Transient stationary waves and angular momentum

We report new transient stationary spherical waves generated by the time evolution of wave functions with angular momentum. In the study the 3D problem of the sudden release of a particle which initially was inside a spherical trap, the exact solution for the particle's time evolution is described by expected traveling incoming and outgoing spherical waves. However, unexpected transient stationary spherical waves are also present. The traveling waves have amplitudes describing diffraction in time, in a way similar to the optical diffraction by a single slit. In striking contrast with the similar 1D problem, the angular momentum generates unexpected transient stationary spherical waves which have their main contribution at points inside the sphere but only for very short times.     

Diffusion-controlled combustion of gases in the absence of forced convection

A mathematical model for the laminar diffusion combustion of gases in the absence of forced convection is developed. This combustion mode is realized near an orifice in the partition that separates the fuel and oxidizer. The stationary solution, size and shape of the flame, temperature distribution, and profiles of the concentrations of fuel, oxidizer, and combustion products are determined. It is shown that the limiting diameter of the diffusion flame is inversely proportional to the burning rate of an equivalent premixed mixture of the same fuel and oxidizer, whereas the flame length is proportional to the diameter of the orifice. The unsteady (quasi-stationary) solution to this problem for the case where the gas is confined in a finite-volume vessel is obtained. The time it takes the flame to approach the partition of the vessel with fuel and enter inside is determined. Experiments on studying the diffusion combustion of natural gas in the absence of forced convection near orifices and a slit in the partition separating the gaseous fuel and oxidizer in a finite-volume vessel are performed. The time of combustion is obtained. Depending on the orifice diameter and slit width, three modes of diffusion combustion were identified: combustion above the partition ending in flame extinction, combustion with a breakthrough, and combustion inside the vessel (submerged flame).     

Microscopic model of the THz field enhancement in a metal nanoslit

We discuss the strong THz-field enhancement effect in a metal slit of dozens of nanometers sizes reported recently. Proposed simple microscopic model considers electric charges induced at the edges of the slit by a polarized incident wave. These charges contribute then to the field in the slit. The model is capable of explaining peculiarities of the field enhancement phenomenon such as an inverse frequency dependence of the enhancement factor. It provides closed-form expressions for the enhancement factor and field mapping inside the slit having only one fitting parameter. The model predicts influence of the slit shape on the field enhancement.     

Most likely ensemble with a given average energy prepared by a single slit

We discuss an ensemble of particle selected by a single slit within the statistical model of quantization reported earlier. We look for the most probable distribution of the position of the particle with a given average energy by applying Jaynes’s maximum entropy principle. We first show that the most likely ensemble with the lowest possible average energy is given by the quantum mechanical ground state of a particle trapped inside the slit. We further show that in general it takes a larger energy to collect the beam of particles into a target position with a higher precision.     

Control of the cross-sectional shape of a hollow microchannel embedded in photostructurable glass by use of a femtosecond laser

Theoretical and experimental investigations have been made of the three-dimensional microchannel fabrication of photostructurable glass by use of a femtosecond (fs) laser. Generally, a microchannel fabricated inside glass by the scanning focal spot of a fs laser perpendicular to the direction of laser propagation assumes an elliptical shape with a cross section of large aspect ratio. We demonstrate that one can greatly reduce the aspect ratio merely by inserting a slit, which is oriented parallel to the laser's scanning direction, before the focusing lens. Computer simulations show that a more symmetrical pattern is obtained in the vicinity of the focal point with the help of such a slit, owing essentially to a diffraction effect.     

Filling of a Plane Slit Volume with a Glow Discharge in a Transverse Magnetic Field and Its Effect on the Discharge Contraction

We consider a dc glow discharge in a plane slit volume with electrodes in the slit plane in a magnetic field transverse to the current, which has been studied experimentally. As in the experiment, the discharge is artificially confined at one of the dielectric boundaries of the volume and propagates to the opposite dielectric boundary until it is stabilized. It is shown using a 2D calculation of the nonstationary process that the discharge in a magnetic field occupies a noticeably larger volume (with a lower current density at the electrodes) than in zero magnetic field. The effect of the magnetic field is also manifested in that it hampers the contraction of the discharge, substantially elevating the threshold current of the diffuse discharge. The discharge contraction is calculated in the approximation of a homogeneous positive column along the current right to the attainment of the stationary state. In calculations with a magnetic field, hysteresis appears in transitions from the diffuse to the contracted state and back.     

Adjustable plasmon resonances through an H-shaped metallic grating

We propose an H-shaped metallic grating and investigate its surface plasmon resonance properties. The result shows the formation process of the transmission spectra of the H-shaped grating by adjusting the depths of the arm cuts, and a band gap is formed on the region of short wavelength. It is also presented that the transmission of the H-shaped grating sensitively depends on the width and position of the arm slit, noticeable magnitude modification, redshift and blueshift, meld and split of the resonance peaks are found. In addition, the resonance peaks exhibit dips in the transmission spectrum when the two slit widths are different, and the dips are tunable by changing any one slit width for fixed another slit. To understand its physical origin, a field-interference mechanism, the Fabry–Pérot-like resonance theory and the phase resonance mechanism have been suggested, respectively. By selecting appropriate structural parameters, an H-shaped metallic grating for optical filter and channel selecting devices can be constructed.     

Self-oscillations in a flow ideal mixing reactor in the region of multiplicity of stationary equilibrium states: a consecutive reaction

A model of a flow ideal mixing reactor for a consecutive two-stage exothermic first-order reaction was considered. The presence of a region of multiplicity of stationary states was established. This multiplicity region can contain regions of three and five stationary states; the region of five states always appears inside the region of three stationary states. Changes in the type of stationary state stability in each of these regions are analyzed. Numerical calculations of phase trajectories in the regions of stationary state stability and instability were performed. A mechanism of the creation of a stable limiting cycle was suggested for the case of three stationary states.     

Extraordinary THz transmission through subwavelength semiconductor slits under antiparallel external magnetic fields

We theoretically study the resonant transmission of electromagnetic waves at the THz frequencies through subwavelength semiconductor slits under external static magnetic fields. The dispersion relations of the surface plasmon polaritons (SPPs) inside a subwavelength slit are analytically derived. It is found that the SPPs propagating along one direction and its reverse are symmetric when parallel external magnetic fields are applied, but are asymmetric when antiparallel external magnetic fields are applied. The transmission properties of periodic subwavelength semiconductor slit arrays with the antiparallel magnetic fields in each unit cell are investigated by the mode expansion technique. The two significant transmission characteristics are observed: (i) The resonant peaks are redshifted with increasing external magnetic fields; (ii) The transmissions in the two opposite directions through the slit arrays are asymmetric. The origin of the transmission asymmetry is reasonably explained by the magnetic-field induced asymmetric SPP propagation losses.     

Inward electromagnetic wave coupling in hybrid subwavelength structures illuminated with secondary imaging

Subwavelength structures hybridized with slits and grooves in metallic films exhibit extraordinary optical properties for manipulation of light. A Green method is developed to investigate the wave coupling physics in the hybrid subwavelength structures, while source-image arrangement in bounded spaces is employed to obtain the Green's functions for the hybrid units. We find that secondary imaging is induced at a horizontal boundary to provide an inward wave propagation mechanism to couple the wave scattered by groove back into slit. Sophisticated self-consistent framework derived from our method that involves the wave couplings is then developed to study the physics origin of the extraordinary optical properties. The case of a slit in a metal film with patterned grooves on the output side for beaming and that of a two-layer metal film with indented double slit for beyond-limit focusing are analyzed. Our Green method, which automatically includes the Fourier high-order modes, is concise in formulation and thus yields accurate solutions. Explicit analytical models are rigorously developed to address wave coupling physics problems in subwavelength structure.     

Theoretical analysis of off beam quartz-enhanced photoacoustic spectroscopy sensor

Off beam quartz-enhanced photoacoustic spectroscopy (OB-QEPAS) sensors are based on a recently developed approach to off-beam photoacoustic (PA) detection which employs a quartz tuning fork (QTF) as an acoustic transducer. A microresonator (mR) with a side slit in the middle is used to enhance PA signal. This paper describes a theoretical model of an OB-QEPAS-based sensor. By deriving the acoustic impedances of the mR at two ends and the side slit in the middle in the model, we obtain a formula for numerically calculating the optimal mRs' parameters of OB-QEPAS-based sensor. We use the model to calculate the optimal mRs' lengths with respect to the resonant frequency of the QTF, acoustic velocities inside mRs, inner diameters of mRs, and acoustic conductivities of the mRs' side slits, and found out that the calculated results closely match experimental data. We also investigated the relationship between the mR selected in “on beam” QEPAS, OB-QEPAS, and an acoustic resonator (AR) excited in its first longitudinal mode used in conventional photoacoustic spectroscopy (PAS).     

Enhancement of spatial coherence by surface plasmons

We report on a method to generate a stationary interference pattern from two independent optical sources, each illuminating a single slit in Young's interference experiment. The pattern arises as a result of the action of surface plasmons traveling between subwavelength slits milled in a metal film. The visibility of the interference pattern can be manipulated by tuning the wavelength of one of the optical sources.     

First-order photon interference of a single photon from a single quantum dot

Photon interference indicating wave-like nature of a single photon emitted from a single quantum dot is demonstrated. Photon state as a superposition of two orthogonal linear polarization modes is prepared inside a solid-state single photon source, which causes the first-order interference analogous to the Young’s double slit experiment. The lack of which-mode information is essential for observing the single photon interference.     

Molecular simulation study of triangle-well fluids confined in slit pores

Grand canonical Monte Carlo simulations are used to study the behaviour of triangle-well (TW) fluids with variable well widths confined inside slit pores. The effect of individual factors influencing the properties of confined fluids such as fluid–fluid interactions, pore size and pore wall–fluid interactions are obtained using simulations as it is difficult to experimentally determine the same. An interesting observation of this study is that inside the narrow pore of slit height h* = 5 at the high-pressure condition of P* = 0.8, for the TW fluid with long-range attraction or for the fluid at a low temperature for even a short-range attraction, the density profiles show layering such that there is a sticking tendency of the particles at centre, while there is a depletion of particles near the wall (as the layers at the centre have higher density peak heights than near the walls).     

Waveguide resonance of subwavelength metallic slits

The transmission characteristics of a metallic film with subwavelength periodic slits are investigated by using the two-dimensional finite-difference time-domain method (2D-FDTD). Two models are constructed to show the dependance of the transmission spectrum on the slit structure. A sandwiched structure is used to exhibit the contribution of the metallic wall inside slits to the extraordinary high transmission. And a filled slit structure is employed to reflect the relation between the average refractive index inside the slits and the transmission spectrum of the structure. The transmission characteristics of two structures can be explained well with the waveguide resonance theory.     

Knudsen Gas in a Finite Random Tube: Transport Diffusion and First Passage Properties

We consider transport diffusion in a stochastic billiard in a random tube which is elongated in the direction of the first coordinate (the tube axis). Inside the random tube, which is stationary and ergodic, non-interacting particles move straight with constant speed. Upon hitting the tube walls, they are reflected randomly, according to the cosine law: the density of the outgoing direction is proportional to the cosine of the angle between this direction and the normal vector. Steady state transport is studied by introducing an open tube segment as follows: We cut out a large finite segment of the tube with segment boundaries perpendicular to the tube axis. Particles which leave this piece through the segment boundaries disappear from the system. Through stationary injection of particles at one boundary of the segment a steady state with non-vanishing stationary particle current is maintained. We prove (i) that in the thermodynamic limit of an infinite open piece the coarse-grained density profile inside the segment is linear, and (ii) that the transport diffusion coefficient obtained from the ratio of stationary current and effective boundary density gradient equals the diffusion coefficient of a tagged particle in an infinite tube. Thus we prove Fick’s law and equality of transport diffusion and self-diffusion coefficients for quite generic rough (random) tubes. We also study some properties of the crossing time and compute the Milne extrapolation length in dependence on the shape of the random tube.     

Scattering mechanism in a step-modulated subwavelength metal slit: a multi-mode multi-reflection analysis

In this paper, the scattering/transmission inside a step-modulated subwavelength metal slit is investigated in detail. We firstly investigate the scattering in a junction structure by two types of structural changes. The variation of transmission and reflection coefficients depending on structural parameters are analysed. Then a multi-mode multi-reflection model based on ray theory is proposed to illustrate the transmission in the step-modulated slit explicitly. The key parts of this model are the multi-mode excitation and the superposition procedure of the scatterings from all possible modes, which represent the interference and energy transfer occurring at the interfaces. The method we use is an improved modal expansion method (MEM), which is a more practical and efficient version compared with the previous one [C. Li, Y.S. Zhou, H.Y. Wang, F.H. Wang, Opt. Express 19, 10073 (2011)]. In addition, some commonly used methods including FDTD, scattering matrix method and improved characteristic impedance method are compared with MEM to highlight the accuracy of these methods.     

D2/H2 quantum sieving in microporous carbons: a theoretical study on the effects of pore size and pressure

The adsorption of hydrogen and deuterium in slit-shaped carbon pores is studied by grand canonical Monte Carlo simulations. All interactions are assumed to be of Lennard–Jones type, while the Feynman–Hibbs expression is used to account for quantum effects. The interaction energy of both isotopes inside the slit pore space is discussed thoroughly. Furthermore, pure component adsorption isotherms of both isotopes were simulated at 77?K for pressures up to 20?bar in slit pores having widths of up to 2.0?nm. According to our simulations, in equilibrium, slit pores reveal slight deuterium selectivity over hydrogen, and this quantum-based selectivity depends both on pressure and pore size.     

New patterns of activity in a pair of interacting excitatory-inhibitory neural fields

In this Letter, we study stationary bump solutions in a pair of interacting excitatory-inhibitory (E-I) neural fields in one dimension. We demonstrate the existence of localized bump solutions of persistent activity that can be maintained by the pair of interacting layers when a stationary bump is not supported by either layer in isolation--a scenario which may be relevant as a mechanism for the persistent activity associated with working memory in the prefrontal cortex and may explain why bumps are not seen in in vitro slice preparations. Furthermore, we describe a new type of stationary bump solution arising from a pitchfork bifurcation which produces a stationary bump in each layer with a spatial offset that increases with the bifurcation parameter.     

Transmission of light through metallic Z-shaped slit array with inner metallic bar

The transmission of a normally incident wave through a Z-shaped channel metallic slit array with metallic bar inside has been investigated by using finite-difference time-domain method. It is obtained that transmission spectra are nearly the same of the slit array with straight channel as that with Z-shaped channel in the condition the material of the slit array the same as that of the inner bar. If the Au bar is replaced by Al of the Au slit array, both resonance modes red shift obviously, especially for the structure with bent channel. Along with the width of the inner bar increasing, the localized waveguide resonance mode red shifts regularly with a tiny decrease of the peak value of all the kinds of composed structure introduced here, and the surface plasmon resonance mode red shifts regularly accompanied by peak value changing uniformly for the structures with only one type of metal. However, the surface plasmon resonance behaves different obviously, its center peak first moves to a larger wavelength fast, then red shifts slowly, for the Au-film Al-bar structure, but that moves in a very small wavelength range for the Al-film Au-bar one. The results obtained here are helpful to design subwavelength optical devices.