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The nanonewton force facility of Physikalisch-Technische Bundesanstalt (PTB), Germany, has been significantly improved. We demonstrate the possibility of using the facility as a calibration device that can accurately determine spring constants of soft cantilevers ( $k ) with traceability to the SI units. This paper is described the possibility of increasing the range of the measured forces to 1 mN. We demonstrate the possibility of using PTB’s nanonewton force facility to accurately determine and compensate for the contact potential difference. To measure the contact potential difference and at the same time the distance between a force sensor and a measured object, a new three-voltage method was developed. For a so-called “plan–plan geometry,” the results of measuring the contact potential difference and the distance in vacuum are presented. A new method of adjusting the parallelism of the plates is also presented. The method used to measure the negative light pressure (light-induced force), which had previously been only theoretically predicted, and the first results of the measurement are presented as well.

The PTB's (Physikalisch-Technische Bundesanstalt, Germany) nanonewton force facility, first presented in work by Nesterov (2007 Meas. Sci. Technol. 18 360–6), Nesterov (2009 Meas. Sci. Technol. 20 084012) and Nesterov et al (2009 Metrologia 46 277–82), has been significantly improved and used to measure the stiffness of a cantilever. The facility is based on a disc pendulum with electrostatic reduction of its deflection and stiffness. In this paper, we will demonstrate that the facility is able to measure horizontal forces in the range below 1 μN with a resolution below 5 pN and an uncertainty below 2.7% for a measured force of 1 nN at a measurement duration of about 20 s. We will demonstrate the possibility of using this facility as a calibration device that can accurately determine spring constants of soft cantilevers (K 0.1 N m−1) with traceability to the SI units. The method and the results of measuring the spring constant of a soft cantilever (K = 0.125 N m−1) in air, in a medium vacuum, in a high vacuum and in nitrogen are presented. We will show that a relative standard uncertainty of the spring constant calibration of better than 0.3% (measurement in a medium vacuum) and a repeatability of better than 0.04% are achieved.

The nanonewton force facility of PTB (Physikalisch-Technische Bundesanstalt, Germany), first presented in [1]–[3], has been significantly improved. In this work, we will demonstrate that the facility is able to measure forces in the range below $1\ \mu \text{N}$ with a resolution below 5 pN and an uncertainty below 2.7 % for a measured force of 1 nN at a measuring duration of about 20 s. We will demonstrate the use of the facility as a calibration device. We will also present measurements methods and the results for the spring constant of a cantilever, the contact potential difference and the negative light pressure.

The attractive plasmon force between two metallic walls when the electromagnetic wave propagates through a narrow slit has been studied earlier for parallel plates and normal incidence. In present paper the effects of imperfect adjustment of plates and laser beam are analyzed. The change of force for non-parallel plates is shown to be of the first order in inclination angle when the wedge is along wave propagation and of the second order for transverse case. The small incidence angle leads to decrease in force due to the antisymmetric waveguide mode appearing in the slit., Comment: 5 figures

For numerous applications in science and engineering, the development of technologies for assembling and manipulating macro-, micro-, and nano-objects by means of laser light is of high interest. Most of these attractive forces require dielectric particles they can act on. In recently published papers, a negative light pressure was predicted which acts on metallic bodies if these are separated by a subwavelength slit and which arises from surface plasmon interaction between the metallic bodies1,2. An experimental demonstration of this force has not yet been carried out. First theoretical calculations showed that, for example, a laser power of 100 mW which is fully absorbed in the slit of a laser with a wavelength of 1550 nm would, in a slit having a width of half the wavelength, generate a force of about 1 nN. However, this is roughly three times the force of the radiation pressure of about 0.33 nN. In this work, we present an experimental setup to measure this force, together with results of refined theoretical calculations and with preliminary results achieved with the experimental setup.

In recent works, a novel light-induced attractive force was predicted between two metal plates. This force arises by the interaction of surface plasmons which are excited at the metal when a transverse magnetic mode propagates through a subwavelength slit between two metal bodies. In this paper, the analytical and numerical calculations of this magnetic field are presented for the perfect metal and for gold. The amplitude and the phase transient curves between the known limiting cases of narrow and wide slits compared to the wavelength are found. The curve is shown to oscillate due to the emergence of new waveguide modes. The analytic solution for the perfect metal is in agreement with the computation for gold by means of the finite element method. The simple asymptotic formula for the light-induced attractive force is found in the limit of a narrow slit.

The similarity between one-dimensional Schrodinger and Helmholtz equations is discussed. The Helmholtz equation in optical coordinate is shown to reduce to the Schrodinger equation with an effective potential. Two examples of scattering problem are considered: sinusoidal Bragg grating with deep modulation and smooth hyperbolic secant layer. The inverse scattering problem is solved numerically for both cases. For the layer an analytical solution is presented as well. The analysis of the effective potential allows one to qualitatively predict some properties of the reflection spectrum.

A one-dimensional inverse scattering problem for the Helmholtz wave equation is considered. The problem consists in reconstruction of the refractive index of transparent inhomogeneous media from a specified complex reflection spectrum. A method previously proposed by the authors for reconstruction of the Bragg gratings in the coupled mode approximation is used. Numerical simulations of the inverse scattering problem for the classical Rayleigh layer and for an exponentially smooth transitional layer are performed. The solutions obtained demonstrate the high efficiency of the proposed approach. The accuracy of refractive index reconstruction turns out to be essentially dependent on the degree of layer smoothness. The proposed approach can be applied in problems of the development of coated and interference optics, in synthesis of the Bragg gratings and multilayer optical mirrors, and in radiophysics and acoustics.

An optimal filter for super-fast fiber-optic communication lines should cause minimal phase distortions. The simplest case of Bragg grating with a symmetric profile is considered. A distortion functional is presented, which is the mean square group delay over the Bragg reflection band at a fixed integral reflectivity. The functional is minimized analytically in the simplest limiting case. Numerical calculations confirm that the optimal reflection spectrum is realizable.

Traditional algorithms for solving the inverse scattering problem for a fiber Bragg grating are described, and a new numerical method for this problem is developed. The method is based on the fast inversion of a matrix using its Toeplitz symmetry and on a special “inner-bordering” procedure. It is shown that the method is equally efficient as the well-known discrete layer peeling method but exceeds the latter in accuracy, especially for high-reflectance gratings. The stability of the proposed method with respect to initial data errors is demonstrated.

Sharp edges of the reflection spectrum of fiber Bragg gratings originate the group delay. As follows from the dispersion relations, the delay of the symmetric grating grows up with the second derivative of the reflectivity with respect to the frequency. The distortion functional is proposed for filter optimization. It is the mean square delay at fixed integral reflectivity. An analytic solution for filters with minimum distortion is obtained in the limit of weak grating.

The inverse scattering problem for fiber Bragg grating reconstruction becomes incorrect with an increasing level of noise in the input data or at a high reflection. The adaptive regularization procedure is proposed to restore the correctness and minimizing the reconstruction error. The proposed method is tested using numerical modeling with the Gaussian statistics of noise.

An analytic solution for Bragg grating with linear chirp in the form of confluent hypergeometric functions is analyzed in the asymptotic limit of long grating. Simple formulas for reflection coefficient and group delay are derived. The simplification makes it possible to analyze irregularities of the curves and suggest the ways of their suppression. It is shown that the increase in chirp at fixed other parameters decreases the oscillations in the group delay, but gains the oscillations in the reflection spectrum. The conclusions are in agreement with numerical calculations., 16 pages, 8 figures, submitted to Opt. Comm

The problem of data communication over a wavelength division multiplexing (WDM) high-data-rate communication link where wave division multiplexing is performed by using quasi-rectangular Bragg filters is studied numerically. It is shown that the optimisation of the mean dispersion of the link, the width and shape of the transfer function of filters provides the increase in the data communication range up to 1550 km.

The problem of probe-field spectrum is considered for a three-level ion placed in a field of an intense standing light wave. The ion interaction with plasma and the velocity-changing Coulomb scattering are taken into account within the weak-collision model. The system of kinetic equations for the density matrix is solved by the expansion in spatial harmonics and eigenfunctions of the collision operator. The profile of nonlinear addition to the probe-wave absorption is determined for various values of the effective ion-ion collision frequencies and various amplitudes and frequencies of standing wave. It is shown that the broadening of the central nonlinear structure in the spectrum is caused by the Coulomb dephasing effect. The computational results are in qualitative agreement with the available experimental data.

Conditions of origination of aeroacoustic resonance phenomena near an axisymmetric body in the form of a thick-walled tube in an air flow in a rectangular channel are studied experimentally. Dependences of the eigenfrequency of acoustic oscillations on the model length are determined. By studying the mechanism of origination of oscillations in the wake flow, it is shown that the process of generation of annular coherent structures in resonant regimes is characterized by evolution of nonlinearities including a subharmonic packet. Possible methods of flow control are discussed.

Single-frequency operation of a 1.03 μm fiber laser with random distributed feedback (RDFB) is demonstrated. The laser cavity is based on a 4 cm long fiber Bragg grating (FBG) consisting of 10 homogeneous subgratings with random phase and amplitude of refractive index modulation inscribed in a polarization maintaining (PM) Yb-doped fiber. Such RDFB laser generates single longitudinal mode with output power up to 25 mW, which is 3.5 times higher than that for a DFB laser based on regular π-shifted FBG of the same length in the same fiber. The single-frequency linewidth is measured to be

The scattering of evanescent wave, one of the main processes of nanophotonics, is studied in 2D geometry using boundary integral equations and special two-domain Green function. The problem is studied for a single, a pair, and a series of nanowires.

Two direct numerical methods of soving Gel'fand--Levitan--Marchenko equations are developed based on bordering procedure, hermiscity, Cholesky decomposistion, Toeplitz symmetry and piecewise-linear approximation. The proposed methods are shown to surpass the discrete layer peeling algorithm in accuracy and stability at high reflectance.

The accuracy of calculation of spectral line shapes in one-dimensional approximation is studied analytically in several limiting cases for arbitrary collision kernel and numerically in the rigid spheres model. It is shown that the deviation of the line profile is maximal in the center of the line in case of large perturber mass and intermediate values of collision frequency. For moderate masses of buffer molecules the error of one-dimensional approximation is found not to exceed 5%., Comment: LaTeX, 24 pages, 8 figures

A new numerical method is developed for solution of the Gel'fand - Levitan - Marchenko inverse scattering integral equations. The method is based on the fast inversion procedure of a Toeplitz Hermitian matrix and special bordering technique. The method is highly competitive with the known discrete layer peeling method in speed and exceeds it noticeably in accuracy at high reflectance., 18 pages, 6 figures

The ionic probe-field spectrum is calculated including scattering in plasma. The peak of higher spatial harmonics is shown to broaden due to Coulomb dephasing. Account of the saturation and population effects provides an agreement with experiment.

A new method to solve the direct Zakharov–Shabat scattering problem is proposed based on the solution for coupled Gel’fand–Levitan–Marchenko integral equations. Speedup of computations is achieved by using the Toplitz symmetry of the matrix and an “inner bordering” procedure. The new algorithm was tested on the exactly solvable potential. It is shown that the suggested algorithm significantly surpasses the traditional transfer matrix method in efficiency.

Coherent preparation of quantum states of atoms and ions by laser light can lead to electromagnetically induced transparency and related effects. In particular, the standing wave at the adjacent transition induces a new type of nonlinear resonance in the probe-field spectrum of a three-level system. The resonance is due to the effect of high-order harmonics of atomic coherence. However, the resonance is broadened and the reason of the broadening was unclear. The paper describes how the velocity changing collisions broaden the resonance. The analytic theory taking into account up to 4-th order of the perturbation theory is presented. The numerical calculations are described. The analytical formulas are shown to describe the experiment qualitatively while the numerical computation demonstrates quantitative agreement. The Coulomb dephasing is discussed as the physical mechanism of the broadening.

Two-dimensional problem of evanescent wave scattering by dielectric or metallic cylinders near the interface between two dielectric media is solved numerically by boundary integral equations method. A special Green function was proposed to avoid the infinite integration. A pattern with a circular and a prolate elliptic cylinders, respectively, is suggested to simulate the sample and the probe in near-field optical microscopy. The energy flux in the midplane of the probe-cylinder is calculated as a function of its position., Comment: 10 pages, 4 figures

The scattering of plane evanescent waves by a cylinder is studied. The Green function for the Helmholtz equation for two dielectrics with flat interface is found and applied for the numerical calculation of the scattered field by the boundary elements method. The Green function keeps close track of scattering, including multiple reflections. The result may be applicable for the data analysis in near-field optical microscopy.

The inverse scattering problem for the one-dimensional Helmholtz wave equation is studied. The equation is reduced to a Fresnel set that describes multiple bulk reflection and is similar to the coupled-wave equations. The inverse scattering problem is equivalent to coupled Gel'fand-Levitan-Marchenko integral equations. In the discrete representation its matrix has Töplitz symmetry, and the fast inner bordering method can be applied for its inversion. Previously the method was developed for the design of fiber Bragg gratings. The testing example of a short Bragg reflector with deep modulation demonstrates the high efficiency of refractive-index reconstruction.

We examine the problem of fiber Bragg grating reconstruction from its reflection coefficient. A direct numerical method of solving the Gel'fand-Levitan-Marchenko integral equations for the problem is developed. The method is based on a bordering procedure, Cholesky decomposition, and piecewise-linear approximation. It is tested using high-reflectance homogeneous and hyperbolic secant profiles. The proposed method is shown to concede the popular discrete layer peeling technique in efficiency but surpasses it in accuracy and stability at high reflectance.