Lateral Interference: Phenomena and Applications

• Lateral interference is the phase-coherent crosstalk among spatially separated subsystems that causes observable constructive or destructive effects based on device geometry.
• In contexts like quantum dot circuits and planar Josephson junctions, this interference modulates electron–phonon coupling and magnetic interference envelopes, impacting excitation rates and critical current patterns.
• Applications span lateral-shearing holography, graphene transport, piezoresponse force microscopy, and plasmonic devices, underlining its role in enhancing measurement accuracy and device optimization.

The lateral interference component refers to geometric, phase-coherent cross-talk or interference effects that arise when spatially separated subsystems interact—via fields, waves, mechanical motion, or measurement—such that the lateral (side-by-side, transverse, or in-plane) arrangement or nonlocal structure of the device determines observable interference, mixing, or distortion in physical signals or operational outcomes. In the quantum, superconducting, plasmonic, piezoelectric, optical, and cognitive/human-interaction contexts, the lateral interference component manifests as a measurable, often detrimental, but sometimes tunable or useful contribution arising from spatially extended systems with finite in-plane geometry, multiple probe points, or anisotropic structure.

1. Quantum Dot Circuits: Coherent Phonon Back-Action

In lateral double- and triple-quantum-dot (DQD, TQD) GaAs circuits, a pronounced back-action effect arises from quantum point contact (QPC)-emitted non-equilibrium acoustic phonons that propagate through the heterostructure and are absorbed by neighboring quantum dots. When the dots are arranged laterally, each phonon's displacement field accumulates a relative phase $\phi(q) = q \cdot d$—$d$ being the vector connecting dot centers. The electron–phonon coupling matrix element is of the form $e^{i q \cdot r_L} - e^{i q \cdot r_R}$, so that phonon absorption amplitudes from each site interfere, leading to oscillations in excitation rates:

$$|M_{\mathrm{DQD}}(q, \mu)|^2 \propto \left| \sin(q d/2) \right|^2.$$

Constructive interference ($q \cdot d = (2n+1)\pi$) maximizes inelastic transitions; destructive interference ($q \cdot d = 2n\pi$) suppresses them. The effect manifests as alternating stripes of transconductance in DQD stability diagrams, with stripe spacing determined by dot separation and sound velocity. Suppressing this lateral interference—by tuning the device to “dark” points (destructive interference) or misaligning the QPC-dot axis—minimizes phonon-mediated back-action during qubit readout, protecting quantum coherence (Granger et al., 2013).

2. Planar Josephson Junctions: Magnetic Interference Envelope

In thin-film planar SNS (superconductor–normal–superconductor) Josephson junctions with finite lateral dimensions (length $L$, width $W$) and various in-plane geometries, the magnetic interference pattern $I_c(B)$ is governed by nonlocal screening currents and the spatial distribution of the phase. The lateral-interference component arises from shape-dependent modulation of the gauge phase:

$$\gamma(d/2, y) = \frac{7 \zeta(3)}{\pi^2} \frac{B W^2}{\Phi_0} \tanh\left[\frac{\pi^3}{28 \zeta(3)} \frac{A}{W^2}\right] f(y/W)$$

with $f(y/W)$ a geometry-dependent dimensionless function. The resulting $I_c(B)$ pattern is a product of a universal period $\Delta B$ (dependent only on $W$ or total area $A$ for $L \ll W$), and a slowly decaying lateral-interference envelope set by $f(y/W)$—producing, e.g., a "sinc" envelope for a rectangle, or a numerically computed envelope for ellipses/rhomboids. Correctly inverting these patterns to reconstruct the critical current density $J_c(y)$ requires explicit inclusion of the lateral-interference form factor; naive analysis leads to gross artifacts (Fermin et al., 2022).

3. Lateral-Shearing Digital Holography: Two-Beam Interference

In subdivided two-beam interference (STBI)-based lateral-shearing digital holographic microscopy (LS-DHM), a lateral interference component is created by using a shear plate to split an object beam into two laterally displaced beams (by $\delta$), which are then recombined on a sensor. The recorded intensity

$$I(x, y) = |A(x, y)|^2 + |A(x-\delta_x, y-\delta_y)|^2 + 2 A(x, y) A(x-\delta_x, y-\delta_y) \cos[\phi(x, y) - \phi(x-\delta_x, y-\delta_y) + \Delta \phi_0]$$

yields high-contrast fringes and depth information, provided careful optical region selection (so only one object-modulated and one blank reference overlap) is implemented. Adjusting the shear to be about half the field of view, the system suppresses “twin-image” artefacts, increases resolution, and achieves phase sensitivity of $\sim 10\,\mathrm{nm}$ (Devinder et al., 2019).

4. Lateral Goos–Hänchen Component in Graphene Transport

In graphene transport through 1D barriers, the lateral (Goos–Hänchen, GH) shift is a phase-coherent displacement of wave packets along the interface direction, proportional to $-\partial \phi_r/\partial k_y$ (or $-\partial \phi_t/\partial k_y$ for transmission). This lateral shift constitutes an interference component in the group delay, contributing an additive term $$\tau_{\mathrm{GH}} = \Delta_{\mathrm{GH}} \sin \theta / v_F$$ to the individual group delay. For the collective group delay (mode-averaged), the GH shift is extracted via weak-field spin-precession conductance measurements. This lateral interference modifies macroscopic transport times and is directly measurable via spintronic approaches (Song et al., 2013).

5. Piezoelectric Domain Walls: Localized Shear in PFM

In piezoresponse force microscopy (PFM) of ferroelectric thin films, the lateral interference component is observed as a sharp, wall-localized signal in lateral PFM (LPFM) phase and amplitude, restricted to domain walls where the out-of-plane polarization is reversed (180°, 109°, 71° walls). Elastic analysis reveals that at such a wall, antiparallel vertical strains produce a net lateral "shear" of magnitude $\Delta u_x \approx 2 \nu d_{33} E t$, with $\nu$ the Poisson ratio, and $d_{33}$ the vertical piezoelectric coefficient. Finite-element modeling and EFM exclude electrostatic or simple tilt artefacts. The LPFM wall signal, with FWHM ∼70 nm, is thus a genuine lateral interference due to mechanical shear, not projection of in-plane polarization (Guyonnet et al., 2010).

6. HCI: Task-Irrelevant Lateral Interference in Cognitive Motor Performance

In human-computer interaction under whole-body motion, the lateral interference component (LI) is operationally defined as the magnitude of residual horizontal acceleration orthogonal to the visually cued response axis:

$$\mathrm{LI} = \|\vec{v}_{\mathrm{side}}\|,\quad \vec{v}_{\mathrm{side}} = \vec{v}_{\mathrm{hor}} - (\vec{v}_{\mathrm{hor}} \cdot \vec{v}_{\mathrm{arrow}})\vec{v}_{\mathrm{arrow}}$$

where $\vec{v}_{\mathrm{arrow}}$ is the response direction and $\vec{v}_{\mathrm{hor}}$ the horizontal motion vector. Empirical mixed-effects modeling shows LI is the principal factor slowing reaction time under motion, with effects heavily amplified in participants with higher motion-sickness susceptibility (MSSQ). In contrast, motion aligned with the cued direction (Directional Congruency) speeds responses and is robust against MSSQ variations. This decomposition guides "motion shaping" strategies for mobile HCI, recommending minimization of LI especially for high-MSSQ users (Wang et al., 19 Jan 2026).

7. Lateral Interference in Plasmonic Ratchet Crystals

In dual-grating-gated two-dimensional electron gases (2DEG), the lateral interference component arises from the nonlinear superposition of "bright" (even under spatial symmetry) and "dark" (odd) plasmon modes in the asymmetric superlattice. The resulting dc ratchet current contains a specific interference term, $$j_{\mathrm{bd}} \propto 1/(\Sigma_{\mathrm{b}}\Sigma_{\mathrm{d}}^*)$$, responsible for parametric amplification of plasmonic peaks. This interference effect creates regime-dependent resonant and super-resonant structures, including a dense super-resonant sub-band comb for relevant damping and coupling ratios, and enables electrical tuning of current amplitude and sign via gate voltages and excitation frequency. The lateral interference thus not only governs peak enhancement but also physical ratchet direction reversals, distinguishing it from minimal (perturbative) models which predict a single resonance only (Gorbenko et al., 17 Jan 2026).

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The lateral interference component is thus a unifying but context-specific concept, describing interference arising from spatially nonlocal, phase-coherent, or transverse interactions set by device geometry, field orientation, or dynamic configuration. It is central to the quantitative analysis, interpretation, or mitigation of back-action in quantum measurement, macroscopic transport in hybrid superconducting and graphene devices, wave packet shifts, shear piezoresponse, optical image formation, plasmonic ultrafast electronics, and even cognitive-motor performance under motion. The careful control and theoretical modeling of this component are essential for optimizing and correctly interpreting the operation of advanced devices and measurement modalities across physics, materials science, electrical engineering, and human factors engineering.