Short Wavelength Limit Research Articles

Quantum Cascade Lasers in the InAs/AlSb Material System

We review the current state of the InAs/AlSb quantum cascade laser (QCL) technology. These materials have brought significant progress in short wavelength QCL due to the high-conduction band offset. The first QCLs emitting below 3 μm have been demonstrated in this system. The short wavelength limit of QCL operation has further been moved down to 2.6 μm. This system is also well suited for far-infrared QCLs because high intersubband gain can be achieved at low transition energies due to the small electron effective mass in InAs. Room temperature operation has been demonstrated in InAs-based QCLs to a wavelength of 21 μm, for the first time for any semiconductor laser emitting above 16 μm. Both short- and long-wavelength single-frequency distributed feedback InAs/AlSb QCLs have been realized, as well as widely tunable external cavity sources for the 3–3.5 μm spectral range.

Athermal directions and their dispersion in KGd(WO4)2 and KLu(WO4)2 crystals

An analysis of the existence of athermal properties for optically biaxial crystals KGd(WO4)2 and KLu(WO4)2 is performed and compared with that of KY(WO4)2 for monolithic and laser cavity configurations. Short-wavelength limits for athermal behavior in the principal planes of optical indicatrix are found. In KGd(WO4)2 they lie near or in the absorption band. In KLu(WO4)2, one of the two isonomal waves and both isonomal waves in the Np–Nm principal plane of KGd(WO4)2 for the laser cavity configuration have also long-wavelength limits. It is shown that for some wavelengths (one or two in the visible spectrum) and light wave polarization, the optical indicatrix axes can be athermal. In KLuW, for the monolithic configuration, the Np axis is athermal at three wavelengths, two of which lie in the IR region (0.843 and 1.975μm). All-space athermal directions are determined for KLu(WO4)2 at 2μm. For the monolithic configuration, they form a cone with its axis parallel to the Np axis and oval cross-section.

Propagation of surface waves and surface resonances along cylindrical cavities in materials with any allowed Poisson's ratio – Part I: Clean inner surface

The dynamics of the inner surface of an infinitely long circular‐cylindrical cavity in an isotropic elastic medium is studied in the whole range of the Poisson's ratio including negative values characteristic of auxetic materials. The existence of the unique long‐lived propagation mode (true surface wave, TSW) has been confirmed on the clean surface with the following properties: (i) existence of a low frequency cut‐off for all the azimuthal indices n except for n = 1 (flexural mode), (ii) polarization tending to that of the Rayleigh wave in the short wavelength limit, (iii) Airy phases (inflection points of dispersion curves) for n < 6 that shift towards short wave region when the Poisson's ratio becomes negative. A number of propagation modes with complex frequencies, i.e., with finite life times (surface leaky waves, pseudo surface waves) are found. The torsional leaky mode transforms into the skimming shear‐horizontal wave (Love wave) in the short wavelength limit. An axial–radial leaky mode, similar to the Rayleigh wave but with reverse elliptical polarization turns out a physical solution except for extremely short wavelengths. A strong radial component of the longitudinal resonance occurs at wavelengths comparable to the cavity's radius especially in the incompressible limit.

Propagation of surface waves and surface resonances along cylindrical cavities in materials with any allowed Poisson's ratio – Part II: Thin‐walled coating

Propagation of infinitely‐lived true surface waves (TSW) and of the evanescent surface resonances (pseudo surface waves, PSW) on the inner surface of a cylindrical cavity in an elastic medium coated with a thin elastic membrane is studied. An analogous flat surface with the same coating is considered as a reference system. The dispersion relations of the true surface waves and of the surface resonances are shown to depend on the interplay between the sound speeds in the substrate and in the covering layer. The short‐wavelength limit of the excitations in the cavity is checked to be consistent with the case of the flat surface. Analytical expressions are obtained for the cut‐offs and for the asymptotic behaviors of the excitations in the long‐wavelength and short wavelength limits. The local surface densities of states (LDOS) as well as the real parts of the Green's functions, i.e., analogues of the reactive power, are calculated. The most eminent anomalies of LDOS, which correspond to the longitudinal resonance, are shown to be located close to the apparently spurious roots of the secular determinant of the surface equations of motion. The roots correspond generally to the total conversion of the longitudinal to transverse bulk waves. These roots show cut‐offs, where the life time of the longitudinal resonance increases to infinity. For still lower wave vectors the maxima of LDOS follow the lines of total conversion transverse‐to‐longitudinal with finite life‐times. The radius dependence of the cut‐off wave vector in the small‐radius limit for a fully symmetric torsional mode is and for a fully symmetric high‐frequency axial–radial TSW follows a 1/a behavior, whereas the analogous dependence for a quasi‐Rayleigh surface wave is proportional to except for a certain range of parameters, where the high‐frequency TSW does not exist.

Self-similar formation of an inverse cascade in vibrating elastic plates.

The dynamics of random weakly nonlinear waves is studied in the framework of vibrating thin elastic plates. Although it has been previously predicted that no stationary inverse cascade of constant wave action flux could exist in the framework of wave turbulence for elastic plates, we present substantial evidence of the existence of a time-dependent inverse cascade, opening up the possibility of self-organization for a larger class of systems. This inverse cascade transports the spectral density of the amplitude of the waves from short up to large scales, increasing the distribution of long waves despite the short-wave fluctuations. This dynamics appears to be self-similar and possesses a power-law behavior in the short-wavelength limit which significantly differs from the exponent obtained via a Kolmogorov dimensional analysis argument. Finally, we show explicitly a tendency to build a long-wave coherent structure in finite time.

Extending the short and long wavelength limits of bacteriochlorin near-infrared absorption via dioxo- and bisimide-functionalization.

Six new bacteriochlorins expanding the range of the strong near-infrared (NIR) absorption (Qy band) to both shorter and longer wavelengths (∼690 to ∼900 nm) have been synthesized and characterized. The architectures include bacteriochlorin-bisimides that have six-membered imide rings spanning the 3,5- and 13,15-macrocycle positions or five-membered imide rings spanning the β-pyrrolic 2,3- and 12,13-positions. Both bisimide types absorb at significantly longer wavelength than the bacteriochlorin precursors (no fused rings), whereas oxo-groups at the 7- or 7,17-positions shift the Qy band to a new short wavelength limit. Surprisingly, bacteriochlorin-bisimides with five-membered β-pyrrolic-centered imide rings have a Qy band closer to that of six-membered bacteriochlorin-monoimides. However, the five-membered bisimides (versus the six-membered bacteriochlorin-monoimides) have significantly enhanced absorption intensity that is paralleled by an ∼2-fold higher fluorescence yield (∼0.16 vs ∼0.07) and longer singlet excited-state lifetime (∼4 ns vs ∼2 ns). The photophysical enhancements derive in part from mixing of the lowest unoccupied frontier molecular orbitals of the five-membered imide ring with those of the bacteriochlorin framework. In general, all of the new bacteriochlorins have excited-state lifetimes (1-4 ns) that are sufficiently long for use in molecular-based systems for photochemical applications.

Rossby waves in an azimuthal wind

Rossby waves in an azimuthal wind are analyzed using an eigen-function expansion. Solutions of the wave equation for the stream-function for Rossby waves are obtained in which depends on where r is the cylindrical radius, is the azimuthal angle measured in the plane relative to the Easterly direction, (the -plane is locally horizontal to the Earth’s surface in which the x-axis points East, and the y-axis points North). The radial eigenfunctions in the -plane are Bessel functions of order and argument kr, where k is a characteristic wave number and have the form in which the satisfy recurrence relations involving , , and . The recurrence relations for the have solutions in terms of Bessel functions of order where is the frequency of the wave and is the angular velocity of the wind and argument . By summing the Bessel function series, the complete solution for reduces to a single Bessel function of the first kind of order . The argument of the Bessel function is a complicated expression depending on r, , a, and kr. These solutions of the Rossby wave equation can be interpreted as being due to wave-wave interactions in a locally rotating wind about the local vertical direction. The physical characteristics of the rotating wind Rossby waves are investigated in the long and short wavelength limits; in the limit as the azimuthal wind velocity ; and in the zero frequency limit in which one obtains a stationary spatial pattern for the waves. The vorticity structure of the waves are investigated. Time dependent solutions with are also investigated.

Application of the Random Coupling Model to Electromagnetic Statistics in Complex Enclosures

The effectiveness of the random coupling model (RCM) in predicting electromagnetic wave coupling to targeted electronic components within a complex enclosure is examined. In the short-wavelength limit with respect to the characteristic length of the enclosure, electromagnetic wave propagation within a large enclosure is sensitive to small changes to the interior, or to the boundaries of the enclosure. Such changes can reduce or invalidate the applicability of deterministic predictions of the electromagnetic fields at radiofrequencies (RF) in large enclosures. Under such circumstances, a statistical approach is needed to provide a better understanding of RF coupling to components within large enclosures. In this paper, we experimentally demonstrate the applicability of a statistical technique, the RCM, to estimate the probabilistic magnitudes of RF fields on electrically large components (i.e., long cables, etc.) that are partially shielded within a complex, 3-D enclosure.

Short wavelength limits of current shot noise suppression

Shot noise in electron beam was assumed to be one of the features beyond control of accelerator physics. Current results attained in experiments at Accelerator Test Facility in Brookhaven and Linac Coherent Light Source in Stanford suggest that the control of the shot noise in electron beam (and therefore of spontaneous radiation and Self Amplified Spontaneous Emission of Free Electron Lasers) is feasible at least in the visible range of the spectrum. Here, we present a general linear formulation for collective micro-dynamics of e-beam noise and its control. Specifically, we compare two schemes for current noise suppression: a quarter plasma wavelength drift section and a combined drift/dispersive (transverse magnetic field) section. We examine and compare their limits of applicability at short wavelengths via considerations of electron phase-spread and the related Landau damping effect.

Modeling of a functionally graded micro-ring segment for the analysis of coupled extensional–flexural waves

Established in this study is a microstructure-dependent continuum model of a micro-ring with a functionally graded material composition in the thickness direction. The developed model is employed to furnish the nature of elastic waves propagation within a segment of the micro-ring. The development of the model is grounded on the modified couple stress theory, the Hamilton’s principle, and the classical rule of mixture. For validation purposes, patterns of wave propagation within homogenous rings and homogeneous micro-rings are analyzed from the reduced forms of the model. Key effects incorporated in the new model include small-scale parameter, power-law index, Winkler–Bach and rotary inertia effects. Dispersion analyses revealed a profile of frequency spectra characterized by distinct frequency zones, each of which is engendered by a bifurcation point. Explicit closed-form expressions are provided for high and low frequency limits as well as the long and short wavelength limits of the coupled waves. Phase speed dispersion curves for the micro-ring are found to have different branches that signify the distinctly flexural and extensional waves. Higher values of the power-law index are found to lead to a marked decrease in the phase speed and a noticeable increase of the group speed of the extensional wave.

Optical beam shaping and diffraction free waves: A variational approach

We investigate the problem of shaping radially symmetric annular beams into desired intensity patterns along the optical axis. Within the Fresnel approximation, we show that this problem can be expressed in a variational form equivalent to the one arising in phase retrieval. Using the uncertainty principle we prove various rigorous lower bounds on the functional; these lower bounds estimate the L2 error for the beam shaping problem in terms of the design parameters. We also use the method of stationary phase to construct a natural ansatz for a minimizer in the short wavelength limit. We illustrate the implications of our results by applying the method of stationary phase coupled with the Gerchberg–Saxton algorithm to beam shaping problems arising in the remote delivery of beams and pulses.

The J and M integrals for a cylindrical cavity in a time-harmonic wave field

The invariant integrals are being widely used in the study of defects and fracture mechanics, mostly in elastostatics. However, the properties and the interpretation of these integrals in elastodynamics, especially in the case of time-harmonic excitation, remain unexplored. This contribution is focused on the derivation of the time average J integral for a cylindrical inhomogeneity and the M integral for a cylindrical cavity placed in a monochromatic plane elastic wave. It is shown in the context of antiplane linear elasticity that the J integral, or the material force acting on the inhomogeneity, resembles the radiation pressure force exerted on a dielectric cylinder by the normally incident electromagnetic wave. Based on the existing solution of this electrodynamic problem and the corresponding acoustic problem, the J integral is expressed as a function of the nondimensional wave number in the form of the partial wave expansion of the scattering theory. Employing the same classical method as with the J integral, the closed-form solution of the time average M integral for a traction-free cavity is also obtained as a function of the nondimensional wave number. The M integral, i.e., the expansion or scalar moment per unit length on an infinitely long circular cavity, is represented in terms of the scattering phase shifts as in the case of the J integral. Alternative expressions that are more convenient for numerical calculations for the cavity are also derived for both integrals. These calculations are carried out for the J and M integrals in a wide spectrum of frequencies. Asymptotic approximations of both integrals for low and high frequencies are presented. The long wavelength approximation, including the monopole and dipole contributions, has been provided for the J integral in the form of a simple analytical expression. The value of M integral in the vanishing frequency limit is also presented. In the opposite short wavelength limit, the corresponding asymptotic values are derived for both integrals. These solutions, which are valid for the empty cavity, are extended to the case of an inviscid fluid-filled cavity. The obtained results have a variety of engineering and geophysical implications. In particular, their applications to the flaw characterization of materials and further development of non-destructive evaluation techniques are briefly discussed in light of the frequency relationships derived for the J and M integrals.

Impedance Matching of Atomic Thermal Interfaces Using Primitive Block Decomposition

We explore the physics of thermal impedance matching at the interface between two dissimilar materials by controlling the properties of a single atomic mass or bond. The maximum thermal current is transmitted between the materials when we are able to decompose the entire heterostructure solely in terms of primitive building blocks of the individual materials. Using this approach, we show that the minimum interfacial thermal resistance arises when the interfacial atomic mass is the arithmetic mean, whereas the interfacial spring constant is the harmonic mean of its neighbors. The contact-induced broadening matrix for the local vibronic spectrum, obtained from the self-energy matrices, generalizes the concept of acoustic impedance to the nonlinear phonon dispersion or the short-wavelength (atomic) limit.

Dispersion and damping of a surface plasmon polariton on a one-dimensional randomly rough metal surface

By the use of the reduced Rayleigh equation for the amplitude of a surface plasmon polariton on a one-dimensional randomly rough metal surface that is in contact with vacuum, we calculate the dispersion and damping of the surface electromagnetic wave to the lowest nonzero order in the rms height of the surface. It is found that the frequency of the surface plasmon polariton is depressed by the surface roughness. The attenuation of the surface plasmon polariton in the long wavelength limit is due primarily to its scattering into other surface plasmon polaritons, while in the short wavelength limit it is due primarily to its roughness-induced scattering into volume electromagnetic waves in the vacuum. The energy mean free path of the surface plasmon polariton is shorter on a randomly rough metal surface than it is on a lossy planar metal surface, and the surface plasmon polariton is more tightly bound to a rough surface than to a planar one.

Nonlinear interaction and parametric instability of kinetic Alfvén waves in multicomponent plasmas

Nonlinear couplings among kinetic Alfvén waves are investigated for a three-component plasma consisting of electrons, protons, and heavy ions. The parametric instability is investigated, and the growth rate is obtained. In the kinetic regime, the growth rate for the parallel decay instability increases with the heavy ion content, but the growth rate for the reverse decay is independent of the latter since the perpendicular wavelength is much larger than the ion gyroradius. It decreases with the heavy ion content when the perpendicular wavelength is of the order of the ion gyroradius. It is also found that in the short perpendicular wavelength limit, the growth rate is only weakly affected by the heavy ions. On the other hand, in the inertial regime, for both parallel and reverse decay cases, the growth rate decreases as the number of heavy ions becomes large.

Anomalous Localization of Light in One-Dimensional Disordered Photonic Superlattices

The Anderson localization of light in one-dimensional disordered photonic superlattices is theoretically studied. The system is considered to be made of alternating dispersive and nondispersive layers of different randomthickness. Dispersive slabs of the heterostructure are characterized by Drude-like frequency-dependent electric permittivities and magnetic permeabilities. Numerical results for the localization length are obtained via an analytical model, only valid in the case of weak disorder, and also through its general definition involving the transmissivity of the multilayered system. Anomalous λ 4 - and λ -4 -dependencies of the localization length in positive-negative disordered photonic superlattices are obtained, in certain cases, in the long and short wavelength limits, respectively. PACS: 78.67.Pt; 42.25.-p; 46.65.+g; 72.15.Rn

If substorm onset triggers tail reconnection, what triggers substorm onset?

Despite the claim that tail reconnection triggers substorm onset, there is an abundance of cases wherein substorm onset triggers tail reconnection. In such cases, the first observable precursor to onset is a periodic rippling (beads) along an equatorward auroral arc. In this study, through an example, we show that substorms arising out of arcs of this type have the classical “inside‐out” evolution, including the triggering of tail reconnection as a possible result. We then investigate what the magnetospheric mode underlying the ripples along the arcs might be. The classical MHD ballooning invoked by some substorm theories is inconsistent with the observation, which exhibits a finite azimuthal wavelength comparable to the local ion gyroradius and the propensity of onset to occur under moderately high (1–10) rather than extremely high plasmaβ. We show that the onset is due to a modified ballooning mode, subject to corrections by the General Ohm's Law and ion heat flux. The net result is that the necessary condition for the instability remains unchanged from the classical MHD, but the growth rate of the instability is heavily attenuated or quenched in the high β and short azimuthal wavelength limits. In the actual magnetosphere, the mode has a wavelength ∼1,500 km, growth timescale ∼10 s, and critical plasma beta in the 3–13 range, all consistent with observations.

Random-matrix theory of amplifying and absorbing resonators with or symmetry

We formulate Gaussian and circular random-matrix models representing a coupled system consisting of an absorbing and an amplifying resonator, which are mutually related by a generalized time-reversal symmetry. Motivated by optical realizations of such systems we consider a or a time-reversal symmetry, which impose different constraints on magneto-optical effects, and then focus on five common settings. For each of these, we determine the eigenvalue distribution in the complex plane in the short-wavelength limit, which reveals that the fraction of real eigenvalues among all eigenvalues in the spectrum vanishes if all classical scales are kept fixed. Numerically, we find that the transition from real to complex eigenvalues in the various ensembles display a different dependence on the coupling strength between the two resonators. These differences can be linked to the level spacing statistics in the Hermitian limit of the considered models.This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Quantum physics with non-Hermitian operators’.

COLLECTIVE MODES IN Q1D ORGANIC CONDUCTORS

We study the weakly damped electromagnetic waves in strongly anisotropic organic conductors with the chain-like character of the intermolecular overlapping at various orientations of an external magnetic field and wave vector. We obtain the analytical expressions for the spectra of the collective modes in a number of limiting cases, in particular, the dispersion relations in a short-wavelength limit when the eigen frequencies are not close to the resonance frequency and its harmonics. The numerical analysis giving full enough description of the dispersion of the weakly damped eigenmodes is presented. We find the spectrum of the eigenmodes owing to electron oscillations along the least conductivity direction. We show that if the orientation of the wave vector k is not too close to the least conductivity direction, the dependence of the eigen frequencies on k has pronounced oscillatory character.

Dependence of LC resonance wavelength on size of silver split-ring resonator fabricated by nanosphere lithography

We fabricated silver split-ring resonators (SRRs) using nanosphere lithography and measured the LC resonance wavelength of single isolated SRRs in optical wavelength range. The SRRs' sizes decreased when smaller polystyrene spheres were used as templates, and their LC resonance wavelength decreased to 721 nm. The LC resonance wavelength corresponding to the observed properties of the SRRs was calculated using the LC circuit model; we confirmed that the observational and calculated results agreed well. The LC resonance frequency of a miniaturized SRR with a constant shape was also calculated. For SRRs of the shape that we fabricated, the estimated short-wavelength limit was 426 nm.