Zero-order Wave Research Articles

Properties of multicomponent achromatic and superachromatic zero-order wave plates

This paper presents the spectral dependences of the phase shift and the position of the optic axis for three-, five-, and seven-component zero-order wave plates fabricated from polymethyl methacrylate, which possesses artificially produced anisotropy. Besides this, the dependences of the phase shift of the wave plates on the angle of incidence of the rays and the temperature are presented, along with the spectral dependence of the transmittance of the plates.

Zero-phonon emission bands of solid hydrogen at 6–12μm wavelength. An astrophysical phenomenon

Infrared emission bands in the wavelength range of 6–12μm observed in the ISO-SWS mission are assigned to rotational zero-phonon bands of solid parahydrogen by using Van Kranendonk’s approximate rigid-lattice method. This method is based on superposed electric quadrupole pair interactions and superposed quadrupole induced dipole moments of pairs in the hcp crystal. Accordingly, the approximate formalism uses zero-order H2 pair wave functions. Symmetry effects of the hcp crystal require preference of rotational pair transitions. The interaction potential of the pairs is confined to the electric quadrupole-quadrupole interaction. Zero-phonon emission bands of H2 pair transitions fitted to the spectrum contain at least one delocalized j=2 state initially and/or finally because of their significantly enhanced emission rates. They also yield the characteristic bandwidths which fit nicely to the widths of the observed features. The frequency positions of the seven pure parahydrogen pair transitions used, obtained from experimentally determined rotational solid hydrogen energy levels, are in perfect agreement with the observed features, whereas the three mixed ortho-parapair transitions need a presently unknown frequency correction, caused by the migration of the ortho-H2 molecules into the parahydrogen crystal prior to emission, the so-called initial excess binding energies. The astrophysical setup of the observed source is discussed in the end of the paper.

Metal nano-grid reflective wave plate

We propose an optical wave plate using a metal nano-grid. The wave plate operates in reflection mode. A single-mode truncated modematching theory is presented as a general method to design such nano-grid wave plates with the desired phase difference between the reflected TM and TE polarizations. This analytical theory allows angled incidence calculations as well, and numerical results agree-well with comprehensive finite-difference time-domain electromagnetic simulations. Due to the subwavelength path-length, the reflective wave plate is expected to have improved broad-band functionality over existing zero-order transmissive wave plates, for which an example is provided. The proposed wave plate is simple and compact, and it is amenable to existing nanofabrication techniques. The reflective geometry is especially promising for applications including liquid-crystal displays and laser feedback experiments.

Direct Evaluation of Cyclic Contributions to the π Energy of Conjugated Hydrocarbons from Strongly Localized Zero-Order Pictures

This paper presents a new procedure for identifying that part of the pi electronic energy of conjugated hydrocarbons which results from cyclic circulation of electrons around a ring. It first shows that one may calculate perturbatively the ground state energy of the Hückel Hamiltonian from a strongly localized Kekulé-type zero-order wave function. The contributions due to cyclic circulation of the electrons appear explicitly, in terms of the interatomic hopping integral t, at the second order in cyclobutadiene (where it is equal to -t (antiaromatic)) and at third order in benzene, where its value is 0.5t (aromatic). Conjugated isomers of benzene are also considered. The cyclic circulation contributions for an N-membered ring are shown to depend strongly on the molecular graph in which it is embedded. A general expression is found for the cyclic contribution to the pi energy of a ring, the Kekulé graph of which contains N double bonds alternating with N single bonds. It is the energy of the ring, plus the sum of the energies of the N subsystems that result from one double-bond removal, minus the sum of the energies of the N open systems that result from one single-bond cut. This new aromaticity index, ACE(MC), may be seen as the enthalpy of a hyperhomodesmotic chemical equation. In contrast to the index ACE(DC) previously defined from a double cut of the ring, the multiple-cut ACE(MC) exhibits the expected asymptotic disappearance of the cyclic energy as the ring size tends to infinity. In the multiple-cut approach, aromaticity persists in bond-alternating rings, but, in contrast to the total pi energy, the purely cyclic contribution tends to resist distortion. Extension of the approach to charged, branched and heterosubstituted rings are discussed, as well as its ab initio transcription.

Cylindrical Invisibility Cloak with Simplified Material Parameters is Inherently Visible

It was proposed that perfect invisibility cloaks can be constructed for hiding objects from electromagnetic illumination [J. B. Pendry, D. Schurig, and D. R. Smith, Science 312, 1780 (2006)10.1126/science.1125907]. The cylindrical cloaks experimentally demonstrated [D. Schurig, Science 314, 977 (2006)10.1126/science.1133628] and theoretically proposed [W. Cai, Nat. Photon. 1, 224 (2007)10.1038/nphoton.2007.28] have however simplified material parameters in order to facilitate easier realization as well as to avoid infinities in optical constants. Here we show that the cylindrical cloaks with simplified material parameters inherently allow the zeroth-order cylindrical wave to pass through the cloak as if the cloak is made of a homogeneous isotropic medium, and thus visible. To all high-order cylindrical waves, our numerical simulation suggests that the simplified cloak inherits some properties of the ideal cloak, but finite scatterings exist.

Fiber loop mirror-based optical transmissivity and optical phase retardation measurement architecture

We introduce and experimentally demonstrate a fiber-connectorized optical system based on the use of a fiber-loop mirror (FLM) to study both the optical transmissivity and the optical phase retardation of a material. Our approach to investigating the optical transmissivity of a test sample is by initially adjusting the optical powers at both FLM output ports to the extremum. A reference and the test sample are then placed one by one at one of the FLM output ports. For the optical phase retardation measurement, we propose placing a test sample inside the FLM and analyzing the ratio of the normalized optical powers from the two FLM output ports in order to eliminate the effect of unwanted optical losses. Our experimental proof of concept using three known zero-order wave plates as our test samples shows promising results that agree very well with our theoretical analysis. Key features include robustness, low optical loss, low polarization dependent loss, and ease of implementation.

Effect of a liquid on the characteristics of antisymmetric lamb waves in thin piezoelectric plates

The effect of a perfectly elastic nonviscous nonconducting liquid on the characteristics of a zero-order antisymmetric Lamb wave (the A 0 wave) in a 128YX LiNbO3 plate, whose thickness is small compared to the wavelength, is studied both theoretically and experimentally. A method for calculating the velocity and attenuation of this wave depending on the value of the parameter hf (h is the plate thickness and f is the wave frequency) is proposed. In addition, the characteristics of an A 0 wave in a piezoelectric plate that is in contact with two different perfectly elastic nonviscous nonconducting liquids on its two sides are investigated. A possibility for the development of a proximate analyzer of liquids on the basis of such a structure is indicated.

Relativistic corrections to the ground-state energy of the positronium molecule

The leading-order relativistic corrections to the ground-state energy of the positronium molecule $({\mathrm{Ps}}_{2})$ have been computed within the framework of perturbation theory. As the zero-order wave function we used a highly accurate nonrelativistic variational expansion in terms of 6000 explicitly correlated Gaussians that yielded the lowest variational upper bound for this system to date. We also report some expectation values representing the properties of ${\mathrm{Ps}}_{2}$.

Many-body calculation of helium1D–3D term intervals for 1snd(n = 12 ∼ 20) high Rydberg states

With many-body perturbation theory,1D–3D term intervals of helium 1snd (n = 12 ∼ 20) configurations are calculated. Based on two different models, Rayleigh-Schrodinger perturbation expansion terms consisting of bound states only, and those of continua are evaluated, respectively. As for bound states, zeroth-order wave functions are strictly generated from self-iteration solutions of the Hartree equation and residues of infinite expansion series are dealt with by the integral processing method, while a simplified hydrogen potential is adopted to get the continua. Using Rayleigh–Schrodinger expansions, we evaluate exchange energy up to third-order terms. It is found that level splittings are mainly attributed to summations over bound states. The fine-structure level splittings yielded here are found to agree quite well with experimental results.PACS Nos.: 31.15.Md, 32.10Fn, 02.60Ed

Band-structure results for elastic waves interpreted with multiple-scattering theory

The band-structure results for elastic wave propagating in a binary phononic crystal are analyzed by employing a multiple-scattering approach. It has been found that there are uncoupling effects at the high symmetry points of the Brillouin zone that open the spectral gaps. At the edge of the first band gap, a self-contained multiple scattering mode has been obtained which comprises only the zeroth-order cylindrical wave component. An analytic relationship for the beginning frequency of the first band gap has been obtained which comprises the periodic structural property and the Mie scattering of a single inclusion simultaneously. By graphic analytic method, the influence of these two properties were evaluated separately and combined.

Hartree−Fock−Heitler−London Method. 2. First and Second Row Diatomic Hydrides

The Hartree-Fock-Heitler-London, HF-HL, method is a new ab initio approach which variationally combines the Hartree-Fock, HF, and the Heitler-London, HL, approximations, yielding correct dissociation products. Furthermore, the new method accounts for nondynamical correlation and explicitly considers avoided crossing. With the HF-HL model we compute the ground-state potential energy curves for H2 [1Sigma+g], LiH [X 1Sigma+], BeH [2Sigma+], BH [1Sigma+], CH [2Pi], NH [3Sigma-], OH [2Pi], and FH [1Sigma+], obtaining in average 80% of the experimental binding energy with a correct representation of bond breaking. Inclusion of ionic configurations improves the computed binding energy. The computed dipole moment is in agreement with laboratory data. The dynamical and nondynamical correlation energies for atomic and molecular systems with 2-10 electrons are analyzed. For BeH the avoided crossing of the two lowest [2Sigma+] states is considered in detail. The HF-HL function is proposed as the zero-order reference wave function for molecular systems. To account for the dynamical correlation energy a post-HF-HL technique based on multiconfiguration expansions is presented. We have computed the potential energy curves for H2 [1Sigma+g], HeH [2Sigma+], LiH [X1Sigma+], LiH [A1Sigma+], and BeH [2Sigma+]. The corresponding computed binding energies are 109.26 (109.48), 0.01 (0.01), 57.68 (58.00), 24.19 (24.82), and 49.61 (49.83) kcal/mol, with the experimental values given in parentheses. The corresponding total energies are -1.1741, -3.4035, -8.0695, -7.9446, and -15.2452 hartrees, respectively, the best ab initio variational published calculations, H2 excluded.

A convenient decontraction procedure of internally contracted state-specific multireference algorithms

Internally contracted state-specific multireference (MR) algorithms, either perturbative such as CASPT2 or NEVPT2, or nonperturbative such as contracted MR configuration interaction or MR coupled cluster, are computationally efficient but they may suffer from the internal contraction of the wave function in the reference space. The use of a low dimensional multistate model space only offers limited flexibility and is not always practicable. The present paper suggests a convenient state-specific procedure to decontract the reference part of the wave function from a series of state-specific calculations using slightly perturbed zero-order wave functions. The method provides an orthogonal valence bond reading of the ground state and an effective valence Hamiltonian, the excited roots of which are shown to be relevant. The orthogonal valence bond functions can be considered quasidiabatic states and the effective valence Hamiltonian gives therefore the quasidiabatic energies and the electronic coupling among the quasidiabatic states. The efficiency of the method is illustrated in two case problems where the dynamical correlation plays a crucial role, namely, the LiF neutral/ionic avoided crossing and the F(2) ground state wave function.

Diffraction of a convergent sound wave by an elastic cylindrical shell with a longitudinal fixation

The problem of the diffraction of a zero-order convergent cylindrical wave by a cylindrical shell with a longitudinal fixation along one of its generatrices is considered. The problem is solved on the basis of using the so-called helical waves, which are aperiodic eigensolutions to the equations of the shell motion. The diffraction field is represented in the form of a convergent series in cylindrical harmonics. The method of the solution allows for a generalization to several cases of longitudinal fixation with conditions of different forms. The calculation of the scattering amplitude of the diffraction field is carried out for various frequencies and shell parameters.

Scaling laws for the critical rupture thickness of common thin films

Despite decades of experimental and theoretical investigation on thin films, considerable uncertainty exists in the prediction of their critical rupture thickness. According to the spontaneous rupture mechanism, common thin films become unstable when capillary waves at the interfaces begin to grow. In a horizontal film with symmetry at the midplane, unstable waves from adjacent interfaces grow towards the center of the film. As the film drains and becomes thinner, unstable waves osculate and cause the film to rupture. Uncertainty stems from a number of sources including the theories used to predict film drainage and corrugation growth dynamics. In the early studies, the linear stability of small amplitude waves was investigated in the context of the quasi-static approximation in which the dynamics of wave growth and film thinning are separated. The zeroth order wave growth equation of Vrij predicts faster wave growth rates than the first order equation derived by Sharma and Ruckenstein. It has been demonstrated in an accompanying paper that film drainage rates and times measured by numerous investigations are bounded by the predictions of the Reynolds equation and the more recent theory of Manev, Tsekov, and Radoev. Solutions to combinations of these equations yield simple scaling laws which should bound the critical rupture thickness of foam and emulsion films. In this paper, critical thickness measurements reported in the literature are compared to predictions from the bounding scaling equations and it is shown that the retarded Hamaker constants derived from approximate Lifshitz theory underestimate the critical thickness of foam and emulsion films. The non-retarded Hamaker constant more adequately bounds the critical thickness measurements over the entire range of film radii reported in the literature. This result reinforces observations made by other independent researchers that interfacial interactions in flexible liquid films are not adequately represented by the retarded Hamaker constant obtained from Lifshitz theory and that the interactions become significant at much greater separations than previously thought.

Calculation of helium 1D—3D term intervals for 1snd(n=4—11) states

With many-body perturbation theory (MBPT), 1D—3D term intervals of helium 1snd(n=4—11) configurations have been calculated. Based on two different models, Rayleigh-Schrdinger perturbation expansion terms only consisting of bound states and those of continua are calculated respectively. For bound states, the zeroth-order wave functions are strictly generated from self-iteration solutions of Hartree equation and residues of infinite perturbation series are dealt with by integral processing method. For continuum parts, a simplified hydrogen potential model is adopted. According to Rayleigh-Schrdinger expansion, the perturbation corrections to Rydberg states have been evaluated up to the third-order terms. From the calculation, the energy splittings are mainly attributed to bound parts. Singlet-triplet level splittings yielded here are found to agree quite well with two sets of experimental results.

A local approach to delocalized electronic systems: semilocal evaluation of the cohesive energies of tight-binding Hamiltonians.

Starting from strongly localized N-electron functions built from either pure atomic orbitals or fully localized bond molecular orbitals, it is possible to evaluate the ground state energy of a periodic lattice ruled by a tight-binding Hamiltonian without explicitly introducing the monoelectronic crystal orbitals. The method consists of a self-consistent perturbation of the zeroth-order wave function which incorporates high order effects and offers reasonable convergence properties. Along this framework, a single variable per bond type is introduced, namely the amplitude of the charge transfer. The method leads to a set of coupled equations which can be numerically solved, if not analytically. Short-range delocalization effects under periodic conditions are explicitly taken into account and relatively accurate cohesive energies are estimated for regular homoatomic and heteroatomic one-dimensional chains as well as for honeycomb lattices. In addition, good agreement with experiment for the distortion amplitude in polyacetylene is obtained. This exploratory tool may be easily extended to more sophisticated Hamiltonians, for which the solutions are not accessible. Since our approach only introduces short-range delocalization effects, its performance questions the importance of the specifically collective delocalization effects.

An application of second-order n-electron valence state perturbation theory to the calculation of excited states

n–electron valence state perturbation theory (NEVPT) is a form of multireference perturbation theory where all the zero-order wave functions are of multireference nature, being generated as eigenfunctions of a two–electron model Hamiltonian. The absence of intruder states makes NEVPT an interesting choice for the calculation of electronically excited states. Test calculations have been performed on several valence and Rydberg transitions for the formaldehyde and acetone molecules; the results are in good accordance with the best calculations and with the existing experimental data.

In Pursuit of the Elusive Bond-Stretch Isomers by ab Initio MethodsBenzocyclobutene, Benzo[1,2:4,5]dicyclobutadiene, and Some Related Substituted Systems

The problem of bond-stretch isomerism in benzocyclobutene (1) and benzo[1,2:4,5]- dicyclobutadiene is addressed by single-state (SS-CASSCF and SS-CASPT2) as well by two-state (TWS-CASSCF and TWS-CASPT2) theoretical formalisms. It is shown beyond reasonable doubt that benzocyclobutene 1 does not exhibit bond-stretch isomerism. The situation is more complex and interesting in the case of benzo[1,2:4,5]-dicyclobutadiene. The TWS-CASPT2 ( π ) + σ approach, based on the TWS-CASSCF(10,10) π zeroth-order wave function, yields two bond-stretch isomers 2 and 3. Their total energies, including the ZPVE contributions, indicate that the structure 3 is slightly favored. Because they are separated by an almost vanishing potential energy barrier (0.4-1.0 kcal/mol), it is concluded that 3 prevails and that bond-stretch isomerism probably does not occur in the case of benzo[1,2:4,5]dicyclobutadiene either. However, the final asnwer will be given only by high level multireference (MR) ab initio calculations. It is important to stress that 3 exhibits a pattern of 10π electrons fully delocalized over the CC bonds of the molecular perimeter and thus represents a planar pseudo-[10]annulene system par excellence. Finally, it is argued that strategic substitution of benzo[1,2:4,5]-dicyclobutadiene might lead to a discrimination of the isomers 2 and 3 and to the isolation of some judiciously selected derivatives in the laboratory. In particular, it is shown that a number of substituted pseudo-[10]annulene systems are possible.

Lower bounds to the dynamic dipole polarizability of beryllium

Hylleraas and Weinhold lower bounds to the frequency dependent dipole polarizability of beryllium atom in the ground state are computed by using exponentially correlated Gaussian wave functions. While Hylleraas approach requires the knowledge of the exact unperturbed wave function Ψ (0), the Weinhold formulae account for the errors in the approximated zero-order wave function Ψ ̃ (0) as measured by the overlap 〈Ψ (0)| Ψ ̃ (0)〉 . Accurate unperturbed wave functions employed in this calculations give, as a by-product, the lowest up to date variational energies of the 2 1S, 3 1S, and 4 1S states.

Perturbative corrections to the equation-of-motion spin–flip self-consistent field model: Application to bond-breaking and equilibrium properties of diradicals

We present perturbative corrections to a recently introduced spin–flip self-consistent field (SF-SCF) wave function. The spin–flip model describes both closed and open shell singlet states within a single reference formalism as spin–flipping, e.g., α→β, excitations from a triplet (Ms=1) reference state for which both dynamical and nondynamical correlation effects are much smaller than for the corresponding singlet state. The simplest spin–flip model employs a SCF wave function for the reference state, and the resulting equations for target states are therefore identical to configuration interaction singles (in spin–orbital form). While being a qualitatively correct zero-order wave function, SF-SCF should be augmented by dynamical correlation corrections to achieve a quantitative accuracy. The results demonstrate that the second-order approximation to the more theoretically complete spin–flip coupled-cluster model (truncated at double substitutions) represents a systematic improvement over the SF-SCF model.