Correlation between optical and topographical images from an external reflection near-field microscope with shear force feedback

An external reflection scanning near-field optical microscope with shear force regulation of the tip-surface distance is described. Near-field optical and shear force topographical images are compared for various samples. It is shown that the most important correlative relationships between these images can be deduced from symmetry considerations. The possibility of extracting additional information from the optical images is demonstrated on images of human blood cells.     

Symmetry considerations in CdSe nanocrystals

Semiconductor nanocrystals or quantum dots show a wide range of physical properties depending on their size or shape. In this paper, we show that symmetry is also an important characteristic that can lead to different electronic and optical properties. We use pseudopotential density-functional theory, within a real space approach, and address the sensitivity of electronic and optical properties with respect to the symmetry point groups associated to CdSe nanocrystals.     

Description of the third-order optical aberrations of near-circular pupil optical systems without symmetry

Many authors, dating back to at least the 1950s, have presented mathematical expansions of the wave-front aberration function for optical systems without symmetry, typically based on limiting assumptions and simplifications, with some of the most recent work being done by Howard and Stone [Appl. Opt. 39, 3232 (2000)]. This paper reveals that in fact there are no new aberrations in imaging optical systems with near-circular aperture stops but otherwise without symmetry. What does occur is that the field dependence of an aberration often changes when symmetry is abandoned. Each aberration type develops a characteristic field behavior in a system without symmetry. Specifically, for example, astigmatism, develops a binodal field dependence; e.g., there are typically two points in the field with zero astigmatism, and typically neither point is on axis. This construct, nodal aberration theory, for understanding the aberrations in systems without symmetry becomes a direct extension of an optical designer's knowledge base. Through the use of real ray-based analysis methods, such as Zernike coefficients, it is possible to understand completely the aberrations of optical systems without symmetry in terms of rotationally symmetric aberration theory with the simple addition of the concept of field nodes.     

Optical symmetry filtering by use of anisotropic self-diffraction in BaTiO3 crystals

We propose what we believe to be a novel and simple method for optical symmetry filtering, using anisotropic self-diffraction in BaTiO(3) crystals. This method allows us to distinguish a centrosymmetric pattern from a noncentrosymmetric pattern easily with scale invariance. It is self-referential; no extra reference element is required. Both the theory and the experiment are demonstrated.     

Optical Bistability and Reversed Switching Effect in a Three-photon Resonant Medium

We have developed, ab initio, a theory for the interaction of coherent laser light in three-photon resonance with two effective levels of a multilevel atom. The theory is developed to consider the optical bistability of homogeneously broadened, three-photon, resonant multilevel atoms inside a ring cavity. It is shown that optical bistable behaviour in the fundamental and the generated third harmonic can be obtained using, for example, Na atoms. The device may be useful in constructing two-channel, optical bistable switches. In certain nonlinear regimes it may be possible to obtain reversed switching between the fundamental and the third harmonic bistability.     

Polarization dependence of two-photon absorption in an AlGaAs waveguide autocorrelator

We have obtained the complete polarization dependence of the two-photon absorption coefficient beta by measuring the orientational dependence and the contrast ratio of the photocurrent in an Al(0.2) Ga(0.8) As waveguide autocorrelator at an optical frequency far above the half-bandgap. The measured polarization dependence is consistent with theory and previous picosecond nonlinear transmission experiments. The cubic symmetry of the nonlinearity provides a contrast ratio that exceeds 2, which is larger than would be obtained assuming an isotropic medium and Kleinmann symmetry. This device was used to obtain an autocorrelation of a mode-locked Nd:YLF laser.     

Independent electromagnetic optimization of the two coating thicknesses of a dielectric layer on the facets of an echelle grating in Littrow mount

Abstract

Electromagnetic investigations using the integral equation system method with parametrization (IESMP) show that the two-coating thicknesses of a dielectric layer on the facets of an echelle grating in a Littrow mount have to be independently optimized. While the optimal coating thickness on the blaze facet is the same for maximal efficiency and minimal absorption in both polarizations, this is not the case for the anti-blaze facet. Therefore, it is only possible to optimize the two-coating thicknesses for one of the purposes. On the blaze facet, a simple formula based on thin-film optical considerations describes the optimal thickness very well. Additionally, we found that resonance anomalies can significantly reduce efficiency if the wrong coating thickness is used on the anti-blaze facet. The coating thickness creating the resonance anomaly can be deduced by investigating the poles of the reflection coefficient of a dielectric coated metallic mirror in grazing incidence. This value can be used to optimize the layer for maximal efficiency. Consequently, we are generally able to describe the optimal coating thicknesses for minimal absorption as well as for maximum efficiency in both, TE- and TM-polarization, using only thin-film optical considerations without any further rigorous calculation.     

Strong thermoelastic and temperature waves in crystalline lattice

We analyze essentially nonlinear system of acoustical and optical vibrations of a complex crystalline lattice consisting of two sublattices. The theory generalizes the Karman–Born–Huang linear theory which prescribes acoustic and optical modes of deformations of the complex lattice. The nonlinear version of the Karman–Born–Huang theory is developed by introducing nonlinear interacting periodic forces between sublattices due to an internal transmitting symmetry in displacement of sublattices for one period and more. Correspondent coupled nonlinear dynamic equations admit large displacements of atoms up to loss of the structural stability and cardinal lattice rearrangement under action of an external force and thermal loads. Moreover, thermal flows interact with acoustic and optical waves, and unusual fast speed temperature waves take place.     

Uniform-load and actuator influence functions of a thin or thick annular mirror: application to active mirror support optimization

Explicit analytical expressions are derived for the elastic deformation of a thin or thick mirror of uniform thickness and with a central hole. Thin-plate theory is used to derive the general influence function, caused by uniform and/or discrete loads, for a mirror supported by discrete points. No symmetry considerations of the locations of the points constrain the model. An estimate of the effect of the shear forces is added to the previous pure bending model to take into account the effect of the mirror thickness. Two particular cases of general influence are considered: the actuator influence function and the uniform-load (equivalent to gravity in the case of a thin mirror) influence function for a ring support of k discrete points with k-fold symmetry. The influence of the size of the support pads is studied. A method for optimizing an active mirror cell is presented that couples the minimization of the gravity influence function with the optimization of the combined actuator influence functions to fit low-order aberrations. These low-spatial-frequency aberrations can be of elastic or optical origin. In the latter case they are due, for example, to great residual polishing errors corresponding to the soft polishing specifications relaxed for cost reductions. Results show that the correction range of the active cell can thus be noticeably enlarged, compared with an active cell designed as a passive cell, i.e., by minimizing only the deflection under gravitational loading. In the example treated here of the European Southern Observatory's New Technology Telescope I show that the active correction range can be enlarged by ~50% in the case of third-order astigmatic correction.     

Exact solution of Eshelby–Christensen problem in gradient elasticity for composites with spherical inclusions

The gradient elasticity theory is employed to solve exactly the problem of Eshelby–Christensen for filled composites with spherical inclusions across length scales. Relying on the fundamental symmetry considerations and using Lagrange’s variational formalism, we derive the governing relations of linear isotropic gradient elasticity. We demonstrate that to avoid spurious solutions, one should necessarily impose some additional symmetry restrictions on the operational strain gradient elastic constants that can be considered as a new correctness condition. By enforcing the “strain gradient” symmetry condition, we offer the variant of the correct applied one-parametric gradient theory of interfacial layer model. To solve the Eshelby–Christensen problem, we employ the generalized Eshelby’s integral representations for the gradient elasticity models that allow to formulate the closing equations in a self-consistent three-phase method, and we also use the generalized Papkovich–Neuber representation to determine the general form of the gradient solution and the structure of the scale effects. As a result, we obtained for the first time an exact solution of Eshelby–Christensen problem for composites reinforced with spherical inclusions in framework of the gradient interfacial layer model. There are known analogs of fundamental results for gradient models related to closed solution for composites with spherical inclusions obtained by R.M. Christensen and K.H. Lo in 1976. The obtained analytical solution of Eshelby–Christensen problem for correct gradient theory is used to determine the stress–strain state and the effective properties of dispersed composites. The analysis of the effect of scale factors is given; the error associated with the use of gradient theories that do not obey the proposed condition of correctness is estimated.     

Exact block diagonalization of large eigenvalue problems for structures with symmetry

We consider large eigenvalue problems for skeletal structures with symmetry. We present an algorithm, based upon a novel combination of group-theoretic ideas and substructuring techniques, that block-diagonalizes such systems exactly and efficiently. The procedure requires only the structural matrices of a repeating substructure, together with the symmetry modes, which are obtained from symmetry considerations alone. We first present a simple paradigmatic example and then follow with several non-trivial applications involving large lattice structures.     

A new method of dark resonance excitation on D<Subscript>2</Subscript> line in <Superscript>87</Superscript>Rb vapor

A new method based on optical pumping is proposed for increasing the parameters of dark resonance excitation on D ₂ line in ⁸⁷Rb vapor. The pumping is provided by linearly polarized two-frequency laser radiation propagating in the direction perpendicular to the probing field directed along the cell with atomic rubidium vapor. This method significantly improves the dark resonance parameters as compared to the case of pumping by a circularly polarized field. Qualitative considerations are confirmed by the results of numerical calculations.     

Graphene–Gold Nano-ring antenna for Dual-resonance optical application

To achieve dual resonance qualification, we are suggested a sub-wavelength dual-ring Nano-antenna based on combination of Graphene and gold where Nano-Antenna with dual-resonance is attractive for spectroscopy and bio-sensing applications. The result shows that with these structures, we could be achieved dual-resonance characteristic of Infra red (IR) and optical regime. In addition, by biasing of the Graphene, we are attained a reconfigurable characteristic for our second resonance. Therefore, in this current research, the extinction, reflection and absorption cross section are studied for every structure and formation. For modeling the prototype Nano-antenna, SiN Substrate is selected with refractive index of 1.98 and silver with Palik optical characteristic for metal layer is modified. Simulation has been done with FDTD method. Of course, because of symmetry of the structure, the prototype Nano-antenna has similar manner for vertical or horizontal polarization. As a result, proposed Nano-antenna is useful for THz medical spectroscopy with simple method of designing and second frequency controlling only with graphene biasing. Here, we are debated about graphene placement and biasing interaction on the bonding and anti-bonding mode where we show that the gold and graphene interaction will affect on E-field distribution by making dipole or quad resonance.     

Graded-index fiber lens proposed for ultrasmall probes used in biomedical imaging

The quality and parameters of probing optical beams are extremely important in biomedical imaging systems both for image quality and light coupling efficiency considerations. For example, the shape, size, focal position, and focal range of such beams could have a great impact on the lateral resolution, penetration depth, and signal-to-noise ratio of the image in optical coherence tomography. We present a beam profile characterization of different variations of graded-index (GRIN) fiber lenses, which were recently proposed for biomedical imaging probes. Those GRIN lens modules are made of a single mode fiber and a GRIN fiber lens with or without a fiber spacer between them. We discuss theoretical analysis methods, fabrication techniques, and measured performance compared with theory.     

Imaging the hidden modes of ultrathin plasmonic strip antennas by cathodoluminescence

We perform spectrally resolved cathodoluminescence (CL) imaging nanoscopy using a 30 keV electron beam to identify the resonant modes of an ultrathin (20 nm), laterally tapered plasmonic Ag nanostrip antenna. We resolve with deep-subwavelength resolution four antenna resonances (resonance orders m = 2-5) that are ascribed to surface plasmon polariton standing waves that are confined on the strip. We map the local density of states on the strip surface and show that it has contributions from symmetric and antisymmetric surface plasmon polariton modes, each with a very different mode index. This work illustrates the power of CL experiments that can visualize hidden modes that for symmetry reasons have been elusive in optical light scattering experiments.     

Bifurcations in dynamical systems with interior symmetry

We propose a definition of interior symmetry in the context of general dynamical systems. This concept appeared originally in the theory of coupled cell networks, as a generalization of the idea of symmetry of a network. The notion of interior symmetry introduced here can be seen as a special form of forced symmetry breaking of an equivariant system of differential equations. Indeed, we show that a dynamical system with interior symmetry can be written as the sum of an equivariant system and a ‘perturbation term’ which completely breaks the symmetry. Nonetheless, the resulting dynamical system still retains an important feature common to systems with symmetry, namely, the existence of flow-invariant subspaces. We define interior symmetry breaking bifurcations in analogy with the definition of symmetry breaking bifurcation from equivariant bifurcation theory and study the codimension one steady-state and Hopf bifurcations. Our main result is the full analogues of the well-known Equivariant Branching Lemma and the Equivariant Hopf Theorem from the bifurcation theory of equivariant dynamical systems in the context of interior symmetry breaking bifurcations.     

Analysis of Inhomogeneous Optical Systems by the Use of Ray Tracing. II. Three-dimensional Systems with Symmetry

We describe a new approach to the index reconstruction of three-dimensional optical systems with rotational symmetry, which is based on sampling ray paths that lie in the sagittal plane. Since the observed rays are distorted by the optical system itself, they cannot be used directly for index reconstruction. We present an iterative procedure to compute the true ray paths and then to find the index distribution. The utility of the method is verified on the model problem.     

Quantitative modelling of the surface plasmon resonances of metal nanoclusters sandwiched between dielectric layers: the influence of nanocluster size, shape and organization

The effects of size, shape and organization on the surface plasmon resonances of Ag nanoclusters sandwiched between Si(3)N(4) layers are studied by transmission electron microscopy and anisotropic spectroscopic ellipsometry. We present an easy-to-handle model that quantitatively links the nanostructure and optical response of the films, which are considered as dielectric/metal:dielectric/dielectric trilayers, with the central nanocomposite layer being an effective medium whose optical properties are described by an anisotropic dielectric tensor. The components of this tensor are calculated using a generalization of the Yamaguchi theory taking into account the real organization, size and shape distributions of ellipsoidal nanoclusters, whose electronic properties are assumed to reflect shape-dependent finite size effects. Using this model, it is shown that the optical response of the films in the visible range is dominated by the excitation of the surface plasmon resonance of the clusters along their in-plane long axis, while no surface plasmon resonance resulting from an excitation along their in-plane short axis can be observed due to damping effects. Moreover, the spectral position of this resonance appears to be mainly affected by the average shape of the clusters, and weakly by their size, their shape distribution and the electromagnetic interaction between them.     

Dispersive mirror in AlGaAs designed by inverse spectral theory

We introduce a new mathematical method, based on the inverse spectral theory of Gel'fand and Levitan, of designing dispersive coatings for use in femtosecond lasers. We fabricated an example in AlGaAs by metal-organic chemical-vapor deposition. The mirror has a high value of group delay dispersion over a bandwidth of 10 nm, reaching an extreme of -1200 fs(2) at the center (805 nm) and falling to -800 fs(2) at the edge of this range. In the same band the reflectivity remains over 95%. We created the design by identifying parameters in the spectral domain, numerically optimizing these parameters, and solving the resulting inverse problem to recover the refractive-index profile. Because we performed the optimization in the spectral domain, we needed only four parameters to obtain a good result. Numerical analysis shows that the excess optical delay at the red end of the stop band can be achieved by use of a mild optical resonance, with the optical field approximately twice the magnitude of that at the blue end.