RU2657344C1 - Method for generating plasmon pulses in collective decay of excitations in ensemble of semiconductor quantum dots - Google Patents

Abstract

FIELD: physics.

SUBSTANCE: invention relates to the method for generating plasmon pulses in the collective decay of excitations in an ensemble of semiconductor quantum dots. It can be used when developing a prototype which specifies the plasmon generator of clock pulses with a characteristic size less than the wavelength of the excited plasmon-polaritons with its subsequent application in plasmon circuits of the information processing, including in the design of terahertz plasmon high-speed data buses. Based on the condition of the transition frequency equality in the quantum dots and the plasmon frequency of the metal plate, the material and the size of semiconductor quantum dots and their concentration are selected based on the condition of the loss compensation in the considered temporal and spatial scales.

EFFECT: obtaining an efficient method for generating short plasmon pulses without using an optical excitation circuit.

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Description

The invention relates to the field of controlling the formation of plasmon-polariton pulses on a flat interface between two media with different dielectric constants and can be used to create a prototype of a master plasmon pulse generator with characteristic dimensions less than the wavelength of the excited plasmon polaritons.

A known method of creating a plasmon waveguide for converting and transmitting a light signal ["Plasmonic waveguide, capable of passing a light signal by using surface plasmon polariton", Korean patent KR 1020090093798, Byoung Ho Lee, Jung Hyun Park, Hwi Kim, priority date 02.29.2008 ]. The method is based on creating a waveguide channel based on Bragg gratings with different refractive indices and combined in such a way as to provide selective transmission of a strictly defined radiation wavelength along the waveguide. The localization of the energy of the electromagnetic wave in the direction perpendicular to the direction of propagation is ensured by a system of antiresonance Bragg gratings that impede the exit of the signal beyond the waveguide channel.

Also known is a method for focusing already formed plasmon polariton waves ["Surface plasmon polariton waveguide focusing device in an MIM structure with an upper metal layer and a lower metal layer including different lengths", Korean patent KR 1020110045201, Myung Hyun Lee, Hae Ryung Park, priority date 10/26/2009]. The method is based on the transfer of plasmon excitations, which manifest themselves in the form of an electromagnetic field of electron density oscillations, from one metal plate of tapering geometry to another, which has significantly smaller geometric dimensions. The plates under consideration are separated from each other by a dielectric layer.

The disadvantages of these methods is that the formation of plasmon polaritons requires devices with sizes larger than or of the order of the wavelength of light, and the process of converting a freely propagating electromagnetic wave (light) into a localized surface wave is associated with a significant level of loss.

Closest to the proposed method is a method for generating plasmon polaritons in the presence of an additional amplifying medium ["Method and apparatus for enhancing plasmon-polariton and phonon polariton resonance", US Patent WO 2005111584, Solaris Nanosciences, Inc., 321 South Main Street, Providence, RI 02903 (USA)]. The method is based on the use of an additional active medium, the resonant frequency of which corresponds to the plasmon frequency in the metal-dielectric interface. Both laser and electronic excitation can serve as a pump for the active medium, which, through the active medium, provides amplification of plasmon-polariton modes.

The limitations of this method are related to the need to combine several devices at once - the plasmon-polariton signal generator, as well as its amplifier, while their characteristic dimensions remain greater than the radiation wavelength.

The problem solved by the invention is to ensure maximum efficiency when converting the energy of an external pump source into plasmon modes at scales strictly less than the wavelength of the generated plasmon-polariton modes.

The proposed problem is solved by the fact that in the method for generating plasmon pulses during collective decay of excitations in an ensemble of semiconductor quantum dots, the process includes radiationless transfer of energy of excited semiconductor quantum dots to plasmon polaritons arising at the metal-insulator interface, characterized by the use of canton plasmon polaritons correlations between individual quantum dots, it becomes possible to carry out a collective process of their decay and leads to the formation of short pulses, the form of which can be obtained from the solution of the nonlinear pendulum equation of the form

, ответственным за учет диссипативных процессов в диэлектрической среде-носителе с квантовыми точками и где θ определяет угол для вектора на сфере Блоха, координаты которого Z=cos(θ) и R=sin(θ) связаны с разностью населенности n₂₁ и поляризацией ρ₁₂ в ансамбле квантовых точек соотношениями

и Z=n₂₁, а К₀=ω_SPt-k_SPz определяется через значения циклической частоты ω_SP и волнового числа k_SP поля плазмонов, распространяющихся во времени t и пространстве z вдоль плоской границы металл-диэлектрик; параметр

выражается через количество квантовых точек N _a в области взаимодействия и константу связи g, тогда как коэффициент u₁ ответственен за диссипативные процессы, связанные с учетом локального поля диэлектрика.with an additional term for

responsible for taking into account dissipative processes in a dielectric carrier medium with quantum dots and where θ determines the angle for the vector on the Bloch sphere whose coordinates Z = cos (θ) and R = sin (θ) are related to the population difference n ₂₁ and polarization ρ ₁₂ in the ensemble of quantum dots by the relations

and Z = n ₂₁ , and K ₀ = ω _SP tk _SP z is determined through the values of the cyclic frequency ω _SP and the wavenumber k _{SP of the} field of plasmons propagating in time t and space z along the plane metal-insulator interface; parameter

is expressed in terms of the number of quantum dots N _a in the interaction region and the coupling constant g, while the coefficient u _{1 is} responsible for dissipative processes associated with taking into account the local field of the dielectric.

Technically, the formation of short plasmon pulses is possible in the process of collective decay in an ensemble of excited quantum dots located in a dielectric layer near a metal plate (Fig. 1), the size of which is selected from the condition that the transition frequency in quantum dots and the plasmon frequency of the metal plate are equal, and the concentration is based on from the condition of compensation for losses on the considered temporal and spatial scales. The dynamics of the formation of plasmon pulses (Fig. 2) is described by a system of self-consistent equations

определяет характерное время установления квантовых корреляций между квантовыми точками и выражается через параметр Бергмана

для границы раздела металл/диэлектрик с диэлектрической проницаемостью ε_d диэлектрика и

металла и с учетом столкновительной частоты γ_p, а также плазмонной частоты

, где

- плазменная частота в металле с массой электронов m₀, зарядом е при их концентрации n_m; ε₀ является электрической постоянной,

постоянной Планка,

- константа связи в объеме V, выражающаяся через частоту Раби Ω₀ и

, где N_p - количество плазмонов в области взаимодействия. Параметр Г_ε в (2а) и (2б) представляет собой суммарную скорость радиационных и нерадиационных потерь для квантовых точек, тогда как параметр

определяет добавку к частоте Раби, появляющуюся вследствие перехода от максвелловского к локальному полю, действующему на квантовые точки. Дисперсионная u_R и диссипативная поправки u₁ имеют физический смысл дополнительных частотной модуляции и эффектов поглощения и возникают за счет учета локального отклика в диэлектрике с комплексным показателем преломления n=n_R+in₁, имеющим действительную n_R и мнимую n₁ части, при определенном выборе которых скорость радиационного затухания квантовых точек может быть скомпенсирована, то есть Г_ε=0.Where

determines the characteristic time of establishing quantum correlations between quantum dots and is expressed in terms of the Bergman parameter

for the metal / dielectric interface with a dielectric constant ε _{d of the} dielectric and

metal and taking into account the collision frequency γ _p , as well as the plasmon frequency

where

- the plasma frequency in a metal with an electron mass m ₀ , a charge e at their concentration n _m ; ε ₀ is the electric constant,

Planck constant,

is the coupling constant in volume V, expressed in terms of the Rabi frequency Ω ₀ and

where N _p is the number of plasmons in the interaction region. The parameter Г _ε in (2a) and (2b) represents the total rate of radiation and non-radiation losses for quantum dots, while the parameter

defines the addition to the Rabi frequency that appears as a result of the transition from the Maxwellian to the local field acting on quantum dots. The dispersion u _R and dissipative corrections u ₁ have the physical meaning of additional frequency modulation and absorption effects and arise due to taking into account the local response in a dielectric with a complex refractive index n = n _R + in ₁ having real n _R and imaginary n ₁ parts, for a certain the choice of which the rate of radiation attenuation of quantum dots can be compensated, that is, Г _ε = 0.

A brief description of the drawings.

; 5 - диэлектрик (пленка); 6 - металл (Au); 7 - объем взаимодействия в диэлектрике V; 8 - накачивающий объем в металле V’; 9 - оптический импульс накачки

; 10 - триггерный плазмонный импульс ε_ex, 11 - формируемый в результате распада экситонов КТ плазмонный импульс ε; 12 - ось Ох; 13 - ось Оу; 14 - ось Oz; 15 - зависимость энергии межзонного перехода 1S_e-1S_h в эВ (ось ординат) от размера D_QD в нм (ось абсцисс) CdS КТ (E_g=2.42 эВ при 0 К для сплошной среды).FIG. 1.1 - Scheme of the formation of plasmon pulses in a layered (planar) metal / dielectric waveguide pumped by CdS CT: 2 - antiresonance Bragg waveguides (ARROW); 3 - diffraction grating; 4 - quantum dots CdS with a dipole moment

; 5 - dielectric (film); 6 - metal (Au); 7 - the amount of interaction in the insulator V; 8 - pumping volume in the metal V '; 9 - optical pump pulse

; 10 — trigger plasmon pulse ε _ex , 11 — plasmon pulse ε formed as a result of QD exciton decay; 12 - axis Oh; 13 - axis Oy; 14 - axis Oz; 15 - dependence of the energy of the interband transition 1S _e -1S _h in eV (ordinate axis) on the size D _QD in nm (abscissa axis) of CdS CT (E _g = 2.42 eV at 0 K for a continuous medium).

вблизи золотой поверхности для случаев нескомпенсированной Г_ε=6.3⋅10¹¹ с^-1 (штриховая линия) и скомпенсированной Г_ε=0 с^-1 при n_R=1.6 n₁=1.23 (сплошная линия) скорости затухания в КТ. Параметры взаимодействия: u₁=-0.1582, γ_R=4.1⋅10¹³ с^-1, g=1.14⋅10¹² с^-1, ξ₀=2.5⋅10¹⁰ с^-1.FIG. 2. The intensity profiles of plasmon pulses I _p in MW / cm ² (ordinate axis) versus time t in ps (abscissa axis) obtained by numerically simulating system (2) with a concentration N = 2.83 2.10 ²² m ^-3 CdS quantum dots with size D _QD = 1.56 nm and initial stochastic polarization

near the gold surface for cases uncompensated T _ε = 6.3⋅10 ¹¹ s ^-1 (dashed line) and a compensated T _ε = 0 s ^-1 at n _R = 1.6 n = ₁ 1.23 (solid line) the attenuation rate RT. Interaction parameters: u ₁ = -0.1582, γ _R = 4.1⋅10 ¹³ s ^-1 , g = 1.14⋅10 ¹² s ^-1 , ξ ₀ = 2.5⋅10 ¹⁰ s ^-1 .

An example implementation of the method.

оказывается равным N_a=200, а величина длительности формируемого плазмонного импульса составит 450 фс с учетом скорости затухания Г_ε=6.3⋅10¹¹ с^-1 или 250 фс при ее компенсации Г_ε=0 с^-1 путем выбора диэлектрика с n_R=1.6, n₁=1.23 (K=-0.0147) (на Фиг. 2); столкновительная частота золота γ_p=4.1⋅10¹³ с^-1, величины константы связи g=1.14⋅10¹² с^-1, параметр Бергмана

, его производная

при ε_d=2.56.An interface in the form of a metal / dielectric waveguide with two-level chromophores in the form of semiconductor CdS quantum dots in FIG. 1 with an average diameter D _QD = 1.56 nm, the inter-level transition wavelength for which is resonant with the plasmon wavelength λ _SP = 192 nm gold (ω _p = 1.37 =10 ¹⁶ s ^-1 ), and the corresponding dipole moment of the interband transition is μ = μ ₁₂ = 5⋅10 ^-29 Kl⋅m. When the concentration of quantum dots N = 2.83⋅10 ²² m ^-3 their number in the interaction region with the volume

turns out to be equal to N _a = 200, and the duration of the generated plasmon pulse will be 450 fs, taking into account the decay rate Г _ε = 6.3⋅10 ¹¹ s ^-1 or 250 fs with its compensation Г _ε = 0 s ^-1 by choosing a dielectric with n _R = 1.6, n ₁ = 1.23 (K = -0.0147) (in Fig. 2); collision frequency of gold γ _p = 4.1⋅10 ¹³ s ^-1 , coupling constant g = 1.14⋅10 ¹² s ^-1 , Bergman parameter

its derivative

at ε _d = 2.56.

Claims (3)

A method for generating plasmon pulses in the collective decay of excitations in an ensemble of semiconductor quantum dots, including the process of non-radiative transfer of energy of excited semiconductor quantum dots to plasmon polaritons arising at the metal-insulator interface, characterized by the use of quantum correlations induced by the plasmon polariton field between individual quantum dots the collective process of their decay and leads to the formation of short pulses, the form of which can be obtained from the solution of the nonlinear pendulum equation of the form

with an additional term for

responsible for taking into account dissipative processes in a dielectric carrier medium with quantum dots, and where θ determines the angle for the vector on the Bloch sphere whose coordinates Z = cos (θ) and R = sin (θ) are related to the population difference n ₂₁ and polarization ρ ₁₂ in the ensemble of quantum dots by the relations

and Z = n ₂₁ , and K ₀ = ω _SP tk _SP z is determined through the values of the cyclic frequency ω _SP and the wavenumber k _{SP of the} field of plasmons propagating in time t and space z along the plane metal-insulator interface; parameter

is expressed in terms of the number of quantum dots N _a in the interaction region and the coupling constant g, while the coefficient u _{I is} responsible for dissipative processes associated with taking into account the local field of the dielectric.

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