Unidirectional Guided Resonances (UGRs)

• UGRs are leaky eigenmodes in open photonic structures that radiate unidirectionally without needing a mirror through engineered interference and symmetry breaking.
• Researchers employ methods like TCMT, perturbation theory, and polarization singularity analysis to design systems with asymmetry ratios up to 65 dB and quality factors reaching 1.6×10⁵.
• Practical implementations of UGRs enable energy-efficient optical couplers, on-chip lasers, and spin-photon interfaces in CMOS-compatible nanophotonic devices.

Searching arXiv for recent and foundational papers on unidirectional guided resonances. Unidirectional guided resonances (UGRs) are leaky eigenmodes of dielectric photonic-crystal slabs or other open periodic photonic structures that radiate entirely toward one side without the need for a reflective mirror on the opposite side (Yin et al., 2022). In one rigorous formulation for a 1D-periodic structure with a single radiation channel, a UGR is a complex-frequency solution satisfying $c_0^+=0$ and $c_0^-\neq0$, so that all power leaks only downward; the opposite choice gives the upward-radiating case (Yuan et al., 2 Oct 2025). Closely related work in nanophotonics demonstrated unidirectional excitation of dielectric waveguide and surface plasmon-polariton modes from an all-dielectric nanoantenna, where asymmetrical excitation of higher multipoles creates a chiral near field that mimics a rotating emitter (Lee et al., 2015). Across these settings, the unifying theme is one-sided coupling to guided or radiative channels by interference, symmetry breaking, and, in many platforms, topological polarization singularities.

1. Definition and distinguishing characteristics

In the photonic-crystal-slab literature, UGRs are usually defined as optical modes that radiate towards one side without the need for mirrors on the other, and are represented from a topological perspective by the merged points of paired, single-sided, half-integer topological charges (Yin et al., 2022). The relevant observable is the asymmetry between the two radiation channels. One commonly used ratio is

$$\eta \equiv \gamma_{\mathrm{top}}/\gamma_{\mathrm{bottom}} \to \infty,$$

which expresses vanishing decay into one side at the UGR point (Yin et al., 2022). Other papers use

$A = 10\log_{10}(P_{\mathrm{up}}/P_{\mathrm{down}})$

for radiation asymmetry (Wang et al., 2023), or

$\tau = |c_0^+/c_0^-|^2$

with UGR corresponding to $\tau=0$ in the one-channel formulation (Yuan et al., 2 Oct 2025).

A persistent misconception is that strict one-sided radiation in planar photonics requires a bottom mirror. The core UGR papers explicitly state the opposite: one-sided leakage is achieved with no mirror placed on the opposite side (Yin et al., 2022, Wang et al., 2023). Another misconception is that UGRs are identical to generic one-way waveguiding. In the gyromagnetic periodic dielectric chain, the reported effect is a unidirectional waveguide mode with $\omega(k)\neq\omega(-k)$ produced by broken time-reversal and inversion-related symmetries, not a one-sided leaky resonance of the mirror-free type emphasized in UGR studies (Li et al., 2019). This suggests a useful distinction between nonreciprocal one-way propagation and reciprocal or quasi-reciprocal one-sided radiation.

2. Topological origin in photonic-crystal slabs

The modern topological picture starts from polarization singularities in momentum space. In the far-field polarization field, an integer topological charge is defined by

$q=\frac{1}{2\pi}\oint_C d\phi(k),$

where $\phi(k)$ is the polarization angle around a closed loop $C$ in $c_0^-\neq0$0-space (Yin et al., 2022). A conventional vortex center or V point has integer charge $c_0^-\neq0$1, while a circular-polarization singularity or C point carries half-integer charge $c_0^-\neq0$2 (Yin et al., 2022).

In broken-symmetry photonic-crystal slabs, a symmetry-protected bound state in the continuum at $c_0^-\neq0$3 can split into half-integer topological charges. Yin and co-workers showed that when a pair of half-integer charges in the polarization field bounce into each other in momentum space, the downward channel is forced to vanish while the upward channel remains finite, producing a unidirectional bound state in the continuum, i.e. a UGR (Yin et al., 2019). In that framework, the asymmetry

$c_0^-\neq0$4

diverges because $c_0^-\neq0$5 while $c_0^-\neq0$6 (Yin et al., 2019).

A particularly explicit realization was given by Wang et al. in a broken-$c_0^-\neq0$7 grating on 340 nm silicon-on-insulator. There, a symmetry-protected BIC at $c_0^-\neq0$8 carries an integer topological charge $c_0^-\neq0$9. Breaking $$\eta \equiv \gamma_{\mathrm{top}}/\gamma_{\mathrm{bottom}} \to \infty,$$0 symmetry in an L-shaped unit cell splits that integer charge into two half-charges $$\eta \equiv \gamma_{\mathrm{top}}/\gamma_{\mathrm{bottom}} \to \infty,$$1, and by tuning the small-block etch depth $$\eta \equiv \gamma_{\mathrm{top}}/\gamma_{\mathrm{bottom}} \to \infty,$$2 the two half-charges re-merge on one side of the downward radiation plane (Wang et al., 2023). Since any downward radiation would have to carry both opposite circular polarizations simultaneously, it vanishes by destructive interference, whereas the upward path remains open (Wang et al., 2023). The reported numerical asymmetry ratio $$\eta \equiv \gamma_{\mathrm{top}}/\gamma_{\mathrm{bottom}} \to \infty,$$3 exceeds $$\eta \equiv \gamma_{\mathrm{top}}/\gamma_{\mathrm{bottom}} \to \infty,$$4, or about $$\eta \equiv \gamma_{\mathrm{top}}/\gamma_{\mathrm{bottom}} \to \infty,$$5 dB (Wang et al., 2023).

3. Mechanisms beyond the canonical broken-$$\eta \equiv \gamma_{\mathrm{top}}/\gamma_{\mathrm{bottom}} \to \infty,$$6 picture

Interband coupling provides a second major route to UGRs. Yin et al. analyzed two slab modes of opposite up-down mirror parity that cross in $$\eta \equiv \gamma_{\mathrm{top}}/\gamma_{\mathrm{bottom}} \to \infty,$$7-space and do not couple in the perfectly symmetric slab. Breaking that symmetry introduces a coupling $$\eta \equiv \gamma_{\mathrm{top}}/\gamma_{\mathrm{bottom}} \to \infty,$$8, hybridizes the modes, and creates circular-polarization singularities from initially trivial polarization fields (Yin et al., 2022). As the tilt angle increases, two half-charges can merge on a high-symmetry line and create a V point with topological charge $$\eta \equiv \gamma_{\mathrm{top}}/\gamma_{\mathrm{bottom}} \to \infty,$$9, producing a UGR with $A = 10\log_{10}(P_{\mathrm{up}}/P_{\mathrm{down}})$0 dB (Yin et al., 2022).

Lee et al. extended this mechanism to one-dimensional zero-contrast gratings. In that system, interband coupling between even-like and odd-like waveguide modes produces quasi-UGRs at small grating thickness and true UGRs when destructive interference in the unwanted port becomes nearly perfect (Lee et al., 2023). With increasing $A = 10\log_{10}(P_{\mathrm{up}}/P_{\mathrm{down}})$1, the directionality evolves from $A = 10\log_{10}(P_{\mathrm{up}}/P_{\mathrm{down}})$2 dB at $A = 10\log_{10}(P_{\mathrm{up}}/P_{\mathrm{down}})$3 to $A = 10\log_{10}(P_{\mathrm{up}}/P_{\mathrm{down}})$4 dB at $A = 10\log_{10}(P_{\mathrm{up}}/P_{\mathrm{down}})$5, and then flips to a downward UGR at $A = 10\log_{10}(P_{\mathrm{up}}/P_{\mathrm{down}})$6 (Lee et al., 2023). The same study also identifies exceptional points and quasi-BICs in the same folded-band setting (Lee et al., 2023).

A third route relies on anisotropy. In anisotropic planar anti-guiding waveguides, UGRs appear only when the so-called polar anisotropy-symmetry is broken; at the UGR point one transmission coefficient vanishes exactly while the other remains finite, and the canceled channel carries a phase singularity with $A = 10\log_{10}(P_{\mathrm{up}}/P_{\mathrm{down}})$7 winding (Mukherjee et al., 2021). Because the UGR condition depends on wavelength, in-plane propagation angle, and polar tilt, the radiation direction can be selected and switched by anisotropy orientation (Mukherjee et al., 2021).

Rigorous perturbation theory places these observations on a broader footing. Yuan and Lu showed that, in the presence of a single radiation channel, a UGR has codimension $A = 10\log_{10}(P_{\mathrm{up}}/P_{\mathrm{down}})$8: under a generic perturbation, one must tune one parameter to maintain $A = 10\log_{10}(P_{\mathrm{up}}/P_{\mathrm{down}})$9 (Yuan et al., 2 Oct 2025). Starting from a generic bound state in the continuum, they further showed that a continuous family of UGRs can always be obtained by tuning one parameter, with

$\tau = |c_0^+/c_0^-|^2$0

as the symmetry-breaking parameter $\tau = |c_0^+/c_0^-|^2$1 (Yuan et al., 2 Oct 2025).

A more recent mechanism relaxes two assumptions that had become common in the field. Near the fourth stop band, competing first- and second-order Fourier harmonics can mediate out-of-plane radiation through two coherent channels; UGRs then arise when the channel cancellation occurs only in one direction (Lee et al., 26 Jun 2026). The authors state explicitly that this mechanism enables UGRs without relying on in-plane symmetry breaking or interband coupling (Lee et al., 26 Jun 2026). This suggests that UGRs are better regarded as a broader radiation-cancellation phenomenon than as the consequence of a single symmetry-breaking recipe.

4. Near-field and nanoantenna realizations

A near-field formulation predates the topological slab literature. In the comment on unidirectional excitation of guided modes under oblique circular illumination, the mechanism is described as the near-field analogue of a Huygens source engineered so that its evanescent spectrum couples asymmetrically into the two counter-propagating branches of a guided or surface mode (Lee et al., 2013). In that picture, interference between electric and magnetic dipoles is central. For the slit geometry, the amplitude ratio can be written as

$\tau = |c_0^+/c_0^-|^2$2

so equal magnitudes and a $\tau = |c_0^+/c_0^-|^2$3 phase shift can suppress one direction exactly (Lee et al., 2013). The same comment argues that the magnetic dipole $\tau = |c_0^+/c_0^-|^2$4, omitted in the original interpretation, is essential, and that the dominant phase-shifted Huygens pair is $\tau = |c_0^+/c_0^-|^2$5, not $\tau = |c_0^+/c_0^-|^2$6 (Lee et al., 2013).

The all-dielectric nanoantenna realization of this idea uses a crystalline silicon sphere with $\tau = |c_0^+/c_0^-|^2$7, sphere radius $\tau = |c_0^+/c_0^-|^2$8 nm, hemispherical notch radius $\tau = |c_0^+/c_0^-|^2$9 nm, and a point dipole located in the notch at distance $\tau=0$0 nm from the center and oriented along the $\tau=0$1-axis (Lee et al., 2015). Because the excitation is off-center, the nanoparticle lacks rotational symmetry and supports higher-order magnetic multipoles in addition to the dipole contribution (Lee et al., 2015). At $\tau=0$2 THz, the magnetic quadrupole dominates; at $\tau=0$3 THz, the magnetic octupole prevails (Lee et al., 2015). The resulting near field is chiral and similar to that of a circularly polarized dipole or quadrupole, which underpins unidirectional coupling to guided modes via spin-orbit interaction (Lee et al., 2015).

The relevant observables in this nanoantenna setting are the local density of states,

$\tau=0$4

and the front-to-back ratio,

$\tau=0$5

(Lee et al., 2015). In simulations, the front-to-back ratio reaches about $\tau=0$6 for a dielectric waveguide at $\tau=0$7 THz, $\tau=0$8 at $\tau=0$9 THz, and $\omega(k)\neq\omega(-k)$0 for a plasmonic gold film at $\omega(k)\neq\omega(-k)$1 THz (Lee et al., 2015).

5. Mathematical formalisms and observables

Several complementary mathematical descriptions recur across the UGR literature. In periodic slabs and gratings, temporal coupled-mode theory is the most common reduced model. For the topological grating coupler, the resonance amplitude $\omega(k)\neq\omega(-k)$2 obeys

$\omega(k)\neq\omega(-k)$3

with outgoing fields

$\omega(k)\neq\omega(-k)$4

so the UGR limit is $\omega(k)\neq\omega(-k)$5, hence $\omega(k)\neq\omega(-k)$6 (Wang et al., 2023). On resonance and neglecting internal loss, the upward coupling efficiency approaches unity, and the insertion loss is $\omega(k)\neq\omega(-k)$7 (Wang et al., 2023).

In interband-coupled ZCGs, the core object is a non-Hermitian $\omega(k)\neq\omega(-k)$8 Hamiltonian with Hermitian near-field coupling $\omega(k)\neq\omega(-k)$9 and anti-Hermitian far-field coupling $q=\frac{1}{2\pi}\oint_C d\phi(k),$0, whose eigenvalues determine the complex frequencies and decay rates of the hybridized modes (Lee et al., 2023). Directionality is then measured by

$q=\frac{1}{2\pi}\oint_C d\phi(k),$1

with $q=\frac{1}{2\pi}\oint_C d\phi(k),$2 dB taken as a true UGR and $q=\frac{1}{2\pi}\oint_C d\phi(k),$3–$q=\frac{1}{2\pi}\oint_C d\phi(k),$4 dB as a quasi-UGR (Lee et al., 2023).

In the perturbative one-channel theory, the outgoing condition is enforced through the amplitudes $q=\frac{1}{2\pi}\oint_C d\phi(k),$5, and the UGR condition is $q=\frac{1}{2\pi}\oint_C d\phi(k),$6 with $q=\frac{1}{2\pi}\oint_C d\phi(k),$7 (Yuan et al., 2 Oct 2025). The perturbation expansion introduces a tunable parameter $q=\frac{1}{2\pi}\oint_C d\phi(k),$8 that must generally be slaved to a fixed perturbation $q=\frac{1}{2\pi}\oint_C d\phi(k),$9 to maintain one-sided radiation to all orders (Yuan et al., 2 Oct 2025).

These formalisms emphasize different aspects of the same object. TCMT is most convenient for device-level loss and coupling calculations, the polarization-singularity picture captures the topological structure of one-sided radiation, and perturbation theory clarifies codimension, tuning requirements, and the $\phi(k)$0-factor scaling near a BIC.

6. Implementations, performance, and applications

The most mature UGR implementation in integrated photonics is the topological grating coupler demonstrated by Wang et al. on a 340 nm silicon-on-insulator platform. By engineering the dispersion and apodizing the grating, they reported a record-low-loss of $\phi(k)$1 dB and bandwidth exceeding $\phi(k)$2 nm at $\phi(k)$3 nm, with a $\phi(k)$4 footprint, standard SOI 340 nm, planar CMOS-compatible, single-etch fabrication, and no mirror placed on the bottom (Wang et al., 2023). The same work reports that a pair of grating couplers can function as an optic via interconnecting two stacked photonic chips with a loss of only $\phi(k)$5 dB (Wang et al., 2023).

Topological photonic-crystal slabs support much larger single-sided quality factors. In the telecommunication regime, the experimentally demonstrated unidirectional bound states in the continuum achieved single-sided quality factor as high as $\phi(k)$6, equivalent to a radiation asymmetry ratio of $\phi(k)$7 dB, with $\phi(k)$8 emission upward (Yin et al., 2019). In 1D ZCGs, true UGRs with $\phi(k)$9 dB arise in a geometry that can be realized in a single lithography-etch step and is compatible with silicon-on-insulator or silicon-nitride platforms (Lee et al., 2023). In the nanoantenna implementation, front-to-back ratios reached $C$0 for a dielectric waveguide and $C$1 for a plasmonic waveguide, demonstrating one-sided launching of guided modes from a subwavelength all-dielectric resonator (Lee et al., 2015).

Platform	Representative result	Source
All-dielectric nanoantenna + dielectric waveguide	FBR$C$2 at $C$3 THz	(Lee et al., 2015)
All-dielectric nanoantenna + Au film	FBR$C$4 at $C$5 THz	(Lee et al., 2015)
Broken-symmetry photonic-crystal slab	Single-sided $C$6 up to $C$7; $C$8 dB directionality	(Yin et al., 2019)
Topological SOI grating coupler	$C$9 dB peak loss; $c_0^-\neq0$00 nm 1 dB bandwidth	(Wang et al., 2023)
1D zero-contrast grating	$c_0^-\neq0$01 dB at $c_0^-\neq0$02	(Lee et al., 2023)

The application space is correspondingly broad. The literature lists energy-efficient grating couplers and optical interconnects (Wang et al., 2023), photonic-crystal surface-emitting lasers and on-chip directional lasers with high efficiency and low threshold (Yin et al., 2019, Yin et al., 2022), enhanced light trapping in photovoltaics (Yin et al., 2022), spin- and orbital-angular-momentum beam generation (Li et al., 2019, Yin et al., 2022), and quantum spin-photon interfaces, optical isolators, and nonreciprocal elements in integrated photonic and quantum networks (Lee et al., 2015). Because several platforms are all-dielectric, low loss, and CMOS compatible (Lee et al., 2015, Wang et al., 2023), UGRs are now treated not merely as a singular topological curiosity, but as a design principle for mirror-free, one-sided radiation control in nanophotonics and integrated optics.