Optical matrix elements

What couples a state to light: the dipole matrix element computed from the states themselves, the selection rules that make transitions allowed or forbidden, and the analytic expression the numbers are checked against.

Lecture 22.1

Optical matrix elements — the dipole matrix element

solve the 10 nm GaAs box with open-nemo's effective-mass model, tilt it with static fields from sunlight strength to beyond the Airy threshold

Lecture 22.2

Optical matrix elements — allowed and forbidden transitions

compute the states of the centred box with open-nemo, check their parity, draw the integrands of the lecture's five example transitions and integrate them

Lecture 22.3

Optical matrix elements — an analytical expression for the dipole matrix element

derive the formula, compare it element by element with the dipole matrix elements of open-nemo's discretized box (and watch the discretization error vanish as the grid is refined), verify the \(i/f^3\) and nearest-neighbour limits