A model has been developed to calculate the Tamm quasi-level in metal-semiconductor structures with Schottky barrier. The model was used to show that electron resonance tunneling from metal to semiconductor through the Schottky barrier can occur with the Tamm quasi-level at the metal-semiconductor interface. The resonance tunneling with the Tamm quasi-level can strongly affect the electron photoemission in plasmonic structures from the metal to the surrounding semiconductor, lowering the red limit of the photoeffect and significantly increasing the internal quantum efficiency of photoemission and the quantum yield of hot carrier generation in plasmonic structures, especially for photochemistry (photocatalysis).

The quantum nonlinear Maxwell-Bloch equations for a single-mode laser with a two-level active medium are solved in the LED regime without adiabatic elimination of the medium polarization, when the population fluctuation spectrum is much narrower than the radiation and polarization spectra. It is shown that population fluctuations significantly increase the output power and collective Rabi splitting of a superradiant LED.

We found that fluctuations in the number of emitters lead to a super-thermal photon statistics of small LEDs in a linear regime, with a strong emitter-field coupling and a bad cavity favorable for collective effects. A simple analytical expression for the second-order correlation function g_2 is found. g_2 increase up to g_2=6 in the two-level LED model is predicted. The super-thermal photon statistics is related to the population fluctuation increase of the spontaneous emission to the cavity mode.

We find that the spontaneous and collective emissions have a strong influence on the excitation of two-level absorbers (atoms, molecules) interacting in resonance with the plasmonic mode near the metal nanoparticle. The spontaneous and collective emissions limit the absorption enhancement by the plasmonic mode and make the enhancement possible only with a fast, picosecond population relaxation of the upper absorbing states. Conditions for the maximum of plasmon-enhanced absorption in the presence of spontaneous and collective emissions are found. The nonlinearity in the nanoparticle-absorber interaction and in collective emission causes the bistability in the plasmon-enhanced absorption at high external field intensities and the plasmonic mode excitation.

Concepts of local and global photoemission directivity patterns are introduced for plasmonic nanoparticles of arbitrary shape, and the relationship between them is established. Formulas for the local photoemission directionality pattern for surface and volume photoemission mechanisms are obtained for a given field distribution in plasmonic modes inside nanoparticles of arbitrary shape. As an illustration of the theory, the local and global photoemission patterns are calculated for spherical nanoparticles with excited dipole or quadruple plasmonic modes. It is shown that the patterns resulting from the surface and volume photoemission differ qualitatively as well as the patterns produced by various plasmonic modes. The findings can be useful in various plasmonic applications, namely, nanostructured photocathodes, photodetectors, in plasmonic photocatalysis, and others.

We theoretically investigated the bistability in a small Fabry-Perot interferometer (FPI) with the optical wavelength size cavity, the nonlinear Kerr medium, and only a few photons, on average, excited by the external quantum field. Analytical expressions for the stationary mean photon number, the bistability domain, the field, and the photon number fluctuation spectra are obtained. Multiple stationary states of the FPI cavity field with different spectra are possible at realistic conditions, for example, in the FPI with the photonic crystal cavity and the semiconductor-doped glass nonlinear medium.

The hot electron generation in plasmonic nanoparticles is the key to efficient plasmonic photocatalysis. Here, the effect of Tamm states (TSs) at the metal–semiconductor interface on hot electron generation and Landau damping (LD) in metal nanoparticles is studied theoretically for the first time. TSs can lead to resonant hot electron generation and to the LD rate enhanced by several times. The resonant hot electron generation is reinforced by the transition absorption due to the jump of the permittivity at the metal–semiconductor interface. Since electron states in the metal and the quasi-discrete TS are coupled coherently (“bound state in continuum”), the absorption spectrum of light by electrons has a Fano-type shape. The results demonstrate clearly the importance of taking into account details of the semiconductor band structure and surface states at the metal–semiconductor interface, including Tamm surface states, for a proper description of the hot carrier generation and LD. The results are in correspondence with earlier experimental works on coherent electron transport and chemical-induced damping in plasmonic nanostructures. Thus, by judicious selection of semiconductor materials with Tamm surface states one can engineer decay rates and hot carrier production for important applications, such as photodetection and photochemistry.

: The hot electron generation in plasmonic nanoparticles is the key to efficient plasmonic photocatalysis. In the paper, we study theoretically for the first time the effect of Tamm states (TSs) at the interface metal-semiconductor on hot electron generation and Landau damping (LD) in metal nanoparticles. TSs can lead to resonant hot electron generation and to the LD rate enhanced by several times. The resonant hot electron generation is reinforced by the transition absorption due to the jump of the permittivity at the metal-semiconductor interface. Since electron states in the metal and the quasi-discrete TS are coupled coher-ently (“bound state in continuum”), the absorption spectrum of light by electrons has a Fano-type shape. Our results demonstrate clearly the importance of taking into account details of the semiconductor band structure and surface states at the metal-semiconductor interface, including Tamm surface states, for a proper description of the hot carrier generation and LD. The results are in correspondence with earlier experimental works on coherent electron transport and chemical-induced damping in plasmonic nanostructures. Thus, by judicious selection of semiconductor materials with Tamm surface states one can engineer decay rates and hot carrier production for important applications, such as photodetection and photochemistry.

We investigate the bistability in a small Fabry-Perot interferometer (FPI) with the optical wavelength size cavity, the nonlinear Kerr medium and only a few photons, on average, excited by the external quantum field. Analytical expressions for the stationary mean photon number, the bistability domain, the field and the photon number fluctuation spectra are obtained. Multiple stationary states of the FPI cavity field with different spectra are possible at realistic conditions, for example, in the FPI with the photonic crystal cavity and the semiconductor-doped glass nonlinear medium.

Spectra of the small Fabry–Perot interferometer (FPI) of the size of the order of the wavelength, with the main mode excited by a quantum field from a nano–LED or a laser, are investigated. The input field is detuned from the FPI mode with only a few photons. We formulate the convenient model for the FPI interacting with a quantum field, and provide novel explicit expressions for the field and the photon number fluctuation spectra inside and outside the FPI, with clearly identified contributions of the quantum and the classical noise. As a result, we found the spectra structures are quite different for the field, the photon number fluctuations inside the FPI, for the transmitted and the reflected fields and note asymmetries in spectra. The quantum noise is colored (or white) inside (or outside) the FPI, which explains differences in spectra. As another novel result, we calculate the second-order time auto–correlation functions for the FPI field; they oscillate and are negative under certain conditions. Results will help the study, design, manufacture, and use of the small elements of quantum optical integrated circuits, such as delay lines or optical transistors.

A laser model is formulated in terms of quantum harmonic oscillators. Emitters in the low lasing states are usual harmonic oscillators, and emitters in the upper states are inverted harmonic oscillators. Diffusion coefficients, consistent with the model and necessary for solving quantum nonlinear laser equations analytically, are found. Photon number fluctuations of the lasing mode and fluctuations of the population of the lasing states are calculated. Collective Rabi splitting peaks are predicted in the intensity fluctuation spectra of the superradiant lasers. Population fluctuation mechanisms in superradiant lasers and lasers without superradiance are discussed and compared with each other.

We investigate the surface photoemission (SPE) and the volume (VPE) photoemission from metal nanoparticles into semiconductor environments with a varied height of the potential barrier at the metal–semiconductor interface. We show that the internal quantum efficiency of the SPE becomes several times larger than the one of the VPE, when the barrier height decreases and the contact on the interface approaches to the ohmic one. Discontinuities in the electron effective mass and in dielectric functions at the interface are taken into account in the calculations. Results are important for efficient generation of hot electrons from metal nanostructures for such applications as photocatalysis and water splitting.

ДИАГРАММА НАПРАВЛЕННОСТИ ПЛОТНОСТИ ФОТОТОКА ИЗ ПЛАЗМОННЫХ НАНОЧАСТИЦ: ФИЗИЧЕСКИЕ ОСНОВЫЯВЛЕНИЯ И ПРИМЕР РАСЧЕТОВ Ихсанов Р

Nonlinear Heisenberg-Langevin equations are solved analytically by operator Fourier-expansion for the laser in the LED regime. Fluctuations of populations of lasing levels are taken into account as perturbations. Spectra of operator products are calculated as convolutions, preserving Bose commutations for the lasing field operators. It is found that fluctuations of population significantly affect spontaneous and stimulated emissions into the lasing mode, increase the radiation rate, the number of lasing photons and broad the spectrum of a bad cavity thresholdless and the superradiant lasers. The method can be applied to various resonant systems in quantum optics.

The Landau damping (LD) mechanism of the localized surface plasmon (LSP) decay is studied for the hybrid nanoplasmonic (metal core/dielectric shell) structures. It is shown that LD in hybrid structures is strongly affected by the permittivity and the electron effective mass in the dielectric shell in accordance with previous observations by Kreibig, and the strength of LD can be enhanced by an order of magnitude for some combinations of permittivity and effective mass. The physical reason for this effect is identified as an electron spillover into the dielectric where the electric field is higher than that in the metal and the presence of quasi-discrete energy levels in the dielectric. The theory indicates that the transition absorption at the metal-dielectric interface is a dominant contribution to LD in such hybrid structures. Thus, by judicious selection of dielectric material and its thickness, one can engineer decay rates and hot carrier production for important applications, such as photodetection and photochemistry.

We find the maximum size of metal nanoparticles, when the surface photoemission (SPE) becomes important, and the size, when SPE exceeds the volume photoemission (VPE). We study dependences of such sizes on the frequency of absorbed field and discontinuities in the dielectric function and in the electron effective mass on the metal–semiconductor interface. We obtain explicitly the size of nanoparticles with equally efficient SPE and VPE near the red limit of the photoeffect and numerically, above the red limit. Such a size is a few tens of nanometers and about 20 nm at the localized plasmon resonance of spherical gold nanoparticles.

A new approach for analytically solving quantum nonlinear Langevin equations is proposed and applied to calculations of spectra of superradiant lasers where collective effects play an important role. We calculate lasing spectra for arbitrary pump rates and recover well-known results such as the pump dependence of the laser linewidth across the threshold region. We predict new sideband peaks in the spectrum of superradiant lasers with large relaxation oscillations as well as new nonlinear structures in the lasing spectra for weak pump rates. Our approach sheds new light on the importance of population fluctuations in the narrowing of the laser linewidth, in the structure of the lasing spectrum, and in the transition to coherent operation.

Enhancement of the surface photoemission from metal into semiconductor by resonance tunneling of photoexcited electrons through (quasi-) discrete level in quantum well, located within Schottky barrier of the metal–semiconductor interface, is studied theoretically taking into account the difference between the electron masses in metal and semiconductor. It is shown, in particular, that resonance tunneling through the discrete level can lead to the redshift of the threshold wavelength of surface photoeffect, higher slope linear growth in photocurrent near the threshold (in contrast to quadratic growth, i.e., Fowler's law), and the possibility to increase substantially the photoemission efficiency similarly to recent experimental results on hot carrier generation in plasmonic structures with a discrete energy level at metal interface. The difference in the effective masses is shown to significantly affect the results. Double-barrier tunneling structures with resonant tunneling may become attractive for applications in photochemistry and in plasmonic photodetectors in near IR and middle IR regions of the spectrum.

Quantum efficiencies of surface (SPE) and volume (VPE) photo-emissions from metal nanoparticles are calculated by quantum mechanical perturbation theory and compared with each other. Along with discontinuities in the potential barrier and dielectric function, the discontinuity in electron effective mass on the metal-environment interface is taken into account. General formulas for quantum efficiencies of SPE and VPE are derived. An example of spherical gold particles with rectangular potential barrier on the interface is considered, analytical formulas for quantum efficiencies of SPE and VPE on the red border of photoemission are derived. It is found that the efficiency of SPE is less decreased with the reduction of the electron effective mass than the efficiency of VPE, so SPE is more efficient that VPE for small particles and large discontinuity in effective mass. Nanoparticle size, when SPE is more efficient than VPE, is found to be tens of nm or less.

Internal surface photoemission of electrons from 1D crystal into a barrier with participation of Tamm state (TS) at the interface crystal barrier is considered theoretically for the first time, to the best of our knowledge. It is shown that resonant tunneling of electrons through a TS could lead to substantial enhancement of the quantum efficiency and lowering the red border to a value defined by the TS. In contrast to the Fowler quadratic law, the photocurrent scales linearly with photon energy near the red border. The results suggest that the efficiency of hot electron generation with plasmonic metal nanoparticles could reach several tens of percent, which is very attractive for application in energy conversion technologies such as water splitting.