Theoretical analysis of the density of states and phase times: Application to resonant electromagnetic modes in finite superlattices

Lahlaouti, M. L. H.; Akjouj, Abdellatif; Djafari‐Rouhani, Bahram; Dobrzyński, L.; Hammouchi, M.; Boudouti, El Houssaine El; Nougaoui, A.; Kharbouch, Bousselham

doi:10.1103/physrevb.63.035312

Cited by 55 publications

(39 citation statements)

References 18 publications

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“…First and foremost, the SLRF points are no longer guaranteed. Not only a relative restriction on constituent elements (25) analogous to the QW condition (2) is required, but also individual constraints on u 0,1 and d 0,1 are necessary, so as to provide special values of β as determined by Eq. (26).…”

Section: Discussionmentioning

confidence: 99%

“…For instance, the "phase time" defined as dϕ/dω is, in general, not equal to the pulse's actual "dwell time" (see [25,27]), although, admittedly, both have a similar frequency dependence and in some cases the phase time is a very good approximation for the dwell time [28]. That said, it is safer not to assign any direct physical meaning to k defined in Eq.…”

Section: Optical and Quantum Density Of Statesmentioning

confidence: 99%

“…The transition from local to integral DOS can be made in a similar manner to the quantum system. In the 1D case (the wave propagation in a multilayer is a 1D problem when only normal-incidence states are taken into account) the modification to the optical DOS ∆N (ω) is also likewise related to the derivative of transmission phase [25]:…”

Section: Optical and Quantum Density Of Statesmentioning

confidence: 99%

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Constraints on transmission, dispersion, and density of states in dielectric multilayers and stepwise potential barriers with an arbitrary layer arrangement

Zhukovsky

Гапоненко

2008

Phys. Rev. E

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Normal-incidence transmission and dispersion properties of optical multilayers and one-dimensional stepwise potential barriers in the non-tunneling regime are analytically investigated. The optical paths of every constituent layer in a multilayer structure, as well as the parameters of every step of the stepwise potential barrier, are constrained by a generalized quarter-wave condition. No other restrictions on the structure geometry is imposed, i.e., the layers are arranged arbitrarily. We show that the density of states (DOS) spectra of the multilayer or barrier in question are subject to integral conservation rules similar to the Barnett-Loudon sum rule but ocurring within a finite frequency or energy interval. In the optical case, these frequency intervals are regular. For the potential barriers, only non-periodic energy intervals can be present in the spectrum of any given structure, and only if the parameters of constituent potential steps are properly chosen.The integral conservation relations derived analytically have also been verified numerically. The relations can be used in dispersion-engineered multilayer-based devices, e.g., ultrashort pulse compressors or ultracompact optical delay lines, as well as to design multiple-quantum-well electronic heterostructures with engineered DOS.

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Section: Discussionmentioning

confidence: 99%

Section: Optical and Quantum Density Of Statesmentioning

confidence: 99%

Section: Optical and Quantum Density Of Statesmentioning

confidence: 99%

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Constraints on transmission, dispersion, and density of states in dielectric multilayers and stepwise potential barriers with an arbitrary layer arrangement

Zhukovsky

Гапоненко

2008

Phys. Rev. E

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“…Besides the information obtained from the imaginary part of the system Green function, giving the frequencies of the system modes [17,29], it is possible to obtain additional information by using the transmission coefficient and the phase time [30].…”

Section: Rudin-shapiro Systemsmentioning

confidence: 99%

“…where T is the phase associated to the transmission coefficient [30]. τ T is indicative of the time needed by a wavepacket to complete the transmission process.…”

Section: Rudin-shapiro Systemsmentioning

confidence: 99%

Properties of elastic waves in quasiregular structures with planar defects

Aynaou

Velasco

Nougaoui

et al. 2002

Superlattices and Microstructures

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One-Dimensional Phononic Crystals

Boudouti¹,

Djafari‐Rouhani²

2012

Springer Series in Solid-State Sciences

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In this chapter, we discuss the vibrational properties of one-dimensional (1D) phononic crystals of both discrete and continuous media. These properties include the dispersion curves of infinite crystals as well as the confined modes and localized (surface, cavity) modes of finite and semi-infinite crystals. A general rule about the existence of localized surface modes in finite and semi-infinite superlattices with free surfaces is presented. We also present the calculations of reflection and transmission coefficients, particularly in view of selective filtering through localized modes. Most of the results presented in this chapter deal with waves propagating along the axis of the superlattice. However, in the last part of the chapter, we also discuss wave propagation out of the normal incidence and, more particularly, we demonstrate the possibility of omnidirectional transmission gap and selective filtering for any incidence angle. A comparison of the theoretical results with experimental data available in the literature is also presented and the reliability of the theoretical predictions is indicated. IntroductionThe one-dimensional (1D) phononic crystals called superlattices (SLs) are of great importance in material science. These structures are, in general, composed of two or several layers repeated periodically along the direction of growth. The layers constituting each cell of the SL can be made of a combination of solid-solid or solid-fluid-layered media. These materials enter now in the category of so-called phononic crystals (see the first chapter of this book and references therein) [1][2][3] constituted by inclusions (spheres, cylinders, etc.) arranged in a host matrix along two-dimensional (2D) and three-dimensional (3D) of the space. After the proposal of SLs by Esaki [4], the study of elementary excitations in multilayered systems has been very active. Among these excitations, acoustic phonons have received increased attention after the first observation by Colvard et al.[5] of a doublet associated to folded longitudinal acoustic phonons by means of Raman scattering. The essential property of these structures is the existence of forbidden frequency bands induced by the difference in acoustic properties of the constituents and the periodicity of these systems leading to unusual physical phenomena in these heterostructures in comparison with bulk materials [6][7][8].With regard to acoustic waves in solid-solid SLs, a number of theoretical and experimental works have been devoted to the study of the band gap structures of periodic SLs [6-10] composed of crystalline, amorphous semi-conductors, or metallic multilayers at the nanometric scale. The theoretical models used are essentially the transfer matrix [7,[11][12][13] and the Green's function methods [6,[14][15][16], whereas the experimental techniques include Raman scattering [5,17,18], ultrasonics [19][20][21][22][23][24][25][26][27][28][29], and time-resolved X-ray diffraction [30]. Besides the existence of the band-gap structures in perfe...

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Theoretical analysis of the density of states and phase times: Application to resonant electromagnetic modes in finite superlattices

Cited by 55 publications

References 18 publications

Constraints on transmission, dispersion, and density of states in dielectric multilayers and stepwise potential barriers with an arbitrary layer arrangement

Constraints on transmission, dispersion, and density of states in dielectric multilayers and stepwise potential barriers with an arbitrary layer arrangement

Properties of elastic waves in quasiregular structures with planar defects

One-Dimensional Phononic Crystals

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