Local-Photon Approach in Photonics

• Local-photon approach is a family of frameworks that characterizes photonic phenomena by using explicitly local quantities such as position-dependent operators and the local density of states (LDOS).
• It enables precise modeling in diverse contexts including structured media, cavity electrodynamics, and quantum network metrology by focusing on local interactions and emission processes.
• The method provides actionable insights for experiments, linking measurable effects like magnon linewidth modifications and entanglement certification directly to local field properties.

The local-photon approach is not a single formalism but a family of research programs in which photonic physics is defined through quantities that are explicitly local: localized bosonic excitations in position space, position-dependent photon operators and local density of states (LDOS) in structured media, local observables for entanglement certification, and local approximations to strong-field QED rates. Across these usages, the shared move is to replace a purely global normal-mode description with objects tied to a position, a detector region, a local coupling channel, or a local background field (Hodgson et al., 2021, Partanen et al., 2014, Yao et al., 2019, Blackburn et al., 2021).

1. Terminological scope

In the literature represented here, “local-photon approach” has several distinct technical meanings. The term therefore functions more as a thematic label than as a universally standardized theory.

Usage	Local object	Representative papers
Position-space quantization	Localized bosonic excitations (“blips”)	(Hodgson et al., 2021, Hodgson, 2023, Southall et al., 2019)
Structured media and cavity electrodynamics	Position-dependent photon operators, LDOS, local field temperature	(Partanen et al., 2014, Partanen et al., 2014, Ge et al., 2015, Yao et al., 2019)
Quantum-network metrology	Local homodyne, local displacement, local click/no-click detection	(Morin et al., 2012, Caspar et al., 2021, Nitsche et al., 2020)
Strong-field QED	Local field approximations such as LCFA, LMA, ULCFA	(Blackburn et al., 2021, King, 2019)
Localization and geometry	Localizable polaritons, eventualization, quasi-local photon surfaces	(Ojima et al., 2015, Cao et al., 2019, Jr, 2017)

A recurrent source of confusion is the assumption that “local” always means a sharply localized photon particle. The cited literature does not support that reading. Depending on context, “local” may instead mean LDOS at the emitter position, a position-dependent ladder operator, a detector acting on one subsystem only, or a local expansion of the background field.

2. Structured media, LDOS, and local photonic environments

One major branch of the local-photon approach treats emission and damping as local-coupling problems inside structured electromagnetic environments. In “Coherent control of magnon radiative damping with local photon states,” a yttrium iron garnet sphere is loaded into a one-dimensional circular waveguide cavity that supports both standing-wave photon modes and travelling-wave photon modes. The Kittel magnon mode radiates into this mixed photonic environment, and the magnon linewidth is written as

$$\mu_0 \Delta H = \mu_0 \Delta H_0 + \frac{\alpha \omega}{\gamma} + 2\pi R \, |\Pi(d,\omega)|,$$

with the key statement that the radiative damping is proportional to LDOS. The same work distinguishes the roles of standing-wave photons, which produce the anticrossing and coherent coupling, from travelling-wave photons, which form the open radiative channel. It reports coherent magnon-photon hybridization with a coupling strength of about $16\,\mathrm{MHz}$, and in one geometry it reports linewidth enhancement by about $20$-fold relative to intrinsic damping at cavity resonance (Yao et al., 2019).

A closely related program appears in position-dependent quantization of layered dielectrics. In “Position-dependent photon operators in the quantization of the electromagnetic field in dielectrics at local thermal equilibrium,” the field is not described by a single global normal mode; instead, a local annihilation operator is tied to the vector potential and normalized by the electric LDOS,

$$\hat a(x,\omega) = \sqrt{\frac{\varepsilon_0 \omega}{2\pi^2 \hbar \rho(x,\omega)}}\,\hat A^+(x,\omega), \qquad \rho(x,\omega)=\frac{2\omega}{\pi c^2 S}\,\mathrm{Im}[G(x,\omega,x)].$$

The resulting local photon number and effective field temperature,

$$T(x,\omega) = \frac{\hbar\omega}{k_B \ln\!\left(1+1/\langle\hat n(x,\omega)\rangle\right)},$$

oscillate in nonequilibrium cavities because left- and right-originating source fields interfere with position-dependent phase. The same framework gives the local balance relation

$$\langle Q(x,t)\rangle_\omega = \hbar\omega^2\,\mathrm{Im}[n(x,\omega)^2]\, \rho(x,\omega)\, \Big[\langle \hat\eta(x,\omega)\rangle-\langle \hat n(x,\omega)\rangle\Big],$$

which connects local emission or absorption to LDOS and the mismatch between reservoir occupation and local field occupation (Partanen et al., 2014).

The extension to a unified electric, magnetic, and total electromagnetic photon-number quantization sharpens this picture. “Unified position-dependent photon-number quantization in layered structures” defines local ladder operators for electric and magnetic fields, corresponding electric and magnetic LDOSs, and a total electromagnetic photon number. Its central qualitative result is that electric and magnetic local field temperatures oscillate with position and photon energy, whereas the effective photon number and field temperature associated with the total electromagnetic field are always position-independent in lossless media (Partanen et al., 2014).

At nanophotonic scales, locality enters through the emitter’s immediate environment. “Quasi-normal mode approach to the local-field problem in quantum optics” treats a finite-size dipole emitter inside a real cavity embedded in a lossy gold nanorod. The local Green function is decomposed into a homogeneous cavity term and a scattering term, and the scattering response is further separated into a quasi-normal-mode contribution and, near a metal boundary, an image-dipole contribution. The analytic decomposition

$$\mathbf{G}_{\rm loc}^{\rm anal} = \mathbf{G}_{\rm loc}^{\rm h} + \mathbf{G}_{\rm loc}^{\rm qsc} + \mathbf{G}_{\rm loc}^{\rm dsc}$$

encodes the local-field correction experienced by the emitter rather than a bulk-medium photon environment (Ge et al., 2015).

In this branch, the local-photon approach does not primarily mean a localized photon particle. It means that emission, damping, energy exchange, and force are governed by the local photonic environment experienced at the point of coupling.

3. Position-space local photons, blips, and locally acting Hamiltonians

A second branch uses “local photons” in the stronger sense of localized field quanta. In “Local photons,” the starting point is that the 1D free Maxwell equation admits wave packets of arbitrary shape that remain localized while propagating at the speed of light. The theory is then built from localized bosonic excitations called blips, labeled by propagation direction $s=\pm1$ and polarization $\lambda\in\{\mathrm H,\mathrm V\}$. Their dynamics are

$$a_{s\lambda}(x,t)=a_{s\lambda}(x-sct,0), \qquad \frac{\partial}{\partial t}a_{s\lambda}(x,t)=-sc\,\frac{\partial}{\partial x}a_{s\lambda}(x,t),$$

with equal-time commutator

$16\,\mathrm{MHz}$0

The electromagnetic field observables are not identical to the blips; they are obtained from them by a nonlocal regularization kernel. The same work emphasizes two structural moves: the explicit direction label $16\,\mathrm{MHz}$1, and the separation between the dynamical Hamiltonian and the positive energy observable. It further states that the formalism simplifies to standard quantum electrodynamics when restricted to an appropriate subspace of states (Hodgson et al., 2021).

“Locally-acting mirror Hamiltonians” develops this position-space quantization for interaction with local optical elements. By including both negative- and positive-frequency solutions of Maxwell’s equations, it constructs annihilation operators for highly localized field excitations with bosonic commutator relations and uses them to build Hamiltonians that act only near a two-sided semi-transparent mirror. The purpose is explicitly local modeling: the mirror Hamiltonian acts where the mirror is, rather than nonlocally on the whole field (Southall et al., 2019).

“A theory of local photons with applications in quantum field theory” generalizes the program to one and three dimensions. It makes a sharp distinction between particles, which can always be localized, and the electric and magnetic fields, which cannot; introduces negative-frequency photons from basic principles by removing the lower bound on the dynamical Hamiltonian; studies a linear optics experiment analogous to Fermi’s two-atom problem; and derives an attractive Casimir force between highly-reflecting metallic plates without invoking regularisation procedures (Hodgson, 2023). This suggests a local-particle, nonlocal-field ontology: the quanta are local, while the observable fields are derived, spatially extended operators.

The same research line has been extended to momentum. “Local-photon model of the momentum of light” defines the momentum of light as the generator for spatial translation,

$16\,\mathrm{MHz}$2

and studies photonic wave packets crossing from air into a denser dielectric medium using a locally acting mirror Hamiltonian. The analysis aligns with Minkowski’s theory and with the definition of the canonical momentum of light in quantum electrodynamics, while also emphasizing that the operator is derived from translation symmetry in the local-photon Hilbert space rather than by direct quantisation of a classical field formula (Waite et al., 2024).

Within this branch, locality is literal: the basic quanta are position-space excitations. The cost is equally literal: one must accept an enlarged Hilbert space, negative-frequency sectors, and a distinction between the generator of time evolution and the positive energy observable.

4. Local measurements, entanglement witnesses, and local operations

A different usage arises in quantum information, where the local-photon approach concerns what can be inferred from strictly local measurements on optical modes. “Witnessing trustworthy single-photon entanglement with local homodyne measurements” targets the delocalized single-photon state

$16\,\mathrm{MHz}$3

Each party measures a local quadrature $16\,\mathrm{MHz}$4 with sign binning, and a CHSH-type correlator is built from the outcomes. In the qubit limit, the ideal maximally entangled value is

$16\,\mathrm{MHz}$5

while the separable bound restricted to the single-photon subspace is

$16\,\mathrm{MHz}$6

The key trustworthy criterion is

$16\,\mathrm{MHz}$7

where $16\,\mathrm{MHz}$8 upper-bounds the multiphoton weight using phase-averaged local homodyne tomography. The experiment collected about $16\,\mathrm{MHz}$9 events per setting and reported $20$0 near $20$1, certifying genuine single-photon entanglement using local homodyne measurements only (Morin et al., 2012).

The multipartite extension replaces homodyne by local displacement followed by on/off detection. “Local and scalable detection of genuine multipartite single-photon path entanglement” constructs a witness for the $20$2 state using the local observable

$20$3

and requires only two basic measurement settings for any number of parties $20$4. For any bipartition, the biseparable bound reduces to the maximum eigenvalue of an $20$5 matrix, which can be computed efficiently. The experiment certified GME for heralded $20$6- and $20$7-partite states, reporting

$20$8

for $20$9, and

$$\hat a(x,\omega) = \sqrt{\frac{\varepsilon_0 \omega}{2\pi^2 \hbar \rho(x,\omega)}}\,\hat A^+(x,\omega), \qquad \rho(x,\omega)=\frac{2\omega}{\pi c^2 S}\,\mathrm{Im}[G(x,\omega,x)].$$0

for $$\hat a(x,\omega) = \sqrt{\frac{\varepsilon_0 \omega}{2\pi^2 \hbar \rho(x,\omega)}}\,\hat A^+(x,\omega), \qquad \rho(x,\omega)=\frac{2\omega}{\pi c^2 S}\,\mathrm{Im}[G(x,\omega,x)].$$1, with $$\hat a(x,\omega) = \sqrt{\frac{\varepsilon_0 \omega}{2\pi^2 \hbar \rho(x,\omega)}}\,\hat A^+(x,\omega), \qquad \rho(x,\omega)=\frac{2\omega}{\pi c^2 S}\,\mathrm{Im}[G(x,\omega,x)].$$2-values $$\hat a(x,\omega) = \sqrt{\frac{\varepsilon_0 \omega}{2\pi^2 \hbar \rho(x,\omega)}}\,\hat A^+(x,\omega), \qquad \rho(x,\omega)=\frac{2\omega}{\pi c^2 S}\,\mathrm{Im}[G(x,\omega,x)].$$3 and $$\hat a(x,\omega) = \sqrt{\frac{\varepsilon_0 \omega}{2\pi^2 \hbar \rho(x,\omega)}}\,\hat A^+(x,\omega), \qquad \rho(x,\omega)=\frac{2\omega}{\pi c^2 S}\,\mathrm{Im}[G(x,\omega,x)].$$4, respectively. The same work estimates scalability to about $$\hat a(x,\omega) = \sqrt{\frac{\varepsilon_0 \omega}{2\pi^2 \hbar \rho(x,\omega)}}\,\hat A^+(x,\omega), \qquad \rho(x,\omega)=\frac{2\omega}{\pi c^2 S}\,\mathrm{Im}[G(x,\omega,x)].$$5 parties under realistic conditions (Caspar et al., 2021).

Locality also appears in the distinction between local and global interference. “Local versus Global Two-Photon Interference in Quantum Networks” studies delocalized single photons distributed across time bins,

$$\hat a(x,\omega) = \sqrt{\frac{\varepsilon_0 \omega}{2\pi^2 \hbar \rho(x,\omega)}}\,\hat A^+(x,\omega), \qquad \rho(x,\omega)=\frac{2\omega}{\pi c^2 S}\,\mathrm{Im}[G(x,\omega,x)].$$6

and defines

$$\hat a(x,\omega) = \sqrt{\frac{\varepsilon_0 \omega}{2\pi^2 \hbar \rho(x,\omega)}}\,\hat A^+(x,\omega), \qquad \rho(x,\omega)=\frac{2\omega}{\pi c^2 S}\,\mathrm{Im}[G(x,\omega,x)].$$7

Local measurements yield standard Hong–Ou–Mandel dips at a given time bin, while global visibility is governed by the overlap $$\hat a(x,\omega) = \sqrt{\frac{\varepsilon_0 \omega}{2\pi^2 \hbar \rho(x,\omega)}}\,\hat A^+(x,\omega), \qquad \rho(x,\omega)=\frac{2\omega}{\pi c^2 S}\,\mathrm{Im}[G(x,\omega,x)].$$8 of the entire delocalized mode structure. The measured reference HOM visibility was $$\hat a(x,\omega) = \sqrt{\frac{\varepsilon_0 \omega}{2\pi^2 \hbar \rho(x,\omega)}}\,\hat A^+(x,\omega), \qquad \rho(x,\omega)=\frac{2\omega}{\pi c^2 S}\,\mathrm{Im}[G(x,\omega,x)].$$9, and the experiment demonstrated cases in which local HOM dips remained strong while global interference vanished because the synthesized mode vectors were orthogonal (Nitsche et al., 2020).

Local operations are equally central in continuous-variable entanglement engineering. “Strategies for enhancing quantum entanglement by local photon subtraction” analyzes local subtraction from a two-mode squeezed state using the entanglement gain $$T(x,\omega) = \frac{\hbar\omega}{k_B \ln\!\left(1+1/\langle\hat n(x,\omega)\rangle\right)},$$0, success probability $$T(x,\omega) = \frac{\hbar\omega}{k_B \ln\!\left(1+1/\langle\hat n(x,\omega)\rangle\right)},$$1, and entanglement gain rate $$T(x,\omega) = \frac{\hbar\omega}{k_B \ln\!\left(1+1/\langle\hat n(x,\omega)\rangle\right)},$$2. In the lossless limit, subtracting a single photon from one mode always produces the highest entanglement gain rate, while under loss there is no general optimal strategy; rather, the optimal subtraction pattern depends strongly on the losses on each mode individually (Bartley et al., 2012). “Increasing and decreasing entanglement characteristics for continuous variables by a local photon subtraction” reaches a complementary conclusion for non-Gaussian resources: local photon subtraction can enhance teleportation fidelity and second-order Einstein–Podolsky–Rosen-type correlation while reducing the degree of entanglement, with the effect being most prominent in the nearly zero-amplitude regime (Lee et al., 2013).

At a more foundational level, “Multiple photon detection and the localization of light energy” recasts detection in terms of phase-space cell filling for an ideal photon gas. The phase space is divided into cells of volume $$T(x,\omega) = \frac{\hbar\omega}{k_B \ln\!\left(1+1/\langle\hat n(x,\omega)\rangle\right)},$$3, and detection probabilities are derived from Bose-Einstein occupation statistics rather than from a continuous instantaneous intensity field. In this formulation, detection is a localization process: the detector probes whether a cell is occupied, and a detector response corresponds to a photon being localized into the detection volume (Lebedev, 2013).

In this entire branch, “local photon” means local access: local measurements, local detectors, local mode operations, and local conditioning. It does not require a commitment to strictly localized photon particles.

5. Local approximations in strong-field QED

In strong-field QED, the local-photon approach concerns the locality of the emission or pair-production rate with respect to the background field. The reference point is the locally constant field approximation (LCFA), whose domain of validity is roughly

$$T(x,\omega) = \frac{\hbar\omega}{k_B \ln\!\left(1+1/\langle\hat n(x,\omega)\rangle\right)},$$4

“From local to nonlocal: higher fidelity simulations of photon emission in intense laser pulses” argues that LCFA becomes unreliable when $$T(x,\omega) = \frac{\hbar\omega}{k_B \ln\!\left(1+1/\langle\hat n(x,\omega)\rangle\right)},$$5, because the process is not local on the scale of a laser cycle and because harmonic structure and interference are absent by construction. The proposed alternative uses the quasimomentum

$$T(x,\omega) = \frac{\hbar\omega}{k_B \ln\!\left(1+1/\langle\hat n(x,\omega)\rangle\right)},$$6

advances trajectories with ponderomotive-force equations, and evaluates emission rates in a locally monochromatic approximation. The total probability takes the form

$$T(x,\omega) = \frac{\hbar\omega}{k_B \ln\!\left(1+1/\langle\hat n(x,\omega)\rangle\right)},$$7

with the local rate built from monochromatic nonlinear Compton channels evaluated at the local cycle-averaged field strength and local frequency. The method captures harmonic peaks, the correct low-$$T(x,\omega) = \frac{\hbar\omega}{k_B \ln\!\left(1+1/\langle\hat n(x,\omega)\rangle\right)},$$8 limit, the first Compton edge, and chirp-induced softening, and it reproduces total probability and average emitted momentum fraction to within a few percent across the explored range, whereas LCFA can be wrong by more than $$T(x,\omega) = \frac{\hbar\omega}{k_B \ln\!\left(1+1/\langle\hat n(x,\omega)\rangle\right)},$$9 even at $$\langle Q(x,t)\rangle_\omega = \hbar\omega^2\,\mathrm{Im}[n(x,\omega)^2]\, \rho(x,\omega)\, \Big[\langle \hat\eta(x,\omega)\rangle-\langle \hat n(x,\omega)\rangle\Big],$$0, especially for yield (Blackburn et al., 2021).

A related development appears for pair creation. “A uniform locally constant field approximation for photon-seeded pair production” improves LCFA for the nonlinear Breit–Wheeler process by retaining the local Airy structure while inserting higher-order information about field variation into the Airy argument. The corrected argument $$\langle Q(x,t)\rangle_\omega = \hbar\omega^2\,\mathrm{Im}[n(x,\omega)^2]\, \rho(x,\omega)\, \Big[\langle \hat\eta(x,\omega)\rangle-\langle \hat n(x,\omega)\rangle\Big],$$1 depends on the local derivatives $$\langle Q(x,t)\rangle_\omega = \hbar\omega^2\,\mathrm{Im}[n(x,\omega)^2]\, \rho(x,\omega)\, \Big[\langle \hat\eta(x,\omega)\rangle-\langle \hat n(x,\omega)\rangle\Big],$$2 and is combined with an intensity filter $$\langle Q(x,t)\rangle_\omega = \hbar\omega^2\,\mathrm{Im}[n(x,\omega)^2]\, \rho(x,\omega)\, \Big[\langle \hat\eta(x,\omega)\rangle-\langle \hat n(x,\omega)\rangle\Big],$$3 to prevent use outside the trusted regime. Benchmarks against exact monochromatic results and numerical short-pulse calculations show that the ULCFA is more accurate than the LCFA in the regime $$\langle Q(x,t)\rangle_\omega = \hbar\omega^2\,\mathrm{Im}[n(x,\omega)^2]\, \rho(x,\omega)\, \Big[\langle \hat\eta(x,\omega)\rangle-\langle \hat n(x,\omega)\rangle\Big],$$4, and can be accurate down to $$\langle Q(x,t)\rangle_\omega = \hbar\omega^2\,\mathrm{Im}[n(x,\omega)^2]\, \rho(x,\omega)\, \Big[\langle \hat\eta(x,\omega)\rangle-\langle \hat n(x,\omega)\rangle\Big],$$5 at the $$\langle Q(x,t)\rangle_\omega = \hbar\omega^2\,\mathrm{Im}[n(x,\omega)^2]\, \rho(x,\omega)\, \Big[\langle \hat\eta(x,\omega)\rangle-\langle \hat n(x,\omega)\rangle\Big],$$6 level in the cases studied (King, 2019).

Here the adjective “local” has yet another meaning. The photon is not a local particle or a local detector event; the rate is local in the sense of being evaluated from the field and its derivatives at the emission phase. The conceptual contrast is therefore between local and nonlocal formation physics, not between global and local photon operators.

6. Localization, ontology, and quasi-local geometry

A more explicitly foundational literature asks whether photons are localizable at all. “Photon localization revisited” treats the Newton–Wigner–Wightman theorem as the basic obstruction: a Lorentz covariant massive system is always localizable, whereas the only localizable massless elementary system has spin zero; a free photon is therefore not localizable. The paper’s proposed resolution is conditional localization: interaction with media, boundaries, or cavities gives the photon an effective mass, producing a polariton-like composite excitation that is localizable. This is embedded in a broader “Quantum Field Ontology,” where the field is primary and localized particle-like manifestations arise through the “Eventualization Principle,” stated as “Quantum fields can effect macroscopic systems only through eventualization” (Ojima et al., 2015).

A different line derives Maxwell theory from a photon Hamilton–Jacobi equation and then interrogates the trajectory picture. “From the Photon to Maxwell Equation” starts from

$$\langle Q(x,t)\rangle_\omega = \hbar\omega^2\,\mathrm{Im}[n(x,\omega)^2]\, \rho(x,\omega)\, \Big[\langle \hat\eta(x,\omega)\rangle-\langle \hat n(x,\omega)\rangle\Big],$$7

and, via a null $$\langle Q(x,t)\rangle_\omega = \hbar\omega^2\,\mathrm{Im}[n(x,\omega)^2]\, \rho(x,\omega)\, \Big[\langle \hat\eta(x,\omega)\rangle-\langle \hat n(x,\omega)\rangle\Big],$$8-form field $$\langle Q(x,t)\rangle_\omega = \hbar\omega^2\,\mathrm{Im}[n(x,\omega)^2]\, \rho(x,\omega)\, \Big[\langle \hat\eta(x,\omega)\rangle-\langle \hat n(x,\omega)\rangle\Big],$$9, obtains the vacuum Maxwell equation $$\mathbf{G}_{\rm loc}^{\rm anal} = \mathbf{G}_{\rm loc}^{\rm h} + \mathbf{G}_{\rm loc}^{\rm qsc} + \mathbf{G}_{\rm loc}^{\rm dsc}$$0. It also writes a Schrödinger-like form of Maxwell’s equations and studies whether the resulting field can define Bohm-like photon trajectories. The conclusion is cautious: pulse reshaping in vacuum, the behavior of the electromagnetic energy-momentum extensor, and a generalized Hamilton–Jacobi equation with a quantum potential all undermine a naive identification of field maxima or flow lines with literal photon trajectories. The work therefore treats the local-photon picture as mathematically suggestive but physically problematic when pushed into a particle-trajectory ontology (Jr, 2017).

In general relativity, locality becomes quasi-local geometry. “Quasi-local photon surfaces in general spherically symmetric spacetimes” defines a photon sphere directly from codimension-$$\mathbf{G}_{\rm loc}^{\rm anal} = \mathbf{G}_{\rm loc}^{\rm h} + \mathbf{G}_{\rm loc}^{\rm qsc} + \mathbf{G}_{\rm loc}^{\rm dsc}$$1 geometry, requiring

$$\mathbf{G}_{\rm loc}^{\rm anal} = \mathbf{G}_{\rm loc}^{\rm h} + \mathbf{G}_{\rm loc}^{\rm qsc} + \mathbf{G}_{\rm loc}^{\rm dsc}$$2

This construction generalizes the Claudel–Virbhadra–Ellis notion without referring to an umbilical hypersurface and explicitly rules out degenerate flat-spacetime examples unrelated to gravity. In the Oppenheimer–Snyder collapse model, the photon surface appears before the event horizon, and for large initial radius the time delay approaches

$$\mathbf{G}_{\rm loc}^{\rm anal} = \mathbf{G}_{\rm loc}^{\rm h} + \mathbf{G}_{\rm loc}^{\rm qsc} + \mathbf{G}_{\rm loc}^{\rm dsc}$$3

In marginally bounded Lemaître–Tolman–Bondi collapse, the photon surface is determined by a second-order differential equation and persists in both black-hole and naked-singularity cases (Cao et al., 2019).

This foundational and geometric literature shows that the local-photon approach can be ontological, dynamical, or quasi-local, depending on whether the central question is localizability of excitations, trajectory language, or confinement of null geodesics by strong gravity.

Across all these branches, the local-photon approach denotes a methodological shift: photonic physics is specified by what is locally available to an emitter, detector, medium, interface, background field, or codimension-$$\mathbf{G}_{\rm loc}^{\rm anal} = \mathbf{G}_{\rm loc}^{\rm h} + \mathbf{G}_{\rm loc}^{\rm qsc} + \mathbf{G}_{\rm loc}^{\rm dsc}$$4 surface, rather than by globally defined normal modes alone. The result is not a single doctrine but a technically heterogeneous framework for re-expressing photon theory in local terms.