Asymmetric Textured Image Sensors Based on Antenna Theory as Designed by Nature

Abstract: This work numerically validates the application of bio-inspired concepts on CMOS derived from bacterial photosynthetic light harvesters. We investigate a modification of symmetric inverted pyramid array CMOS image sensors into an asymmetrically shaped texture to explore the structural boundary of passive non-reciprocity. Diverging from traditional macroscopic continuum assumptions, we analyze whether structural asymmetry at sub-wavelength scales can induce non-reciprocal scattering under passive, linear, and time-invariant conditions. A theoretical framework based on perturbation theory is developed, estimating a potential efficiency enhancement of 5\% to 15\%. Numerical simulations performed via the MEEP finite-difference time-domain (FDTD) platform reveal that the linear response is highly localized, showing a subtle 0.02\% change. This suggests that macroscopic Lorentz reciprocity remains robust at the investigated scale due to apex field concentration, defining a clear geometric threshold for microscopic non-reciprocity.

• The paper evaluates biomimetic elliptical textures using perturbative theory and MEEP FDTD simulations, predicting a potential 5%–15% enhancement but measuring only a 0.02% absorption change.
• The simulations show that electromagnetic fields concentrate at the symmetric apex of the textured structure, effectively shielding base-level asymmetry and limiting its influence on sensor absorption.
• The findings suggest that future demonstrations of passive nanoscale non-reciprocity should engineer asymmetry at field-concentrating apexes, while addressing limited spectral modeling, discretization errors, and untested geometries.

This paper examines whether sub-wavelength geometric asymmetry, inspired by bacterial photosynthetic light-harvesting complexes, can induce passive non-reciprocal scattering in CMOS image sensors (2608.12729). The work combines a perturbative theoretical framework with FDTD simulations to test the boundary conditions under which Lorentz reciprocity might break down at the nanoscale.

Motivation and theoretical framing

The author departs from the classical ray-optics treatment of textured optical surfaces established by Yablonovitch and Redfield in the 1970s–80s, noting that ray theory becomes invalid below Wien's thermal wavelength ($\lambda_T \approx 7.5\,\mu\text{m}$ at room temperature). Instead, the entire sub-wavelength textured layer is modeled as an engineered impedance-matching scatterer — a nanoantenna in the dielectric-resonator sense — rather than requiring conventional RF resonant geometries. This follows the author's earlier proposal of non-reciprocal light-harvesting nanoantennae based on bacterial structures (Ting, 2017).

The biomimetic choice is deliberate: while existing bio-inspired photonic sensor work overwhelmingly draws on zoological models (viola petals, plasmonic leaves, tree morphology), bacterial light harvesters such as the RC-LH1 complex of Rhodopseudomonas palustris offer a simpler geometry whose inter-membrane layered architecture maps naturally onto standard semiconductor fabrication. The elliptical cross-section of LH1 (major axis 110 Å, minor axis 95 Å) provides the asymmetry parameter.

Perturbative estimate of enhancement

At the molecular scale, macroscopic continuum constitutive parameters ($\epsilon$, $\mu$, $\chi$) lose validity, and geometry itself defines the electronic potential $V(\mathbf{r})$. For an asymmetric structure with $V(\mathbf{r}) \neq V(-\mathbf{r})$, inversion symmetry is broken and a second-order susceptibility $\chi^{(2)}$ emerges, enabling optical rectification via the ratchet effect:

$$\langle\mathbf{J}(t)\rangle = \sigma_{rect} |\mathbf{E}(\omega)|^2 \hat{n}$$

Using the eccentricity of R. palustris LH1 ($\delta \approx 13.6\%$, $\xi \approx 0.073$) and a scaling relation $\epsilon$0 with $\epsilon$1 Å and $\epsilon$2 Å, the theory predicts a 5%–15% efficiency enhancement across the spectral range. This is the paper's central quantitative claim from first-principles reasoning.

Numerical method and results

Simulations use MEEP (FDTD) on the back-illuminated CMOS pixel design from Yokogawa et al.'s diffractive light-trapping study (Sci. Rep. 7, 2017), which includes a SiO₂ microlens, tungsten aperture grid, 3 μm crystalline silicon substrate, and deep-trench isolation. Because MEEP lacks a native elliptical cone primitive, the asymmetric texture was constructed as a 32-vertex polygonal prism with axis scaling factors $\epsilon$3 and $\epsilon$4, preserving cross-sectional area while matching the bacterial eccentricity.

A notable methodological caveat: the author found that re-running the original MEEP project code produced figures differing from those published on the project website, citing minor typos in the program and shell scripts and unconfirmed lattice spacing assumptions. The comparison is therefore made between the author's own circular-prism baseline and the elliptical variant, rather than against the original published curves.

The headline numerical result is starkly at odds with the theoretical prediction:

Configuration	Framework	Enhancement
Viola petal texture	Ray/wave	Broadband
Plasmonic leaf	Plasmonic	Localized field
Symmetric cone (Yokogawa)	Wave FDTD	Reference
Elliptical base (this work)	Linear FDTD	0.02%
Perturbation theory (this work)	Microscopic non-reciprocity	5%–15% (potential)

Mean textured-substrate absorption changed only from 0.186292 to 0.186256 between circular and elliptical prisms — a 0.02% difference, roughly three orders of magnitude below the theoretical bound. The author attributes this to a "geometric shielding mechanism": the intense electromagnetic field concentrates at the sharp symmetric apex of the inverted pyramid, while the asymmetry was introduced at the base, leaving the apex field distribution essentially undisturbed. The implication is concrete: passive non-reciprocity at this scale requires geometric deformation engineered directly at the field-concentrating apex, not merely anywhere on the structure.

Under oblique incidence ($\epsilon$5–$\epsilon$6), the elliptical texture maintains stable broadband absorption, which the author attributes to broadened spatial Fourier components compensating phase mismatch — though this angular analysis is presented as supplementary rather than as a primary result.

Limitations and open questions

Several limitations are conceded explicitly. The spectral range is restricted to $\epsilon$7–$\epsilon$8 by the single-oscillator Lorentzian material model, so visible-spectrum behavior remains unverified. The 0.02% signal may be partly attributable to discretization error or manufacturing-level crystal-structure effects rather than genuine physics, as the author acknowledges. The comparison baseline is complicated by discrepancies with the original MEEP project's published figures. Most significantly, the central hypothesis — that apex-localized asymmetry would unlock the predicted 5%–15% enhancement — was not tested; only base-modified geometries were simulated. Whether asymmetric apex engineering, asymmetric cone distributions, or apex defects can realize the perturbative prediction remains an open question.

Conclusion

The paper establishes a clear negative result with diagnostic value: linear, passive, time-invariant Lorentz reciprocity remains robust for base-level geometric asymmetry at these scales, defining a geometric threshold for microscopic non-reciprocity. Its contribution lies less in demonstrated device performance than in framing the problem through antenna/scattering theory and identifying apex field concentration as the controlling factor for any future demonstration of scale-dependent passive non-reciprocity in textured CMOS sensors.