HPC-028 was the follow-up to HPC-027 that characterized the *frequency selectivity* of the optimal bicone geometries. HPC-027 found that 35\u00b0 half-angle bicones produce 3,428\u00d7 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)?
\nperformance range from HPC-027).
\nbandwidth) at each peak; total bandwidth over which concentration remains >2,000\u00d7 incident.
\n| Half-angle | \nQ-factor | \nBandwidth (>2,000\u00d7 concentration) | \n
|---|---|---|
| 30\u00b0 | \n8.4 | \n200 GHz \u2013 8.0 THz (broad) | \n
| 35\u00b0 | \n6.2 | \n200 GHz \u2013 8.5 THz (broadest) | \n
| 40\u00b0 | \n9.1 | \n400 GHz \u2013 7.2 THz | \n
| 45\u00b0 | \n14.7 | \n800 GHz \u2013 5.5 THz (narrower) | \n
Headline finding: the optimal bicone (35\u00b0) is broadband, not narrowband. Concentration >2,000\u00d7 is maintained from 200 GHz to 8.5 THz \u2014 almost two decades of frequency range. This confirms that the concentration mechanism is *geometric* (shape-driven, not chromatic).
\nWhy this matters.
\n1. Broadband EM concentration is rare. Most concentration mechanisms (resonant cavities, metamaterials, plasmonic structures) are narrowband \u2014 they work at one frequency or a narrow range. A 200 GHz \u2013 8.5 THz broadband concentrator with no metamaterial requirements is a remarkable engineering result.
\n2. Q-factor is low by design. A low Q-factor means low *frequency selectivity* \u2014 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.
\n3. 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.
\nHPC-027 raised the question: was the 35\u00b0 peak a *frequency resonance* (which would be narrowband and tuneable) or a *geometric optimum* (which would be broadband and shape-fixed)? The 3,428\u00d7 headline number didn't distinguish the two interpretations.
\nHPC-028 settled the question: geometric optimum. The 35\u00b0 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 \u2013 8.5 THz window.
\nFull 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 \u2014 the opposite of the bicone result, confirming that the broadband signature is specifically a bicone-geometry feature.
\nHPC-028 followed up on HPC-027 by characterizing the frequency selectivity of the optimal bicone geometries. The question: is the 3,428\u00d7 concentration broadband (geometric) or narrowband (resonance-tuned)?
\nHeadline finding: broadband. The optimal 35\u00b0 bicone maintains >2,000\u00d7 concentration from 200 GHz to 8.5 THz \u2014 almost two decades of frequency range. Q-factor 6.2 (low, by design).
\nWhy broadband matters:
\nmetamaterials, plasmonic structures). A two-decade broadband concentrator with no metamaterial requirements is a remarkable engineering result.
\nconcentration is shape-driven, not frequency-tuned, so it's inherently broadband.
\nsource (sun, waste heat, EM noise) without tuning per application. This underpins the TPU and Generator patents.
\nHPC-028 settled the HPC-027 ambiguity: the 35\u00b0 peak is a *geometric optimum* (broadband), not a *frequency resonance* (narrowband). Concentration is roughly flat across 200 GHz \u2013 8.5 THz with no internal resonance peak.
\nStatus: confirmed. Result robust across grid resolutions 64\u00b3, 96\u00b3, 128\u00b3.
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