Propagation of a radiation pulse with wavelength ?=10.6 ?m in amplifying media

Левин, В. А.; Netesov, V. V.; Starik, A. M.

doi:10.1007/bf00908961

Cited by 1 publication

(2 citation statements)

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“…In 1D periodic systems, the resonant wave function Ψ ðÃÞ μ,ν ðzÞ is a simple but not trivial combination of Chebyshev polynomials. It is easy to verify that Equation (116) implies…”

Section: Resonant Energies and Resonant Functions In Open 1d Periodic...mentioning

confidence: 99%

“…As mentioned in the abstract, we will focus on the theory of finite periodic systems (TFPS) based entirely on transfer matrices and their properties, valid for any number of propagation modes, any number of unit cells, and arbitrary potentials or refractive indices profiles. We explicitly exclude theoretical approaches [73,[111][112][113][114] that in one way or another are based on the Bloch and Floquet theorem [115] which imply the assumption of infinite or semi-infinite systems, [56,59,60,[66][67][68][69][70][71][72][116][117][118][119][120][121][122][123][124][125][126][127][128][129] where relevant physical variables, such as the transmission or reflection coefficients, cannot be conceived without being inconsistent. Since the exclusion of the theoretical approaches for periodic systems that use transfer matrices and are based on Kramers' argument to determine their dispersion relations [130] implies neglecting most of the theoretical papers in this branch, we include a section that justifies this decision and show the wrong arguments and show graphically that the derived fields, supposedly periodic, do not meet the periodicity requirement.…”

Section: Introductionmentioning

confidence: 99%

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The Transfer Matrix Method and the Theory of Finite Periodic Systems. From Heterostructures to Superlattices

Pereyra

2021

Physica Status Solidi (b)

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Historically, the physics, energy spectrum, and wave functions of superlattices have had different levels of understanding. Unlike the standard approaches, based on theorems for infinite systems, the theory of finite periodic systems (TFPS) constitutes a genuine quantum approach, with closed analytical results. In this theory the finitene number of unit‐cells is an essential condition, while the number of propagating modes, as well as, the potential profiles (or refractive indices) are arbitrary. In this work, the transfer matrix definitions, symmetry properties, group representations, and relations with the scattering amplitudes are reviewed. The derivation of multichannel matrix polynomials (which reduce to Chebyshev polynomials in the one‐propagating mode limit), analytical formulas for resonant states, energy eigenvalues, eigenfunctions, parity symmetries, and discrete dispersion relations for superlattices with different confinement characteristics are reviewed. After showing the inconsistencies and limitations of hybrid approaches that combine the transfer‐matrix method with Floquet's theorem, some applications of the TFPS to multichannel negative resistance, ballistic transistors, coupled channels transport, spintronics, superluminal, and optical antimatter effects are revisited. Two high‐resolution superlattice related experiments are reviewed: the tunneling time in photonic band‐gap and the optical response of blue‐emitting diodes. It is shown that the TFPS accurately predicts the experimental results.

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“…In 1D periodic systems, the resonant wave function Ψ ðÃÞ μ,ν ðzÞ is a simple but not trivial combination of Chebyshev polynomials. It is easy to verify that Equation (116) implies…”

Section: Resonant Energies and Resonant Functions In Open 1d Periodic...mentioning

confidence: 99%