Unidirectional Mode Excitation Strategy

• Unidirectional mode excitation strategy is a method that uses asymmetric excitation, structural bias, and tailored detection to launch a specific mode in one propagation direction.
• It employs mechanisms such as chiral near fields, symmetry breaking, and interference between dynamical pathways to achieve high isolation and mode selectivity.
• The approach enhances directional control in devices, enabling improved signal routing and modal suppression in systems ranging from spin-wave waveguides to photonic circuits.

Searching arXiv for the cited topics to ground the synthesis.

Searching for the central spin-wave waveguide paper.

Unidirectional mode excitation strategy denotes a class of excitation, coupling, and biasing schemes in which a selected mode is launched preferentially into one propagation direction, or a selected modal subspace is populated while the opposite direction or competing modes are suppressed. Across the literature, this strategy appears in spin-wave waveguides, bosonic networks, gyromagnetic photonics, optomechanical systems, elastic lattices, ring lasers, surface magnetoplasmons, nanoantennas, piezoelectric structural excitation, and single-molecule rotors, with the common objective of converting symmetry breaking, phase-sensitive interference, chirality, or non-Hermitian asymmetry into directional modal control (Vanderveken et al., 2019, Wanjura et al., 2022, Chen et al., 2019, Li et al., 2019, Brandão et al., 27 May 2026, Kacmoli et al., 2022, Liu et al., 2024, Lee et al., 2015, Qiu et al., 2021, Au-Yeung et al., 2024).

1. Definition and scope

In its most general form, a unidirectional mode excitation strategy combines three ingredients: a mode-selective excitation field, a structural or dynamical asymmetry that distinguishes opposite propagation directions or symmetry channels, and a detection or transport geometry that preserves the selected directionality. In many implementations, the underlying dispersion remains reciprocal, so the directional behavior originates from asymmetric coupling rather than from a nonreciprocal band structure. This is explicit, for example, in non-uniformly magnetized spin-wave waveguides, where $f_n(+k)=f_n(-k)$ in the absence of interfacial Dzyaloshinskii–Moriya interaction, and the observed unidirectionality arises from excitation nonreciprocity (Vanderveken et al., 2019).

The concept includes both real-space direction selection and modal selectivity in an internal basis. In quadrature nonreciprocity, transport is unidirectional only for specific mode quadratures resolved with respect to an external reference phase, even though the Hamiltonian is time-reversal symmetric (Wanjura et al., 2022). In parametrically driven coupled quantum oscillators, the same language refers to selective excitation of one normal mode while the other remains close to its ground state, with only even quantum numbers populated in each normal mode (Seshadri, 25 May 2026). In structural dynamics, distributed $d_{15}$ piezoelectric strips synthesize an in-plane traction field whose symmetry matches one target mode and suppresses coupling to others (Qiu et al., 2021).

A recurring distinction is between strategies based on directional coupling and those based on directional propagation. Chiral Oersted fields, magneto-dipolar gratings, gyromagnetic time-mirror symmetry breaking, quadrature-sensitive interference between beamsplitter and two-mode-squeezing couplings, non-Hermitian skin-effect feedback, and asymmetric gain/loss with a nonlinear defect all realize directionality by modifying how energy is launched or amplified (Vanderveken et al., 2019, Chen et al., 2019, Li et al., 2019, Wanjura et al., 2022, Brandão et al., 27 May 2026, Landers et al., 2024). By contrast, some topological surface-wave systems use a bandgap supporting one-way edge or surface states, so the directional response is built into the modal spectrum itself (Liu et al., 2024).

2. Underlying physical mechanisms

Several distinct physical mechanisms recur across the cited works.

Chiral near fields and asymmetric overlap form one major class. In spin-wave systems, an inductive antenna produces an Oersted field with in-plane and out-of-plane components and a phase relation that favors nonreciprocal coupling to Damon–Eshbach-like waves; in a thicker strip, this yields higher intensity for $+x$ than for $-x$ propagation, while the mode profiles remain the same in both directions (Vanderveken et al., 2019). In a Co nanowire grating on ultrathin YIG, the dynamic dipolar field of the nanowire Kittel mode is chiral with respect to the film plane, and the coupling to $+k$ or $-k$ exchange spin waves is selected by the relative magnetic configuration of nanowires and film (Chen et al., 2019). All-dielectric nanoantennas exploit a related idea: asymmetric excitation of higher multipoles inside a notched silicon nanoparticle produces a chiral near field that couples to the transverse spin of guided modes or surface plasmon polaritons (Lee et al., 2015). The comment on near-field interference emphasizes that, under oblique circularly polarized illumination of a nanoslit, an effective magnetic dipole $m_x$ generated by induction currents is essential to the observed directional launching (Lee et al., 2013).

Symmetry breaking in the excitation profile is equally central. In non-uniformly magnetized waveguides, the average magnetization tilt modifies width-mode symmetry and phase-front orientation, so that a symmetric excitation field can couple more strongly to the second-order mode than to the first (Vanderveken et al., 2019). In $d_{15}$-actuated structures, the excitation field is not electromagnetic but mechanical: the bonded strips generate pure in-plane shear traction, and selective excitation is obtained by arranging the spatial traction symmetry to match the target mode and to cancel the generalized force on non-target modes (Qiu et al., 2021). In gyromagnetic rod chains, breaking the combined time-mirror symmetry $T\circ M_x$ makes $\omega(k)\neq\omega(-k)$, converting a periodic dielectric chain into a one-way waveguide; rotating the T-shaped rod restores or reverses this behavior (Li et al., 2019).

Interference between dynamical pathways underlies the bosonic and coherent-wave realizations. Quadrature nonreciprocity arises from interference between excitation-conserving beamsplitter couplings and excitation-non-conserving two-mode-squeezing couplings. At resonance and for $d_{15}$0, destructive interference suppresses one cross-quadrature transmission element while leaving the opposite direction finite; rotating the measurement quadratures can maximize, reverse, or eliminate the asymmetry (Wanjura et al., 2022). In coherent control via metasurfaces, unilateral excitation of evanescent harmonics makes the reflection matrix triangular, suppresses the time-reversed diffraction channels, and forces the output to remain in one reflection direction while its amplitude is tuned by the phase difference between two asymmetric inputs (Zhong et al., 2023).

Gain/loss asymmetry and nonlinear state dependence provide another route. In a three-mode optomechanical system with optical gain introduced into the optomechanical cavity, forward transmission and backward transmission obey different nonlinear equations because the mechanics couples only to one cavity; the result is optical nonreciprocal transmission with unidirectional amplification (Song et al., 2019). In the frozen-mode regime near a stationary inflection point, a short lossy section, a longer gain section, and a single Kerr defect produce direction-dependent nonlinear mismatch: forward incidence experiences weak interaction at the defect and is amplified, whereas backward incidence reaches the defect with stronger local intensity and is predominantly reflected (Landers et al., 2024). In spatially periodic feedback lattices, non-Hermitian asymmetry from the feedback matrix produces directional attenuation or amplification associated with the non-Hermitian skin effect (Brandão et al., 27 May 2026).

Driven bistability and latching characterize ring-laser and molecular realizations. In quantum cascade ring lasers, an evanescently coupled active waveguide injects amplified spontaneous emission into one traveling-wave direction, perturbing the bistable CW/CCW dynamics and selecting the desired attractor; once selected, the state remains latched (Kacmoli et al., 2022). In single-molecule rotation on Au(111), chirality and the STM electric field set the rotation sense on the excited-state surface, while quantum mixing between ground and excited electronic states allows thermal energy to assist a semi-classical, still directional, step in a restricted voltage and temperature window (Au-Yeung et al., 2024).

3. Mathematical formulations

The mathematical description of unidirectional mode excitation is usually built from overlap, scattering, or Floquet formalisms.

In spin-wave mode selection, the excitation efficiency of width mode $d_{15}$1 is written as

$d_{15}$2

or, for width selection,

$d_{15}$3

These expressions make explicit that directionality and modal preference depend on the symmetry of the excitation field, the transverse mode profile, and the equilibrium magnetization texture (Vanderveken et al., 2019). In piezoelectric structural excitation, the same logic appears in mechanical form through the generalized modal force

$d_{15}$4

with selectivity obtained by designing $d_{15}$5 to maximize coupling to the target mode and cancel overlap with other modes (Qiu et al., 2021).

Scattering-matrix formulations dominate coherent-wave and bosonic settings. In quadrature nonreciprocity, the susceptibility matrix is

$d_{15}$6

and the scattering matrix is

$d_{15}$7

For the resonant dimer with equal damping and $d_{15}$8, the unrotated susceptibility has nonzero elements only for one cross-quadrature direction, while a global quadrature rotation redistributes these matrix elements according to $d_{15}$9 and $+x$0 factors (Wanjura et al., 2022). In metasurface coherent control, the reflection matrix is

$+x$1

or, for a grounded dielectric substrate,

$+x$2

with unilateral Fourier content in the surface admittance making the matrix triangular and thereby suppressing selected diffraction channels (Zhong et al., 2023).

Periodic or parametrically driven systems are analyzed with Bloch–Floquet or effective parametric Hamiltonians. In gyromagnetic rod chains, broken time-mirror symmetry manifests directly as asymmetric Bloch dispersion $+x$3 (Li et al., 2019). In space-time-modulated lattices, a plane-wave expansion with sidebands $+x$4 yields a block quadratic eigenvalue problem in the normalized frequency $+x$5, and directional band gaps emerge because the traveling modulation couples $+x$6 to $+x$7 differently for opposite signs of $+x$8 (Brandão et al., 27 May 2026). In coupled quantum oscillators, modulation of the inter-oscillator coupling produces two normal modes with time-dependent frequencies $+x$9; near $-x$0, the effective Hamiltonian contains single-mode squeezing terms $-x$1 and $-x$2, enforcing the even-parity selection rule and enabling selective excitation of one normal mode by choosing the detuning inside one Mathieu-like resonance window and outside the other (Seshadri, 25 May 2026).

Non-Hermitian and nonlinear descriptions extend this framework. In optomechanics, forward and backward amplitudes obey different cubic transmission equations because the effective nonlinearities $-x$3 and $-x$4 are not equal, which is the necessary condition for nonreciprocity at equal input powers (Song et al., 2019). Near a stationary inflection point, the frozen-mode regime is described by a Bloch dispersion with vanishing first and second derivatives,

$-x$5

and the nonlinear defect is solved self-consistently through a cubic equation in the defect intensity $-x$6 (Landers et al., 2024).

4. Representative implementations across physical platforms

The strategy is not tied to a single field; rather, it appears as a transferable design pattern.

Platform	Direction-selective mechanism	Representative outcome
Spin-wave waveguides	Chiral Oersted field or strain-shaped overlap	Nonreciprocal antenna radiation; mode-selective but bidirectional magnetoelastic excitation (Vanderveken et al., 2019)
Exchange spin waves in YIG	Chiral magneto-dipolar coupling from Co nanowire grating	Nearly perfect unidirectionality with $-x$7 for exchange modes with $-x$8 (Chen et al., 2019)
Gyromagnetic photonic chains	Broken $-x$9 symmetry	$+k$0 dB isolation at $+k$1 for $+k$2 (Li et al., 2019)
Bosonic dimers and rings	BS–TMS interference in quadrature space	Direction switched by quadrature rotation; reciprocal at $+k$3 (Wanjura et al., 2022)
Optomechanical cavities with gain	Asymmetric nonlinear response and reduced $+k$4	Strong forward amplification with suppressed reverse transmission (Song et al., 2019)
QCL ring lasers	ASE injection into bistable CW/CCW states	Deterministic switching with $+k$5 modulation of the electrical input (Kacmoli et al., 2022)

In spin-wave waveguides, the mesoscopic strip geometry is decisive. A $+k$6 nm wide, $+k$7 nm thick CoFeB strip at $+k$8 mT has an average magnetization tilt of approximately $+k$9, and the resulting tilted phase fronts alter the apparent parity of the width modes. This makes the second mode couple more strongly than the first under a symmetric Oersted excitation field, while normal and shear strain states redistribute the magnetoelastic field toward the center or the edges and thereby favor different modes (Vanderveken et al., 2019). By contrast, in the Co/YIG grating system, the periodicity directly selects exchange-spin-wave wavevectors $-k$0 for even $-k$1, and the P versus AP magnetic configuration flips the launched direction from $-k$2 to $-k$3 (Chen et al., 2019).

Photonic and plasmonic implementations emphasize geometry and material tensors. In the periodic dielectric chain of T-shaped YIG rods, $-k$4 and $-k$5 break the combined time-mirror symmetry and produce unidirectional guided modes, whereas $-k$6 and $-k$7 restore reciprocal propagation (Li et al., 2019). In YIG-sandwiched waveguides, symmetric bias supports even-symmetric and odd-symmetric unidirectional surface magnetoplasmons in the band $-k$8, while asymmetric bias can open a single EA-mode window $-k$9, enabling robust unidirectional multimode interference, splitters, and mode converters (Liu et al., 2024). In the diamond ELFA+BG emitter, the elliptical facet and Bragg grating create an asymmetric mode-conversion path toward a nanofiber, with forward coupling of approximately $m_x$0, backward coupling of approximately $m_x$1, and a chirality constant approaching $m_x$2 for larger etched length (Murmu et al., 2021). In the all-dielectric nanoantenna, the notched silicon sphere supports higher magnetic multipoles that create the chiral near field needed for directional excitation of dielectric-waveguide or plasmonic modes, with front-to-back ratios up to $m_x$3 and $m_x$4, respectively (Lee et al., 2015).

Mechanical, elastic, and molecular systems broaden the notion of “mode.” In periodic elastic lattices, space-time modulation creates directional band gaps, whereas spatially periodic feedback produces broad direction-dependent attenuation or amplification through the non-Hermitian skin effect (Brandão et al., 27 May 2026). In structural mechanics, distributed $m_x$5 transducers selectively excite bending, torsional, or longitudinal modes over a broad frequency range by matching traction symmetry to mode symmetry (Qiu et al., 2021). In molecular rotation, the “mode” is a chiral rotational degree of freedom rather than a waveguide eigenmode, but the same logic of directional bias through non-equilibrium excitation applies: the DMNI-P rotor exhibits $m_x$6 one-step rotation in the same direction at $m_x$7 mV and $m_x$8 K, while moderate heating in the $m_x$9–$d_{15}$0 K and $d_{15}$1–$d_{15}$2 mV window accelerates the directional rate without eliminating directionality (Au-Yeung et al., 2024).

5. Control variables, diagnostics, and performance metrics

Unidirectional mode excitation is typically characterized by a small set of repeated metrics: overlap efficiency, forward/backward power ratio, isolation ratio, mode purity, and propagation filtering.

In spin-wave systems, directionality can be inferred from spatial intensity asymmetry and from propagation-dependent modal decay. At $d_{15}$3 GHz in the mesoscopic CoFeB strip, the decay lengths are $d_{15}$4 and $d_{15}$5, so the initially stronger $d_{15}$6 mode decays faster than $d_{15}$7, and the crossover distance

$d_{15}$8

serves as a measure of relative excitation efficiencies under different strain states (Vanderveken et al., 2019). In the Co nanowire grating, the experimental directionality metric

$d_{15}$9

approaches $T\circ M_x$0 for exchange modes with $T\circ M_x$1 (Chen et al., 2019).

Quadrature-sensitive and coherent-wave systems rely on phase-dependent transfer functions. In the bosonic dimer at resonance with $T\circ M_x$2, the scattering magnitude is $T\circ M_x$3; for $T\circ M_x$4, this gives $T\circ M_x$5, corresponding to approximately $T\circ M_x$6 dB gain without reverse transmission in the selected quadrature basis (Wanjura et al., 2022). In the metasurface coherent-control experiment, the reflected amplitude in the fixed direction follows

$T\circ M_x$7

for equal inputs, so the response is continuously tuned from coherent perfect absorption at $T\circ M_x$8 to coherent maximum reflection at $T\circ M_x$9 (Zhong et al., 2023). In the gyromagnetic dielectric chain, isolation is measured directly as

$\omega(k)\neq\omega(-k)$0

and exceeds $\omega(k)\neq\omega(-k)$1 dB in the reported one-way window (Li et al., 2019).

Optomechanical and laser systems add gain and switching thresholds. In the gain-assisted optomechanical system, the optimal forward transmission is

$\omega(k)\neq\omega(-k)$2

while the isolation ratio is reported analytically and numerically in terms of forward versus backward transmission (Song et al., 2019). In the QCL ring laser, the control variable is electrical rather than optical phase: full CW/CCW switching is obtained with $\omega(k)\neq\omega(-k)$3 mA, or approximately $\omega(k)\neq\omega(-k)$4 of $\omega(k)\neq\omega(-k)$5 mA, and a $\omega(k)\neq\omega(-k)$6 ns spike up to approximately $\omega(k)\neq\omega(-k)$7 A can flip the state during a $\omega(k)\neq\omega(-k)$8 ns pulse (Kacmoli et al., 2022).

Structural and molecular implementations are diagnosed differently but with analogous intent. In $\omega(k)\neq\omega(-k)$9-actuated bars, the natural frequency is extracted as $d_{15}$00 and the quality factor as $d_{15}$01, while the selective suppression of competing modal families is confirmed by conductance, susceptance, and laser vibrometry (Qiu et al., 2021). In the single-molecule rotor, the action spectrum is cast as a rotation yield per electron,

$d_{15}$02

and fitted by a threshold kernel with vibrational energies near $d_{15}$03 meV and $d_{15}$04 meV; the measured values span from approximately $d_{15}$05 rotations/electron at $d_{15}$06 mV to approximately $d_{15}$07 rotations/electron above $d_{15}$08 mV (Au-Yeung et al., 2024).

6. Limitations, misconceptions, and future directions

A common misconception is that unidirectionality always implies nonreciprocal dispersion or broken time-reversal symmetry. The surveyed literature shows that this is not generally the case. In mesoscopic spin-wave waveguides, the dispersion remains reciprocal and the directionality originates from asymmetric coupling (Vanderveken et al., 2019). Quadrature nonreciprocity explicitly preserves time-reversal symmetry of the Hamiltonian; the directional behavior appears only in a quadrature-resolved basis set by an external phase reference, and reciprocity is restored at a special quadrature rotation (Wanjura et al., 2022). Similarly, coherent control via unilateral evanescent-wave excitation preserves reciprocity while engineering the available scattering channels (Zhong et al., 2023).

Another misconception is that mode selectivity and unidirectionality are interchangeable. They often coexist, but not always. Magnetoelastic transducers in non-uniformly magnetized waveguides provide mode selectivity without chirality and therefore radiate symmetrically into $d_{15}$09 (Vanderveken et al., 2019). Thickness-shear piezoelectric strips can selectively excite one structural mode over a broad band without introducing any directional propagation asymmetry in the host (Qiu et al., 2021). A plausible implication is that “unidirectional mode excitation strategy” should be treated as a family of related but not identical design objectives: direction selection, modal selection, and their combination.

Limitations differ by platform. In spin-wave and photonic systems, directional behavior is often sensitive to geometry, edge pinning, thickness, or exact bias orientation (Vanderveken et al., 2019, Li et al., 2019). In gain-based systems, one must remain below lasing or instability thresholds and account for added noise, although the reported optomechanical example achieves $d_{15}$10 in the stated operating region (Song et al., 2019). In space-time modulation, the stable region shrinks with increasing chain length, modulation depth, and modulation frequency, so Floquet multipliers must be checked explicitly (Brandão et al., 27 May 2026). In the frozen-mode regime, directional amplification is intensity-dependent and tends toward reciprocal behavior at very low or very high input power, with the useful asymmetry confined to an intermediate operating window (Landers et al., 2024). In molecular rotation, heating assists directionality only in a restricted moderate-voltage, moderate-temperature regime; above $d_{15}$11 K the motion becomes stochastic (Au-Yeung et al., 2024).

The main directions for extension are already visible in the cited works. Spin-wave studies suggest combining chiral antennas with interfacial DMI or engineered edge pinning to strengthen directional selectivity (Vanderveken et al., 2019). Bosonic-network results indicate that even-$d_{15}$12 rings and cavity arrays can support even–odd quadrature pairing and exponential end-to-end gain (Wanjura et al., 2022). Topological surface-magnetoplasmon work points toward robust multimode interference, splitter design, and mode conversion in disorder-tolerant unidirectional channels (Liu et al., 2024). The mass–spring comparison suggests that spatially periodic feedback and space-time modulation should be viewed as complementary design paradigms rather than competing ones, one favoring broad passband asymmetry and the other narrow directional gaps (Brandão et al., 27 May 2026). Across all these settings, the enduring theme is that unidirectional mode excitation is achieved not by a single universal mechanism, but by deliberately matching excitation symmetry, modal structure, and directional asymmetry so that only the desired channel remains accessible.