The researchers used a two-pronged approach combining theoretical analysis with numerical simulations. First, they developed mathematical models using what's called the T-matrix method to evaluate how light would interact with their proposed structures. They focused particularly on nanospheres made of silicon, arranged in regular patterns to form a metasurface. These spheres were chosen to be about 210.6 nanometers in radius, spaced at three times their radius - dimensions carefully selected to support specific resonant behaviors. The team then validated their theoretical predictions using detailed computer simulations that accounted for real-world factors like material losses and coupling between different nanospheres.

The key findings showed that their resonant approach could achieve momentum bandgaps 350 times wider than conventional non-resonant designs, while requiring only a 1% change in material properties instead of the previously required 100%. The team demonstrated this effect for both surface waves (confined to the metasurface) and propagating waves (traveling through space). Importantly, they showed their design could maintain substantial amplification even with realistic material losses, specifically when the material's damping factor stayed below about 5% of the resonance frequency - a condition easily met by silicon in the infrared range.

While promising, the research does have important boundaries. The current design works best in the infrared spectrum, and extending it to visible light would require different materials or structural adaptations. The team also notes that practical implementation would require precise control over the temporal modulation of the material properties. Additionally, while their calculations account for material losses, real-world fabrication imperfections could introduce additional challenges not covered in their theoretical analysis.

This work represents a fundamental rethinking of how to achieve photonic time crystal effects. Rather than pushing against the limitations of material properties, the team showed how structural resonances could dramatically enhance the desired effects. Their approach opens new possibilities for experimental demonstrations and practical applications, though significant engineering work would be needed to realize these possibilities. The research also suggests similar resonant approaches might be valuable in other areas of physics and engineering where weak effects need to be enhanced.

The research was conducted within the "Wave phenomena: analysis and numerics" Collaborative Research Center, funded by the German Research Foundation (DFG), and is embedded in the Helmholtz Association's Information research field. Additional support came from multiple institutions including the Max Planck School of Photonics, the Research Council of Finland, and various university programs. The collaborative effort involved researchers from Harbin Engineering University, Karlsruhe Institute of Technology, University of Eastern Finland, and Aalto University, with no declared competing interests.