Start each investigation by identifying the object, its environment, the incident wave, and the response being measured. These original drawings depict the models used in this book. The ridge and film cuts show a finite visible portion of structures that extend indefinitely; a drawn edge does not create a simulated finite device.
A map from structure to result¶
| Chapter | Object or model | What the result describes |
|---|---|---|
| 1 | Ideal sheet with two equivalent response channels | Analytical specular reflection and transmission; no particle shape assigned |
| 2 | Planar interface, uniform film, electric sheet, or specified Jones element | Boundary scattering, interference, or polarization in that restricted model |
| 3 | Identical dielectric ridges repeated along x, invariant along y | Complex scattering of a periodic ridge environment as its width changes |
| 4 | A periodic interface with stated period and illumination | Allowed diffraction channels; motif shape and scattering powers are not solved |
| 5 | Six different ridges forming one repeated supercell | Collective reflected/transmitted order powers; separate scalar/Jones exercises use their own models |
| 6 | A uniform dielectric slab, infinite along x and y | Numerical approximation to a known film-scattering problem |
| 10 | Synthetic analytical resonant sheet | Learning and inverse-search performance on analytical data; no fabricated unit cell |
Chapter 3: one ridge width, repeated everywhere¶
The dashed boundaries enclose one unit cell. The neighboring ridges have the same width; changing the slider changes that width in every cell. The visible ridge ends are illustrative cuts along the invariant y direction. The numerical field varies in x and z, with electric field along y.
Read the phase and power as the response of this entire repeated environment. The material indices are ideal model inputs, not a claim about a measured material. The unit-cell explorer updates the drawing from the selected saved width.
Chapter 5: six widths act together¶
This is the saved expanded beam-steering design. Its full six-ridge sequence repeats with L = 6Λ = 3.90 µm. A purple boundary marks the whole supercell. The solver calculates the collective scattering of this geometry, including coupling and every open diffraction order.
Changing a case in the synthesis explorer changes the widths and common height in the drawing together with the saved results. Reversing the sequence mirrors the design and exchanges positive/negative order powers. These ridges are not a finite metalens: the later focus plots propagate prescribed scalar aperture fields and do not simulate a fabricated focusing structure.
Chapter 6: a film benchmark, with numerical nodes¶
The slab is physically uniform along x and y. Only z is discretized. Dots denote numerical field nodes, not extra material layers. In the reference drawing N = 8 and the computational boundaries lie on the two film faces; exterior padding moves those boundaries. Reflection is referenced to z = 0, transmission to z = d.
The numerical explorer changes the displayed mesh count and padding annotation with its controls. Refining N changes the numerical approximation while preserving the physical film. Its fields and errors benchmark a solver method; they are not the results of a patterned metasurface simulation.
Chapters 1 and 10: draw the equivalent model honestly¶
The ideal sheet is a two-port boundary description. No pillar, ring, split-ring, or physical thickness has been assigned. Chapter 1 varies equivalent response channels; Chapter 10’s abstract design coordinate tunes its analytical generator rather than a specified nanostructure.
A learned response does not establish a physical geometry. Connecting it to a ridge or another manufactured shape requires a geometry-dependent electromagnetic dataset and fresh verification.
Before interpreting any plot¶
Point to the object and name every direction in which it repeats or remains invariant.
Read the geometric parameters, material indices, wavelength, illumination, and polarization.
Identify the physical reference planes and distinguish numerical nodes/boundaries from material interfaces.
Name the plotted quantity: field, complex amplitude, incident-normalized order power, scalar intensity, or model-prediction error.
Keep the geometry and model label with exported results. These drawings use the book’s saved parameter files and the original shared renderer
templates/model-geometry.js; they are generated without external artwork.
The same six-ridge geometry now anchors ms-09 spectral sweeps, ms-10 local/supercell comparisons, and ms-11 bounded width optimization. Their browser drawings follow the saved wavelength, width contrast or selected candidate.