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Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Bulgakov E. N., Sadreev A. F.
Заглавие : Bound states in photonic Fabry-Perot resonator with nonlinear off-channel defects
Коллективы :
Место публикации : Phys. Rev. B: AMER PHYSICAL SOC, 2010. - Vol. 81, Is. 11. - Ст.115128. - ISSN 1098-0121, DOI 10.1103/PhysRevB.81.115128
Примечания : Cited References: 73. - The work was partially supported by RFBR under Grant No. 09-02-98005 "Siberia." We are greatly acknowledge Konstantin Pichugin for many discussions.
Предметные рубрики: CRYSTAL WAVE-GUIDES
STATIONARY LOCALIZED STATES
COUPLED-MODE THEORY
OPTICAL RESONATORS
NUCLEAR REACTIONS
UNIFIED THEORY
MICROCAVITIES
TRANSMISSION
CONTINUUM
CIRCUITS
Аннотация: We consider a Fabry-Perot resonator (FPR) comprised of two off-channel nonlinear defects coupled to the photonic waveguide. For the linear case FPR can support bound states in the form of standing waves between the defects if a distance between them is quantized. For the nonlinear case the bound states appear for arbitrary distance between the defects if electromagnetic intensity is quantized. For transmission through the FPR we reveal additional resonances which are the result of coupling of incident wave with the bound states because of nonlinearity of the defects. The resonances are spaced at the eigenfrequencies of bound states with a width proportional to the input amplitude. The theory of the FPR based on the simple Wang and Fan model [Phys. Rev. E 68, 066616 (2003)] is complemented by the tight-binding one. The results for the transmission and bound states in these models agree with computations in real two-dimensional photonic crystal waveguide coupled with two off-channel defects fabricated from a Kerr-type material.
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Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Bulgakov E. N., Rotter I., Sadreev A. F.
Заглавие : Correlated behavior of conductance and phase rigidity in the transition from the weak-coupling to the strong-coupling regime
Место публикации : Phys. Rev. B: AMER PHYSICAL SOC, 2007. - Vol. 76, Is. 21. - Ст.214302. - ISSN 1098-0121, DOI 10.1103/PhysRevB.76.214302
Примечания : Cited References: 42
Предметные рубрики: OPEN QUANTUM-SYSTEMS
NUCLEAR CROSS-SECTIONS
UNIFIED THEORY
FLUCTUATIONS
CONTINUUM
BILLIARD
STATES
Аннотация: We study the transmission through different small systems as a function of the coupling strength v to the two attached leads. The leads are identical with only one propagating mode xi(E)(C) in each of them. In addition to the conductance G, we calculate the phase rigidity rho of the scattering wave function Psi(E)(C) in the interior of the system. Most interesting results are obtained in the regime of strongly overlapping resonance states where the crossover from staying to traveling modes takes place. The crossover is characterized by collective effects. Here, the conductance is plateaulike enhanced in some energy regions of finite length while corridors with zero transmission (total reflection) appear in other energy regions. This transmission picture depends only weakly on the spectrum of the closed system. It is caused by the alignment of some resonance states of the system with the propagating modes xi(E)(C) in the leads. The alignment of resonance states takes place stepwise by resonance trapping, i.e., it is accompanied by the decoupling of other resonance states from the continuum of propagating modes. This process is quantitatively described by the phase rigidity rho of the scattering wave function. Averaged over energy in the considered energy window, G is correlated with 1-rho . In the regime of strong coupling, only two short-lived resonance states survive each aligned with one of the channel wave functions xi(E)(C). They may be identified with traveling modes through the system. The remaining M-2 trapped narrow resonance states are well separated from one another.
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Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Rotter I., Sadreev A. F.
Заглавие : Singularities caused by coalesced complex eigenvalues of an effective hamilton operator
Разночтения заглавия :авие SCOPUS: Singularities caused by coalesced complex eigenvalues of an effective Hamilton operator
Место публикации : Int. J. Theor. Phys.: SPRINGER/PLENUM PUBLISHERS, 2007. - Vol. 46: 25th International Colloquium on Group Theoretical Methods in Physics (AUG 02-06, 2004, Cocoyoc, MEXICO), Is. 8. - P1914-1928. - ISSN 0020-7748, DOI 10.1007/s10773-006-9328-4
Примечания : Cited References: 38
Предметные рубрики: UNIMOLECULAR REACTION-RATES
EXCEPTIONAL POINTS
OVERLAPPING RESONANCES
NUCLEAR REACTIONS
QUANTUM-SYSTEMS
UNIFIED THEORY
S-MATRIX
CONTINUUM
PHASE
DEGENERACY
Ключевые слова (''Своб.индексиров.''): effective hamilton--complex eigenvalue--quantum dots--branch points--branch points--complex eigenvalue--effective hamilton--quantum dots
Аннотация: The S matrix theory with use of the effective Hamiltonian is sketched and applied to the description of the transmission through double quantum dots. The effective Hamilton operator is non-hermitian, its eigenvalues are complex, the eigenfunctions are bi-orthogonal. In this theory, singularities occur at points where two (or more) eigenvalues of the effective Hamiltonian coalesce. These points are physically meaningful: they separate the scenario of avoided level crossings from that without any crossings in the complex plane. They are branch points in the complex plane. Their geometrical features are different from those of the diabolic points.
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Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Sadreev A. F., Bulgakov E. N., Rotter I.
Заглавие : S-matrix formalism of transmission through two quantum billiards coupled by a waveguide
Место публикации : J. Phys. A. - 2005. - Vol. 38, Is. 49. - P.10647-10661. - ISSN 0305-4470, DOI 10.1088/0305-4470/38/49/012
Примечания : Cited References: 32
Предметные рубрики: CIRCULAR BENDS
DOTS
TRANSPORT
CONTINUUM
SYSTEMS
STATES
Аннотация: We consider a system that consists of two single-quantum billiards (QBs) coupled by a waveguide and study the transmission through this system as a function of length and width of the waveguide. To interpret the numerical results for the transmission, we explore a simple model with a small number of states which allows us to consider the problem analytically. The transmission is described in the S-matrix formalism by using the non-Hermitian effective Hamilton operator for the open system. The coupling of the single QBs to the internal waveguide characterizes the 'internal' coupling strength u of the states of the system while that of the system as a whole to the attached leads determines the 'external' coupling strength v of the resonance states via the continuum (waves in the leads). The transmission is resonant for all values of v/u in relation to the effective Hamiltonian. It depends strongly on the ratio u/u via the eigenvalues and eigenfunctions of the effective Hamiltonian. The results obtained are compared qualitatively with those from simulation calculations for larger systems. Most interesting is the existence of resonance states with vanishing widths that may appear at all values of v/u. They cause zeros in the transmission through the double QB due to trapping of the particle in the waveguide.
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Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Rotter I., Sadreev A. F.
Заглавие : Avoided level crossings, diabolic points, and branch points in the complex plane in an open double quantum dot
Место публикации : Phys. Rev. E: AMERICAN PHYSICAL SOC, 2005. - Vol. 71, Is. 3. - Ст.36227. - ISSN 1063-651X, DOI 10.1103/PhysRevE.71.036227
Примечания : Cited References: 49
Предметные рубрики: BERRY TOPOLOGICAL PHASE
EXCEPTIONAL POINTS
GEOMETRIC PHASES
NUCLEAR REACTIONS
RESONANCE STATES
UNIFIED THEORY
S-MATRIX
CONTINUUM
REPULSION
INTERFEROMETER
Ключевые слова (''Своб.индексиров.''): branch points in the complex plane (bpcp)--diabolic points (dp)--geometric phases--riemann sheets--eigenvalues and eigenfunctions--electron energy levels--functions--hamiltonians--quantum theory--resonance--topology--semiconductor quantum dots
Аннотация: We study the spectrum of an open double quantum dot as a function of different system parameters in order to receive information on the geometric phases of branch points in the complex plane (BPCP). We relate them to the geometrical phases of the diabolic points (DPs) of the corresponding closed system. The double dot consists of two single dots and a wire connecting them. The two dots and the wire are represented by only a single state each. The spectroscopic values follow from the eigenvalues and eigenfunctions of the Hamiltonian describing the double dot system. They are real when the system is closed, and complex when the system is opened by attaching leads to it. The discrete states as well as the narrow resonance states avoid crossing. The DPs are points within the avoided level crossing scenario of discrete states. At the BPCP, width bifurcation occurs. Here, different Riemann sheets evolve and the levels do not cross anymore. The BPCP are physically meaningful. The DPs are unfolded into two BPCP with different chirality when the system is opened. The geometric phase that arises by encircling the DP in the real plane, is different from the phase that appears by encircling the BPCP. This is found to be true even for a weakly opened system and the two BPCP into which the DP is unfolded.
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Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Rotter I., Sadreev A. F.
Заглавие : Influence of branch points in the complex plane on the transmission through double quantum dots
Место публикации : Phys. Rev. E: AMER PHYSICAL SOC, 2004. - Vol. 69, Is. 6. - Ст.66201. - ISSN 1539-3755, DOI 10.1103/PhysRevE.69.066201
Примечания : Cited References: 25
Предметные рубрики: ELECTRON-ATOM SCATTERING
S-MATRIX
DOUBLE POLES
CONTINUUM
SYSTEM
MODEL
Ключевые слова (''Своб.индексиров.''): eigenvalues and eigenfunctions--hamiltonians--mathematical models--matrix algebra--probability--resonance--scattering--wave propagation--branch points--open quantum systems--propagating modes--quantum computing devices--semiconductor quantum dots
Аннотация: We consider single-channel transmission through a double quantum dot system consisting of two single dots that are connected by a wire and coupled each to one lead. The system is described in the framework of the S matrix theory by using the effective Hamiltonian of the open quantum system. It consists of the Hamiltonian of the closed system (without attached leads) and a term that accounts for the coupling of the states via the continuum of propagating modes in the leads. This model allows one to study the physical meaning of branch points in the complex plane. They are points of coalesced eigenvalues and separate the two scenarios with avoided level crossings and without any crossings in the complex plane. They influence strongly the features of transmission through double quantum dots.
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Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Bulgakov E. N., Rotter I., Sadreev A. F.
Заглавие : Phase rigidity and avoided level crossings in the complex energy plane
Место публикации : Phys. Rev. E: AMERICAN PHYSICAL SOC, 2006. - Vol. 74, Is. 5. - Ст.56204. - ISSN 1539-3755, DOI 10.1103/PhysRevE.74.056204
Примечания : Cited References: 40
Предметные рубрики: OPEN QUANTUM-SYSTEMS
FANO RESONANCES
S-MATRIX
DOT
CONTINUUM
TRANSMISSION
COHERENCE
TRANSPORT
BILLIARDS
PROBE
Ключевые слова (''Своб.индексиров.''): eigenvalues and eigenfunctions--hamiltonians--resonance--rigidity--semiconductor quantum dots--biorthogonal eigenfunctions--open quantum system--phase rigidity--quantum theory
Аннотация: We consider the effective Hamiltonian of an open quantum system, its biorthogonal eigenfunctions phi(lambda), and define the value r(lambda)=(phi(lambda)parallel to phi(lambda))/phi(lambda)parallel to phi(lambda) that characterizes the phase rigidity of the eigenfunctions phi(lambda). In the scenario with avoided level crossings, r(lambda) varies between 1 and 0 due to the mutual influence of neighboring resonances. The variation of r(lambda) is an internal property of an open quantum system. In the literature, the phase rigidity rho of the scattering wave function Psi(E)(C) is considered. Since Psi(E)(C) can be represented in the interior of the system by the phi(lambda), the phase rigidity rho of the Psi(E)(C) is related to the r(lambda) and therefore also to the mutual influence of neighboring resonances. As a consequence, the reduction of the phase rigidity rho to values smaller than 1 should be considered, at least partly, as an internal property of an open quantum system in the overlapping regime. The relation to measurable values such as the transmission through a quantum dot, follows from the fact that the transmission is, in any case, resonant at energies that are determined by the real part of the eigenvalues of the effective Hamiltonian. We illustrate the relation between phase rigidity rho and transmission numerically for small open cavities.
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Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Bulgakov E. N., Sadreev A. F.
Заглавие : Bound States in Photonic Fabry-Perot Resonator Comprised of Two Nonlinear Off-Channel Defects
Коллективы : Russian Foundation for Basic Research [09-02-98005-Siberia]
Место публикации : JETP Letters. - 2009. - Vol. 90, Is. 12. - P.744-749. - ISSN 0021-3640, DOI 10.1134/S0021364009240023
Примечания : Cited References: 32. - We thank Kostya Pichugin for many helpful discussions. The work was partially supported by the Russian Foundation for Basic Research, project no. 09-02-98005-Siberia.
Предметные рубрики: SCATTERING-THEORY
WAVE-GUIDE
CONTINUUM
MODES
Аннотация: Two off-channel nonlinear defects coupled to the photonic waveguide constitute the Fabry-Perot interfer-ometer (FPR). The defects are made from a Kerr-like nonlinear material. For the linear case such a FPR can support the bound states in the form of standing waves between the defects if the distance between them is quantized. For the nonlinear case the bound states appear for arbitrary distance between the defects however for an quantized electromagnetic intensity. For the transmission through FPR we reveal new resonances and show these are a result of coupling of the bound states with incident wave because of nonlinearity of the defects. The resonances are spaced at the eigen frequencies of bound states.
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Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Bulgakov E. N., Sadreev A. F.
Заглавие : Propagating Bloch bound states with orbital angular momentum above the light line in the array of dielectric spheres
Коллективы : Ministry of Education and Science of the Russian Federation (Minobrnauka) [N 3.1845.2017]; Russian Foundation for Basic Research (RFBR) [16-02-00314]
Место публикации : J. Opt. Soc. Am. A: Optical Society of America, 2017. - Vol. 34, Is. 6. - P.949-952. - ISSN 1084-7529, DOI 10.1364/JOSAA.34.000949. - ISSN 1520-8532(eISSN)
Примечания : Cited References:37. - Ministry of Education and Science of the Russian Federation (Minobrnauka) (N 3.1845.2017); Russian Foundation for Basic Research (RFBR) (16-02-00314).
Предметные рубрики: GUIDED-WAVES
CONTINUUM
BEHAVIOR
GRATINGS
Аннотация: We present propagating Bloch bound states in the radiation continuum with orbital angular momentum in an infinite linear periodical array of dielectric spheres. The bound states in the continuum demonstrate a giant Poynting vector spiraling around the array. They can be excited by a plane wave with incident linear polarization with a small tilt relative to the axis of the array.
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10.

Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Bulgakov E. N., Sadreev A. F.
Заглавие : Scattering plane waves by a dielectric cylinder with periodically modulated permittivity at oblique incidence
Коллективы : Ministry of Education and Science of Russian Federation [3.1845.2017]; Russian Foundation for Basic Research [16-02-00314]
Место публикации : Phys. Rev. A. - 2018. - Vol. 97, Is. 6. - Ст.063856. - ISSN 2469-9926, DOI 10.1103/PhysRevA.97.063856. - ISSN 2469-9934(eISSN)
Примечания : Cited References: 24. - We acknowledge discussions with A. A. Bogdanov and D. N. Maksimov. This paper was partially supported by Ministry of Education and Science of Russian Federation (State Contract No. 3.1845.2017) and Russian Foundation for Basic Research Grant No. 16-02-00314.
Предметные рубрики: BOUND-STATES
FANO RESONANCE
LIGHT LINE
CONTINUUM
ARRAYS
Аннотация: For scattering of electromagnetic waves by a dielectric cylinder with periodically modulated permittivity we focus on the vicinity of the frequency of the wave with regard to the eigenfrequencies of bound states in the continuum. Then response of the cylinder becomes extremely sensitive to the angle of incidence and polarization of the plane wave. The cross section of the scattering of electromagnetic waves with mixed polarization undergoes crucial change from the Bragg shape to the Fano shape by rotation of the polarization that paves a way to tuning of Fano resonances by an external source.
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