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Designing Phased Arrays and Metamaterials with Floquet Unit-Cell Analysis
- RF & Microwave
- Aerospace & Defense
- Telecommunications
- Quantum Computing
What This Simulation Does
The cylinder_floquet example applies a Floquet periodic boundary condition linking the two end faces of the cell at a fixed phase shift. This turns the geometry into a unit cell of an infinite periodic structure and computes the modes for a prescribed propagation constant — the workflow behind phased arrays and periodic waveguides.
- Floquet–Bloch condition — E(r + a) = E(r)·e−j k·a between donor and receiver faces, with Floquet wave vector k = [0, 0, 0.2] here
- Dispersion (band) diagram — sweeping k traces the frequency-vs-phase relationship of the periodic cell, mapping pass and stop bands
- Order-4 elements on a tetrahedral mesh; the inter-cell phase shift (scan angle) is imposed directly through the boundary
Key Parameters
- Problem type: Eigenmode, tetrahedral mesh, length unit L0 = 1 cm
- Material: dielectric fill, εr = 2.08, μr = 1.0, loss tangent 0.0004
- Boundaries: end faces = Periodic (Floquet wave vector [0, 0, 0.2]); side wall = PEC
- Eigensolver: 15 eigenpairs, target 2.0 GHz, tolerance 1e-8
- Inner solve: GMRES + multigrid preconditioner, GPU device (order 4)
The core transferable physics: an infinite periodic structure can be analyzed from a single unit cell by imposing a Bloch phase between its faces. Sweeping that phase yields the dispersion diagram — the band structure that governs how waves propagate, scan, or are blocked. This is the foundation of phased-array scanning, frequency-selective surfaces, and metamaterials.
What Makes This Capability Unique
Infinite array from one cell.
Floquet periodicity captures the full infinite-array behavior from a single unit cell, cutting the model size by orders of magnitude.
Scan angle as a knob.
The inter-cell phase is imposed directly, so scanning an array or shifting a band is a parameter sweep, not a re-mesh.
Full dispersion diagram.
Sweeping the Floquet vector produces the band diagram that reveals pass-bands, stop-bands, and scan blindness.
High-order, GPU-fast.
Order-4 tets on GPU resolve the cell accurately while keeping scan/band sweeps quick.
Domain Applications
Select a domain to see how this simulation applies, with industry-specific scenarios and ROI.
The Problem
Frequency-selective surfaces (FSS), electromagnetic band-gap structures, and metamaterials are engineered periodic media whose behavior is defined entirely by their unit cell and its dispersion. Designing them by simulating a large finite tile is prohibitively expensive and still misses the true infinite-array response.
Without unit-cell analysis, teams iterate on fabricated panels — each etched or machined panel costing $5K–$50K and weeks — to find the pass/stop bands empirically.
Floquet eigenmode analysis delivers the dispersion diagram directly, so the band edges and responses are known before fabrication.
Applications
| Application | How this simulation maps |
|---|---|
| Frequency-selective surfaces | Dispersion diagram gives pass/stop bands vs incidence phase |
| Metamaterial / EBG design | Band gaps located directly from the Floquet sweep |
| Periodic waveguide filters | Bloch modes set the periodic-structure pass-band |
Quantifiable Business Value
Scenario: An FSS/metamaterial group builds 15 periodic-panel designs/year at 6 fabricated iterations each. Unit-cell analysis cuts iterations to 2.
Correct band placement on the first fabricated panel also unlocks faster program milestones for radomes and reflectarrays.
Recommended Next Steps
Model your unit cell
Replace the geometry with your periodic cell and set the Floquet wave vector for the scan/phase of interest.
Sweep the phase
Vary the Floquet vector to trace the dispersion diagram and locate pass/stop bands and blindness angles.
Compare periodicity types
Contrast with cylinder_waveguide (translational periodicity) and the closed cylinder_cavity_pec baseline.
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