Filter performance parameters for vectorial high-aperture wave fields

Performance parameters have been presented that can be used to compare the focusing performance of different optical systems, including the effect of pupil filters. These were originally given for the paraxial case and recently extended to the high-aperture scalar regime. We generalize these parameters to the full vectorial case for an aplanatic optical system illuminated by a plane-polarized wave. The behavior of different optical systems is compared.     

A non-relativistic wave equation of second order in time for scalar fields

In this paper a generalization of the traditional non-relativistic Schrödinger equation is considered. It is a wave equation of second order in time and fourth order in the space coordinates for scalar fields. The equation has certain features, which make it a closer analogue of the Klein-Gordon equation than the traditional Schrödinger equation. However, the equation maintains the non-relativistic relation between energy and momentum.The implications of this generalized wave equation and the quantized field theory based on it are studied. The theory can be shown to be charge symmetric and allows to introduce anti-particles and pair creation. We compare the Green functions for this theory with those of conventional non-relativistic quantum theory.The theory allows to formulate a transformation for charge conjugation. The PCT-theorem is valid for it. The usual spin-statistics connection holds.     

Raster method for recording optical wave fields

We propose a new method for recording the wave field. The method is based on that the angular spectrum of the field is modulated using an amplitude mask. It is shown that the new method ensures high spatial and angular resolutions. An optical scheme for implementing the method and an algorithm for reconstructing the wave-field phase from the measurement data are developed. Computer simulation of the experiment for recording the wave field on the basis of the proposed method is performed.     

Diffraction method for recording optical wave fields

We propose a method for recording an optical wave field that is based on diffraction of the optical wave field by two screens that are complementary to each other. We show that the new method ensures the measurement of the phase of the wave field with a high accuracy and spatial resolution. An optical scheme for implementing the diffraction method and an algorithm for reconstructing the phase of the wave field from the measurement data are developed. We perform a computer simulation of the experiment on recording the optical wave field based on the method proposed.     

Parabolic nondiffracting optical wave fields

We demonstrate the existence of parabolic beams that constitute the last member of the family of fundamental nondiffracting wave fields and determine their associated angular spectrum. Their transverse structure is described by parabolic cylinder functions, and contrary to Bessel or Mathieu beams their eigenvalue spectrum is continuous. Any nondiffracting beam can be constructed as a superposition of parabolic beams, since they form a complete orthogonal set of solutions of the Helmholtz equation. A novel class of traveling parabolic waves is also introduced for the first time.     

Foundations of the unified theory of gravitational,electromagnetic, and scalar fields

A particular case of bimetrical unified field theory is considered, which is based on Hilbert's proposal of obtaining a complete system of independent equations for unified theory. The action depends on two symmetrical tensors g_μν and g _μν ^° , the second leading to a zero curvature tensor, which results in the theory being invariant under the Poincaré group, and in ten conservation laws. The field equations obtained when varying the action with respect to g_μν have the form of Einstein equations whose righthand side is not defined independently, but is rather a function of g_μν and g _μν ^° . The vector and scalar gauge transformations corresponding to variations δS of special form are defined. With the aid of these transformations, the electromagnetic and scalar fields are introduced within the framework of the unified theory. The basic equations of the theory under consideration contain a new dimensional physical constant, which connects gravitation and electromagnetism. A numerical estimate of this constant is given.     

A Jost-Schroer theorem for string fields

It is shown that the truncated Wightman functions of three or more string-localized fields vanish if they are solutions of a Klein-Gordon equation in each variable. As an application it is shown that a string field is a free field if its two-point functions are those of a free field. Another application to perturbation theory is pointed out.     

Dynamic shaping of vectorial optical fields based on two-dimensional blazed holographic grating

We propose a vectorial optical field generation system based on two-dimensional blazed grating to high-efficiently generate structured optical fields with prescribed amplitude, phase, and polarization. In this system, an optimized blazed grating hologram is written on a spatial light modulator(SLM) and can diffract the majority of the incident light into the first-order diffractions of the x and y directions, which then serve as base vectors for synthesizing desired vector beams.Compared with the conventional cosine grating used in the previous work, the proposed two-dimensional, blazed grating has a much higher efficiency. Both computer simulation and optical experiment validate that a conversion efficiency up to 5 times that of the former work is achieved. Our method can facilitate applications of the optical field manipulation.     

A grand unified wave function

A variant of wave functions describing all fundamental fermions (quarks and leptons) is presented. It represents a peculiar pattern of generations, of which the first consists of (v_e, e, u, d; v_μ, μ, c, s) and the second contains quarks and leptons with unorthodox electric charges as well as τ, v_τand b.     

Analytical solution of the scalar wave equation for slightly deformed optical Bragg waveguide

Using a simple analytical method, we study the electromagnetic-wave propagation in an optical Bragg waveguide which is slightly deformed at one side. We show the results of computations in the form of dispersion curves and provide a comparison with standard circular Bragg waveguides and step-index circular waveguides. We show that the correspondence between the cutoff V values for the standard step-index fiber and the new Bragg waveguide, which is slightly flattened on one side, is quite close for the lowest mode under the weak guidance condition.     

A commutation theorem and duality for free Bose fields

We first present an elementary commutation theorem for operator algebras on Hilbert space. This theorem is then applied to give an elementary proof of duality for free Bose fields.     

A pinching theorem for the normal scalar curvature of invariant submanifolds

We prove some inequalities relating intrinsic and extrinsic curvature invariants for invariant submanifolds of Kaehlerian and Sasakian space forms. When we restrict to invariant submanifolds of odd-dimensional unit spheres or invariant submanifolds of complex Euclidean space, one of the inequalities gives a positive answer to a conjecture, proposed in [P.J. De Smet, F. Dillen, L. Verstraelen, L. Vrancken, A pointwise inequality in submanifold theory, Arch. Math. (Brno) 35 (1999) 115–128].     

Field-dependent coupling strength for scalar fields

Effective Lagrangians with a nonlinear coupling between the scalar density of the nucleons and the scalar meson field are investigated within the framework of relativistic mean-field theories. This phenomenological coupling acts as a field-dependent coupling strength and is supposed to take into account renormalization effects within a mean-field picture. The parameters of the model are adjusted to saturation properties of nuclear matter and predictions for the real part of the optical potential are compared with experimental data. For that relativistic and nonrelativistic optical model fits are examined and an experimental standard is deduced which covers the energy range from ? 50 MeV to 1000 MeV. A definition for the real part of the optical potential is given which is not linear in the energy but has the proper limits for momentum zero and infinity. It is shown that for a special choice of the field-dependent coupling strength the meanfield theory can describe the nuclear equation of state and the momentum dependence of the single particle energy without further parameters up to momenta where the intrinsic structure of nucleon becomes relevant.     

Variational principle and limit relations in the unified theory of gravitational,electromagnetic, and scalar fields

Within the framework of a special version of unified bimetrical field theory [1], starting from the explicit form of the Lagrangian L, the principal expressions are derived: the field equations, the energy-momentum tensor, the generalized equations of electrodynamics, the conservation laws. Various limiting cases are considered. It is shown that the equations for the electromagnetic field can be obtained as a consequence of the conservation law for the energy-momentum of the unified field.     

Geometric phases for scalar wave superpositions

Geometric phases are defined for superpositions of scalar waves of various nature. The geometric phases possess similar properties to those of polarized light wave ones, but require a different parametric space. An appropriate parametric space is constructed on the basis of a modified Poincaré sphere. An example considering spherical scalar waves is presented.     

Hamiltonian and recursion operators for two-dimensional scalar fields

The equation for the Noether operator is obtained. It gives the necessary conditions for complete integrability of the field equations. For several double-component models the Hamiltonian pairs and the recursion operators are presented.     

Retrieval of Green's function and generalized optical theorem for the scattering of complete dyadic fields

Green's function retrieval has been widely used in different research fields due to the fact that the Green's function can be extracted by cross-correlating the records at two receivers. In this paper, the retrieval of the dyadic Green's function is studied by investigating the representation theorem. The generalized optical theorem for the dyadic fields is derived based on the elastic dynamic interferometric equation. By addressing the cross-correlation recorded at two receivers, the important role of the generalized optical theorem and energy equipartition in retrieving the exact Green's function is shown. The presented derivation also shows the Newton-Marchenko equation holdsif the condition of equipartition is not satisfied.