Application of electromagnetics formalism to quantum-mechanical electron-wave propagation in semiconductors

Embedded energy state in an open semiconductor heterostructure

“…By comparing of (3) and (6a), (6b) and the corresponding boundary conditions, a direct analogy between the semiconductor and electromagnetic cases is obtained, see Table I. Table I also reveals that the presented electron-light analogy for spherical waves is very similar to that for plane waves [31][32][33][34].…”

Quantum State Engineering Based on Electromagnetic Analogies and Numerical Methods for Semiconductor Intersubband Lasers

“…These have been developed in Ref. 10. Generally phase effects like path differences and wave interference for both elec tromagnetic and electron waves can be described by the phase propagation constant.…”

“…photons primarily do not experience dispersion effects. 10 Therefore, the equivalence between an optical and a electron-wave filter is exact for one energy only, E. This largely does not pose any difficulties since the wave-electron filters used for intersubband-laser design requires increased confinement at the upper sin gle lasing-state. While the use of Aj/4 layers to increase the lifetime of an eigenstate is an obvious result from the application of equivalent electromagnetic optics prin ciples to quantum mechanics, it has also been proven theoretically in Refs.…”

Influence of light polarization on the analogy between ballistic nanostructures and the electromagnetic field

“…These analogies are based on the formal similarity between the Helmholtz equation and the Schrödinger [3][4][5][6][7][8] or Dirac [9][10][11][12][13][14] equations satisfied by charge carriers, and have been useful for developing research fields such as electron optics [15], photonic band crystals [16], or random lasers [17]. Even quantitative electron-light analogy has been developed for ballistic structures confined in one [18], two [19], or three dimensions [20], in which the quantum wavefunction and the electromagnetic field have the same values in corresponding layers.…”