Numerical Modeling of Photonic Time Crystals

Research training in time-varying photonics through Floquet band calculations and time-domain simulations

Platform
Time-varying photonics
My role
Numerical modeling
Status
Ongoing research training

Context: Ongoing research training in time-varying and spatiotemporal photonics.

Research focus

I am studying how temporal modulation changes electromagnetic wave propagation. This training connects frequency-domain descriptions of periodic media with direct time-domain simulations.

Numerical approach

  • Plane-wave expansion for band calculations in time-varying and spatiotemporal media.
  • Temporal transfer matrices for independent checks of band calculations.
  • MATLAB FDTD simulations, field reconstruction, and comparisons with published reference problems.

My current emphasis is on understanding the assumptions of each method and checking agreement between complementary numerical approaches.

Numerical training examples

FDTD training simulations comparing pulse dynamics in a pass band and a momentum gap
My FDTD reproduction using parameters from Lustig, Sharabi, and Segev, Optica 5, 1390–1395 (2018). The panels compare pulses in a pass band and a momentum gap. These are numerical training results based on a published reference problem; the two panels use different color scales.
Calculated Floquet bands and momentum gaps for a two-step temporal modulation
My temporal transfer-matrix calculation for a two-step modulation model, showing real-quasifrequency pass bands and momentum gaps. This is a numerical method check within the training project.
Probe-based spectral reconstruction from finite wave-packet simulations
My FFT-based reconstruction from finite wave-packet simulations and fixed probes. The horizontal coordinate is the source center wavevector, so this plot is a probe-based numerical response rather than an exact infinite-medium eigenvalue spectrum.

Selected background reading

  1. E. Lustig, Y. Sharabi, and M. Segev, “Topological aspects of photonic time crystals,” Optica 5, 1390–1395 (2018). doi:10.1364/OPTICA.5.001390
  2. J. Park and B. Min, “Spatiotemporal plane wave expansion method for arbitrary space-time periodic photonic media,” Optics Letters 46, 484–487 (2021). doi:10.1364/OL.411622
  3. D. Ramaccia, A. Alù, A. Toscano, and F. Bilotti, “Temporal multilayer structures for designing higher-order transfer functions using time-varying metamaterials,” Applied Physics Letters 118, 101901 (2021). doi:10.1063/5.0042567