Full-wave · openEMS

Full-wave validation with openEMS — a free FDTD solver running on the machine that hosts this page. Configure below and run: a rectangular waveguide with your chosen wall material. Tick which simulations to run (guided wave, reflection, S-parameters, field/loss map, angle sweep); the charts overlay this tool's fast analytical model so you can see how well they agree.

Run on openEMS — automated

Pick the configuration and run the full-wave solver directly. (Requires the local bridge: start openEMS/openems_server.py and open this page at http://localhost:8731.)

Configuration

Band

X (8–12 GHz)Ku (12–18 GHz)K (18–27 GHz)

Material

MXene-coated basswood

Coats

Length (mm)

Structure

Rectangular waveguide

Ports

2-port · thru (S11 + S21) 1-port · reflection (S11)

Mesh

Coarse · λ/15 (fast) Normal · λ/20 Fine · λ/30 (slow)

Field view

Time-domain (animation) Frequency-domain (steady |E| at f₀)

Simulations

▦ Preview geometry Run on openEMS

Multi-layer coating stack block + up to 3 stacked layers (Layer 1 = innermost, faces the wave). Overrides the Material selector above.

Block substrate

Layer 1 · innermost

Coats

Layer 2

Coats

Layer 3 · outer

Coats

Set the layers to see the analytical stack readout; Run to solve on openEMS with the stack's effective wall.

Checking whether the solver bridge is reachable…

Summary Copy summary Show math ⬇ Run manifest (JSON) Download results

What you're looking at

• The 3-D box with the bright green outline is the waveguide itself — the wall material you chose (e.g. basswood) with its inner conductive coating (e.g. MXene) lining the inside. The coating is only microns thick, so it is represented by the inner surface, not drawn to scale.
• The glowing colour is the electric-field strength |E| (see the colour bar, in V/m): bright/red = strong field, dark = little or no field.
• The wave is launched at one end (the input port) as the TE₁₀ mode and travels along the guide's long axis (left → right in the view).
• Any colour outside the green outline is signal leaking through the wall — large for a poor conductor (bare wood, too-thin coating), negligible for a good one (MXene, copper, silver).
• Guided wave = the travelling signal (transmission). Reflection = a wall placed across the far end so the wave bounces back into a standing-wave pattern (fixed bright/dark bands); a strong, stationary pattern means a near-perfect reflector.
• In Field view → frequency-domain the picture is a single steady |E| snapshot at the band-centre frequency instead of an animation.

Simulated field — what the animation shows ⓘ

Renders come from openEMS. The insertion-loss chart below uses the openEMS S-parameters from the guided run.

1 · Insertion loss — openEMS vs modelⓘ

openEMS S21 loads automatically after a run; the model's predicted loss over the same length is overlaid.

2 · S-parameters — S11 (reflection) & S21 (transmission)ⓘ

From the openEMS solve when the S-parameters simulation is ticked. S11 = fraction bouncing back at the input (more negative dB = better matched); S21 = fraction getting through (closer to 0 dB = lower loss).

3 · Far-field radiation pattern — the guide's open end (aperture antenna)ⓘ

A waveguide's open end radiates like an aperture antenna. The analytical open-ended TE10 pattern (Balanis) is shown instantly for the current band — E-plane (φ=90°) and H-plane (φ=0°), normalized to the main beam. Tick "Far-field radiation pattern" in the Simulations picker and Run to overlay the full-wave openEMS NF2FF result automatically (or load a CSV manually below).

4 · Reflection / transmission / absorption — openEMS vs modelⓘ

Transfer-matrix model R/T/A (current Materials test material), shown automatically. Load an openEMS R/T/A file to overlay.

5 · R/T/A vs incidence angle — modelⓘ

Oblique-incidence (TE) model vs angle at band centre, shown automatically. Load an angle-sweep file to overlay.

Horn antenna · analytical design (instant)

Design a horn instantly from its dimensions (analytical aperture theory, this tab), then validate the full 3-D structure with the openEMS FDTD solve (the Full-wave sub-tab). An antenna is a different problem from a closed waveguide — it uses open (PML) boundaries and a near-field-to-far-field transform for gain.

Horn antenna · inverse design & sweep

Inverse design & parametric sweep

Size the shortest optimal-gain horn for a target gain, or sweep aperture × flare and rank the results — all instant (analytical). Uses the frequency/type from the Horn design sub-tab.

Horn antenna · comparison & coating trade

Design comparison & lightweight-coating trade

Pin designs on the Horn design sub-tab (📌) and they overlay here. Below, the core project trade: a thin conductive coating on a light basswood shell vs a solid-metal horn — gain penalty against mass saved.

Horn antenna · full-wave (openEMS)

Full-wave validation (openEMS)

Upload a CAD design (or use the loaded WR-90 horn), run a full 3-D FDTD solve, and compare gain, S11, pattern and the per-coating loss against the instant analytical design.

Full-wave validation — run on openEMS

Requires the local bridge: start openEMS/openems_server.py and open this page at http://localhost:8731. A run takes ~1–2 minutes. Leave the file empty to use the loaded WR-90 X-band horn.

Configuration

CAD design (.step)

Choose .step (default horn)

Band

X (8–12 GHz)Ku (12–18 GHz)K (18–27 GHz)

Inner coating

MXeneCopperSilverAluminumPEC (ideal)

Mesh

Normal · λ/15 Fine · λ/20 (slow) Finer · λ/25 (slower)

Field view

Frequency-domain (steady |E|) Time-domain (animation)

▦ Preview geometry Run antenna sim

Checking whether the solver bridge is reachable…

⬇ Download Excel (all data) ⬇ Download files (PNG · CSV · text) Summary Show math ⬇ Run manifest (JSON)

Field scale dB Linear

Simulated field · interactive 3-Dⓘ

Volume Cut-plane Reset view

Gain vs frequencyⓘ

S11 vs frequencyⓘ

Radiation pattern at f₀ — E-plane (φ=90°) & H-plane (φ=0°)ⓘ

Geometry · interactive 3-Dⓘ Reset view

Coating comparison — gain penalty vs solid metalⓘ

Conductor loss on the horn walls, computed from the full-wave field via the surface-impedance method (the surface-impedance boundary method for finite conductivity). Radiation efficiency = radiated ÷ accepted power.

Radar cross section · openEMS

How detectable is a target by radar — and how much does a coating hide it? A plane wave illuminates the target in openEMS; a near-field-to-far-field box captures the scattered field and returns the radar cross section (RCS). The instant analytical curve (exact Mie series for a sphere [37], physical optics for a plate [38]) is overlaid so you can see the full-wave solve tracks it. Coating a metal target with a lossy absorber (magnetite, carbonyl iron, …) lowers the RCS — the reason radar-absorbing materials exist.

Run on openEMS — automated

Pick the target and run the full-wave RCS solver. (Requires the local bridge: start openEMS/openems_server.py and open this page at http://localhost:8731.) A coated run also solves the bare metal target for the reduction figure, so it takes about twice as long.

Scattered-field animationⓘ

An animation of the radar wave (green arrow, entering from the left) washing over the target; colour is the electric field. It shows the total field (incident + scattered) inside the excitation box, so you can watch three things: the incoming wavefronts, the standing-wave ripples where the reflection off the front interferes with the incoming wave, and the shadow cast behind the target. A stronger reflector makes sharper ripples; a good absorber softens them. Toggle to a steady peak-|E| snapshot: AnimationSteady |E|

3-D scattering lobeⓘ Interactive 3-DRendered GIF

The target's scattering shown as a 3-D surface: it bulges outward in directions where the target scatters strongly and pinches in where it scatters little; colour is RCS in dBsm. The green arrow is the incoming radar direction — the bulge pointing away from it is forward-scatter, and the return back along it is the monostatic echo. Unlike the field animation, this is the pure scattered far field (the incident wave removed), so it is exactly what a radar network would measure. Drag to rotate, scroll to zoom the interactive view.

The full theory — how RCS is defined (the far-field σ limit and dBsm), the scattering mechanisms, and how full-wave methods (FDTD, MoM) differ from the high-frequency asymptotic methods (PO, PTD, SBR) used for whole vehicles — now lives on the The physics ↗ tab, alongside the waveguide and horn derivations. Every formula there is cited.

Inverse design · radar-absorbing material

Design me the coating

Instead of testing one coating, set the target — "≥ X dB RCS reduction across the band" — and the tool searches absorber materials, thicknesses and layer counts to find the lightest coating that hits it. It evaluates each candidate with the exact metal-backed transfer-matrix (the same physics as a flat coated reflector), returns the Pareto frontier of reduction vs areal mass, seeds the classic Salisbury / Dallenbach / Jaumann archetypes, and shows the Rozanov thickness bound — the hard physical limit on bandwidth for a given thickness. One click sends the winner to the RCS tab to validate on a real 3-D target.

Radar-absorbing material · saved materials

Material library — compare your saved materials

Every material you pin with 📌 Pin material to library on the Reflection-loss (RL) tab lands here. This page overlays their reflection-loss curves so you can see, side by side, which material absorbs best and over what bandwidth — and the same library feeds the per-part coating dropdowns on the CAD-RCS tab. Everything is analytical and instant; the library is stored in your browser and survives between sessions.

RCS · batch parameter sweep

Sweep one parameter, unattended

Vary one parameter — coating thickness, conductivity, loss, target size or incidence — across a range, and the tool runs a full openEMS RCS solve at each value in sequence, plotting how the RCS (and coating reduction) responds. Leave it running; each solve is 20–60 s.

Answering "how thick does the absorber need to be?" Start on Fast material search instead — it evaluates thousands of ε/μ and thickness combinations in closed form in a few seconds. Come back here to confirm the winner with real full-wave solves, which is what this tab is for.

How the batch runner works

• Each step is a real openEMS solve (monostatic only, coarse mesh) sent to the same /run_rcs bridge as the RCS tab. They run one at a time — the bridge writes to fixed paths, so concurrent solves would collide.
• The chart fills in live after each solve; press Stop after current to halt cleanly. Rough time = steps × 20–60 s.
• For a coating/solid sweep, the bare-metal reference is solved once per step too, so the reduction curve is honest at every point.
• Results are downloadable as CSV for plotting elsewhere.

Scripting it yourself (headless API)

The bridge is a plain JSON API, so you can drive these sweeps from Python/curl for unattended overnight runs. Every field on the RCS tab maps to a key in the /run_rcs POST body:

import requests
for t_mm in [0.5, 1, 2, 3, 4]:
    r = requests.post("http://localhost:8731/run_rcs", json={
        "shape":"sphere", "size1":15, "band":"X",
        "construct":"coated", "sigma":5, "epsr":15, "epspp":3,
        "mur":3, "mupp":1.5, "thick":t_mm/1000,     # metres
        "cells":18, "nfreq":51, "endcrit":1e-4,
        "sims":["monostatic"]
    }).json()
    mid = r["coated"]["freq"][len(r["coated"]["freq"])//2]
    print(t_mm, "mm →", round(mid["dbsm"],2), "dBsm  · reduction",
          r["reduction_db"], "dB")

Response keys: bare/coated (each with freq, bistatic, …), reduction_db, polar, files, seconds, errors. The keys above are the complete set; the defaults live in openEMS/openems_server.py.

Radar-absorbing material · reflection loss & RCS

Reflection loss from measured ε/μ — then RCS

Type a material's ε and μ (or upload a measured dispersion file straight from your lab — CSV, text or Excel) and get the reflection loss of a metal-backed absorber for every thickness at once, the thickness–frequency map that locates the optimum, the effective absorption bandwidth, impedance matching and attenuation — then turn the same material straight into a coated-plate RCS reduction. This reproduces the standard microwave-absorber workflow from the reference papers [47]–[51] in one place. The engine is the exact metal-backed transmission-line formula RL = 20·log₁₀|(Z_in−1)/(Z_in+1)|, Z_in = √(μ_r/ε_r)·tanh(j·2πfd/c·√(μ_rε_r)) — validated against the reference Excel to ~0.01 dB.

Radar cross section · imported CAD · analytical PO + PTD

CAD-RCS — radar signature of an uploaded model

Upload a 3-D model (STEP or STL — a rocket, drone, satellite fitting…) and get its analytical, instant monostatic radar cross section versus look-angle, plus how a radar-absorbing coating on each part cuts it down. The engine is Physical Optics (the specular "tiny-mirrors" surface return) + first-order Ufimtsev PTD edge diffraction, with the coating applied per-facet through the same reflection-loss physics as the RL tab — the standard asymptotic method used for electrically-large targets that full-wave solvers cannot fit [38][40]. Honest scope: PO+PTD captures specular + first-order edge returns (validated vs openEMS full-wave on a plate: broadside 0.15 dB, wide-angle/edge floor ~3.5 dB — while PO alone is up to 70 dB wrong at grazing). It does not model multiple bounces / cavities (corner reflectors, nozzles), creeping or travelling waves, tip diffraction, or ray self-occlusion (shadowing is per-facet by surface normal only). Curved-edge PTD is approximate. Use the openEMS tab for cavities, coatings-on-edges, and resonances. Everything here is analytical; the "Verify on openEMS" button cross-checks a small part with full-wave.

Radar-absorbing material · parametric sweep

Sweep the design space — find what absorbs most

Run thousands of reflection-loss calculations at once, varying coating thickness, frequency and the material's ε/μ, and rank every combination by how strongly it absorbs. Reflection loss is closed-form, so this is instant — no full-wave solves (that is the difference from the openEMS Batch sweeps tab, which runs one slow full-wave solve per point and is for validating a shortlist). Built for mapping a material design space for a paper: sweep → rank → export.

Inverse design · waveguide

Design the optimal lightweight guide

Instead of picking a material and reading the performance, set the target and what to minimize. The optimizer searches every coating / substrate / number-of-coats combination in the catalog — plus every solid metal — on the validated analytical engine, and returns the Pareto-optimal designs: the best achievable trade-off between signal loss and mass, cost, or carbon.

Optimize ▸ searches the whole catalog for the best design in the band selected above. Trade-space report (X/Ku/K) ▸ runs that search for all three satellite bands at once — using your current objective, max-loss and launch-cost settings — and opens a clean, printable one-page table naming the single best design for each band (loss, mass, delivered cost and CO₂). It's the "hand-in / save-with-the-run" summary; use Save report as PDF in the print dialog.

Design space — loss vs the objectiveⓘ

Every dot is one buildable design. The green frontier is the Pareto-optimal set — designs where you cannot lower one axis without raising the other. The orange marker is the recommendation for your target. Both axes are logarithmic; lower-left is better.

Best designs for your target

Measurement → simulation bridge

Extract your coating's real conductivity from a measurement

Upload a measured transmission curve (S21) from a vector network analyser — CSV or Touchstone .s2p — and the tool fits the effective conductivity of the wall that reproduces your data. It closes the loop between the lab bench and the model: coat a guide, measure it, and read off the RF conductivity your process actually achieved.

Upload a CSV (freq_ghz, s21_db) or a Touchstone .s2p file to begin.

Space survivability

Can this part actually survive in orbit?

Low loss is necessary but not sufficient — before an RF part flies, two vacuum-specific failure modes decide whether it works: multipaction (an electron avalanche that collapses the signal and can damage the part) and overheating (in vacuum a wall can only shed absorbed power by radiation). These first-order screens flag both. They're the go/no-go questions no generic EM tool asks.

1 · Multipaction screeningⓘ

At high power in hard vacuum, electrons knocked off the wall can multiply in resonance with the RF field and avalanche — destroying the signal. Susceptibility scales with the frequency×gap product and the peak gap voltage.

2 · Power handling & heating in vacuumⓘ

The wall absorbs a little of the signal as heat. In air that convects away; in vacuum the wall can only radiate it. This finds the steady-state wall temperature and the maximum power before the coating degrades.

Material comparison

The leading waveguide candidates — solid metals and metal/MXene-coated lightweight blocks — with their analytical metrics computed instantly (no solver needed). Press Run on any row to validate that material with the openEMS full-wave solver (needs the local bridge running). Then Generate summary of whatever you ran and Download all — images, field animations, and CSV files of every curve.

Loss = mid-band conductor attenuation (dB/m, lower is better). Weight & delivered cost are per metre of guide (four walls). Break-even = launch cost above which the material beats solid copper to orbit. openEMS S21 = the full-wave transmission through the simulated section: how much signal reaches the far end, in decibels (0 dB = nothing lost; each −3 dB ≈ half the power). The % next to it is that in power, 10^(S21/10); the second line is the loss per metre. Press Expand on any row to see its 3-D field animations and S-parameter graphs in a pop-up. openEMS columns fill in after you Run a row.

Everything the simulator computes comes from one chain of physics: an electromagnetic wave travels down a hollow rectangular pipe, and the imperfectly-conducting walls steal a little energy from it on every bounce. Here is the full derivation, in order.

Inside a rectangular guide of internal width $a$ and height $b$ (with $a>b$), the lowest-order wave pattern that can travel is the TE10 mode — the standard operating mode for satellite waveguides. Maxwell's equations, solved for this geometry, give every result below (Pozar, Microwave Engineering [6]).

Every material enters Maxwell's equations through three numbers: conductivity $\sigma$, permittivity (its electric response) and permeability (its magnetic response). The last two are quoted relative to free space [6]:

with $\varepsilon_0 = 8.854\times10^{-12}$ F/m and $\mu_0 = 4\pi\times10^{-7}$ H/m. Permittivity $\varepsilon_r$ sets how the material stores electric energy; permeability $\mu_r$ how it stores magnetic energy. Together they fix the wave impedance and how fast/short the wave is inside the material:

For a conductor the free-electron response dominates and is folded into a complex permittivity:

A waveguide is a high-pass filter: below a cutoff frequency $f_c$, the wave cannot propagate at all. For TE10 it depends only on the width $a$ [6]:

where $c$ is the speed of light. This is why each band uses a different guide size — wider guides for lower frequencies.

At microwave frequencies the wall current crowds into an extremely thin surface layer. Its characteristic depth is the skin depth $\delta$ [6]:

$f$ = frequency, $\mu_0\mu_r$ = permeability ($\mu_r\approx1$ for these non-magnetic materials), $\sigma$ = conductivity. This is the single most important quantity in the whole MXene story: because MXene conducts ~58× worse than copper, and skin depth scales as $1/\sqrt{\sigma}$, its skin depth is about $\sqrt{58}\approx8\times$ larger (~5 µm vs ~0.66 µm at 10 GHz). A coating thinner than the skin depth lets the wave "leak" straight through it. (A magnetic material with $\mu_r>1$ has a thinner skin depth and therefore higher wall loss — that is how permeability enters.)

The energy lost per bounce is set by the wall's surface resistance $R_s$. For a thick wall [6]:

But a thin coating on a non-conducting substrate (MXene on wood) is not a thick wall. If the coating thickness $t$ is comparable to or smaller than $\delta$, the effective resistance rises sharply (thin-film surface impedance [6]):

When $t \gg \delta$, $\tanh \to 1$ and the coating behaves like solid metal. When $t \ll \delta$, $R_s^{\text{eff}}$ blows up — a useless wall. As a rule of thumb the coating needs $t \gtrsim 3\delta$; that is exactly the "coating ÷ skin depth" indicator on the simulator, and why stacking ~15–20 coats matters.

The TE10 conductor attenuation (Pozar, Microwave Engineering [6]) gives how fast the signal decays along the guide, in nepers per metre:

where $\eta_0 = \sqrt{\mu_0/\varepsilon_0} \approx 376.7\ \Omega$ is the impedance of free space. Converting to decibels:

This $\alpha_{\text{dB/m}}$ is the curve plotted on the simulator's first chart.

How strongly a material couples to a microwave field is captured by its complex permittivity and permeability — the real parts store energy, the imaginary parts $\varepsilon_r''$ and $\mu_r''$ dissipate it as heat [11]:

The ratio of loss to storage is the loss tangent. Including the ohmic (conduction) contribution, the effective loss tangent is [6][11]:

The power absorbed per unit volume has three channels — conduction/Joule heating, dielectric loss, and magnetic loss [11]:

The penetration depth $D_p$ is how far the field reaches into the material before its amplitude falls to $1/e$ [11]:

with $\varepsilon' = \varepsilon_0\varepsilon_r'$ and $\mu' = \mu_0\mu_r'$. For a good conductor ($\sigma \gg \omega\varepsilon'$) this collapses to the skin depth $\delta$ of step 3 — so $D_p$ is simply its general form. Finally, the rate a lossy material heats under the field [11]:

where $\rho$ is density and $C_p$ the specific heat. These four quantities are reported on the Simulator cards (loss tangent, penetration depth, dominant loss mechanism).

A section is four thin walls. With perimeter $P = 2(a+b)$, wall thickness $t_{\text{wall}}$, length $L$ and density $\rho$ (densities [5][15][16]):

For coated basswood, the wood core and the (micron-thin) coating are summed. The weight win comes from replacing dense metal ($\rho_{\text{Cu}}\approx 8960$) with light basswood ($\rho\approx 415$ kg/m³).

The real cost of a part in orbit is what you pay to build it plus what you pay to launch its mass (launch cost [9]):

With launch around \$7,000/kg, the launch term usually dwarfs the material term. That is the whole argument for lightweight waveguides: a cheap-but-heavy copper guide can cost far more to fly than an expensive-but-light coated-wood one.

Assumptions & limits

• Dominant TE10 mode only; air-filled guide; smooth walls (no surface-roughness penalty).
• Conductivity constant over each band.
• 1-D layered treatment of the wall — a full 3-D field solver (FEM/FDTD) would refine numbers slightly but not change the conclusions.
• Does not model the physical space-qualification tests (radiation, vibration, vacuum) — those are separate lab checks, not electromagnetic calculations.

A horn is an open, radiating structure, so unlike the closed waveguide it is solved with FDTD using open (PML) boundaries and a near-field-to-far-field (NF2FF) transform. A WR-waveguide feed launches the TE10 mode into a flared aperture. The relations below are the antenna figures of merit reported on the Horn tab — standard antenna theory (Balanis [25]), validated against a rated 15 dBi standard-gain horn and matched to the metric set of Sarpanah Sourkouhi et al. [26].

Aperture, directivity & gain

Feed cutoff and the free-space wavelength at the operating frequency $f_0$ [6]:

The far-field radiation intensity $U$ and directivity $D$ follow from the radiated field $E_{\text{ff}}(\theta,\phi)$ — this is exactly what the NF2FF transform computes [10][25]:

For an inner aperture of size $A_x \times A_y$, the ideal (uniform-illumination) directivity and the aperture efficiency are [25]:

Beam shape

From the principal-plane patterns the tool extracts the half-power beamwidth (the −3 dB angular width around boresight), the first sidelobe level (peak-to-first-lobe ratio) and the front-to-back ratio [25]:

Quick pyramidal-horn cross-checks: $\text{HPBW}_E \approx 56\,\lambda/A_y$ and $\text{HPBW}_H \approx 67\,\lambda/A_x$ (degrees). The co-/cross-polarization patterns come from the two far-field components — E-plane: co $=|E_\theta|$, cross $=|E_\phi|$; H-plane: co $=|E_\phi|$, cross $=|E_\theta|$.

Input match: S11, VSWR, impedance

At the feed port the reflection coefficient $\Gamma$ (= $S_{11}$) is the ratio of reflected to incident wave; from it come the return loss, its phase, the VSWR and the input impedance [6][25]:

The impedance bandwidth is the frequency span where $|S_{11}| \lt -10$ dB (i.e. $|\Gamma| \lt 0.316$). The mismatch efficiency is the fraction of incident power the antenna accepts:

Radiation efficiency & realized gain

The radiation efficiency is radiated over accepted power; the realized gain folds in both wall loss and the input mismatch [25]:

Wall (coating) loss — surface-impedance method

FDTD cannot mesh a good conductor's skin depth (≪ the cell size), so conductor loss on the horn walls is obtained by the surface-impedance perturbation of the full-wave field: solve once with perfect walls (PEC), then integrate the tangential magnetic field over the walls for each coating conductivity $\sigma$ [6][26]:

The gain penalty of a coating versus ideal metal is $10\log_{10}(e_{\text{rad}})$ dB. Because $P_c \propto 1/\sqrt{\sigma}$, a single PEC solve yields the result for every coating.

A waveguide's open end radiates like an aperture antenna. For the TE10 aperture (broad wall $a$, narrow wall $b$) the normalized principal-plane patterns are (Balanis [25]):

with $k=2\pi/\lambda$. The E-plane ($\phi=90^\circ$) uses the uniform aperture field across the narrow wall $b$; the H-plane ($\phi=0^\circ$) the cosine field across the broad wall $a$. The full-wave openEMS Far-field simulation instead computes the pattern directly from the recorded near fields via the near-field-to-far-field (NF2FF) transform [10] — enclosing the aperture in a Huygens box and applying the equivalence principle — which also yields the directivity $D = 4\pi U_{\max}/P_{\text{rad}}$. Both are overlaid on the Full-wave tab's far-field chart.

The Inverse-design tab turns the model around: instead of scoring one wall, it evaluates every catalog design and finds the best trade-off between signal loss and a resource cost. Each design's loss is the TE10 attenuation $\alpha_{\text{dB/m}}$ (§5, using the multilayer $R_s^{\text{eff}}$ where coated); its per-metre mass, delivered cost and embodied carbon are

where $P=2(a+b)$ is the wall perimeter and $t,\rho,p,g$ are each layer's thickness, density, price and embodied-carbon factor, and $c_{\text{launch}}$ the launch cost per kg. With two objectives (loss and, e.g., mass) a design $\mathbf{x}$ dominates $\mathbf{y}$ when it is no worse on both and strictly better on one:

The Pareto-optimal frontier is the set of non-dominated designs — the curve where loss cannot fall without adding mass/cost/carbon, or vice-versa. The tool returns that frontier plus the lowest-objective design meeting your loss target (Marler & Arora [28]).

The Measurement-fit tab inverts the same loss model. Given a measured transmission $S_{21}^{\text{meas}}(f_i)$ over a guide of length $L$, the modelled transmission for a trial conductivity is $S_{21}^{\text{mod}}(f;\sigma) = -\alpha_{\text{dB/m}}(f;\sigma)\,L$. The effective wall conductivity is the least-squares best fit

solved by a golden-section search on $\log_{10}\sigma$ (Kiefer [31]). The reported confidence range is the span of $\sigma$ for which the RMS residual stays within a tolerance of its minimum. The extraction assumes wall-dominated loss (a matched guide); connector or mismatch loss biases $\sigma^\star$ low.

Several inputs are genuinely uncertain — above all MXene's conductivity, reported anywhere from $\sim\!10^4$ to $2.4\times10^6$ S/m across the literature [1][2]. Quoting a single loss number would be false precision. The honest approach is to treat each uncertain input as a probability distribution, propagate many samples through the model, and report the distribution of the output rather than one value (JCGM 101 Monte-Carlo method [30]).

For an output $y=g(\mathbf{x})$ with uncertain inputs $\mathbf{x}\sim p(\mathbf{x})$, draw $N$ samples $\mathbf{x}^{(k)}$ and evaluate:

Reporting, e.g., "loss $=0.9$ dB/m, 90% CI $[0.4,\,2.1]$" makes the conclusion robust to the input spread. A first-order sensitivity — how much of the output variance each input explains (Sobol indices, or one-at-a-time variation) — then shows which property (here almost always $\sigma$ and the coat count) dominates and is worth pinning down experimentally.

Radar cross section (RCS) answers one question: when a radar wave hits a target, how strongly does that target scatter energy back toward the receiver? Everything the openEMS solve and the analytical overlay on the RCS (openEMS) tab compute is a route to that single number.

Formally, RCS $\sigma$ is defined in the far field as the equivalent area that would intercept the incident power and re-radiate it isotropically to produce the observed scattered field [38][25]:

where $E_i$ is the incident field, $E_s$ the scattered field measured at range $R$, and the limit removes the observer's distance. Crucially, $\sigma$ is not the target's geometric area — it is a hypothetical, equivalent area (in m²) that captures how much incident power the target intercepts and throws back at the radar as if from an isotropic scatterer. A shape can have an RCS far larger than its physical size (a flat metal plate seen head-on) or far smaller (an angled, absorber-coated facet). Because returns span many orders of magnitude, RCS is quoted in decibels relative to one square metre (dBsm) [38]:

RCS depends strongly on the target's shape, its surface material (a bare conductor versus a lossy absorber), the frequency, the wave's polarization, and — most sharply — the aspect angle from which it is viewed. The same object can change by tens of dB as it rotates just a few degrees.

How a target scatters — the mechanisms

The return from a real object is the sum of several distinct physical effects [38]:

• Specular reflection — mirror-like bounce off flat or gently curved surfaces. A flat plate held normal to the beam gives a huge, narrow return spike; tilt it and that spike swings away from the radar.
• Edge diffraction — sharp edges, corners and wedges scatter energy over a wide range of angles, and dominate the return once the specular flash has been steered away.
• Surface / creeping waves — waves that travel around the shadowed side of a smooth curved body and re-radiate where the surface curvature changes or ends.
• Cavity reflections — open structures such as engine intakes and cockpits trap the wave in multiple internal bounces and re-radiate it strongly back toward the source.

How RCS is simulated — full-wave vs asymptotic

Which numerical method applies is decided by the target's electrical size — its physical dimension measured in wavelengths, $L/\lambda$. Two regimes result.

Full-wave (exact) solvers discretize Maxwell's equations directly and make no high-frequency approximation. They are accurate but expensive, needing a mesh finer than a fraction of a wavelength everywhere:

• Method of Moments (MoM) — a surface integral-equation method: it meshes only the conductor surface into patches and solves for the induced surface currents, from which the scattered field follows [39].
• Finite-Difference Time-Domain (FDTD) — a differential method: it fills a 3-D volume with Yee cells and time-steps an electromagnetic pulse through the grid, reading off the scattered field [10][35]. This is the engine behind the RCS tab.

High-frequency asymptotic approximations take over when the object is much larger than the wavelength — for example a 15 m aircraft at 10 GHz, where $\lambda\approx3$ cm makes the target roughly 500 wavelengths across, far beyond any full-wave mesh:

• Physical Optics (PO) — approximates the current on each illuminated patch as that of a locally-flat mirror and sets the current in the shadow to zero, then integrates for the scattered field [38]. The dashed plate / cylinder / dihedral overlays on the RCS tab are PO.
• Physical Theory of Diffraction (PTD) — adds edge line-currents that correct PO where it fails, at sharp boundaries (Ufimtsev's extension) [40].
• Shooting and Bouncing Rays (SBR) / ray tracing — launches millions of rays, follows their multiple bounces across the geometry, and is essential for the cavity and corner returns that PO alone misses [41].

The generic high-frequency workflow used across industry is: import and clean the CAD geometry (suppressing sub-wavelength detail the solver cannot use) → assign materials (a perfect conductor, or a complex $\varepsilon/\mu$ for a radar-absorbing coating) → excite with a plane wave at a chosen azimuth $\phi$, elevation $\theta$ and polarization → solve the ray or current problem → transform the near field to the far field to build a 2-D or 3-D RCS pattern.

The analytical references the RCS tab overlays are the exact Mie series for a conducting sphere [37] and physical optics for a flat plate, a broadside cylinder ($\sigma=2\pi a h^2/\lambda$) and a dihedral corner ($\sigma=8\pi a^2 h^2/\lambda^2$, the large-reflector upper bound) [38].

Physical optics gives a surface an induced current $\mathbf{J}_s = 2\,\hat{n}\times\mathbf{H}^{inc}$ on its lit side and nothing on its shadowed side, so the scattered far field of a facet is the phase integral of that current over its area. The consequence that dominates low-observable design is that a flat or singly-curved surface radiates a narrow specular lobe about its own normal: for a flat plate of dimension $a$ the return falls as $\mathrm{sinc}^2(ka\sin\theta)$, whose first null is only $\theta \approx \lambda/2a$ away from broadside [38]. A 1 m panel at 10 GHz therefore drops tens of decibels for a few degrees of tilt, which no practical absorber can match — a coating multiplies the lobe by $|\Gamma|^2$, but shaping decides whether the lobe points at the radar at all.

The same argument runs for edges. First-order Ufimtsev PTD makes an edge radiate on the Keller cone about itself, so an edge perpendicular to the line of sight throws its diffraction lobe straight back at the radar, while a swept edge throws it elsewhere [40]. That is the physics behind planform alignment — aligning every leading and trailing edge of an airframe to a few common sweep angles, so the whole aircraft has only a handful of narrow edge-flash azimuths instead of dozens.

What the search on the CAD-RCS tab actually does. It applies closed-form vertex deformations to the imported mesh — nose ogive power, aft boat-tail, body taper, cross-section ellipticity, planform shear, appendage roll, and tilt or slimming of whichever part dominates — and for each candidate re-runs the identical PO+PTD solve used elsewhere in the tool over the threat sector you select. There is no surrogate model and no scoring heuristic: every number is the same physics on a genuinely different geometry. The stacking is coordinate descent — adopt the single best change, then search the remaining levers on top of it — which is why the recipe it prints is a short, explainable list rather than an opaque parameter vector.

Two constraints keep the answers honest. First, RCS falls trivially if the target simply gets smaller, so every deformation preserves the overall length along the body axis (the levers that move axial coordinates re-normalise the span afterwards), and the enclosed volume and maximum diameter of each candidate are measured and reported — a 14 dB win that costs 30 % of the internal volume is a trade you should see, not a victory. Second, the reduction is reported as the sector mean and sector peak, because moving a flash a few degrees out of a narrow sector is a real gain against a known threat axis but not against an unknown one.

The Inverse RAM design tab searches coatings by scoring each candidate on a metal-backed reflector. A stack of layers on a perfect conductor has an input impedance built by the transmission-line recursion, from the short-circuit at the metal outward through each layer of complex permittivity $\varepsilon=\varepsilon'-j\varepsilon''$ and permeability $\mu=\mu'-j\mu''$ [6]:

starting from $Z=0$ (the metal). The front-face reflection and the reflection loss in dB are

The classic archetypes are special cases: the Dallenbach absorber is one lossy layer on metal; the Jaumann is two; and the Salisbury screen places a resistive sheet ($R_s\approx 377\,\Omega$) a quarter-wavelength above the metal so the short-circuited spacer transforms to an open at the sheet, leaving only $R_s$ matched to free space — a near-perfect but narrowband absorber [44]. There is a hard physical limit relating a magnetic absorber's total thickness $d$ to the bandwidth over which it can suppress reflection — the Rozanov bound [44]:

with $\mu_{s,i}$ the static permeability of each layer. The tab reports how close the winning design sits to this ceiling — you cannot beat it with any passive magnetic coating of that thickness. Reflection loss is the flat-reflector proxy; the openEMS RCS tab confirms the reduction on a real 3-D target.

A target's backscatter measured across a frequency band $H(f)$ carries, in its phase, where along the line of sight each echo originated. The inverse Fourier transform of the (windowed) stepped-frequency return is the down-range impulse response — the same synthetic-range-profiling principle behind ISAR imaging (Mensa) [46]:

Each peak is a scattering center — the front-face specular return near $r=0$, and delayed peaks from edges or a creeping wave that travels the extra path around a curved body before re-radiating. The range resolution $\Delta r$ is set only by the bandwidth $B$; the tool exports the complex backscatter from the monostatic solve to compute this.

The full polarization behaviour of a target is the $2\times2$ Sinclair matrix relating the scattered field to the incident one in the vertical/horizontal basis:

obtained here from two solves (the chosen polarization plus a flipped-polarization solve). The Pauli decomposition splits it into three orthogonal mechanisms whose powers classify the dominant scatterer [46]:

A sphere or flat plate is a single reflection: $S_{VV}\approx S_{HH}$, so the odd-bounce term dominates and cross-pol is negligible. A dihedral corner is a double reflection whose second bounce flips the phase: $S_{VV}\approx -S_{HH}$, so the even-bounce term dominates — the tool reproduces exactly this, a clean validation.

The radar-range equation gives the range at which the received power equals the receiver's minimum detectable signal. But detection is statistical: for a chosen false-alarm probability $P_{fa}$ the threshold is set, and the probability of detection $P_d$ rises with signal-to-noise ratio. For a steady (Swerling 0) target the single-pulse $P_d$ follows the North approximation; for a fluctuating (Swerling 1) target there is a closed form [45]:

Because SNR $\propto\sigma/R^4$, a coating that lowers $\sigma$ by $\Delta$ dB moves the whole $P_d$-vs-range curve inward by the factor $10^{-\Delta/40}$ — the operational meaning of an RCS reduction: the radar must come that much closer to keep the same detection odds.

Edit any value below and press Apply to re-run the simulator with your own material. Defaults are MXene-coated basswood vs copper & aluminum. Conductivity in S/m, density in kg/m³, price in \$/kg, CO₂ in kgCO₂e/kg. Magnetic materials (magnetite Fe₃O₄, carbonyl iron) carry μr″ > 0 — pick them from the coating/block dropdown to auto-fill their complex ε/μ.

This tool tests whether lightweight coated materials — flagship MXene-coated basswood — could replace solid metal for satellite waveguides and horn antennas: far lighter, but do they still carry, reflect and radiate microwave signals well? It answers four questions: what a material costs you in waveguide loss, mass and launch cost; how a horn antenna built from it performs; how much radar reflection a coating absorbs, from your own measured ε/μ; and what radar cross section a real 3-D model has, part by part. Each answer comes two ways — a fast built-in model that runs instantly in your browser, and a full-wave solver (openEMS) that runs the real 3-D electromagnetic simulation — plus design/characterization tools that pick the optimal material for you and read a real conductivity back from a lab measurement. It runs on macOS or Windows (setup in step 6).

A simulator is a calculator with physics behind it: you describe a situation (a wave, a material, a shape) and it predicts what happens, using equations we know are correct, instead of building hardware. That lets you ask "what if the coating were thicker?" or "what about a higher frequency?" and get an answer in seconds. Everything here rests on Maxwell's equations — the laws governing electromagnetic waves. A material enters those equations as just a few numbers: its conductivity (how well it carries current), permittivity, and permeability.

The analytical model (Simulator, Compare, Materials tabs) solves the equations with exact formulas — instant, runs in the browser, great for exploring. A full-wave simulation (Full-wave tab, via openEMS) instead chops space into a 3-D grid and steps the fields through time (the FDTD method) — slower, but it produces the real field patterns and animations and validates the fast model. Commercial tools like openEMS performs this full-wave simulation — free and Mac-native.

• Waveguide ▾ → Analytical Simulator — the headline results: signal loss vs frequency across the X/Ku/K bands, mass and delivered launch cost, all recomputed instantly as you move the sliders. Start here.
• Waveguide ▾ → Full-wave (openEMS) — runs the real 3-D solver on a waveguide and brings back field animations, S-parameters and R/T/A. Needs the bridge.
• Waveguide ▾ → Inverse design — you set a target (band, maximum loss) and what to minimise (mass, delivered cost or CO₂e); it returns the Pareto-optimal design.
• Waveguide ▾ → Measurement fit — upload a measured S21 (CSV or Touchstone .s2p) and it back-fits the effective conductivity of your real sample.
• Waveguide ▾ → Space survival — two first-order vacuum screens: multipaction susceptibility and how hot the wall runs with no air to cool it.
• Waveguide ▾ → Compare — a side-by-side table of the leading candidates, with a Run button per row to validate any of them on openEMS.
• Horn ▾ → Horn design (analytical) — type feed, aperture and flare dimensions (pyramidal or conical) and get gain, beamwidth and patterns instantly.
• Horn ▾ → Inverse & sweep — the horn that hits a target gain, plus an aperture × flare sweep ranked into a table.
• Horn ▾ → Compare & trade — pinned designs overlaid, and the project's core trade: a coated light shell against solid metal, gain penalty against mass saved.
• Horn ▾ → Full-wave (openEMS) — the same horn solved rigorously: gain vs frequency, radiation patterns, S11 and the interior field in 3-D.
• RCS + RL ▾ → RCS (openEMS) — how big a target looks to a radar. A plane wave illuminates a sphere, plate, cylinder, dihedral or an imported mesh; the headline is the dB by which a coating shrinks the echo.
• RCS + RL ▾ → Reflection loss (RL) — the measured-material workflow: give it a material's ε/μ (typed, or uploaded from your VNA) and it returns reflection loss for every thickness at once, plus the coated-plate RCS that follows.
• RCS + RL ▾ → Fast material search (analytical) — thousands of closed-form evaluations in seconds, to find which ε/μ and thickness absorb best. No solver involved.
• RCS + RL ▾ → Inverse RAM design — searches absorber recipes (Salisbury, Dallenbach, Jaumann, multilayer) and plots reduction against the mass you pay for it, with the Rozanov thickness bound for context.
• RCS + RL ▾ → Material library — the shelf. Materials you pin here are the ones offered on the RCS tab and on every part of an imported CAD model.
• RCS + RL ▾ → Full-wave batch (openEMS) — sweeps one parameter unattended, one real full-wave solve per point. Slow and rigorous; the opposite of Fast material search.
• RCS + RL ▾ → CAD-RCS (STEP/STL) — upload a 3-D model and get its radar signature part by part, which part dominates, what a coating buys you, and a search over real deformations of the geometry for a lower signature.
• Materials (in both the Waveguide and Horn menus — it is one page, listed twice) — define any material and the whole tool recomputes around it.
• Learn ▾ → The physics — every equation behind every number, each with a literature citation. It opens with a contents index.
• Learn ▾ → Instructions — this tab.
• Learn ▾ → References — every value and formula, with its source.

Every openEMS chart and animation, and every page, has a small ⓘ button that opens a plain-language explanation (with an English / Emirati-Arabic toggle).

Open the Materials tab, edit the test material (a coating on a substrate, or a solid block) and the two baselines, then press Apply. The Simulator and Compare tabs immediately recompute. A Quick pick dropdown loads any of the ten preset candidates, and per-layer dropdowns let you build any coating + substrate (or solid block) combination. The file material_properties.txt in your project folder lists ready values for copper, aluminum, silver, gold, MXene, graphene and several substrates.

Beyond simulating a material you choose, the tool can choose one for you and read one back from a measurement:

• Inverse design — pick a band, a maximum acceptable loss, and what to minimize (mass, delivered-to-orbit cost, or embodied CO₂). The optimizer searches thousands of designs (every coating × substrate × coat-count, plus every solid metal) and plots the Pareto-optimal frontier with a ranked table and one recommended design. Press ▸ Send to Full-wave (openEMS) on the recommendation to jump to the Full-wave tab pre-loaded with that exact design, ready to Run.
• Measurement fit — if you have measured a real coated guide on a vector network analyser, upload its S21 (CSV freq_ghz,s21_db or Touchstone .s2p). The tool fits the effective conductivity your coating actually achieved, with a confidence range, and overlays measured vs modelled.
• Multi-layer coating stack (Full-wave tab) — tick it to build the wall from a substrate plus up to three stacked coatings (Layer 1 = innermost, facing the wave); the transfer-matrix model computes the exact layered behaviour and hands openEMS an effective wall.

Quick view (no install): double-click waveguide_simulator.html — it opens in your browser and the Simulator, Inverse design, Measurement fit, Compare, Physics, Materials, Instructions and References tabs all work immediately (needs internet for fonts, charts and equations). Only the openEMS full-wave runs — the Run buttons on the Full-wave and Horn tabs — need the one-time toolchain below. Pick your operating system:

In the Full-wave tab, choose band, material, coats and length, and optionally the number of ports (1-port = reflection / S11 only; 2-port = through, S11 + S21) and the mesh density (finer = more accurate but more RAM — the estimated cell count and memory are shown live). The Simulations tick-box (also on the Compare tab) picks which analyses to run — six options: guided wave (transmission field render), reflection (standing wave), S-parameters (S11/S21 vs frequency), field & wall-loss map (where the wall heats), angle-of-incidence sweep (R/T/A vs angle, analytical), and far-field radiation pattern (the open end's beam via the openEMS NF2FF transform). Tick any subset and press Run on openEMS; each full-wave analysis takes a couple of minutes (the angle sweep is instant).

• Insertion loss (dB/m) — how much signal is lost travelling down the guide; lower is better.
• R / T / A — fractions reflected, transmitted, absorbed; they sum to 100%. For a good waveguide wall you want high reflection (≈99.8% for MXene-coated basswood — like metal).
• Weight & delivered cost — MXene-coated basswood is ~95% lighter than copper (≈46 vs ≈890 g per metre of X-band guide), and once the ~$7,000/kg launch cost is counted, far cheaper to put in orbit.

• The analytical model is exact for the idealized 1-D layered problem; openEMS adds the real 3-D field behavior. Cite openEMS (Liebig et al., 2012) in any writeup.
• openEMS conductor-loss magnitude at this mesh resolution is approximate — the precise loss number comes from the validated analytical model; the field visuals and reflection behavior are the full-wave payoff.
• Radar-chart Sustainability axis is a fixed 0–100 rating the author assigned to the four default materials — it is not computed from anything, and it does not update for a material you define yourself. The env-friendly score IS derived, from embodied-carbon (CO₂/kg) figures that are themselves approximate — treat both as ballpark, not measured values.
• The physical space-qualification tests (radiation, vibration, vacuum) are separate lab checks, not part of this electromagnetic tool.

Every number the simulator uses, what it is, its value, and where it comes from. Conductivity and density are well-established handbook/measured values; MXene and price figures carry more uncertainty and are drawn from recent literature.

Rangwala, H. T. (2026). EM Waveguide & RCS Simulator (Version 3.8) [Computer software]. Khalifa University, Abu Dhabi. Full-wave results computed with openEMS (Liebig, doi:10.1002/jnm.1875).

Material properties (default values)

εr′/εr″ (real/imaginary permittivity) and μr′/μr″ (real/imaginary permeability) are editable in the Materials tab. MXene, copper, aluminium and wood are all non-magnetic (μr′ ≈ 1, μr″ = 0). *MXene's microwave loss is dominated by conduction, already captured by σ through the complex permittivity εc = ε₀εr′ − jσ/ω, so its explicit εr″ defaults to 0 to avoid double-counting. Set εr″/μr″ > 0 only to add extra dielectric or magnetic (ferrite) loss. The imaginary parts feed the loss-tangent, penetration-depth and absorption calculations, and the waveguide loss via σ_eff = σ + ωε₀εr″. Magnetite (Fe₃O₄) and carbonyl iron are magnetic (μr′ > 1, μr″ > 0), so they exercise the magnetic-loss term πf μ₀μr″|H|²; the metals and polymers are non-magnetic (μr′ ≈ 1, μr″ = 0).

Conductor coatings & solid blocks — full catalog

Conductivities are room-temperature handbook/measured values; graphene film σ is a best-quality-film value (published range ≈10⁶–10⁸ S/m [20]); graphite is the in-plane value. Prices are market ballpark and move over time; embodied-carbon (CO₂e) figures are cradle-to-gate ballpark [19] and *MXene's is an order-of-magnitude estimate.

Substrate cores — full catalog

†Plated-metal cores are modelled with εr = 1 — the thin conductive coating sets the RF behaviour, the core sets the mass. Polymer εr are microwave datasheet/measured values [15][23][24]; CFRP permittivity is anisotropic and filler-dependent, so ≈5 is representative [24].

Candidate waveguide materials (Compare tab)

These are the presets in the Compare tab; the Materials tab lets you build any coating + substrate (or solid block) combination from the same catalogs. Conductivities are room-temperature handbook values; silver/gold/commodity prices move with the market — treat $/kg as ballpark. Coated designs put a thin (µm-scale) high-σ layer over a light structural core, so RF loss is set by the coating while mass is set by the core.

Other parameters

References

1. A. Lipatov et al., high electrical conductivity of Ti₃C₂Tₓ MXene films — "Scalable Manufacturing of Free-Standing, Strong Ti₃C₂Tₓ MXene Films with Outstanding Conductivity" (PubMed 32309891).
2. Improved-synthesis Ti₃C₂Tₓ reaching ~2.4×10⁴ S/cm — Mathis et al., "Improved Synthesis of Ti₃C₂Tₓ MXene..." (ResearchGate).
3. MXene microwave response is dielectric/conductive, not magnetic (μr≈1) — "Ti₃C₂ MXene: a promising microwave absorbing material" (PMC9077445); permeability only appears in ferrite composites: M-type hexagonal ferrite + Ti₃C₂Tₓ (ScienceDirect).
4. Dry-wood relative permittivity ≈1.8–2 at 8–12 GHz — "Microwave testing... dielectric constant of spruce from 8 GHz to 12 GHz", Eur. J. Wood Wood Prod. (2017).
5. Metal conductivities & densities (Cu, Al) — CRC Handbook of Chemistry and Physics, CRC Press — official online edition.
6. D. M. Pozar, Microwave Engineering, 4th ed., Wiley, ISBN 978-0-470-63155-3 — TE10 attenuation, waveguide dimensions, transfer-matrix method.
7. MXene production cost — "Cost analysis of MXene..." (ScienceDirect); commercial pricing e.g. Nanografi/Nanochemazone (~$15–40/g).
8. Rectangular-waveguide WR band designations — EIA RS-261-B / IEC 60153-2 standard rectangular-waveguide sizes (WR designations); the WR-90 / WR-62 / WR-42 dimensions used here are tabulated in Pozar [6].
9. Launch cost to LEO — an input assumption, not a measured constant: the app exposes it as a slider precisely because published figures span roughly \$2,000–20,000/kg depending on vehicle, orbit and contract, and no single value is authoritative. The default is a representative mid-range figure; set it to your own programme's number before quoting any delivered-cost result.
10. T. Liebig, A. Rennings, S. Held, D. Erni, "openEMS – a free and open source FDTD simulation platform," Int. J. Numer. Modelling, 2012. DOI: 10.1002/jnm.1875.
11. A. E. Elkaffas et al., "Microwave synthesis of gram scale millimeter size layered transition metal oxide crystals," NPG Asia Materials, 2026. DOI: 10.1038/s41427-026-00637-8. — microwave–matter interaction framework: complex permittivity/permeability, loss tangent, power absorption (Eq. S1), penetration depth (Eq. S2) and heating rate (Eq. S3).
12. Metallized (silver/copper-plated) 3-D-printed polymer waveguides — lightweight, low-loss microwave components for space/satellite: "3D Printed Metalized Plastic Waveguides for Microwave Components" (Int. Symp. Microelectronics, 2017); silver-coated polymer hollow waveguide, 0.73 dB/m at 220 GHz: "Pd-free activation for low-loss silver-coated polymer waveguides" (Mater. & Design).
13. Copper/metal-plated carbon-fibre (CFRP) waveguides & antennas for space — lightweight, low-CTE, dimensionally stable: "A slotted waveguide array antenna from CFRP for the European space SAR" (Acta Astronautica).
14. Silver-plated aluminium / Invar RF waveguides for space (autocatalytic silver with nickel undercoat; Invar for thermal stability): "Autocatalytic silver-plating of aluminium RF waveguides… for space applications"; 3-D-printed Invar filter with high thermal stability (IEEE MTT).
15. Elemental / alloy electrical conductivity (Ag 6.3×10⁷, Cu 5.8×10⁷, Au 4.1×10⁷, Al 3.5×10⁷, brass ≈1.5×10⁷, Ni 1.43×10⁷ S/m) — reference table of elemental electrical conductivity and CRC Handbook; polymer densities & dielectric constants (PLA εr≈2.7, PEEK≈3.2, PTFE≈2.1, PC≈2.9, FR4≈4.4) from standard materials datasheets.
16. Basswood (Tilia) density ≈415 kg/m³ (12% MC) — The Wood Database, "Basswood"; dry-wood microwave permittivity εr≈1.8–2 at 8–12 GHz (density-dependent) — Eur. J. Wood Wood Prod. (2017) and "Dielectric properties of hardwood species at microwave frequencies", J. Wood Sci.
17. Complex permittivity & permeability of magnetite (Fe₃O₄) and carbonyl-iron composites at X-band (representative εr′, εr″, μr′, μr″ used here) — "Complex permittivity and permeability of carbonyl iron powders at microwave frequencies"; "Permittivity and permeability of epoxy–magnetite powder composites at microwave frequencies". Values vary strongly with filler fraction — treat as typical, not exact.
18. Polyurethane microwave permittivity εr≈2.5–3.5 (low loss, common absorber matrix) and density ≈1100–1200 kg/m³ — supplier datasheets for cast polyurethane resins and the standard dielectric-materials tables in von Hippel, Dielectric Materials and Applications (Artech House, ISBN 978-1-58053-123-6). Treated as a range throughout, not a single value.
19. Embodied carbon (CO₂e per kg): timber ≈0.4–0.5, copper ≈3.5, aluminium ≈9 (primary), silver ≈150, gold ≈35,000, PLA ≈2, PEEK/PTFE/CFRP higher — representative cradle-to-gate figures from the ICE (Inventory of Carbon & Energy) database and life-cycle-assessment literature. MXene CO₂ is not well established; the ≈15 used here is an order-of-magnitude estimate. Treat all CO₂/kg values as ballpark.
20. Graphene-film electrical conductivity — CVD monolayer measured at ≈1.46×10⁶ S/m by conductive-AFM: "Measurements of the Electrical Conductivity of Monolayer Graphene Flakes…", Nanomaterials (2021); high-quality multilayer/graphitic films span ≈10⁶–10⁸ S/m ("Towards standardisation of… electrical measurements of CVD graphene", Sci. Rep. (2020)). The ≈1×10⁷ S/m used here is a good-film value.
21. Graphite in-plane electrical conductivity ≈10⁵ S/m — "Electrical conductivity of compacts of graphene, multi-wall carbon nanotubes, carbon black, and graphite powder", Powder Technology (2012); rolled/pressed graphite foils ≈5×10⁴–1.7×10⁵ S/m in-plane ("Electrical Conductivity in Graphite Foils Produced by Rolling and Pressing" (2024)).
22. Silver conductive paint/coating conductivity ≈10⁵–10⁶ S/m (from datasheet volume resistivity) — MG Chemicals "Super Shield 842" silver conductive coating technical datasheet.
23. ABS microwave relative permittivity εr≈2.7–2.9 — "Characterization of Acrylonitrile Butadiene Styrene for 3D Printed Patch Antenna" (εr≈2.74); complex permittivity of common plastics at ~10 GHz ("Complex permittivity measurements of common plastics…").
24. CFRP (carbon-fibre-reinforced polymer) X-band relative permittivity (representative εr′≈5, anisotropic and fibre-fraction dependent) — "X-band microwave characterisation and analysis of carbon fibre-reinforced polymer composites", Composite Structures (2019); "Microwave axial dielectric properties of carbon fiber", Sci. Rep. (2015).
25. Antenna figures of merit — directivity, gain, aperture efficiency, HPBW, sidelobe level, front-to-back, VSWR, input impedance, realized gain and co-/cross-polarization (the horn-antenna equations in the Physics tab): C. A. Balanis, Antenna Theory: Analysis and Design, 4th ed., Wiley, ISBN 978-1-118-64206-1 (standard reference).
26. Z. Sarpanah Sourkouhi, J. Alhourani, Y. Gogotsi, M. H. Zarifi, "MXene-Coated 3D Printed Horn Antennas for Ku Frequency Band," Advanced Materials Technologies, 2026. DOI: 10.1002/admt.202502239 — the horn-antenna metric set (S11, gain, radiation pattern, efficiency) mirrored by the Horn tab.
27. Horn validation reference — Pasternack PE9856B-15, WR-90 waveguide standard-gain horn, 8.2–12.4 GHz, nominal 15 dBi gain (the rated part the full-wave directivity is checked against): product page / datasheet.
28. Multi-objective (Pareto) optimization for engineering design — the dominance test and Pareto frontier used by the Inverse-design tab: R. T. Marler and J. S. Arora, "Survey of multi-objective optimization methods for engineering," Structural and Multidisciplinary Optimization, 26:369–395, 2004. DOI: 10.1007/s00158-003-0368-6.
29. Touchstone® file format (.s2p), parsed by the Measurement-fit tab — Touchstone® File Format Specification v2.0, IBIS Open Forum (ratified 24 Apr 2009): specification PDF.
30. Monte-Carlo uncertainty quantification (propagation of distributions) — basis of the Physics-tab UQ section: JCGM 101:2008, Evaluation of measurement data — Supplement 1 to the GUM: Propagation of distributions using a Monte Carlo method, BIPM/JCGM: document PDF.
31. Golden-section search — the 1-D minimizer used to invert the loss model for effective conductivity (Measurement-fit tab): J. Kiefer, "Sequential minimax search for a maximum," Proc. Amer. Math. Soc., 4(3):502–506, 1953. DOI: 10.2307/2032161.
32. Multipaction (multipactor) design/test for vacuum RF hardware — the frequency×gap susceptibility framework behind the Space-survival multipaction screen: ECSS-E-ST-20-01C, "Space engineering — Multipactor design and test", ECSS/ESA, 15 June 2020: standard PDF.
33. Ti₃C₂Tₓ MXene thermal stability — oxidation onset ≈ 322–360 °C in air, structurally stable to ≈ 600 °C in inert/vacuum (the coating's safe-temperature limit in the vacuum-thermal screen): S. Gao et al., "Thermal Stability of MXene: Current Status and Future Perspectives," Small (2025) link; high-temperature-stable Ti₃C₂Tₓ, Nature Communications (2022) link.
34. Radiative heat transfer in vacuum — Stefan–Boltzmann law $P=\varepsilon\sigma_{SB}A(T^4-T_{\text{env}}^4)$ used for the vacuum power-handling screen: T. L. Bergman & A. S. Lavine, Fundamentals of Heat and Mass Transfer, 8th ed., Wiley, 2017, ISBN 978-1-119-32042-5.
35. Full-wave method — the finite-difference time-domain (FDTD) solver and the running-DFT extraction of frequency-domain fields and spectra from a single time-domain run (the basis of the openEMS solve, the S-parameter/far-field results, and the Field-view time/frequency toggle): A. Taflove & S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd ed., Artech House, 2005, ISBN 978-1-58053-832-9.
36. Conductor surface-roughness loss — the Hammerstad–Jensen correction factor applied to the surface resistance in the Coating-quality (real-world coating) panel: E. O. Hammerstad and Ø. Jensen, "Accurate Models for Microstrip Computer-Aided Design," IEEE MTT-S International Microwave Symposium Digest, 1980, pp. 407–409. DOI: 10.1109/TMTT.1980.1130118.
37. Mie scattering — the exact series solution for a plane wave scattered by a sphere, used as the analytical anchor on the RCS tab (openEMS is validated against it): G. Mie, "Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen," Annalen der Physik, 330(3):377–445, 1908. DOI: 10.1002/andp.19083300302. Perfectly-conducting-sphere backscatter and the resonance/optical regimes follow the standard Riccati-Bessel formulation (e.g. Balanis [25], Bohren & Huffman).
38. Physical optics & radar cross section — the flat-plate PO estimate (broadside σ = 4πA²/λ²) and RCS conventions used on the RCS tab: E. F. Knott, J. F. Shaeffer, M. T. Tuley, Radar Cross Section, 2nd ed., SciTech/Artech House (standard reference). publisher page. openEMS RCS follows the plane-wave (TF/SF) + near-field-to-far-field method of its own RCS-sphere tutorial (Taflove & Hagness FDTD [35]).
39. Method of Moments (MoM) — the surface integral-equation method (mesh the conductor surface, solve the induced surface currents) that underlies the exact full-wave regime described on the RCS tab: R. F. Harrington, Field Computation by Moment Methods, IEEE Press, 1993 (reissue of the 1968 Macmillan edition). DOI: 10.1109/9780470544631.
40. Physical Theory of Diffraction (PTD) — the edge-wave correction that adds edge line-currents to physical optics, used to explain the high-frequency asymptotic regime on the RCS tab: P. Ya. Ufimtsev, Fundamentals of the Physical Theory of Diffraction, 2nd ed., Wiley–IEEE Press, 2014. DOI: 10.1002/9781118753767.
41. Shooting and Bouncing Rays (SBR) — the multi-bounce ray-tracing method for electrically large targets and cavities cited on the RCS tab: H. Ling, R.-C. Chou and S.-W. Lee, "Shooting and bouncing rays: calculating the RCS of an arbitrarily shaped cavity," IEEE Transactions on Antennas and Propagation, 37(2):194–205, 1989. DOI: 10.1109/8.18706.
42. Standard CEM validation targets (NASA/EMCC benchmark suite) — the canonical smooth-target family (almond, ogive, cone-sphere) used to validate computational-electromagnetics RCS codes, referenced by the "Standard RCS benchmarks" panel on the RCS tab: A. C. Woo, H. T. G. Wang, M. J. Schuh and M. L. Sanders, "Benchmark radar targets for the validation of computational electromagnetics programs," IEEE Antennas and Propagation Magazine, 35(1):84–89, 1993. DOI: 10.1109/74.210840. (Almond: two-segment parametric surface, overall length L = 9.936 in = 252.37 mm; canonical monostatic test frequencies 1.19 and 7 GHz.)
43. Radar range equation — the detection-range relation used by the "Radar range / detectability" calculator on the RCS tab, R = [P_t G_t G_r λ² σ / ((4π)³ P_min L)]^1/4: M. I. Skolnik, Introduction to Radar Systems, 3rd ed., McGraw-Hill, 2001, ISBN 978-0-07-288138-7 (§1.2, the radar equation).
44. Radar-absorbing-material thickness bound — the physical limit relating a magnetic absorber's total thickness to the bandwidth over which it can suppress reflection, used by the Inverse RAM design tab's "Rozanov bound": K. N. Rozanov, "Ultimate thickness to bandwidth ratio of radar absorbers," IEEE Transactions on Antennas and Propagation, 48(8):1230–1234, 2000. DOI: 10.1109/8.884491. The Salisbury screen (resistive sheet a quarter-wave above a ground plane) and Dallenbach/Jaumann lossy-layer absorbers are standard: R. L. Fante and M. T. McCormack, "Reflection properties of the Salisbury screen," IEEE Trans. Antennas Propag., 36(10):1443–1454, 1988, DOI: 10.1109/8.8632; and Knott/Shaeffer/Tuley, Radar Cross Section [38] (Ch. on RAM). Metal-backed reflection is the transmission-line/transfer-matrix input-impedance recursion (Pozar, Microwave Engineering [6]).
45. Detection probability & target fluctuation — the P_d-vs-range curves on the RCS radar panel: the non-fluctuating (Swerling 0) single-pulse detection uses the North/Albersheim approximation, and the fluctuating case uses the closed-form Swerling 1 result P_d = P_fa^1/(1+SNR). P. Swerling, "Probability of detection for fluctuating targets," IRE Trans. Information Theory, 6(2):269–308, 1960, DOI: 10.1109/TIT.1960.1057561; D. O. North, "An analysis of the factors which determine signal/noise discrimination in pulsed-carrier systems," Proc. IEEE, 51(7):1016–1027, 1963 (reprint), DOI: 10.1109/PROC.1963.2383.
46. Polarimetric decomposition — the 2×2 Sinclair scattering matrix and the Pauli (odd-/even-/volume-bounce) decomposition on the RCS polarimetric panel: S. R. Cloude and E. Pottier, "A review of target decomposition theorems in radar polarimetry," IEEE Trans. Geoscience and Remote Sensing, 34(2):498–518, 1996. DOI: 10.1109/36.485127. The down-range profile is the standard inverse-DFT of the stepped-frequency backscatter (synthetic range profiling / ISAR), Mensa, High Resolution Radar Cross-Section Imaging, Artech House, 1991.
47. Reflection-loss / RCS reference paper (dielectric absorber, CuS/ZnS) replicated on the Reflection-loss (RL) tab: S. B. Jamali, T. H. Qamar, S. ul Hassan, et al., "3D CuS/ZnS snowflakes as multi-waveband microwave absorbers," Materials Chemistry and Physics 340 (2025) 130821. DOI: 10.1016/j.matchemphys.2025.130821. Source of the metal-backed reflection-loss workflow, RL-vs-thickness maps and CST plate-RCS comparison.
48. RL / RCS reference paper (magnetic FeCu/MWCNT): F. Zare-Nazari, M. Dehghani-Dashtabi, M. Mohebbi, H. Hekmatara, "FeCu/MWCNT nanocomposite with a broad microwave absorption band and highly reduced radar cross section," Advanced Electronic Materials 11 (2025) e00965. DOI: 10.1002/aelm.202400965.
49. RL / RCS reference paper (magnetic carbon foam, MFNC): J. Yu, H. Luo, Z. Wang, et al., "Surface morphology of magnetic carbon foam regulated electromagnetic properties for microwave absorption," Journal of Alloys and Compounds 971 (2024) 172757. DOI: 10.1016/j.jallcom.2023.172757. Uses a 200 mm PEC-backed plate for its RCS study.
50. RL / RCS reference paper (CoFe@C@PPy fibers; 180 mm plate, θ −90…+90°): T. Sun, Z. Dong, Z. Yan, et al., "Dual-shelled CoFe@C@PPy hybrid fibers toward efficient microwave absorption, wide-angle RCS suppression and hydrophobic performance," Carbon 258 (2026) 121775. DOI: 10.1016/j.carbon.2026.121775. Source of the bare-PEC 180 mm plate RCS anchor (+14.1 dBsm at 13.2 GHz, matching 4πA²/λ²).
51. RL / RCS reference paper (CB/FeCo dual-loss fibers; 180 mm plate, θ −90…+90° at φ=90°): Y. Li, W. Zhou, S. Zhou, et al., "Flexible electromagnetic functional fibers with synergistic dual-loss mechanisms," Journal of Materials Chemistry A (submitted 2026), manuscript TA-ART-02-2026-001662. Source of the advisor's coated-plate RCS geometry (θ −90…+90°, φ=90°).

Commodity prices (Cu, Al) and MXene prices move over time — treat $/kg figures as ballpark. The material-properties file material_properties.txt in the project folder lists the same values.