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Comparative Performance of Graphene-Enabled Transmitarray Antenna and Reflectors for Wide-Angle Terahertz Beam Steering

Somayeh Komeylian, Truong Nguyen, Christopher Paolini

arXiv:2609.05803v1cs.NI

TL;DR

The paper compares a hemispherical graphene-based transmitarray with its geometrically corresponding planar reflector for wide-angle THz beam steering. It formulates the planar reflector framework and evaluates both configurations, reporting wider elevation steering and lower HPBW variation for the transmitarray.

  • Problem

    THz links use narrow, highly directional beams, but that beamwidth restricts spatial coverage for tracking dynamic targets, while conventional phased arrays face hardware-complexity and power constraints.

    Source: §I · p. 1

  • Method

    The work formulates and numerically evaluates a planar graphene reflector as the geometrically corresponding comparator for the hemispherical transmitarray, alongside comparisons with reported experimental results.

    Source: §I · p. 2, §VIII · p. 19

  • Results

    HPBW variation is 26.48° for the planar reflector versus 13.1° for the transmitarray; elevation steering is ±60° versus ±78°, respectively, with 360° azimuthal coverage.

    Source: §VIII · p. 19

  • Takeaways & Limitations

    The results establish the hemispherical transmitarray as a viable architecture for electronically reconfigurable, wide-angle, three-dimensional beam steering in future THz and 6G systems.

    Source: §VIII · p. 19

Abstract

from arXiv · show

This work compares a hemispherical graphene-based transmitarray antenna with its planar reflector counterpart for wide-angle beam steering in the THz regime. The theoretical framework of the planar reflector is formulated and numerically evaluated, yielding an elevation beam-steering range of \pm60{\deg}. In contrast, the transmitarray extends the elevation steering range to \pm78{\deg} while maintaining full 360{\deg} azimuthal coverage. The planar reflector exhibits a larger HPBW variation of 26.48{\deg}, compared with 13.1{\deg} for the transmitarray, resulting in a broader reflected-beam distribution and reduced directional power density, directivity, and gain. Meanwhile, the transmitarray maintains a more stable and controllable beamwidth response with greater directional power concentration over a wide steering range. The performance advantages of the transmitarray are demonstrated through comparisons with experimental results reported in the literature for planar reflectors and antennas. We further provide a comprehensive assessment of the performance advantages of the transmitarray over planar configurations across the remaining metrics.

I. INTRODUCTION

The paper compares a graphene-based hemispherical transmitarray with its geometrically corresponding planar reflector for wide-angle THz beam steering, while outlining the planar reflector’s theoretical basis. It presents the transmitarray’s wider steering range and describes graphene control and fabrication considerations.

I. INTRODUCTION

  • The hemispherical geometry provides nearly normal incidence at local elements, while multilayer cells and isolated graphene sectors support element-level phase control across the conformal aperture.The metallic patches and dielectric media boost local fields near graphene, so modest conductivity changes can significantly change transmission phase.Source: §I · pp. 1–2
  • The reported transmitarray efficiency ranges from 71% to 80%, with a 5% degradation across the scanning range attributed to practical fabrication imperfections.The cited work presents these metrics as suitable for real-time moving-target tracking.Source: §I · p. 2
  • The transmitarray reaches ±78° elevation steering with 40% relative bandwidth, while the planar reflector provides ±60° steering and full 360° azimuthal coverage.The comparison is specifically between the proposed transmitarray and its geometrically corresponding planar reflector, not a general comparison of antenna classes.Source: §I · p. 2
  • A hierarchical biasing architecture groups or multiplexes DC control lines for 121 independently tunable patches, reducing routing complexity while preserving the desired spatial phase distribution.Patches requiring identical chemical potentials can share a bias network; the lines are designed for high RF impedance to limit electromagnetic loading.Source: §I · p. 2

II. THEORETICAL BACKGROUND AND ANALYTICAL FORMULATIONS FOR THE PLANAR REFLECTOR

  • The planar reflector counterpart uses 121 independently controlled graphene sectors on a planar surface, with chemical potential tunable from 0.1–1.0 eV.Its sectors are physically and electrically isolated for independent electrostatic biasing and reconfigurable operation.Source: §II · p. 3

A. Graphene conductivity

  • At room temperature and sufficiently high chemical potential, the graphene conductivity expression reduces to the conventional intraband Drude formulation.The passage states that interband thermal excitation across the Dirac point is negligible when µc ≫ kBT.Source: A. Graphene conductivity · p. 3

B. Complete Unit-Cell Geometry in the Cylindrical Coordinate System

The planar reflector’s sectors are located in cylindrical coordinates, with ring populations and a separately modeled central apex defining its complete unit-cell geometry.

B. Complete Unit-Cell Geometry in the Cylindrical Coordinate System

  • The geometry locates reflector sectors by radial position and azimuth, with each ring’s population governing its azimuthal sector positions.The center of each (n, k)-th sector is defined from its ring and sector indices.Source: B. Complete Unit-Cell Geometry in the… · pp. 4–5
  • The linear ring-population model gives Nn = 8n for a = 8 and β = 1, producing 8, 16, 24, 32, and 40 sectors in the five active rings.Here, a sets the first ring’s unit-cell count and β controls how the count increases outward.Source: B. Complete Unit-Cell Geometry in the… · pp. 4–5
  • The central apex disk is modeled separately from the annular sectors, with its own region defined from the origin and its radial boundary.The apex spans the full azimuthal angle from 0 to 2π.Source: B. Complete Unit-Cell Geometry in the… · p. 5

C. Local Dimensions of Each Graphene Sector

The planar reflector’s sector dimensions account for local radial and azimuthal geometry, finite isolation gaps, and the effective area used in its equivalent circuit model.

C. Local Dimensions of Each Graphene Sector

  • Each sector’s radial width is set by Δρ, while its azimuthal periodicity follows the local arc length rather than the transmitarray’s sin θn scaling.Physical isolation introduces finite gaps in both radial and azimuthal directions.Source: C. Local Dimensions of Each Graphene… · p. 5
  • For symmetric rings, gap dimensions determine the equivalent RLC circuit parameters for each electrically isolated graphene sector.The azimuthal cell dimension depends on local arc length at radius ρn.Source: C. Local Dimensions of Each Graphene… · p. 5

D. Area of the Graphene Sector

  • The sector-area treatment distinguishes an exact annular-sector area from the effective physical area used in the equivalent circuit, which accounts for separation between adjacent sectors.The small-unit-cell area is approximated, and the effective area excludes the finite gaps rather than counting the entire annular sector.Source: D. Area of the Graphene Sector · p. 5

E. Resistance of each Graphene Sector

The planar reflector’s isolated graphene sectors are modeled with direction-dependent resistance and inductance based on their geometry and current orientation. The equivalent inductance combines graphene kinetic and geometric contributions.

E. Resistance of each Graphene Sector

  • Finite annular-sector geometry makes the effective surface impedance direction-dependent despite graphene’s scalar conductivity, with a scalar RLC impedance chosen along the dominant current direction.The aspect ratio compares radial width with azimuthal arc length.Source: E. Resistance of each Graphene Sector · p. 6
  • Radial and azimuthal current orientations yield separate effective sector-resistance expressions, using the corresponding geometry and graphene sheet resistance.The radial-current model assumes current flows along the radial dimension; coupled current components near resonance may require verification.Source: E. Resistance of each Graphene Sector · p. 6

F. Kinetic and Geometrical Inductance

  • Total inductance is modeled as the sum of graphene kinetic inductance, which depends primarily on chemical potential, and geometric inductance from the magnetic field of the current path.The lumped impedances account for sector aspect ratios and are expressed in ohms, unlike the sheet-impedance tensor in ohms per length.Source: F. Kinetic and Geometrical Inductance · p. 6

G. Capacitance of an Electrically Isolated Graphene Sector

The sector capacitance model combines coupling to the PEC ground plane with inter-sector and edge-fringing contributions. It also accounts for the multilayer dielectric stack and graphene’s quantum capacitance.

  • The total capacitance combines graphene-to-PEC coupling, inter-sector capacitive coupling, and finite-edge fringing effects.Electrically isolated neighboring sectors couple through electric fields and displacement current, not direct conductive current.Source: G. Capacitance of an Electrically… · pp. 7–8
  • Quantum capacitance accounts for graphene’s finite electronic density of states, and its value depends on sector area and tunable chemical potential.The chemical potential is controlled by the bias voltage applied to each graphene sector.Source: G. Capacitance of an Electrically… · p. 7
  • The oxide-stack capacitance represents electrostatic coupling through the hBN–SiO2 layers, with effective capacitance depending on sector area and equivalent dielectric thickness.Increasing graphene area raises this capacitance, while increasing equivalent dielectric thickness lowers it.Source: G. Capacitance of an Electrically… · p. 7, Figure 5 · p. 7
  • Fringing fields across finite radial and azimuthal gaps couple adjacent sectors, while fields extending beyond sector edges add edge capacitance.The radial-gap fringing capacitance is treated with a first-order approximation.Source: G. Capacitance of an Electrically… · pp. 7–8

H. Equivalent RLC Model

The planar reflector unit cell is represented by an equivalent RLC model whose response is electrically tuned through each isolated graphene sector’s chemical potential. The model links the sector’s inductance and capacitance to its resonance behavior.

  • The equivalent RLC model represents the impedance of each graphene sector, with total inductance comprising kinetic and geometric terms and total capacitance combining several contributions.The capacitance includes graphene-to-PEC, inter-sector-gap, and edge-fringing contributions.Source: H. Equivalent RLC Model · p. 8
  • Increasing chemical potential reduces graphene kinetic inductance and shifts the unit-cell resonance frequency upward, enabling direct electrical tuning of its response.Electrically isolated sectors can have their chemical potentials independently controlled through their corresponding gate voltages.Source: H. Equivalent RLC Model · p. 8
  • For greater electrostatic-model accuracy, additional capacitance contributions should be included, particularly at low chemical potentials.Source: H. Equivalent RLC Model · p. 8

III. ARRAY FACTOR OF THE PLANAR REFLECTOR

The planar-reflector array factor combines each sector’s local reflection, physical area, and horn illumination, then uses phase synthesis to direct the reflected beam. The synthesis selects feasible graphene chemical potentials while accounting for phase error and reflection magnitude.

III. ARRAY FACTOR OF THE PLANAR REFLECTOR

  • Each sector’s array-factor contribution combines its physical area, horn illumination, and local graphene reflection coefficient before far-field propagation phase is incorporated.The planar reflector’s incident-field amplitude varies spatially with feedhorn pattern, distance spreading, incidence angle, and polarization mismatch.Source: §III · p. 8, B. Phase Synthesis for Dynamic Beam… · pp. 9–10

B. Phase Synthesis for Dynamic Beam Steering

  • Beam steering requires phase coherence across the aperture: each sector’s tuned reflection phase matches the required phase so reflected fields align toward the desired far-field direction.The required phase accounts for incident-feed phase and propagation toward the target direction.Source: §III · pp. 8–9, B. Phase Synthesis for Dynamic Beam… · pp. 9–10

A. Annular-Sector Geometry

  • The area centroid provides a representative radial location for an annular sector because its area is nonuniformly distributed radially; the arithmetic midpoint is only a first-order approximation.The sector’s physical area is also incorporated into the array-factor amplitude coefficients.Source: A. Annular-Sector Geometry · p. 9

B. Phase Synthesis for Dynamic Beam Steering

  • Chemical-potential selection first enforces physical realizability and sufficient reflection magnitude, then minimizes phase error among attainable phase states.The feasible set is constrained by the graphene biasing range and a minimum allowable reflection magnitude.Source: B. Phase Synthesis for Dynamic Beam… · pp. 10–11

C. Array factor of the Planar Reflector

The planar-reflector array factor accounts for contributions from the graphene apex and annular sectors. The section defines efficiency and beam-quality metrics, then maps desired directions to sector bias conditions.

C. Array factor of the Planar Reflector

  • The reflector array factor combines contributions from the graphene apex and annular sectors using their positions and excitation amplitudes.The sector contributions are represented by their element patterns and array factors.Source: C. Array factor of the Planar Reflector · p. 11
  • Beam-pointing errors, normalized peak array-factor gain, and sidelobe level quantify steering accuracy, relative peak response, and undesired radiation.A lower sidelobe level indicates better suppression outside the main-beam region.Source: C. Array factor of the Planar Reflector · pp. 11–12
  • Reflector efficiency is the ratio of reflected to incident power, separating reflector losses from feed and illumination-path losses.Beam efficiency measures the incident power delivered into the desired reflected-beam region.Source: C. Array factor of the Planar Reflector · pp. 11–12
  • Dynamic steering maps the desired beam direction to a reflection phase and then to chemical-potential values across the graphene sectors.The sector chemical potentials provide the spatial bias distribution for steering.Source: C. Array factor of the Planar Reflector · p. 12

IV. BROADBAND BEAM-STEERING PERFORMANCE OF THE HEMISPHERICAL TRANSMITARRAY ANTENNA

This section contrasts the planar reflector with the hemispherical transmitarray and evaluates representative reflector steering configurations across frequency. The reflector’s assessment extends to 350 GHz.

IV. BROADBAND BEAM-STEERING PERFORMANCE OF THE HEMISPHERICAL TRANSMITARRAY ANTENNA

  • The reflector’s frequency evaluation extends to 350 GHz to further assess its beam-steering consistency.The comparison with the hemispherical transmitarray focuses on steering range and angular coverage over 200–300 GHz.Source: §IV · p. 12
  • Fig. 8 pairs graphene-sector bias distributions with reflected beams for four directions under vertical incidence across 200–300 GHz.The feedhorn is positioned approximately 41.7λ0 above the reflector.Source: Figure 8 · p. 12
  • Fig. 9 presents corresponding bias distributions and reflected-beam directions for oblique incidence at (θinc, ϕinc) = (40°, 20°).Its reported evaluation also spans 200–300 GHz.Source: Figure 9 · p. 13
  • Table I evaluates representative reflector bias distributions through reflected-beam characteristics and HPBW across 200–350 GHz.Source: Table I · p. 14

A. Broadband Beam-Steering Performance from 200 to 300 GHz

Across 200–300 GHz, the planar reflector’s steering performance depends on incidence angle and degrades near its large-angle limit. The hemispherical transmitarray supports wider steering through a more uniform aperture phase response.

A. Broadband Beam-Steering Performance from 200 to 300 GHz

  • Tailored graphene-sector biases produce spatial reflection-phase variation that directs the planar reflector’s beam electronically.Each desired direction corresponds to a unique bias-voltage distribution.Source: A. Broadband Beam-Steering Performance… · p. 14
  • Oblique illumination adds spatial phase variation across the planar aperture, progressively degrading patterns at large steering angles.Under normal incidence, the reflector has a more symmetric and stable phase distribution and wider steering angles.Source: A. Broadband Beam-Steering Performance… · p. 14
  • The hemispherical transmitarray steers approximately from −78° to +78°, beyond the planar reflector’s practical limit of approximately 60° elevation.The hemispherical geometry maintains more uniform phase differences across its aperture at large scan angles.Source: A. Broadband Beam-Steering Performance… · p. 14

B. Broadband Beam-Steering Performance from 200 to 350 GHz

The planar reflector’s reported performance across 200–350 GHz differs under normal and oblique illumination: consistent steering is reported, but oblique illumination does not maintain stability across that range.

B. Broadband Beam-Steering Performance from 200 to 350 GHz

V. ENHANCEMENT OF HALF-POWER BEAMWIDTH IN THE HEMISPHERICAL TRANSMITARRAY ANTENNA

The section compares beamwidth stability and bandwidth behavior in the hemispherical transmitarray and planar reflector, then relates radiation-performance characteristics to aperture excitation and FCC elements.

V. ENHANCEMENT OF HALF-POWER BEAMWIDTH IN THE HEMISPHERICAL TRANSMITARRAY ANTENNA

  • The transmitarray's HPBW variation is 13.1°, and its variation is reduced by approximately 50.6% under oblique and 46.4% under normal incidence versus the planar reflector.The transmitarray also provides a more stable, controllable HPBW response; the wider reflected-beam distribution of the flat reflector reduces power density, directivity, and gain.Source: §V · pp. 14–15

VI. SUBSTANTIAL BANDWIDTH IMPROVEMENT WITH FRACTAL CONCENTRIC CIRCULAR ELEMENTS

  • The FCC-ring optimization maximizes minimum phase span while keeping mean transmission above −12 dB; α=0.73 was rounded to 0.8, corresponding to 40% fractional bandwidth with |S11| below −10 dB over 200–300 GHz –[20].The ring dimensions are progressively scaled by 0.8 between successive concentric rings.Source: §VI · pp. 15–16
  • Beam-steering performance remains stable from 240–300 GHz with S11 below −10 dB; 3D radiation patterns show consistent steering and stable gains across 240–360 GHz, despite S11 degrading to approximately −5 dB at 360 GHz.Source: §VI · pp. 16–17

VII. MORE COMPARISON OF THE HEMISPHERICAL TRANSMITARRAY ANTENNA AND ITS PLANAR REFLECTOR COUNTERPART

  • The comparison assesses wave alignment, parasitic mitigation, mutual-coupling suppression, and moving-target tracking; the authors attribute radiation-control characteristics to hemispherical topology and FCC unit cells.The stated mechanisms include more efficient aperture excitation, radiation-pattern control, and consistent high-gain performance over a broad steering range.Source: §VII · p. 17

A. Intrinsic Feed-Wave Alignment and Spatial Phase Uniformity

The hemispherical aperture aligns the feed wave with its radial element positions, reducing feed-induced phase variation; the planar reflector instead needs phase compensation. The section also compares their steering performance and discusses the transmitarray’s geometry, elements, and tracking scope.

A. Intrinsic Feed-Wave Alignment and Spatial Phase Uniformity

  • Approximately 0° RMS phase error in the hemispherical aperture contrasts with the planar aperture’s nonuniform feed phase, which requires individual phase compensation.The hemispherical feed-wave and radial-position alignment minimizes feed-induced phase variation; compensation gives a uniform aperture phase for broadside radiation and a spatial phase gradient for steering.Source: Figure 14 · p. 17, A. Intrinsic Feed-Wave Alignment and… · pp. 17–18

B. Mitigation of Edge Diffraction and Parasitic Radiation

  • The hemispherical lens mitigates ground-plane surface-current propagation and edge diffraction, keeping radiated power concentrated in the intended main beam over broad-angle scanning.For planar arrays, currents can diffract from ground-plane edges and produce spurious radiation that makes apparent spherical coverage sidelobe-dominated.Source: B. Mitigation of Edge Diffraction and… · p. 18

C. Ohmic Loss Reduction Strategy

  • The transmitarray uses hollow FCC elements to reduce conductive material while preserving resonant paths and phase control, with full-wave analysis accounting for current concentration, diffraction, and coupling trade-offs.Its aperture primarily uses dielectric materials to avoid substantial ohmic dissipation associated with all-metal implementations.Source: C. Ohmic Loss Reduction Strategy · p. 18

D. High-Directivity FCC Elements for Mutual Coupling Suppression

  • FCC geometry improves individual-element performance and mitigates mutual coupling, supporting stable directivity, radiation efficiency, and sidelobe levels during large-angle scanning.Mutual coupling can reduce element directivity, distort the overall pattern, and degrade array aperture efficiency.Source: D. High-Directivity FCC Elements for… · pp. 18–19

E. Application for tracking moving targets

  • Practical moving-target tracking also depends on bias switching, graphene-device RC charging, controller update latency, and tracking-algorithm speed; their comprehensive evaluation is deferred to future work.Source: E. Application for tracking moving… · p. 19

VIII. CONCLUSION

  • ±78° versus ±60° elevation steering, with 360° azimuthal coverage in both; HPBW variation falls from 26.48° for the planar reflector to 13.1° for the transmitarray.The transmitarray’s lower beamwidth variation is associated with more stable radiation and greater directional power concentration, directivity, and gain, particularly at large steering angles.Source: §VIII · p. 19
  • The transmitarray’s beam-steering consistency and stability are verified across 240–360 GHz, with an operating frequency of 300 GHz.The paper also reports a 200–300 GHz steering frequency range with |S11| < −10 dB, corresponding to 40% fractional bandwidth, in prior work –[20].Source: §VIII · p. 19
  • Comparisons with reported planar reflectors and antennas highlight the hemispherical architecture’s steering range, beamwidth stability, and directional performance.The conclusion attributes the performance to the combination of hemispherical geometry and FCC elements.Source: §VIII · p. 19
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