Concept 40 of 42 · Frontiers, Experiments and Design

Numerical methods: FDTD and FEM

Computational electromagnetics predicts nanophotonic resonances and field patterns.

01 / Mathematical framework

$$\nabla\times\mu^{-1}\nabla\times\mathbf E=\omega^2\epsilon\mathbf E$$

Physical intuition

Computational electromagnetics predicts nanophotonic resonances and field patterns. This is the starting point for understanding how nanoscale optical geometry changes the states or dynamics accessible to light and matter.

Deep dive: how the mechanism works

FDTD evolves discretized Maxwell equations in time; FEM solves variational boundary-value problems and eigenmodes.

How the quantum phenomenon appears

A simulation extracts Q, mode volume and waveguide transmission. To distinguish a genuinely quantum signal from a classical optical response, connect the device physics to a measurement such as photon correlations, interference visibility, energy-level structure or quantum-state tomography where appropriate.

Assumptions and limitations

Mesh convergence, absorbing boundaries and material dispersion must be validated.

Research and simulation exercise

Identify the tunable parameters, predict the observable from the stated model, and sweep one parameter while holding the others fixed. Compare against a simpler reference model, quantify loss and uncertainty, and state which observations would falsify the hypothesis.

Connect the ideas

Fabrication and disorder Quantum-optical simulation workflow

See the chapter guide and further reading.

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λNumerical methods: FDTD and FEM