Heat Reshapes Light Channels in Silicon Photonic Crystals

Light traveling through the heart of a computer chip does not move through copper wires but through channels carved in silicon, the same material that powers the electronics beside it. Silicon photonics has matured over two decades into a technology capable of moving data between chips at extraordinary speeds, using waveguides, filters, beam splitters and sharp optical bends all built with standard semiconductor fabrication processes. Yet a quiet vulnerability has always shadowed these devices: temperature. When integrated chips operate in demanding environments, whether packed server racks, near-Sun satellite missions, or landers exploring the surfaces of Mercury and Venus, temperatures can climb by hundreds of kelvin. Because the refractive indices of silicon and silicon dioxide both drift with heat, the optical pathways designed at room temperature may not behave the same way once the chip warms up. A new theoretical study published in Results in Optics now maps, in unusual detail, exactly how rising temperatures reshape the photonic band gaps of a two-dimensional silicon dioxide-silicon hexagonal photonic crystal, offering designers a practical guide to which optical features can be trusted when things get hot.

The research, carried out by Chia-Ching Li, Sih-Yuan Wang, Sheng-Chun Weng, Qi-Lin Yang and Ting-Han Pei, focuses on a structure that is deliberately simple to fabricate: a silicon dioxide substrate perforated with a hexagonal array of holes, each filled with silicon. Photonic crystals of this kind control light the way semiconductor crystals control electrons, using periodic modulation of refractive index to open forbidden frequency ranges, called photonic band gaps, where light simply cannot propagate. The hexagonal lattice was chosen over a square one because its higher structural symmetry consistently supports wider band gaps and offers greater design flexibility, a conclusion the authors confirmed through direct comparison. The material pairing matters too. Pure silicon dioxide photonic crystals, whether square or hexagonal, struggle to produce clear band gaps at all, so embedding high-index silicon into the low-index silica background provides the dielectric contrast needed to trap and steer light while remaining fully compatible with chip manufacturing.

What distinguishes this work from earlier thermal studies is the rigor of the optical input data. Rather than treating refractive index as a constant or assuming it varies linearly with temperature, the team coupled experimentally based, wavelength- and temperature-dependent refractive-index models directly into their band-structure calculations. For silicon dioxide, they employed two independent descriptions: the semi-empirical Ghosh model, which explicitly accounts for thermal expansion and the temperature-induced shift of the material’s excitonic band gap, and a modified Sellmeier equation whose fitting parameters vary with temperature. The two models agreed closely, predicting a silica refractive index of about 1.44415 at 314 kelvin rising to 1.44873 at 754 kelvin at the telecommunications wavelength of 1.55 micrometers, with differences between the models so small they are practically negligible. For silicon, the researchers adopted the classic experimentally grounded model published by H. H. Li in 1980, valid from 1.2 to 14 micrometers and from 100 to 750 kelvin, which captures the distinctly nonlinear behavior of silicon’s refractive index with temperature.

The computational engine behind the study is the plane wave expansion method, a workhorse technique more than three decades old that exploits the periodicity of photonic crystals by expanding the electromagnetic fields and the inverse dielectric function into Fourier series. Substituting these expansions into Maxwell’s equations converts the problem of finding allowed light frequencies into a matrix eigenvalue problem in reciprocal space. The authors built their own MATLAB implementation, verified it against worked examples in Kazuaki Sakoda’s standard textbook, and pushed convergence hard, testing truncation sizes from 41 by 41 up to 91 by 91 plane waves. The Bloch wave vector was scanned along the high-symmetry path from M through Gamma to K in the first Brillouin zone, and band gaps were confirmed wherever the minimum frequency of an upper band exceeded the maximum frequency of the band below it. All calculations were performed in the transverse-electric polarization mode at the 1.55 micrometer telecommunications wavelength, deep within silicon’s transparency window, where band-to-band absorption is absent and free-carrier absorption remains negligible even at 600 kelvin.

The results reveal a photonic crystal with a rich thermal personality. Eight band gaps initially emerged below a normalized frequency of 1.1, though one of them, Gap 6, proved so vanishingly narrow that it was excluded from quantitative analysis as a likely numerical artifact. Of the seven reliable gaps that remained, the lower-order ones behaved like thermal bedrock. The first gap, between the first and second bands, held a normalized width of roughly 0.022 with almost no change from 200 to 600 kelvin. The second, the widest of all at a normalized width near 0.035, was similarly indifferent to heating. In stark contrast, the higher-order gaps widened noticeably as temperature climbed. The seventh gap grew by more than 50 percent, from a normalized width of 0.006 to 0.0095, while the eighth expanded by more than 25 percent, from about 0.018 to 0.023. The third, fourth and fifth gaps showed gentler but measurable widening. This split behavior arises because different photonic bands distribute their electric fields differently between the silicon and silica regions, so each gap responds uniquely to the changing refractive-index contrast.

Perhaps the most practically valuable finding concerns the mid-gap positions. Across the entire 400-kelvin temperature span, the centers of all identified gaps shifted only slightly and gradually, meaning the frequencies at which the crystal blocks light stay roughly put even as the gaps themselves breathe. That stability is a gift for engineers, but the study also quantifies how much tolerance designers actually have. For the eighth gap, the team found that its lower edge at 200 kelvin nearly coincides with its upper edge at 600 kelvin, a warning that devices targeting this gap must be designed with care. Operating at the gap center at 250 kelvin, corresponding to a normalized frequency of about 1.007, yields a lattice constant of 1.5609 micrometers at 1.55 micrometers, with a fabrication tolerance of only plus or minus 9.3 nanometers. The second gap is far more forgiving: centered at a normalized frequency of 0.37, it permits a lattice constant of 0.5735 micrometers with a tolerance of plus or minus 27.1 nanometers, roughly three times looser.

The authors also confronted the physical effects they chose to set aside, and the reasoning holds up under scrutiny. Thermal expansion of the silica substrate changes the hole radius by only about 0.02 percent over the full 200-to-600-kelvin range, a variation too small to matter. Differential expansion between silicon and silica does generate compressive stress in the silicon-filled holes, and strain is known to alter silicon’s refractive index by as much as 1.4 percent under extreme conditions, but the estimated internal stress in this geometry falls far below the gigapascal-scale strains required for such shifts, especially compared with the 1.8 percent refractive-index change silicon undergoes purely from heating across 300 kelvin. The photoelastic contribution is therefore safely negligible. The main limitations the authors acknowledge are the boundaries of their material models, which exclude wavelengths shorter than 1.2 micrometers or longer than 14 micrometers, temperatures below 200 or above 600 kelvin, and the absence of direct experimental verification, though every refractive-index input rests on experimentally fitted data.

Placed alongside recent literature, the study carves out a clear niche. Earlier work on diamond-lattice silicon photonic crystals used linearized refractive-index formulas and reported a temperature sensitivity of about 0.0518 nanometers per kelvin at the first band-gap center, hinting at applications in optical temperature sensing and biosensing chips. Other groups have demonstrated thermally tunable silicon valley photonic crystal rings, mapped heat spread from thermo-optic devices, and built photonic crystal temperature sensors from defect-mode resonance shifts. By contrast, this work spans a broader temperature range, covers multiple band gaps simultaneously, and applies nonlinear, experimentally validated refractive-index functions to a structure directly relevant to silicon photonic waveguides. The practical upshot is a design map: lower-order gaps for thermally robust passive components such as filters and waveguides that must survive harsh environments unchanged, and higher-order gaps for thermally tunable or temperature-sensing applications where deliberate sensitivity is the point. As silicon photonics pushes into hotter, harsher and more ambitious territory, knowing exactly where the light is allowed to travel, and how much that map shifts with heat, may prove as important as the circuits themselves.

Subject of Research: Thermal effects on the photonic band gaps of a two-dimensional SiO2-Si hexagonal photonic crystal for silicon photonics

Article Title: The thermal effects on the photonic band gaps of the two-dimensional SiO 2 -Si hexagonal photonic crystal

Article References: Li, C.-C., Wang, S.-Y., Weng, S.-C., Yang, Q.-L., & Pei, T.-H. (2026). The thermal effects on the photonic band gaps of the two-dimensional SiO2-Si hexagonal photonic crystal. Results in Optics, 25, Article 101146. https://doi.org/10.1016/j.rio.2026.101146

Image Credits: AI Generated

DOI: 10.1016/j.rio.2026.101146

Keywords: silicon photonics, photonic crystals, photonic band gaps, thermo-optic effect, plane wave expansion method, silicon dioxide, refractive index, hexagonal lattice, telecommunication wavelength, thermal stability, waveguide design, high-temperature applications