BiDex: Hybrid Airy-Plasmonic Systems

• BiDex System is a reconfigurable hybrid Airy-plasmonic photonic platform that exploits graphene and dielectric waveguides to achieve long-range, self-accelerating surface waves.
• It employs an exponentially truncated Airy beam design to ensure non-diffracting, self-healing, and self-bending propagation characteristics.
• Enhanced by real-time graphene chemical potential tuning, the BiDex system overcomes conventional plasmonic limitations by extending propagation lengths and enabling adjustable beam trajectories.

The BiDex system is not directly referenced in the provided preprints. However, within the scope of advanced plasmonic beam engineering and specifically hybrid Airy plasmonic systems, the principal factual foundation derives from the study of hybrid Airy plasmons in graphene-based waveguides, as established in "Hybrid Airy Plasmons with Dynamically Steerable Trajectories" (Li et al., 2016). The following article synthesizes the theory, implementation, and implications of these hybrid surface wave systems, as these constitute the substantive research context for "BiDex" if that is an editorial label for reconfigurable, subwavelength Airy-plasmonic photonic systems.

Hybrid Airy plasmons exploit the interplay between dielectric and plasmonic guiding, employing graphene's tunability to realize nondiffracting, self-accelerating surface waves with dynamically controllable trajectories. This class of systems is central to next-generation photonic manipulation, flat-optics, and on-chip THz signal technologies.

1. Theoretical Framework: Paraxial Model and Mode Hybridization

Hybrid Airy plasmon systems are realized in planar waveguides featuring a tightly confined quasi-TM field. The primary geometry consists of a trilayer graphene–PTFE channel adjacent to a GaAs dielectric slab, yielding strong transverse confinement and hybridization of electromagnetic modes.

The field is expressed as

$$\Phi(x, y, z) = H_y(x, y, z) = \psi(y, z) \Phi_0(x) e^{i \beta z}$$

where $\Phi_0(x)$ is the transverse mode profile and $\beta = \beta_r + i \beta_i$ is the complex propagation constant. Insertion into the Helmholtz equation and projection onto $\Phi_0(x)$, under the paraxial approximation, leads to a one-dimensional Schrödinger-type equation for the slowly varying envelope $\psi(y, z)$: $$i \frac{\partial \psi}{\partial \xi} + \frac{\partial^2 \psi}{\partial s^2} = 0,$$ with scaled variables $s = y/y_0$, $\xi = z/(2 \beta y_0^2)$. The validity of this reduction requires $\sqrt{a} \beta_r y_0 \gg 1$, where $a$ is the truncation parameter of the Airy beam.

Hybrid mode dispersion derives from the interface conditions at $\Phi_0(x)$0, with trilayer graphene modeled as a sheet conductivity $\Phi_0(x)$1. This produces a transcendental equation relating modal $\Phi_0(x)$2 to physical and tunable parameters, interpolating between pure dielectric slab and pure graphene plasmonic channel limits.

2. Airy Plasmon Solution, Trajectory, and Beam Properties

The analytical solution for a finite-energy Airy plasmon beam is derived by imposing an exponentially truncated Airy initial field: $\Phi_0(x)$3 The resulting paraxial propagation is: $\Phi_0(x)$4 Key physical features include:

• Non-diffraction: The main lobe width remains $\Phi_0(x)$5 over significant distances.
• Self-acceleration: The peak follows a parabolic path $\Phi_0(x)$6.
• Self-healing: The beam reconstructs beyond small transverse obstacles.

The hybrid approach leverages the moderate quality factor ($\Phi_0(x)$7) and reduced loss of the coupled dielectric-plasmonic mode compared to pure SPP modes, preserving pronounced parabolic bending while greatly extending propagation length.

3. Figures of Merit: Propagation Length and Self-Bending

Quantitative comparison between pure and hybrid modes is essential for system optimization. Analytical metrics include: $\Phi_0(x)$8 where $\Phi_0(x)$9 is the 1/e power decay length and $\beta = \beta_r + i \beta_i$0 is the total lobe-peak displacement over $\beta = \beta_r + i \beta_i$1. Numerical simulations yield:

• For a pure plasmonic mode at 1.75 THz ($\beta = \beta_r + i \beta_i$2m, $\beta = \beta_r + i \beta_i$3): $\beta = \beta_r + i \beta_i$4, $\beta = \beta_r + i \beta_i$5m, $\beta = \beta_r + i \beta_i$6m.
• For a pure dielectric mode: $\beta = \beta_r + i \beta_i$7, $\beta = \beta_r + i \beta_i$8, but negligible self-deflection.
• For the hybrid (HOHM) mode: $\beta = \beta_r + i \beta_i$9, $\Phi_0(x)$0m, $\Phi_0(x)$1m.

These metrics demonstrate that hybrid Airy plasmons enable two orders of magnitude longer range than pure plasmons, with significant trajectory curvature—addressing major limitations of early SPP Airy beam implementations (Li et al., 2016).

4. Dynamic Beam Steering via Graphene Chemical Potential

Central to hybrid Airy plasmon systems is the capability for real-time control of beam trajectories through electrical gating. Adjusting the graphene chemical potential $\Phi_0(x)$2 alters the conductivity $\Phi_0(x)$3, thereby modulating both $\Phi_0(x)$4 and $\Phi_0(x)$5:

$\Phi_0(x)$6(eV)	$\Phi_0(x)$7	$\Phi_0(x)$8m)$\Phi_0(x)$9	$\psi(y, z)$0m)$\psi(y, z)$1
0.2	40	410	18
0.3	61.4	538	24
0.4	93	722	32

Propagating trajectory and self-acceleration can thus be tuned in situ, with effective deflection angle $\psi(y, z)$2, conferring a degree of beam steering not accessible in purely metallic SPP platforms. This enables reconfigurable photonic routing and dynamic manipulation (Li et al., 2016).

5. Experimental Implementation and Numerical Simulation

Field distributions for hybrid Airy plasmons are verified through full-wave electromagnetic simulations, employing the numerically calculated HOHM transverse profile $\psi(y, z)$3. Simulations at 1.75 THz demonstrate:

• Distinct diffraction-free Airy lobes persisting over $\psi(y, z)$4–$\psi(y, z)$5m.
• Beam trajectories matching analytic parabolic predictions.

For fabrication, GaAs/PTFE slabs are prepared and CVD-grown graphene is transferred via wet methods. Airy-like beams are typically launched using gratings or nanopit structures engineered to impart cubic phase modulation to incident light, ensuring efficient modal excitation. These approaches draw from phase mask strategies established for Airy plasmonics in noble metals (Minovich et al., 2011, Li et al., 2011).

6. Applications and Advantages over Conventional Plasmonic Airy Systems

Hybrid Airy plasmon systems address key limitations of conventional SPP Airy beams: short range and lack of tunability. The combination of subwavelength confinement, long-range nondiffracting behavior, and reconfigurable trajectories supports advanced on-chip functionalities:

• Optical tweezing and tractor-beaming of micro-particles.
• Reconfigurable sorting and transport of biological cells.
• Super-resolution THz imaging and focal-line scanning.
• On-chip THz signal routing, interferometry, and dynamically tunable beam-splitters.

A plausible implication is that this hybrid strategy may generalize to broader classes of flat-optics platforms, enabling sustained, steered, non-diffracting wavefronts in regimes where materials offer strong tunability (e.g., multilayer graphene, phase-change dielectrics).

7. Context within Broader Airy Plasmonics Research

The development of hybrid Airy plasmons extends foundational work on Airy SPP beams on noble metal surfaces (Minovich et al., 2011, Li et al., 2011), which established the experimental feasibility and unique field control afforded by Airy beams. Subsequent advances in caustic design (Epstein et al., 2013) and advanced structured light approaches (e.g., Hermite-Gaussian Airy SPPs (Martínez-Herrero et al., 30 Apr 2025)) provide complementary methods for field tailoring. However, only hybrid graphene–dielectric systems enable simultaneously large trajectory reconfiguration and long propagation lengths, crucial for next-generation plasmonic manipulation and adaptive photonic systems (Li et al., 2016).