessible predictions for chirality-controlled oscillations, polarization dynamics, and orbital angular momentum conversion in structured optical fields.
The hydrodynamic formulation of the Dirac equation has historically been hindered by the inability to close the system of physical variables without resorting to infinite moment hierarchies. We resolve this longstanding issue by developing a fully covariant chiral-hydrodynamic formulation of the Dirac field in curved spacetime. Working in the Weyl representation, we introduce two independent null vectors, PLμ and PRμ, which decouple the left and right chiral components. This allows us to define chiral geodesic and stochastic velocities, yielding a closed system of exactly eight real equations that corresponds directly to the Dirac field degrees of freedom. Remarkably, this formulation naturally isolates the spin-orbit coupling (q/2)σμνFμν while demonstrating the vanishing of the spin-gravity coupling in torsion-free general relativity. To demonstrate the analytical power of this framework, we specialize to the Schwarzschild geometry. We obtain exact radial solutions in terms of confluent Heun functions and directly compute the quasi-bound state spectrum (fermionic resonances), quasinormal mode frequencies, and greybody factors. Furthermore, by establishing an exact energy balance equation -- representing the first law of thermodynamics for Dirac fields -- we derive the Hawking radiation flux purely from chiral flux conservation at the event horizon. This work not only provides a closed hydrodynamic theory for spin-1/2 fluids but also establishes a unified framework for analyzing quantum information and fermion dynamics in strong gravitational backgrounds.
The theory of quantum electrodynamics is employed in the description of linear and \nnonlinear optical effects. We study the effects of using a two energy level \napproximation in simplifying expressions obtained from perturbation theory, \nequivalent to truncating the completeness relation. However, applying a two-level \nmodel with a lack of regard for its domain of validity may deliver misleading results. \nA new theorem on the expectation values of analytical operator functions imposes \nadditional constraints on any atom or molecule modelled as a two-level system. We \nintroduce measures designed to indicate occasions when the two-level approximation \nmay be valid. \nAnalysis of the optical angular momentum operator delivers a division into spin \nand orbital parts satisfying electric-magnetic democracy, and determine a new \ncompartmentalisation of the optical angular momentum. An analysis is performed on \nthe recently rediscovered optical chirality, and its corresponding flux, delivering \nresults proportional to the helicity and spin angular momentum in monochromatic \nbeams. A new polarisation basis is introduced to determine the maximum values that \nan infinite family of optical helicity- and spin- type measures may take, and disproves \nrecent claims of ‘superchiral light’. A theoretical description of recent experiments \nrelate helicity- and spin- type measures to the circular differential response of \nmolecules, and show that nodal enhancements to circular dichroism relate only to \nphoton number-phase uncertainty relation and do not signify ‘superchiral’ regions. \nThe six-wave mixing of optical vortex input, in nonlinear media, demonstrates the \nquantum entanglement of pairs of optical vortex modes. The probability for each \npossible output pair displays a combinatorial weighting, associated with Pascal’s \ntriangle. \nA quantum electrodynamic analysis of the effect of a second body on absorption \ncan be extended by integrating over all possible positions of the mediator molecules, \nmodelling a continuous medium. This provides links with both the molecular and \nbulk properties of materials.
Conventional optical materials are characterized by either a dissipative response, which results in polarization-independent absorption, or by a gain response that leads to wave amplification. In this work, we study a peculiar class of materials with chiral-gain properties, where gain selectively amplifies waves of one polarization handedness, while dissipation suppresses the opposite handedness. We uncover a novel phenomenon, gain-momentum locking, at the boundary of chiral-gain media, where surface plasmons are amplified or attenuated based on their direction of propagation. This effect, driven by the interplay between spin-momentum locking and polarization-sensitive non-Hermitian responses, enables precise control over unidirectional wave propagation. Our findings open the door to photonic devices with unprecedented capabilities, such as lossless unidirectional edge-wave propagation and the generation of light with intrinsic orbital angular momentum.
The study investigate control of the optical force and its modification with variation of the driving field’s strength in the system levels of the chiral medium for left and right circular polarized light. In addition to orbital and magnetic and spin quantum numbers of applied fields, significant vector field arrows of optical force in chiral media are examined using spatial coordinates, detuning , Rabi frequency and decay rates. The parameters of the probe and control fields’ detuning along with their decay rates and phases are provided to determine the optical force in chiral medium both for left and right circularly polarized fields. The optical force is a function of orbital, magnetic and spin quantum numbers. Using phase, detuning, and Rabi frequency of the control fields as variables, the minimum value of optical force measure is 0.003pN for probe detuning and spatial coordinate while the maximum value of optical force for normalized detuning and transverse radial coordinate is measured to be 0.2pN. Potential uses of optical force in fundamental optics, molecular physics, optomechanics, material science, nanoscience, quantum physics, radar, waveguide, antennas and optical tweezers technology are demonstrated by the results.
Can a chiral cavity turn a free electron into a Landau-like orbiting particle? We answer with exact solutions of three quadratic electron--cavity models in the dipole limit, valid at arbitrary coupling. A single linearly polarized mode dresses the electron mass, which delays its flight, slows the spreading of a wavepacket and entangles the packet with the cavity. The complete transverse field, with both circular helicities, keeps two commuting, gapless translations at any coupling, mode number and helicity splitting, so the electron stays ballistic and no synthetic magnetic field appears. Keeping a single helicity gives two inequivalent models that are not related by a gauge transformation: reducing before the Power--Zienau--Woolley transformation gives ballistic motion, whereas reducing after it gives a Landau-like crossed-quadrature Hamiltonian. They differ by a real uniform field B=sλ2/(2ωc) (ωc the mode frequency, λ the coupling, s=±1 the helicity). In the complete theory the frequency ω−s of the partner helicity, measured against g2=λ2/(2ωc), decides between them: the electron is ballistic for a stiff partner, and Landau-like only at the soft-partner point, through an exact canonical reorganization that holds for the active sector but not for observables such as the electron--photon entanglement. Projecting onto one helicity after the PZW transformation is therefore not by itself a mechanism for synthetic magnetism; the mode content of the cavity is.
We explore the underlying spin-orbit coupling (SOC) mechanism for the interactions between complex structured light fields in a four-level tripod electromagnetically induced transparency (EIT) system. Because one coupling field in the system is a Bessel beam, the susceptibility of the EIT medium can be modulated quasiperiodically in the radial dimension. The paraxial propagation and evolution of a rotating spinor image as the probe field in the medium can be described by a Pauli-like equation with the SOC term. We calculate the spatial distributions of the diffracted patterns of the image in the near field and clearly show the tunable SOC-induced radial splitting of the oppositely polarized pseudospin states. Our scheme may be useful for all-optical processing of spatial multimode signals in coherent media.