Directional Waveguide–Emitter Coupling Interface

• Directional waveguide–emitter coupling is a light–matter interface where emitters asymmetrically interact with counterpropagating guided modes via spin–orbit effects and mirror-symmetry breaking.
• Key mechanisms include local spin–orbit interactions, multi-emitter interference, and antenna-based phase engineering that create direction-selective emission.
• This interface underpins applications in quantum routing, nonreciprocal photonic devices, and integrated circuits by exploiting tailored evanescent fields and emitter alignment.

Directional waveguide–emitter coupling interface denotes a class of light–matter interfaces in which a localized emitter couples asymmetrically to the two counterpropagating modes of a waveguide, so that spontaneous emission, scattering, absorption, or collective decay become direction-selective. In the literature, this asymmetry is realized through non-transversal guided fields and spin–orbit interaction of light, mirror-symmetry breaking and evanescent angular spectra, multi-emitter interference at fixed propagation phase, and engineered antenna or cavity geometries. Representative platforms include vacuum-clad silica nanofibers with atoms, glide-plane photonic-crystal waveguides with quantum dots, quarter-wavelength-spaced superconducting qubits in microwave transmission lines, planar TiO$_2$ waveguides assisted by Yagi–Uda antennas, and wavelength-scale deformed microdisks (Mitsch et al., 2014, Söllner et al., 2014, Kannan et al., 2022, Yu et al., 2024, Redding et al., 2011).

1. Electrodynamic definition and symmetry structure

A standard formulation resolves the spontaneous-emission rate of an emitter with dipole operator $\mathbf d$ at position $\mathbf r_0$ into the two counterpropagating guided modes,

$$\Gamma_+ = \frac{2\pi}{\hbar}\,|\mathbf d\cdot \mathbf E_+(\mathbf r_0)|^2\,\rho_+(\omega_0),\qquad \Gamma_- = \frac{2\pi}{\hbar}\,|\mathbf d\cdot \mathbf E_-(\mathbf r_0)|^2\,\rho_-(\omega_0),$$

or, equivalently,

$$\Gamma_{\pm}=\frac{2\omega_0^2}{\hbar\epsilon_0 c^2}\,\mathbf d^{T}\cdot \mathrm{Im}\,G_{\pm}(\mathbf r_0,\mathbf r_0;\omega_0)\cdot \mathbf d^*.$$

In tightly confined guides, $\mathbf E_{\pm}(\mathbf r_0)$ is neither purely transverse nor symmetric under $z\rightarrow -z$, and the local polarization ellipticity depends on propagation direction. In the nanofiber HE$_{11}$ mode, the electric spin density

$$S_e(\mathbf r)=\frac{\epsilon_0}{4\omega}\,\mathrm{Im}\!\left[\mathbf E^*(\mathbf r)\times \mathbf E(\mathbf r)\right]$$

reverses sign when the propagation direction is reversed, which allows a dipole of given helicity to couple preferentially to one direction (Mitsch et al., 2014).

A compact measure of asymmetry is the directionality parameter

$D=\frac{P_+-P_-}{P_++P_-}\in[-1,+1].$

A symmetry-based treatment shows that, for emitters near a waveguide invariant under mirror operations, directionality is mostly due to mirror-symmetry breaking caused by the axial character of the angular momentum of the emitted light. For a centered emitter with both relevant mirror symmetries, $\mathbf d$0 at $\mathbf d$1, while for single-mode planar waveguides the dependence takes the explicit form

$\mathbf d$2

with the exponential dependence traced to a property of the evanescent angular spectrum (Lamprianidis et al., 2019). This establishes that the sign of the angular momentum along an axis transverse to the waveguide determines the preferential coupling direction, while helicity-dependent effects can appear when displacement breaks another mirror symmetry.

2. Physical mechanisms of directional coupling

One mechanism is local spin–orbit interaction of light in subwavelength confinement. In the nanofiber geometry of Mitsch et al., a circular dipole $\mathbf d$3 can couple nearly exclusively to one propagation direction, whereas a $\mathbf d$4 transition $\mathbf d$5 couples equally to both directions because the HE$\mathbf d$6 modes are always $\mathbf d$7-polarized along $\mathbf d$8 (Mitsch et al., 2014). Closely related behavior underlies chiral photonic-crystal waveguides, where time-reversal symmetry implies $\mathbf d$9, so a $\mathbf r_0$0 dipole overlaps strongly with one guided mode and weakly with its counterpropagating partner (Söllner et al., 2014).

A second mechanism is interference between spatially separated emitters. For two qubits separated by $\mathbf r_0$1, the right- and left-going output fields can be written as

$\mathbf r_0$2

$\mathbf r_0$3

and the off-diagonal coherences produce destructive interference in one direction and constructive interference in the other. Preparing

$\mathbf r_0$4

yields purely right- or left-going emission in the idealized lossless case (Gheeraert et al., 2020).

A third mechanism uses antenna-mediated phase engineering. In a planar TiO$\mathbf r_0$5 waveguide, a gold Yagi–Uda antenna consisting of a feed rod, one reflector and three directors is designed so that scattering from its elements acquires an approximately $\mathbf r_0$6 phase difference. Constructive interference on the forward side and destructive interference on the backward side then yield in-plane directivity into the guided TE$\mathbf r_0$7 mode (Yu et al., 2024).

A fourth mechanism is wave-optical splitting of clockwise and counter-clockwise pseudo-orbits in wavelength-scale resonators. In a deformed microdisk, the Goos–Hänchen shift

$\mathbf r_0$8

and Fresnel filtering generate a spatial separation of the CW and CCW ray orbits; by placing a waveguide tangentially at a suitable boundary location, one selectively extracts one circulation sense while leaving the opposite circulation inside the cavity (Redding et al., 2011).

3. Optical realizations

The paradigmatic nanofiber–atom realization uses cesium atoms near a vacuum-clad silica nanofiber with fiber radius $\mathbf r_0$9, refractive indices $$\Gamma_+ = \frac{2\pi}{\hbar}\,|\mathbf d\cdot \mathbf E_+(\mathbf r_0)|^2\,\rho_+(\omega_0),\qquad \Gamma_- = \frac{2\pi}{\hbar}\,|\mathbf d\cdot \mathbf E_-(\mathbf r_0)|^2\,\rho_-(\omega_0),$$0 and $$\Gamma_+ = \frac{2\pi}{\hbar}\,|\mathbf d\cdot \mathbf E_+(\mathbf r_0)|^2\,\rho_+(\omega_0),\qquad \Gamma_- = \frac{2\pi}{\hbar}\,|\mathbf d\cdot \mathbf E_-(\mathbf r_0)|^2\,\rho_-(\omega_0),$$1, single-mode guidance of the fundamental HE$$\Gamma_+ = \frac{2\pi}{\hbar}\,|\mathbf d\cdot \mathbf E_+(\mathbf r_0)|^2\,\rho_+(\omega_0),\qquad \Gamma_- = \frac{2\pi}{\hbar}\,|\mathbf d\cdot \mathbf E_-(\mathbf r_0)|^2\,\rho_-(\omega_0),$$2 mode at $$\Gamma_+ = \frac{2\pi}{\hbar}\,|\mathbf d\cdot \mathbf E_+(\mathbf r_0)|^2\,\rho_+(\omega_0),\qquad \Gamma_- = \frac{2\pi}{\hbar}\,|\mathbf d\cdot \mathbf E_-(\mathbf r_0)|^2\,\rho_-(\omega_0),$$3, and an evanescent decay length $$\Gamma_+ = \frac{2\pi}{\hbar}\,|\mathbf d\cdot \mathbf E_+(\mathbf r_0)|^2\,\rho_+(\omega_0),\qquad \Gamma_- = \frac{2\pi}{\hbar}\,|\mathbf d\cdot \mathbf E_-(\mathbf r_0)|^2\,\rho_-(\omega_0),$$4. The atoms are trapped in a single-color dipole trap at $$\Gamma_+ = \frac{2\pi}{\hbar}\,|\mathbf d\cdot \mathbf E_+(\mathbf r_0)|^2\,\rho_+(\omega_0),\qquad \Gamma_- = \frac{2\pi}{\hbar}\,|\mathbf d\cdot \mathbf E_-(\mathbf r_0)|^2\,\rho_-(\omega_0),$$5 plus $$\Gamma_+ = \frac{2\pi}{\hbar}\,|\mathbf d\cdot \mathbf E_+(\mathbf r_0)|^2\,\rho_+(\omega_0),\qquad \Gamma_- = \frac{2\pi}{\hbar}\,|\mathbf d\cdot \mathbf E_-(\mathbf r_0)|^2\,\rho_-(\omega_0),$$6 blue-detuned light, with trap minima at $$\Gamma_+ = \frac{2\pi}{\hbar}\,|\mathbf d\cdot \mathbf E_+(\mathbf r_0)|^2\,\rho_+(\omega_0),\qquad \Gamma_- = \frac{2\pi}{\hbar}\,|\mathbf d\cdot \mathbf E_-(\mathbf r_0)|^2\,\rho_-(\omega_0),$$7 and a bias field of $$\Gamma_+ = \frac{2\pi}{\hbar}\,|\mathbf d\cdot \mathbf E_+(\mathbf r_0)|^2\,\rho_+(\omega_0),\qquad \Gamma_- = \frac{2\pi}{\hbar}\,|\mathbf d\cdot \mathbf E_-(\mathbf r_0)|^2\,\rho_-(\omega_0),$$8 along $$\Gamma_+ = \frac{2\pi}{\hbar}\,|\mathbf d\cdot \mathbf E_+(\mathbf r_0)|^2\,\rho_+(\omega_0),\qquad \Gamma_- = \frac{2\pi}{\hbar}\,|\mathbf d\cdot \mathbf E_-(\mathbf r_0)|^2\,\rho_-(\omega_0),$$9. For the cycling transition $$\Gamma_{\pm}=\frac{2\omega_0^2}{\hbar\epsilon_0 c^2}\,\mathbf d^{T}\cdot \mathrm{Im}\,G_{\pm}(\mathbf r_0,\mathbf r_0;\omega_0)\cdot \mathbf d^*.$$0, only $$\Gamma_{\pm}=\frac{2\omega_0^2}{\hbar\epsilon_0 c^2}\,\mathbf d^{T}\cdot \mathrm{Im}\,G_{\pm}(\mathbf r_0,\mathbf r_0;\omega_0)\cdot \mathbf d^*.$$1 emission is possible. On the left side, $$\Gamma_{\pm}=\frac{2\omega_0^2}{\hbar\epsilon_0 c^2}\,\mathbf d^{T}\cdot \mathrm{Im}\,G_{\pm}(\mathbf r_0,\mathbf r_0;\omega_0)\cdot \mathbf d^*.$$2 of the guided photons go into $$\Gamma_{\pm}=\frac{2\omega_0^2}{\hbar\epsilon_0 c^2}\,\mathbf d^{T}\cdot \mathrm{Im}\,G_{\pm}(\mathbf r_0,\mathbf r_0;\omega_0)\cdot \mathbf d^*.$$3 and $$\Gamma_{\pm}=\frac{2\omega_0^2}{\hbar\epsilon_0 c^2}\,\mathbf d^{T}\cdot \mathrm{Im}\,G_{\pm}(\mathbf r_0,\mathbf r_0;\omega_0)\cdot \mathbf d^*.$$4 into $$\Gamma_{\pm}=\frac{2\omega_0^2}{\hbar\epsilon_0 c^2}\,\mathbf d^{T}\cdot \mathrm{Im}\,G_{\pm}(\mathbf r_0,\mathbf r_0;\omega_0)\cdot \mathbf d^*.$$5; on the right side, $$\Gamma_{\pm}=\frac{2\omega_0^2}{\hbar\epsilon_0 c^2}\,\mathbf d^{T}\cdot \mathrm{Im}\,G_{\pm}(\mathbf r_0,\mathbf r_0;\omega_0)\cdot \mathbf d^*.$$6 go into $$\Gamma_{\pm}=\frac{2\omega_0^2}{\hbar\epsilon_0 c^2}\,\mathbf d^{T}\cdot \mathrm{Im}\,G_{\pm}(\mathbf r_0,\mathbf r_0;\omega_0)\cdot \mathbf d^*.$$7 and $$\Gamma_{\pm}=\frac{2\omega_0^2}{\hbar\epsilon_0 c^2}\,\mathbf d^{T}\cdot \mathrm{Im}\,G_{\pm}(\mathbf r_0,\mathbf r_0;\omega_0)\cdot \mathbf d^*.$$8 into $$\Gamma_{\pm}=\frac{2\omega_0^2}{\hbar\epsilon_0 c^2}\,\mathbf d^{T}\cdot \mathrm{Im}\,G_{\pm}(\mathbf r_0,\mathbf r_0;\omega_0)\cdot \mathbf d^*.$$9, corresponding to an imbalance ratio $\mathbf E_{\pm}(\mathbf r_0)$0. For the multibranch decay $\mathbf E_{\pm}(\mathbf r_0)$1 with $\mathbf E_{\pm}(\mathbf r_0)$2, the measured asymmetries were $\mathbf E_{\pm}(\mathbf r_0)$3 on the left side and $\mathbf E_{\pm}(\mathbf r_0)$4 on the right side, consistent with symmetric $\mathbf E_{\pm}(\mathbf r_0)$5 decay and chiral $\mathbf E_{\pm}(\mathbf r_0)$6 decay (Mitsch et al., 2014).

A photonic-crystal implementation employs a glide-plane waveguide in a GaAs membrane. The structure is engineered with hole radius $\mathbf E_{\pm}(\mathbf r_0)$7, membrane thickness $\mathbf E_{\pm}(\mathbf r_0)$8, GaAs refractive index $\mathbf E_{\pm}(\mathbf r_0)$9, and a guided band below the light line at $z\rightarrow -z$0 with group index $z\rightarrow -z$1. The glide operation removes the mirror plane and produces modes with local circular polarization. Experimentally, a single quantum dot emitted into the waveguide with directionality of more than $z\rightarrow -z$2, waveguide-coupling efficiency $z\rightarrow -z$3, and directional $z\rightarrow -z$4-factor $z\rightarrow -z$5. For the best single-QD line, the measured directionality factor was $z\rightarrow -z$6 (Söllner et al., 2014).

A hybrid plasmonic/photonic realization places a gold Yagi–Uda antenna atop an $z\rightarrow -z$7 TiO$z\rightarrow -z$8 slab of refractive index $z\rightarrow -z$9 on glass. A CdSe/CdS quantum dot placed $_{11}$0 from the feed tip excites the antenna at $_{11}$1. After optimization, the antenna dimensions are $_{11}$2, $_{11}$3, $_{11}$4, $_{11}$5, and $_{11}$6. Full-wave FEM gives $_{11}$7 and directivity $_{11}$8 with $_{11}$9, corresponding to $$S_e(\mathbf r)=\frac{\epsilon_0}{4\omega}\,\mathrm{Im}\!\left[\mathbf E^*(\mathbf r)\times \mathbf E(\mathbf r)\right]$$0 of the plasmonically enhanced emission propagating toward $$S_e(\mathbf r)=\frac{\epsilon_0}{4\omega}\,\mathrm{Im}\!\left[\mathbf E^*(\mathbf r)\times \mathbf E(\mathbf r)\right]$$1. Experimentally, the coupling efficiency was $$S_e(\mathbf r)=\frac{\epsilon_0}{4\omega}\,\mathrm{Im}\!\left[\mathbf E^*(\mathbf r)\times \mathbf E(\mathbf r)\right]$$2 and the front-to-back ratio was $$S_e(\mathbf r)=\frac{\epsilon_0}{4\omega}\,\mathrm{Im}\!\left[\mathbf E^*(\mathbf r)\times \mathbf E(\mathbf r)\right]$$3, so that $$S_e(\mathbf r)=\frac{\epsilon_0}{4\omega}\,\mathrm{Im}\!\left[\mathbf E^*(\mathbf r)\times \mathbf E(\mathbf r)\right]$$4 of guided photons propagate in the $$S_e(\mathbf r)=\frac{\epsilon_0}{4\omega}\,\mathrm{Im}\!\left[\mathbf E^*(\mathbf r)\times \mathbf E(\mathbf r)\right]$$5 direction; polarization analysis confirmed the TE nature of the guided mode (Yu et al., 2024).

An asymmetry-based dielectric implementation uses a GaAs photonic wire waveguide with a two-step stair-like cross section. For the optimum asymmetry $$S_e(\mathbf r)=\frac{\epsilon_0}{4\omega}\,\mathrm{Im}\!\left[\mathbf E^*(\mathbf r)\times \mathbf E(\mathbf r)\right]$$6, FEM yields $$S_e(\mathbf r)=\frac{\epsilon_0}{4\omega}\,\mathrm{Im}\!\left[\mathbf E^*(\mathbf r)\times \mathbf E(\mathbf r)\right]$$7 and $$S_e(\mathbf r)=\frac{\epsilon_0}{4\omega}\,\mathrm{Im}\!\left[\mathbf E^*(\mathbf r)\times \mathbf E(\mathbf r)\right]$$8, with $$S_e(\mathbf r)=\frac{\epsilon_0}{4\omega}\,\mathrm{Im}\!\left[\mathbf E^*(\mathbf r)\times \mathbf E(\mathbf r)\right]$$9 only approximately $D=\frac{P_+-P_-}{P_++P_-}\in[-1,+1].$0 below the symmetric rectangular-waveguide $D=\frac{P_+-P_-}{P_++P_-}\in[-1,+1].$1. Full 3D FDTD with $D=\frac{P_+-P_-}{P_++P_-}\in[-1,+1].$2 independent circular dipoles gives $D=\frac{P_+-P_-}{P_++P_-}\in[-1,+1].$3, confirming that approximately $D=\frac{P_+-P_-}{P_++P_-}\in[-1,+1].$4 of the ensemble emission is steered into a single direction. Wrapping the same stair profile into a $D=\frac{P_+-P_-}{P_++P_-}\in[-1,+1].$5-diameter microdisk gives a TE$D=\frac{P_+-P_-}{P_++P_-}\in[-1,+1].$6 mode at $D=\frac{P_+-P_-}{P_++P_-}\in[-1,+1].$7 with $D=\frac{P_+-P_-}{P_++P_-}\in[-1,+1].$8, and the bus-coupled structure yields $D=\frac{P_+-P_-}{P_++P_-}\in[-1,+1].$9 (Lin et al., 2019).

In deformed microdisk lasers, a straight dielectric waveguide separated by a sub-wavelength gap $\mathbf d$00 from a deformed cavity of refractive index $\mathbf d$01 enables selective extraction of CW or CCW lasing emission. Full-wave calculations and experiment show peaks of $\mathbf d$02 near $\mathbf d$03 and $\mathbf d$04, and experimentally $\mathbf d$05, $\mathbf d$06, and $\mathbf d$07. Lasing threshold at $\mathbf d$08 was $\mathbf d$09 (Redding et al., 2011).

4. Microwave and collective waveguide-QED interfaces

In superconducting circuits, a central architecture is the artificial molecule of two qubits coupled to a bidirectional waveguide a quarter wavelength apart. For $\mathbf d$10, waveguide-mediated exchange gives $\mathbf d$11, and a direct tunable coupling $\mathbf d$12 cancels it. The same device can operate as a directional emitter, a directional receiver, or a transparent pass-through element. For a time-symmetric $\mathbf d$13 wave packet,

$\mathbf d$14

the required decay modulation is

$\mathbf d$15

In resonator-mediated schemes, $\mathbf d$16 gives pulse fidelity above $\mathbf d$17; residual coupling-cancellation errors of order $\mathbf d$18 reduce directionality by less than $\mathbf d$19, and separation errors $\mathbf d$20 or frequency mismatch $\mathbf d$21 still keep $\mathbf d$22 (Gheeraert et al., 2020).

An experimental realization uses two frequency-tunable transmon qubits strongly coupled to a bidirectional coplanar waveguide with $\mathbf d$23. The total exchange is $\mathbf d$24, and the operation point $\mathbf d$25 cancels the static waveguide-mediated term. When the qubits are prepared in

$\mathbf d$26

interference routes the emitted photon to a chosen direction. Experimentally, for $\mathbf d$27 the measured photon number was $\mathbf d$28 with $\mathbf d$29, giving single-photon fidelity $\mathbf d$30 to $\mathbf d$31; for $\mathbf d$32 the results were $\mathbf d$33 and fidelity $\mathbf d$34 to $\mathbf d$35. The extinction ratio exceeded $\mathbf d$36 and the emission efficiency was approximately $\mathbf d$37 (Kannan et al., 2022).

A related two-qubit analysis identifies the jump operators

$\mathbf d$38

with null-eigenstates

$\mathbf d$39

Under the controlled antiresonance conditions $\mathbf d$40 and $\mathbf d$41, one obtains $\mathbf d$42 and $\mathbf d$43. Starting from $\mathbf d$44, the first quantum jump projects onto $\mathbf d$45 or $\mathbf d$46 with equal probability $\mathbf d$47, and the second photon must emerge in the same direction, yielding the two-photon N00N state $\mathbf d$48 up to overall phase (Maffei et al., 2024).

Long-range collective directionality has also been realized with two quantum dots embedded in a bidirectional photonic-crystal waveguide and separated by $\mathbf d$49, corresponding to $\mathbf d$50 effective wavelengths. The guided mode mediates dissipative coupling $\mathbf d$51 and dispersive coupling $\mathbf d$52, producing dressed states $\mathbf d$53 with shifted energies $\mathbf d$54. Choosing the relative driving phase $\mathbf d$55 yields $\mathbf d$56 and emission entirely to the right, while $\mathbf d$57 yields $\mathbf d$58 and emission entirely to the left. In the same platform, continuous driving gives direction-dependent photon statistics, and under pulsed full inversion the measured same-port correlations $\mathbf d$59 and $\mathbf d$60 show partial bunching of approximately $\mathbf d$61–$\mathbf d$62, while $\mathbf d$63 (Henke et al., 7 Apr 2026).

5. Figures of merit and design rules

The literature uses several closely related performance measures. For guided-mode loading, the usual $\mathbf d$64-factor is

$\mathbf d$65

with directional variants

$\mathbf d$66

and

$\mathbf d$67

Other common measures are the power asymmetry

$\mathbf d$68

the coupling efficiency $\mathbf d$69, and the antenna front-to-back ratio $\mathbf d$70 (Söllner et al., 2014, Lamprianidis et al., 2019, Yu et al., 2024).

Practical design rules differ by platform but show recurring themes. For nanofibers, reported guidelines are $\mathbf d$71, emitter placement at $\mathbf d$72, use of a pure circular dipole transition $\mathbf d$73 aligned to the local transverse spin, a quantization axis perpendicular to the fiber axis and in the plane of dipole emission, and suppression of $\mathbf d$74-dipole decay to reduce symmetric background (Mitsch et al., 2014). From the symmetry perspective, maximizing the steepness of $\mathbf d$75 versus transverse angular momentum favors operation near the single-mode cutoff so that $\mathbf d$76 is as large as possible, with emitters kept close to the evanescent field and the transverse axis chosen for quantization to achieve strict sign locking (Lamprianidis et al., 2019).

In antenna-assisted planar waveguides, the design process starts from effective wavelengths $\mathbf d$77 and $\mathbf d$78, then scales feed, reflector, director, and spacing dimensions according to RF Yagi–Uda rules before full FEM optimization. The cited design uses $\mathbf d$79, $\mathbf d$80, a dipole parallel to $\mathbf d$81 at $\mathbf d$82, and a $\mathbf d$83 feed gap (Yu et al., 2024). In microwave two-emitter interfaces, optimal directionality requires inter-emitter spacing $\mathbf d$84 and control coupling chosen so that the coherent exchange is canceled, namely $\mathbf d$85 or, equivalently in the antiresonant condition, $\mathbf d$86 (Maffei et al., 2024). For long-range photonic-crystal molecules, the reported guidelines are to choose the coupling phase near $\mathbf d$87, work near the band edge to boost $\mathbf d$88, and use independently tunable segments to align emitters into resonance; in the cited device, $\mathbf d$89 was achieved (Henke et al., 7 Apr 2026).

6. Conceptual clarifications, applications, and extensions

A recurrent misconception is that all directional coupling can be reduced to a single notion of spin–momentum locking. The symmetry analysis shows a more specific statement: independently of emitter displacement, directionality is mostly due to mirror-symmetry breaking caused by the axial character of the angular momentum of the emitted light, whereas the chiral character of the handedness of the emission yields a binary and less pronounced effect when displacement breaks another mirror symmetry. The same work also shows that choosing a different angular-momentum axis changes whether strict locking exists and how directionality depends on angular momentum (Lamprianidis et al., 2019).

Functionally, directional interfaces support single-photon routing, quantum switching, non-reciprocal emission, and cascaded interactions. The nanofiber platform explicitly identifies integrated quantum photonic circuits, on-chip optical isolators, chiral quantum networks, and single-photon diodes and circulators as target applications (Mitsch et al., 2014). In chiral photonic circuits, near-unity directional coupling enables optical diodes and circulators at the single-photon level and motivates a deterministic photon–photon CNOT gate with entanglement fidelity $\mathbf d$90 and worst-case fidelity $\mathbf d$91 (Söllner et al., 2014). A $\mathbf d$92-type emitter coupled to a chiral waveguide extends the same interface concept to quantum-memory and gate operations: for a Gaussian photon pulse of bandwidth $\mathbf d$93 and coupling ratio $\mathbf d$94, the reported averages are $\mathbf d$95, $\mathbf d$96, $\mathbf d$97, $\mathbf d$98, and $\mathbf d$99, $\mathbf r_0$00 (Li et al., 2018).

The interface also has non-Markovian and network-level extensions. Near a waveguide continuum edge, the density of states singularity produces a non-local memory kernel and allows exact control-pulse prescriptions for shaped emission and absorption in a $\mathbf r_0$01-type system; with free-space leakage $\mathbf r_0$02, the cited fidelities exceed $\mathbf r_0$03, and for slow pulses with partial photonic-crystal cladding the interface fidelity exceeds $\mathbf r_0$04 (Chen et al., 2011). At the network scale, phase-tunable waveguide-QED architectures use engineered propagation and coupling phases so that coherent exchange and collective dissipation balance to suppress the backward channel while retaining a finite forward channel. In that framework, perfect nonreciprocity corresponds to $\mathbf r_0$05, equivalently $\mathbf r_0$06, and the giant-small-emitter mirror-terminated configuration simultaneously achieves perfect nonreciprocity and battery-dominated storage (Guo et al., 21 May 2026).

Taken together, these results suggest that a directional waveguide–emitter coupling interface is not a single device architecture but a unifying operational principle. Across atomic, semiconductor, plasmonic, cavity, and superconducting implementations, the central task is the same: engineer the local vectorial mode structure or the collective interference pattern so that one propagation channel becomes bright while the opposite channel becomes dark.