Concept 02 of 42 · Light confined below the wavelength

Maxwell equations in matter

Nanophotonics starts with electromagnetic boundary-value problems in structured media.

01 / Mathematical framework
$$\nabla\times\mathbf E=-\partial_t\mathbf B,\quad\nabla\times\mathbf H=\mathbf J+\partial_t\mathbf D$$

Physical intuition

Nanophotonics starts with electromagnetic boundary-value problems in structured media. 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

Material permittivity, permeability, geometry and boundary conditions determine resonances and local fields; dispersive media require frequency-dependent constitutive relations.

How the quantum phenomenon appears

Finite-element eigenmode calculations predict a dielectric nanocavity spectrum. 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

At nanometre scales, nonlocal response and quantum material effects may invalidate simple local permittivity models.

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

See the chapter guide and further reading.

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