The heart of the device is a two-dimensional photonic crystal, a periodic lattice of air holes etched into a thin silicon slab that manipulates the flow of light in much the same way that a semiconductor crystal manipulates electrons. Because the refractive index alternates periodically between silicon and air, the structure exhibits a photonic band gap, a range of wavelengths that cannot propagate through the crystal. By introducing defects into this lattice, engineers can trap light in tiny resonant cavities whose transmission spectrum contains extremely sharp peaks. When something changes the optical properties of the surrounding material, such as mechanical stress altering the refractive index of silicon, those peaks shift in a measurable and repeatable way, turning a purely optical effect into a sensitive physical measurement.

Earlier work by the same community showed that a single hexagonal ring resonator in a photonic crystal suffers from relatively low sensitivity and a modest quality factor, the figure of merit that describes how long photons circulate inside a resonator before leaking away. A high quality factor translates directly into narrow resonance linewidths, and narrow linewidths make it possible to detect very small wavelength shifts. The new design therefore couples two hexagonal ring resonators in series, an arrangement that dramatically improves optical confinement and extends the effective photon lifetime within the structure. The result is a resonance that is both sharper and more responsive to external perturbations than anything a single ring can deliver.

The physical architecture of the sensor is a study in miniaturisation. A silicon substrate 450 micrometres thick and 14 by 14 micrometres in lateral size supports a three-micrometre silicon dioxide layer, on top of which sits the 220-nanometre-thick photonic crystal slab. The active sensing region measures 12 by 12 micrometres and contains an array of 40 by 34 air holes arranged in a hexagonal lattice, with a hole radius of 136 nanometres and a lattice constant of 420 nanometres. The researchers chose the hexagonal lattice deliberately, citing studies showing that it delivers wider photonic band gaps and better performance metrics than triangular or square alternatives. The ratio of hole radius to lattice constant falls between 0.3 and 0.4, a range chosen to keep the design realistic for existing fabrication processes.

Beneath the photonic crystal lies a cavity that leaves the diaphragm free to deform downward when pressure is applied. The team computed the photonic band structure of the defect-free lattice using the plane wave expansion method, finding a band gap spanning wavelengths from 1.3506 to 1.9425 micrometres, comfortably encompassing the 1550-nanometre telecommunications band where the sensor is designed to operate. When the input port is excited with a broadband source, a prominent resonance peak appears at 1.56674 micrometres with a full width at half maximum of just 0.03 nanometres, corresponding to a quality factor of 52,224. Field distribution maps at the resonant and off-resonant conditions confirm that light is efficiently coupled into the double-ring structure only on resonance, the behaviour required for reliable wavelength-shift readout.

The opto-mechanical side of the sensor was analysed with the finite element method, while the optical behaviour was simulated with the finite-difference time-domain technique, a combination that captures both the structural deformation under load and the resulting electromagnetic response. When pressure is applied to the diaphragm as a boundary load, the membrane deflects downward and surface stress rises. Stress changes the refractive index of silicon through the photoelastic effect, governed by a stress coefficient of 1.56 times ten to the minus eleven, and this refractive index change shifts the resonance wavelength. The stress distribution across the diaphragm is not uniform: it oscillates between high and low values as the edge alternates between air holes and solid silicon, reaching maxima at the midpoints of the diaphragm edges and a minimum at the centre.

The numerical results, tabulated across the full 0 to 12 megapascal operating range, show a beautifully linear response. At one megapascal the resonance sits at 1.57842 micrometres; by twelve megapascal it has moved to 1.7104 micrometres. Intriguingly, the quality factor does not degrade as pressure increases but actually climbs, from 52,224 at zero load to 57,013 at the top of the range, because the resonance wavelength itself increases while the linewidth remains fixed at 0.03 nanometres. The researchers also calculated the burst pressure of the diaphragm using the fracture stress of silicon, arriving at a maximum safe operating pressure of approximately twelve megapascals, which conveniently defines the sensor’s full measurement span.

How does this compare with the existing literature? The authors assembled a comparison table of photonic crystal pressure sensors that makes the advance strikingly clear. A two-dimensional photonic crystal Mach-Zehnder interferometer reported in 2018 managed a sensitivity of just 0.02237 nanometres per megapascal, while a 2023 ring resonator design reached only 0.003. Even the strongest earlier entries from the same research group, a photonic crystal microring resonator diaphragm sensor with a sensitivity of 1.37 nanometres per megapascal and a quality factor of 26,180, are surpassed by nearly an order of magnitude in sensitivity and doubled in quality factor. The new device also achieves a minimum detectable pressure of 0.00253 megapascal, roughly seventeen times finer than the earlier diaphragm sensor’s 0.0437 megapascal.

The significance of the work extends beyond the raw numbers. Because the entire sensor is built on a silicon-on-insulator platform using standard photonic crystal geometries, it is inherently compatible with the same semiconductor manufacturing infrastructure that produces computer chips, opening a plausible route to mass production of optical pressure sensors that are immune to electromagnetic interference and capable of operating in harsh environments. The researchers suggest the design could serve applications ranging from industrial process monitoring to biomedical instrumentation, wherever small pressures must be measured with high precision on a chip-scale footprint.

There remain, of course, the usual caveats that separate simulation from product. The reported performance comes from finite element and finite-difference time-domain modelling rather than from a fabricated and tested device, and real-world fabrication tolerances, surface roughness and coupling losses will inevitably erode some of the simulated quality factor. Nevertheless, the design parameters were deliberately constrained to fabrication-friendly values, and the underlying physics of serially coupled resonators is well established experimentally. If the laboratory results survive contact with a cleanroom, serially coupled hexagonal photonic crystal resonators may well become a standard building block for the next generation of chip-scale optical pressure sensors, proving once again that in photonics, as in so much of engineering, the cleverest tricks often come from coupling simple things together in the right way.

Subject of Research: Photonic crystal ring resonator pressure sensor design and simulation

Article Title: Highly sensitive and high Q-factor photonic crystals serially coupled hexagonal resonator for pressure sensing

Article References: Basavaprasad, Kolli, V. R., P.R., Y., K.B., S. K., Ramesh, M., Manivannan, G. S., & Talabattula, S. (2026). Highly sensitive and high Q-factor photonic crystals serially coupled hexagonal resonator for pressure sensing. Results in Optics, 25, Article 101167. https://doi.org/10.1016/j.rio.2026.101167

Image Credits: AI Generated

DOI: 10.1016/j.rio.2026.101167

Keywords: photonic crystals, pressure sensor, hexagonal ring resonator, silicon-on-insulator, quality factor, FDTD, finite element method, optical sensing, photonic band gap, microelectromechanical systems, wavelength shift, silicon photonics

The refractive index, a measure of how much light slows and bends as it passes through a material, is far more than an optical curiosity in this context. Because the index shifts systematically with the concentration of dissolved lithium bromide, engineers can use optical techniques such as interferometry and inline refractometry to monitor solution strength without ever touching the fluid. That matters enormously in absorption refrigeration, where the concentration of the lithium bromide solution must be tightly controlled. Let the concentration drift too high and crystals form, clogging pumps and heat exchangers in one of the most feared failure modes of the technology. Accurate, real-time optical sensing is therefore a safety and efficiency tool, not merely a laboratory convenience.

Until recently, the optical data available for lithium bromide solutions were sparse. Most historical measurements were taken at a single wavelength, the sodium D-line at 589.3 nanometers, over narrow ranges of temperature and composition, and the resulting datasets were often inconsistent. A major change came when Pérez de Luco and colleagues published a comprehensive experimental database spanning multiple wavelengths, a wide sweep of lithium bromide mass fractions, and temperatures from 23 to 47 degrees Celsius, with and without 150 parts per million of 1-octanol, a surfactant commonly added to enhance heat and mass transfer. The new study builds directly on that dataset, which contains 3,185 individual refractive index measurements, to construct predictive models that capture all of these variables simultaneously.

The researchers benchmarked five machine learning architectures: CatBoost, a gradient-boosting method; a multilayer perceptron neural network; a heterogeneous ensemble combining support vector machines, decision trees, and k-nearest-neighbor regressors; AdaBoost; and Random Forest. Rather than hand-tuning their models, the team employed Coupled Simulated Annealing, an optimization strategy that runs multiple search trajectories in parallel under a shared acceptance rule. This cooperative scheme helps the search escape local minima that trap conventional single-path optimizers. The tuning was performed strictly on a validation subset carved out of the training data, with an independent test set of 637 points held back until the very end, a discipline designed to prevent the subtle data leakage that can inflate reported accuracy.

The verdict was emphatic. CatBoost emerged as the clear winner, achieving a coefficient of determination of 0.99988 on the test set, a root mean square error of 0.00069, and an average absolute relative error of just 0.0366 percent. That error is within roughly one to three times the stated experimental uncertainty of the underlying measurements, which stands at plus or minus 0.0003 in refractive index. The neural network and the heterogeneous ensemble followed closely, while AdaBoost and Random Forest trailed with errors roughly double those of CatBoost. Notably, the gap between training and testing performance for CatBoost was a mere 1.47 percent in RMSE, strong evidence that the model genuinely learned the underlying physics rather than memorizing its training examples.

Perhaps the most scientifically interesting result came from a Monte Carlo sensitivity analysis, which quantified how strongly each input variable drives the refractive index. Wavelength dominated with a sensitivity index of 6.97, consistent with the well-known phenomenon of optical dispersion. Temperature ranked second at 4.95, reflecting its dual influence on solution density and molecular polarizability. But in third place, with an index of 3.67, sat surfactant presence, ahead of lithium bromide mass fraction itself at 1.52. Comparing matched experimental pairs, the team found that adding 150 ppm of 1-octanol consistently lowers the refractive index by about 0.0004 to 0.0012 units, a small but systematic effect that earlier optical models of absorption systems had universally ignored.

The practical consequences of that neglected effect are striking. According to the authors’ analysis, an optical diagnostic calibrated on surfactant-free solutions but deployed on a surfactant-containing system would misread the lithium bromide concentration by roughly 1.5 to 2.5 weight percent. In an absorption chiller, where crystallization prevention depends on knowing concentration to within about half a percent, that is an error no operator can afford. The new models are, to the authors’ knowledge, the first predictive tools to explicitly and accurately quantify this surfactant-induced optical shift across the full experimental range, allowing engineers to interpret optical signals correctly even when heat-transfer additives are present.

The team also stress-tested the winning model with a grouped leave-one-out validation scheme, deliberately withholding entire physical regimes rather than random data points. When all measurements at 655 nanometers were excluded, the model had to extrapolate to an unseen wavelength, and its RMSE rose from 0.00069 to 0.00124. Excluding the high-temperature band of 44 to 47 degrees Celsius and the high-concentration region above 0.55 mass fraction produced similar, slightly smaller degradations. Even under these demanding conditions, the coefficient of determination never fell below 0.9979, and the translated concentration error of about 0.39 percent remains within the tolerances of typical chiller monitoring. Intriguingly, the wavelength-exclusion test produced the largest error, mirroring the Monte Carlo finding that dispersion is the dominant variable, an agreement between two independent analyses that strengthens confidence in the physical interpretation.

Speed matters as much as accuracy for real-world deployment, and here the models also shine. Once trained, CatBoost delivers predictions in milliseconds with a small memory footprint, making it suitable for embedding in optical sensors, computational fluid dynamics codes, and digital twin platforms for absorption chillers. The authors envision the model serving as a surrogate that replaces expensive property calculations inside cycle simulators and CFD solvers, or feeding real-time control strategies that keep systems safely away from the crystallization boundary. Designers of lab-on-a-chip devices and liquid-core optical fibers that might contact lithium brine fluids could likewise use the models to predict optical behavior without extensive characterization campaigns.

The study is candid about its limits. The models are data-driven and valid only within the training domain of 23 to 47 degrees Celsius, wavelengths from 436.1 to 655 nanometers, and mass fractions up to 0.6199 kilograms per kilogram; extrapolation beyond these bounds is not recommended. The binary surfactant variable also captures only the fixed 150 ppm dosage used in the source experiments, and the sensitivity ranking for a discrete on-off variable must be interpreted differently from that of continuous inputs. Still, the authors argue that the framework itself, from Coupled Simulated Annealing optimization to grouped cross-validation, is fully generalizable, and future work could embed physical constraints such as molar refractivity and thermodynamic consistency directly into the training process. For now, the message is clear: with the right algorithm and rigorous validation, machine learning can turn a sprawling optical dataset into a fast, trustworthy instrument in its own right, one that sees both the salt and the subtle fingerprint of the surfactant dissolved within it.

Subject of Research: Machine learning prediction of the refractive index of surfactant-containing aqueous lithium bromide solutions

Article Title: Accurate refractive index modeling of surfactant-containing LiBr–water solutions via optimized machine learning techniques

Article References: Al Bustanji, S., Mostafa, S. A., Prajapati, A. A., Gowrishankar, J., Shakir, A. K., Bharti, R., Ernazarov, M., Madaminov, B., & Hekmatyar, Z. (2026). Accurate refractive index modeling of surfactant-containing LiBr–water solutions via optimized machine learning techniques. Results in Chemistry, 31, Article 103874. https://doi.org/10.1016/j.rechem.2026.103874

Image Credits: AI Generated

DOI: 10.1016/j.rechem.2026.103874

Keywords: refractive index, lithium bromide, machine learning, CatBoost, surfactant, absorption chillers, Coupled Simulated Annealing, interferometry, sensitivity analysis, Monte Carlo simulation, optical sensing, hyperparameter optimization

The heart of the innovation lies in the cladding. Photonic crystal fibers, first proposed by Philip Russell and co-workers in the 1990s, replace the doped glass of conventional fiber with a periodic lattice of air holes running along the entire length. Because air has a refractive index close to 1.0, while silica sits near 1.45, the air-hole lattice lowers the effective refractive index of the cladding far more aggressively than doping ever could. In the new design, nine solid silica cores—one at the center and eight arranged symmetrically in an octagonal ring—stand out as the highest-index regions in the structure, each trapping its own light. The surrounding triangular lattice of air holes, with a hole diameter of 2 micrometers and a pitch of 2.7 micrometers, provides the optical barrier that keeps the channels isolated.

Geometry is everything in this architecture. Each core has a diameter of 50 micrometers, and the inter-core distances of 250 and 194 micrometers were deliberately chosen so that every core sits at least seven core radii from its neighbors, a threshold beyond which coupling between cores becomes practically negligible. The researchers confirmed this with full-vectorial finite element method simulations, solving the Helmholtz equation for the transverse permittivity profile and extracting the coupling coefficient between adjacent cores from the overlap of even and antisymmetric supermodes. The result was a coupling coefficient of roughly 3 × 10⁻⁷ per meter, which translates into the −90.5 decibel crosstalk figure. For comparison, conventional weakly coupled multicore fibers typically manage only −60 to −80 decibels.

The air-hole cladding also delivers a high numerical aperture of 0.3, corresponding to a critical acceptance angle of 11.8 degrees. That matters for practical systems: a wide acceptance cone makes it far easier to couple light efficiently from inexpensive sources such as vertical-cavity surface-emitting lasers and light-emitting diodes, which is precisely the regime relevant for short- and medium-reach links. Conventional multicore fibers, with numerical apertures around 0.1 to 0.2, demand more precise and more expensive launch optics. The trade-off is a relatively large outer cladding diameter of 720 micrometers, which imposes larger bending radii than standard telecom fiber, but the authors argue this is acceptable for fixed links, laboratory systems, and spatial-division multiplexing platforms where the benefits of high channel density and simplified integration outweigh the handling constraints.

To predict how signals actually behave over distance, the team turned to the power flow equation, a computationally efficient framework first formulated by Detlef Gloge in 1972 that describes how optical power redistributes among the guided modes of a multimode fiber. Mode coupling in real fibers arises from unavoidable imperfections—microbending, diameter fluctuations, density inhomogeneities—that scatter power between modes as light propagates. Using an explicit finite difference method with a coupling coefficient of 6.4 × 10⁻⁶ radians squared per meter, the researchers simulated two Gaussian launch conditions with angular widths of 1 degree and 5 degrees, tracking the output power distribution along all nine cores at distances from 10 meters up to nearly 2 kilometers.

The simulations reveal a clear and quantitatively rich picture of how the fiber reaches equilibrium. In short fibers, power concentrates in low-order modes, but as light travels, coupling progressively shifts energy toward higher-order modes until the distribution settles into the equilibrium mode distribution. For the narrower 1-degree launch, this occurs at a coupling length of about 705 meters; for the wider 5-degree launch, at about 624 meters. A fully steady-state distribution arrives even later, at roughly 1850 meters and 1700 meters respectively. Wider launch beams therefore shorten the characteristic lengths, because the light starts out spread across more modes and has less distance to travel before mixing completes.

Bandwidth tells the complementary story. At 10 meters, the narrow launch delivers a −3 dB optical bandwidth of 54 gigahertz, versus just 4 gigahertz for the wide launch, because a tightly collimated beam excites fewer high-order modes and suffers less modal dispersion. By 100 meters the figures fall to 0.97 gigahertz and 0.31 gigahertz, and by 500 meters they converge to tens of megahertz. Beyond the steady-state length, the bandwidth becomes entirely independent of how the light was launched, settling at about 12 megahertz. The practical conclusion is that this nine-channel fiber is best suited to short- and medium-haul transmission up to roughly 500 meters, where narrow launch beams can dramatically boost per-channel bandwidth, rather than to long-haul submarine or terrestrial backbone routes.

What elevates the design beyond a communication curiosity is its sensing potential. Because the nine channels are so well isolated, each core can be selectively functionalized to interact with a different analyte, and local changes in refractive index modulate that channel’s effective propagation constant without contaminating its neighbors. The architecture naturally supports differential sensing, in which unfunctionalized cores serve as reference paths that compensate for ambient temperature and mechanical fluctuations in real time. The authors envision parallel, real-time detection of multiple chemical and biological species for environmental surveillance, biomedical diagnostics, and chemical process monitoring—applications where conventional fibers offer only single-parameter or spatially limited sensing.

Fabrication, the team argues, is within reach of existing technology. The fiber can be made by the standard stack-and-draw procedure, in which silica capillaries are stacked into the triangular lattice while solid rods occupy the nine core positions, with multi-stage drawing and active pressure control preventing hole collapse. Alternatively, high-precision CNC ultrasonic drilling or laser-assisted preform machining can fix the core positions before the capillaries are inserted. Standard manufacturing tolerances of ±1 percent on hole diameter and ±0.5 percent on pitch introduce only negligible shifts in cladding index and numerical aperture, and the analysis shows that even with a ±1 micrometer core-position deviation, the inter-core separation stays well above the critical coupling threshold, keeping crosstalk isolation above 88 decibels.

The work arrives amid a broader surge of interest in multicore and photonic crystal fiber architectures, from polymer-fiber multiplexers for short-reach routing to eight-channel C-band demultiplexers built on multicore photonic crystal fibers. By combining an octagonal nine-core layout, an air-silica microstructured cladding, and a rigorous power-flow analysis of bandwidth and mode coupling, the Serbian and Chinese team has sketched a single component that could serve simultaneously as a compact spatial-division multiplexing platform and a nine-channel parallel sensor. As data demand keeps climbing and sensing systems grow ever more parallel, fibers that keep their channels whisper-quiet to one another may prove to be exactly the kind of quiet revolution optical networks need.

Subject of Research: Design and bandwidth analysis of a nine-core multimode step-index silica photonic crystal fiber for space-division multiplexed communication and multi-channel optical sensing.

Article Title: Design and analysis of multimode step-index multicore silica photonic crystal fibers for communication and sensing applications

Article References: Simović, A., Drljača, B., Savović, M., Deng, X., & Savović, S. (2026). Design and analysis of multimode step-index multicore silica photonic crystal fibers for communication and sensing applications. Results in Optics, 25, Article 101155. https://doi.org/10.1016/j.rio.2026.101155

Image Credits: AI Generated

DOI: 10.1016/j.rio.2026.101155

Keywords: photonic crystal fiber, multicore fiber, space-division multiplexing, inter-core crosstalk, optical bandwidth, mode coupling, silica fiber, optical sensing, power flow equation, fiber optics, refractive index, telecommunications