Grid-Based Beam Steering

• Grid-based beam steering is a technique that employs spatially discretized elements, such as phased arrays and metasurfaces, to control beam direction through engineered phase gradients.
• Various platforms, including RF phased arrays, integrated optical phased arrays, and metasurfaces, implement this method to enable agile communications, imaging, and LiDAR systems.
• Advanced algorithms and analytical models optimize element settings to suppress sidelobes and counteract challenges like mutual coupling and quantization artifacts.

Grid-based beam steering refers to the systematic control and redirection of electromagnetic or optical beams using arrays of discrete radiating or scattering elements arranged on a spatial grid. These arrays—phased arrays, metasurfaces, or multi-element waveguide systems—coordinate element-level phase, amplitude, or state to synthesize a desired radiation pattern and steer the main lobe or focus in a programmable or dynamically tunable manner. This paradigm encompasses a broad spectrum of physical mechanisms, device platforms, and algorithmic strategies, allowing fine-grained manipulation of beams for communications, sensing, imaging, and adaptive optics.

1. Fundamental Principles of Grid-Based Beam Steering

The essential feature of grid-based steering is that a spatially discretized set of elements (antennas, waveguides, or subwavelength scatterers) forms the basis set for spatial control of the outgoing or incoming field. The spatial phases $\Delta\phi_n$ or amplitude weights assigned to each element on the grid determine the far-field (or near-field) pattern by forming a coherent superposition, as dictated by the Fourier transform of the complex aperture distribution. In classical phased arrays, the current or phase at each antenna element is tuned as

$a_n = \exp(j \Delta\phi_n)$

where the set $\{\Delta\phi_n\}$ encodes the beam direction $\theta_s$ via a linear relationship:

$\Delta\phi_n = k d n \sin \theta_s$

with $d$ the inter-element spacing and $k$ the wavenumber. This approach generalizes in optical phased arrays to the application of optical phase shifters (e.g., via Pockels effect, thermo-optics, or carrier injection) and in metasurfaces to spatially patterned static or dynamic phase gradients engineered on the subwavelength scattering elements.

A unifying spectral viewpoint is that the grid of elements serves as a “sampling” of the desired aperture function $a(x,y)$; the resulting angular spectrum or far-field radiation is its spatial Fourier transform, and beam steering corresponds to imparting a global phase tilt or, more generally, an engineered phase profile across the grid.

2. Physical Implementations and Device Architectures

Grid-based steering spans diverse physical implementations, each exploiting the grid paradigm:

• RF/microwave phased arrays: Arrays of dipoles, microstrip patches, or slot antennas use discrete electronic phase shifters or true-time delay elements per element, supporting rapid and flexible beam steering (e.g., (Ghasemi et al., 2017, Shad et al., 2019)).
• Integrated optical phased arrays (OPAs): Silicon or thin-film lithium niobate ridge waveguide arrays combine high-confinement waveguides with integrated phase shifters (thermo-optic (Kossey et al., 2017), electro-optic via Pockels effect (Li et al., 27 Jun 2025)) at subwavelength spacing, achieving fine angular resolution and wide field-of-view.
• Metasurfaces/metamaterials: Arrays of meta-atoms (metallic or dielectric resonant subwavelength scatterers) are programmed for spatial phase response—either passively via static design (gradient-index, impedance-matched metasurfaces (Dang et al., 2020)) or actively via external bias (graphene-based coding metasurfaces (Hosseininejad et al., 2020) or PIN-controlled elements (Jahangiri et al., 5 May 2024)).
• MEMS- and mechanically actuated arrays: Microelectromechanical (MEMS) actuation in grating or metastructure arrays (e.g., (Errando-Herranz et al., 2018, Deng et al., 2022)) enables beam steering via geometric transformation (e.g., gap dilation, in-plane shifting), harnessing grid periodicity for low-power, analog control.
• Multi-layer LC systems and hybrid solutions: Stacked grids of birefringent nematic LC cells (for shifting, steering, and expansion) yield programmable amplitude and phase control via electric fields (Mur et al., 2022).

Designs may exploit non-uniform arrays (Li et al., 27 Jun 2025) or hybrid grid approaches (superlattice OPA, multi-row or multi-face metasurfaces (Jahangiri et al., 5 May 2024)) to optimize for crosstalk, sidelobe suppression, and angular coverage.

3. Algorithmic and Mathematical Models

Beam steering on a grid is fundamentally an optimization problem over the set of discrete element settings (phase, amplitude, polarization state, coded bit, etc.). Two primary modeling approaches are prevalent:

a) Direct Phase/State Optimization

For classical arrays, the steering is commonly formulated as:

$\mathbf{a} = \mathcal{F}\{\mathbf{w}\}$

where $\mathbf{w}$ is the vector of element weights, and $\mathcal{F}$ denotes the spatial Fourier transform.

For digital/coding metasurfaces, element states are restricted (e.g., $b_i \in \{0, \pi\}$ for 1-bit, or a set of quantized phase states for $q$-bit designs). The overall array response becomes a sum over coded elements with discretized phase:

$E(\theta) = \sum_{n=1}^N a_n \exp[j(n-1)(\phi_n)]$

Optimizing $\{\phi_n\}$, given state and platform constraints, to minimize sidelobes or achieve precise steering, is typically performed via:

• Grid-based search over discretized angle/phase space (Eroglu et al., 2018, Eroglu et al., 2019) for performance metrics such as sum rate or fairness.
• Sparsity-constrained or $\ell_0$/$\ell_q$-relaxed combinatorial formulations (e.g., using majorization-minimization algorithms (Eroglu et al., 2018, Eroglu et al., 2019)).
• Evolutionary/global optimizers: Particle Swarm Optimization (PSO) and deep neural networks (Transformer) for low-dimensional control or compressed representation (Xia et al., 2022).

b) Analytical Physical Models

• Generalized Snell’s Law and phase gradient methods:

$$\sin\theta_r - \sin\theta_i = \frac{\lambda_0}{2\pi n_i} \frac{d\phi}{dy}$$

for metasurface beam steering (Jahangiri et al., 5 May 2024).

• Multipolar and lattice sum models in dielectric metalattices, incorporating lattice-induced modification of Mie scattering multipoles to engineer asymmetric (steered) scattering (Liu et al., 2017).
• Electromagnetic full-wave and transfer-matrix calculations for optical, THz, and metamaterial platforms (Dang et al., 2020, Hosseininejad et al., 2020).

Comprehensive modeling must also account for near-field/far-field mapping (Simončič et al., 25 Mar 2024), polarization effects, and other physical effects such as crosstalk, mutual coupling, quantization-induced quantized beam patterns, or combinatorial constraints in constrained hardware (limited number of controllers, bit resolution).

4. Performance Metrics and Optimization Criteria

Performance evaluation in grid-based beam steering systems focuses on:

• Beamwidth and angular resolution: Defined by array aperture, element spacing, and design optimization; e.g., FWHM of $0.99^\circ \times 0.63^\circ$ in a lithium-niobate OPA (Li et al., 27 Jun 2025), or $17^\circ$ in a silicon OPA (Kossey et al., 2017).
• Steering range/field of view (FOV): Expressed in degrees, typically limited by element spacing (to avoid grating lobes), modulation range (max achievable phase shift), or physical design (e.g., metasurface geometry, electrode design, or MEMS displacement limits).
• Sidelobe levels (SLL): Measured relative to the main lobe, high suppression (e.g., $-20$ dB in (Li et al., 27 Jun 2025)) is vital for spatial selectivity and communication link integrity.
• Insertion/absorption loss, energy efficiency: Maximized transmittance, minimized reflection or absorption when desired; e.g., sub-$\mu$W power in MEMS optical beam steering (Errando-Herranz et al., 2018), absorption S-parameter $< -10$ dB in metasurfaces (Jahangiri et al., 5 May 2024).
• Operational bandwidth: Measured over GHz bands in microwave or THz regimes; e.g., broadband $3-12$ GHz operation in an SPMT-based device (Zhang et al., 5 Sep 2025).
• Dynamic/tunable operation: Time/frequency agility, e.g., 100%-duty-cycle 9.8 GHz ultrafast scans in EO comb-based arrays (Seshadri et al., 6 Apr 2024), or high modulation rates ($6$ kHz) in 2DOF metasurface mechanical systems (Deng et al., 2022).
• Topological and polarization control: Degree of freedom in topological charge or handedness, critical in advanced optical/quantum communication (e.g., BIC nanolasers with tunable topological charge, (Chen et al., 19 Jul 2024)).

Optimizers or machine learning models (Transformer, PSO) can yield non-uniform, dimension-reduced, or compressed representations for reduced controller count, trading a small compromise in beam fidelity for major savings in hardware complexity (Xia et al., 2022).

5. Practical Applications and System-Level Implications

Grid-based beam steering finds application across diverse domains:

• Wireless communications and 5G/6G: Rapid beam alignment for mmWave links, RIS-based smart environments, high-gain, wide-FOV, and agile base station or user equipment antennas (Shad et al., 2019, Roberts et al., 2022, Jahangiri et al., 5 May 2024).
• Optical wireless, LiDAR, and imaging: High-resolution mapping, high speed LiDAR with low crosstalk, large FOV OPAs with rapid scanning (Kossey et al., 2017, Li et al., 27 Jun 2025), and projection systems with reconfigurable patterns (Mur et al., 2022).
• Integrated photonics and compact beam control: MEMS and EO platform advances for chip-scale high-precision OPAs, ultracompact nanolaser beam steering combining generation and steering in a single device (Errando-Herranz et al., 2018, Chen et al., 19 Jul 2024).
• Metamaterials and terahertz components: Flat optics, lenses, cloaking, and beam steering in THz with high efficiency (Dang et al., 2020, Hosseininejad et al., 2020).
• Multi-functional systems: Devices performing beam steering alongside beam compressing, shifting, and shaping; e.g., SPMT for simultaneous steering and beamwidth compression (Zhang et al., 5 Sep 2025), layered LC structures imparting shifting, steering, and expansion (Mur et al., 2022).
• Resource-constrained environments: Satellite, IoT, and deep-space missions benefit from dimensionality-reduced arrays for lower-cost, lower-power operation (Xia et al., 2022).

Trade-offs persist among design parameters (aperture, bit-depth, active controller count, loss budget, beam shape), which are explored in performance and scalability studies (Hosseininejad et al., 2020), including programmability and integration with controller/FPGA logic.

6. Advanced Concepts and Future Directions

Recent research identifies several frontiers and emerging themes:

• Dynamic/ultrafast beam steering: EO comb arrays for GHz-rate, full-duty-cycle scans, eliminating reliance on slow thermal or mechanical tuning (Seshadri et al., 6 Apr 2024).
• Compressive and AI-driven beamforming: Leveraging SVD, PSO, and Transformer models for compressed, low-controller beam steering in massive arrays (Xia et al., 2022).
• Topological and singularity-based steering: BIC nanolaser arrays exploit topological charge control for directional lasing and OAM mode generation (Chen et al., 19 Jul 2024).
• Multi-degree-of-freedom actuation: Mechanically actuated metasurface doublets demonstrate high-speed, wide-FOV beam control with only two DOF, matching the parameterization of the planar output wavefront (Deng et al., 2022).
• Non-planar and conformal grid systems: Dual-faced and curved metasurfaces enable advanced beam control on complex surfaces, mitigating quantized beam artifacts (Jahangiri et al., 5 May 2024).
• Simultaneous multifunctional operation: Devices simultaneously steering and compressing beams, providing enhanced control for high-density, broadband communication systems (Zhang et al., 5 Sep 2025).
• Fundamental limits and moiré-based models: Moiré effect theory provides a physical lens for understanding beam steering as spatial interference between source and mask distributions, elucidating the role of geometric transformation (scaling, rotation, translation) in grid-based systems (McGuyer et al., 2021).

7. Challenges, Limitations, and Outlook

Despite major advances, several persistent challenges remain:

• Crosstalk and mutual coupling: High-density arrays require superlattice and non-uniform designs to mitigate crosstalk.
• Quantization artifacts: Low-bit metasurfaces may yield staircase or quantized beams unless specifically engineered (e.g., via dual-face geometries).
• Scalability and integration: Achieving large aperture, low-loss, and high-speed performance on a monolithic or integrated platform remains a central objective (Li et al., 27 Jun 2025, Seshadri et al., 6 Apr 2024).
• Polarization and polarization mismatch: Especially in near-field steering, polarization artifacts must be managed to retain efficiency (Simončič et al., 25 Mar 2024).
• Complexity and hardware budget: Reducing controller count, power, and footprint—while retaining agility and fidelity—underscores ongoing work in compressed beamforming and reconfigurable IC integration.

Grid-based beam steering thus remains a core enabling technology for current and future wave-based engineering across the electromagnetic spectrum, with continuing innovation in devices, algorithms, and system architectures defining the research landscape.