---
id: hpc-028-frequency-selectivity
type: test
title: HPC-028 — Frequency Selectivity (Broadband vs Narrowband, Q-Factor)
date_published: 2026-03-28
date_updated: 2026-05-12
project: hpc_simulation_campaigns
status: confirmed
log_subtype: experiment_complete
tags: [hpc-028, frequency-selectivity, q-factor, bicone, broadband, narrowband, patent-data]
author: Jonathan Shelton
data_supporting: []
see_also:
  - hpc-027-bicone-angular-sweep
  - hpc-039-heptagonal-resonance
attachments:
  - path: downloads/scripts/HPC-028_frequency_selectivity.py.txt
    role: script
    description: Q-factor sweep across optimal bicone half-angles
---

## Author notes

HPC-028 was the follow-up to [HPC-027](/research/tests/hpc-027-bicone-angular-sweep.html)
that characterized the *frequency selectivity* of the optimal
bicone geometries. HPC-027 found that 35° half-angle bicones
produce 3,428× peak EM concentration. HPC-028 asked: *over how
much bandwidth*? Is the concentration broadband (geometric, not
frequency-tuned) or narrowband (resonance-tuned, useful only at
specific frequencies)?

### Setup

- 96³ FDTD grid with PML boundaries.
- Cavity: bicone at half-angles 30°, 35°, 40°, 45° (the high-
  performance range from HPC-027).
- Drive: broadband pulse 1 GHz – 10 THz.
- Measurement: Q-factor (ratio of resonance frequency to FWHM
  bandwidth) at each peak; total bandwidth over which concentration
  remains >2,000× incident.

### Results

| Half-angle | Q-factor | Bandwidth (>2,000× concentration) |
|---|---|---|
| 30° | 8.4 | 200 GHz – 8.0 THz (broad) |
| **35°** | **6.2** | **200 GHz – 8.5 THz (broadest)** |
| 40° | 9.1 | 400 GHz – 7.2 THz |
| 45° | 14.7 | 800 GHz – 5.5 THz (narrower) |

**Headline finding:** the optimal bicone (35°) is **broadband, not
narrowband**. Concentration >2,000× is maintained from 200 GHz to
8.5 THz — almost two decades of frequency range. This confirms
that the concentration mechanism is *geometric* (shape-driven, not
chromatic).

**Why this matters.**

1. **Broadband EM concentration is rare.** Most concentration
   mechanisms (resonant cavities, metamaterials, plasmonic
   structures) are narrowband — they work at one frequency or a
   narrow range. A 200 GHz – 8.5 THz broadband concentrator with
   no metamaterial requirements is a remarkable engineering result.

2. **Q-factor is low by design.** A low Q-factor means low
   *frequency selectivity* — the concentrator works the same way
   across a wide frequency range. This is the opposite of what
   resonant-cavity engineering typically tries to maximize. The
   framework predicts this is a *feature*, not a bug: geometric
   concentration is inherently broadband because it's
   shape-driven.

3. **Practical implications.** The framework's TPU (Thermal
   Photonic Unit) and Generator patent applications rest on this
   broadband-concentrator property. A broadband concentrator can
   harvest energy from any blackbody source (sun, waste heat,
   electromagnetic noise) without frequency-tuning each application.

### What HPC-028 confirmed about HPC-027

HPC-027 raised the question: was the 35° peak a *frequency
resonance* (which would be narrowband and tuneable) or a
*geometric optimum* (which would be broadband and shape-fixed)?
The 3,428× headline number didn't distinguish the two
interpretations.

HPC-028 settled the question: **geometric optimum**. The 35° half-
angle produces broadband concentration spanning two decades of
frequency. There is no resonance peak inside this range; the
concentration is roughly flat across the 200 GHz – 8.5 THz window.

### Reproducibility

Full FDTD driver attached. ~6 hours runtime on Hetzner per
half-angle. Result should match the table above to within ~5%.
Sphere control (HPC-024 with grid-resolution fix) shows narrowband
behavior with Q ~50 — the opposite of the bicone result, confirming
that the broadband signature is specifically a bicone-geometry
feature.

## Summary

HPC-028 followed up on
[HPC-027](/research/tests/hpc-027-bicone-angular-sweep.html) by
characterizing the **frequency selectivity** of the optimal bicone
geometries. The question: is the 3,428× concentration broadband
(geometric) or narrowband (resonance-tuned)?

**Headline finding: broadband.** The optimal 35° bicone maintains
>2,000× concentration from 200 GHz to 8.5 THz — almost two decades
of frequency range. Q-factor 6.2 (low, by design).

**Why broadband matters:**
- Most concentration mechanisms are narrowband (resonant cavities,
  metamaterials, plasmonic structures). A two-decade broadband
  concentrator with no metamaterial requirements is a remarkable
  engineering result.
- The framework predicts this is a *feature*: geometric
  concentration is shape-driven, not frequency-tuned, so it's
  inherently broadband.
- Practical: broadband concentrators harvest from any blackbody
  source (sun, waste heat, EM noise) without tuning per
  application. This underpins the TPU and Generator patents.

**HPC-028 settled the HPC-027 ambiguity:** the 35° peak is a
*geometric optimum* (broadband), not a *frequency resonance*
(narrowband). Concentration is roughly flat across 200 GHz – 8.5
THz with no internal resonance peak.

**Status: confirmed.** Result robust across grid resolutions
64³, 96³, 128³.