Self-Organized Optical Pathways in Optofluidic Photonic Crystals

Steven Motta

physics.opticsMar 26, 2026

Self-Organized Optical Pathways in Optofluidic Photonic Crystals

Authors: Steven Motta

Abstract

This paper reports FDTD simulations of optofluidic reconfiguration in two-dimensional silicon photonic crystal waveguides, treating structural plasticity (the creation and destruction of optical pathways) via selective fluid infiltration. Using MPB eigenmode analysis, we decouple bandgap narrowing from defect-mode weakening, showing that defect weakening dominates (2.4 times faster transmission decay than bandgap narrowing at CS_2 indices). Infiltration topology controls signal routing (L-bend selectivity S = 0.98), though modulation depth is weak (Delta varepsilon/ varepsilon_ textSi = 11 %). A phenomenological optothermal feedback model produces self-organized pathways that achieve 63 % of a hand-designed waveguide's bandgap transmission (7.6 times the heavily suppressed empty-crystal baseline). Amplitude competition between counter-propagating sources produces strong, monotonic pathway steering (DeltaCOM_x from +0.03 to +4.92 ;a), while pulsed spike-timing-dependent plasticity yields a predictable null result: the timing-sensitive cross-term is suppressed by >10^2 when pulse delays exceed the temporal pulse width. The results provide benchmarks and identify physical limits for bio-inspired reconfigurable optofluidic photonics.

Figures & tables

Figure 1: Optofluidic structural plasticity concept. Left: empty photonic crystal, where the bandgap blocks light propagation. Center: fluid-infiltrated pathway; filling a line of holes with CS 2 creates a defect mode that guides light. Right: biological analogy; filling/flushing holes corresponds to synaptogenesis/pruning of neural connections. The process is fully reversible.

Figure 2: Weight plasticity vs. structural plasticity in photonic systems. Left: conventional neuromorphic photonics (Tait, Feldmann) uses fixed waveguide connections with tunable weights ( $O(N^{2})$ elements for $N\times N$ mapping). Right: our optofluidic approach reconfigures which connections exist by filling/flushing holes in a photonic crystal ( $2^{N}$ possible topologies from $N$ holes). The structural approach trades modulation depth for combinatorial richness.

Figure 3: Simulation geometry (top-down view). Triangular lattice of air holes (white) in silicon (gray), with a line of CS 2 -infiltrated holes (blue) forming the waveguide channel. A Gaussian source (red) launches TE-polarized light; a flux monitor (green) records transmission. PML absorbing boundaries (hatched) surround the domain. Inset: unit cell with $r/a=0.3$ .

Figure 4: Photonic band structure along high-symmetry directions ( $r/a=0.3$ , $\varepsilon_{\text{Si}}=11.56$ ). Blue: TE modes; red dashed: TM modes. (a) Air holes: 39.2% TE bandgap. (b) CS 2 -infiltrated: 30.0% bandgap.

Holes	Integrated flux	Regime
1	$0.111\pm 0.014$	Localized defect
3	$0.083\pm 0.011$	Localized defect
5	$0.095\pm 0.012$	Transition
7	$0.159\pm 0.021$	Resonant coupling
9	$0.212\pm 0.028$	Peak resonance
11	$0.060\pm 0.008$	Post-resonance decay

Table 1: Integrated bandgap transmission (

f=0.22

–

0.28\;c/a

) for infiltration line lengths from 1 to 17 holes (CS 2 ,

n=1.52

). Uncertainties are

\pm 13\%

from resolution convergence (Appendix A ); adjacent values within these error bars are not statistically distinguishable.

Figure 5: Waveguide creation via fluid infiltration. (a) Transmission spectra for selected line lengths. (b) Integrated bandgap transmission vs. number of infiltrated holes showing non-monotonic behavior.

Figure 6: Integrated bandgap transmission vs. fluid refractive index for an 11-hole infiltrated line. Transmission decreases with increasing fluid index above $n\approx 1.1$ .

Figure 7: Decoupling bandgap narrowing from defect weakening. (a) Bandgap edges (blue shading) and integrated transmission (red) vs. fluid index. (b) Normalized comparison: both quantities relative to their $n=1.0$ values. Transmission drops $2.4\times$ faster than bandgap width, proving defect weakening dominates. (c) Rate of change $d/dn$ for both quantities.

Configuration	Port A	Port B	$S_{\text{raw}}$	$S_{\text{corr}}$
Route A (straight)	0.0080	0.0053	0.20	0.29
Route B (L-bend)	0.0006	0.0111	0.89	0.98
Y-split	0.0046	0.0054	0.08	0.06
Blocked (baseline)	0.0119	0.0106	0.06	—

Table 2: Rerouting results: integrated bandgap flux at each port, raw directional selectivity

S_{\text{raw}}

, and background-corrected selectivity

S_{\text{corr}}

(see text). The blocked configuration serves as the scattered-light baseline.

Figure 8: Signal routing via infiltration topology. Integrated bandgap flux at Port A and Port B for four configurations. The L-bend configuration achieves $S=0.89$ directional selectivity.

Topology	$F_{A}$	$F_{B}$	$F_{AB}$	$\frac{F_{AB}}{F_{A}+F_{B}}$
Pass A	0.012	0.018	0.020	0.67
Pass B	0.004	0.046	0.055	1.11
Dual-path	0.011	0.056	0.045	0.66
Junction	0.008	0.036	0.037	0.83
Blocked	0.020	0.025	0.042	0.93

Table 3: Input-output mapping results.

F_{A}

F_{B}

F_{AB}

: output flux for A-only, B-only, and both-inputs-active states.

F_{AB}/(F_{A}+F_{B})

: superposition ratio (1.0 = linear,

>

1 = cooperative,

<

1 = destructive interference). S/B: signal-to-background ratio vs. blocked configuration.

Figure 9: Configurable input-output mappings via infiltration topology. (a) Normalized output flux for five topologies and four input states. (b) Comparison of topology responses. The “blocked” configuration transmits non-negligible scattered flux, limiting the effective signal-to-background ratio.

Configuration	Integrated flux
Reference (no holes)	32.93
Empty crystal (3D)	25.58
Line-infiltrated (3D)	27.48
W1 waveguide (3D)	33.47
Route B, Port A	26.56
Route B, Port B	3.50

Table 4: 3D membrane validation: total integrated spectral flux for each configuration (resolution 24 pixels/

a

h/a=0.55

Figure 10: 3D membrane validation ( $h/a=0.55$ ). Transmission spectra for intact crystal and infiltrated waveguide. The bandgap and infiltration effects persist in realistic 3D geometries.

Figure 11: The optothermal Hebbian feedback loop. Six steps cycle iteratively: (1) MEEP CW electromagnetic solve, (2) field energy extraction at each hole, (3) absorbed power computation with $\eta_{\text{seed}}$ floor, (4) normalized temperature map with thermal diffusion, (5) fill fraction update (hot holes fill, cold holes drain), (6) geometry update with new dielectric values. The cycle repeats for 40 iterations, spanning optical (ps), thermal ( $\mu$ s), and fluidic (ms) timescales.

Figure 12: Self-organized pathway formation via optothermal feedback. Top row: final fill-fraction maps ( $\eta$ , color scale) after 40 iterations for three source configurations. Bottom row: total fill fraction convergence. (a) Single input: 10 holes $>$ 50% filled. (b) Dual inputs: 12 holes $>$ 50% filled, two distinct pathways. (c) Competing inputs: 14 holes $>$ 50% filled, symmetric infiltration.

Figure 13: Time-lapse of pathway self-organization for the single-input scenario at iterations 1, 10, 20, 30, and 40. The pathway progressively extends from the source (left edge) into the crystal, with initially seeded holes reaching full saturation while neighboring holes are activated through thermal diffusion.

Figure 14: Absorption–loss tradeoff: number of holes exceeding 50% fill fraction as a function of absorbing-dye concentration $\text{Im}(\varepsilon)$ . All three values produce similar pathway topologies, confirming that the self-organization is robust across an order of magnitude in absorption strength.

Figure 15: Sensitivity to the seeding parameter $\eta_{\text{seed}}$ . Two orders of magnitude variation ( $0.001$ – $0.1$ ) produces consistent pathway topologies: 10 holes $>$ 50% filled in all cases, with total $\Sigma\eta$ varying by only 12%.

Figure 16: Broadband transmission through self-organized pathways. (a) Spectra comparing empty crystal, hand-designed line (11 holes), and Hebbian single-input pathway. (b) Integrated bandgap flux for all configurations. The self-organized pathway achieves 63% of the hand-designed waveguide’s transmission; the competing-inputs scenario self-assembles a through-channel with $40\times$ enhancement.

Figure 17: Activity-dependent pathway competition. Top row: fill-fraction change maps ( $\Delta\eta$ ) starting from the Hebbian single-input state, for $\Delta t=-20$ , $0$ , $+20$ (a/ $c$ ). All three maps are nearly identical, confirming timing insensitivity. Bottom left: “STDP learning window” showing $\Delta$ COM x flat across all delays (red), far above the single-source control (dashed). Bottom right: center-of-mass evolution showing all delay cases collapsing onto a single trajectory.

Figure 18: Phase-controlled standing wave test. $\Delta$ COM x vs. phase (bottom left) shows a single outlier at $\varphi=\pi/4$ ; the remaining four phases cluster within $\pm 0.1\;a$ . We conclude the result is inconclusive.

Figure 19: Amplitude competition: rate-coded pathway steering. Top: $\Delta\eta$ maps for A:B $=$ 3:1, 1:1, 1:3, showing progressively rightward extension. Bottom left: $\Delta$ COM x vs. power fraction, showing monotonic steering from $+0.03$ (A only) to $+4.92\;a$ (B only). Bottom right: COM evolution showing smooth trajectory separation.

Quantity	Value
TE bandgap (air holes)	0.187–0.279 $c/a$
TE bandgap (CS 2 , $n{=}1.52$ )	0.184–0.249 $c/a$
Gap-midgap ratio (air / CS 2 )	39.2% / 30.0%
Peak infiltration flux	0.212 (9 holes)
Bandgap retention at $n{=}1.52$	71.2%
Transmission retention at $n{=}1.52$	29.2%

Table 5: Summary of key quantitative results. Uncertainties reflect the

\sim

13% systematic error from resolution convergence (Appendix A ).

Appendix figures & tables8 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 20: Resolution convergence for 2D infiltrated waveguide transmission. Non-monotonic behavior across resolutions 32–48 pixels/ $a$ indicates $\sim$ 13% systematic uncertainty.

Figure 21: Disorder robustness: transmission spectra for 20 realizations with $\pm 10\%$ random dielectric perturbations (CV $=10.8\%$ ). Shaded regions show $\pm 1\sigma$ and $\pm 2\sigma$ envelopes.

Figure 22: Integrated bandgap transmission vs. partial fill fraction (0% = air, 100% = full CS 2 ). The monotonic trend supports analog modulation.

Panel of Figure 23 — Figure 23: Transverse $|H_{z}|$ profiles at $x=0$ for four configurations.

Figure 25: $H_{z}$ field distribution (CW, $f=0.25\;c/a$ ) for four infiltration configurations.

Figure 26: Energy balance verification for three configurations. $R+T+\text{Loss}\approx 1$ within numerical precision, confirming simulation correctness.

Figure 27: TE bandgap dependence on hole refractive index (MPB). (a) Bandgap edges vs. fluid index showing asymmetric narrowing. (b) Bandgap width, declining from 39.2% to 4.4% as $n$ increases from 1.0 to 3.0.

Figure 28: Failed analytical model fits. Black: FDTD data. Blue: coupled-cavity ( $R^{2}<0$ ). Red: Fabry-Pérot ( $R^{2}<0$ ). Both models are worse than a constant mean.

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Reliability-Aware Bayesian Optimization of 1310 nm PCSELs with FDTD Verification

Jinglin Yu, Feiyang Wu, Longying Wen, Chongxian Yuan+2

School of Science and Engineering (SSE), The Chinese University of Hong Kong, Shenzhen, Shenzhen 518172, China · Nick Holonyak Micro and Nanotechnology Laboratory, University of Illinois Urbana-Champaign, Urbana, IL 61801 USA

Bayesian Optimization

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Near 1310 nm photonic-crystal surface-emitting lasers (PCSELs) are attractive narrow-beam sources for optical communication and sensing, but their final design refinement is costly. Small geometry changes simultaneously shift the band-edge resonance, cavity leakage, far-field divergence, and the numerical stability of a high-

Q

decay fit, while every full-wave trial requires a time-domain simulation. We couple a commercial finite-difference time-domain solver to a reliability-aware Bayesian optimization (BO) loop over eight local design variables. Each completed simulation updates the surrogate used to choose the next geometry. Candidate ranking combines wavelength and beam-quality requirements with a reliability-adjusted metric

Q_{\mathrm{eff}}

derived from the solver-reported relative fit-error estimate

dQ/Q

. Across three 80-evaluation runs from the same reference model, BO produced 5--15 candidates per run that passed the joint filter. Designs reconstructed from fresh model copies retained

Q_{\mathrm{eff}}=4.33\times10^6

7.76\times10^6

, a 60--108-fold increase over the baseline metric, at 1308.23--1310.90~nm with approximately

0.84^{\circ}

divergence. Under equal budgets, BO gave the highest mean strict-filter yield (9.0 candidates), compared with differential evolution (7.0) and Latin-hypercube sampling (1.5), although the controls occasionally matched the peak

Q_{\mathrm{eff}}

. Field maps, resonance spectra, and local perturbations further identify an index-related wavelength handle and a hole-size-related leakage handle. The resulting FDTD budget produces a pool of wavelength-compatible, narrow-beam, and reproducible high-

Q

PCSEL candidates without trusting a single optimistic decay fit.

Abstract

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