Formation of required distributions on the basis of decomposition by vortex eigen functions of a bounded non-paraxial propagation operator

The solution of the problem of overcoming the diffraction limit based on the representation of an optical signal in the form of a superposition of communication modes matched with the vortex eigenfunctions of a bounded (in the object and spectral regions) nonparaxial propagation operator in free space is considered. Nonparaxial propagation of laser beams is described using an expansion in terms of conic waves based on the m-th order Fourier-Hankel transform. The eigenfunctions of such an operator, which have near-unity eigenvalues, determine the number of degrees of freedom and characteristics of an optical signal transmitted without distortion over a given distance. Based on the considered approach, a parametric method was developed for solving the inverse diffraction problem, including overcoming the diffraction limit.

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Topologically protected optical signal processing using parity–time-symmetric oscillation quenching

Nanophotonics ◽

10.1515/nanoph-2021-0215 ◽

2021 ◽

Vol 0 (0) ◽

Author(s):

Sunkyu Yu ◽

Xianji Piao ◽

Namkyoo Park

Keyword(s):

Signal Processing ◽

Degrees Of Freedom ◽

Quantum Hall ◽

Optical Signal ◽

Pt Symmetry ◽

Coupled Systems ◽

Fermi Surfaces ◽

Topological States ◽

Topological Geometry ◽

Quenching Mechanisms

Abstract The concept of topology is universally observed in various physical objects when the objects can be described by geometric structures. Although a representative example is the knotted geometry of wavefunctions in reciprocal space for quantum Hall family and topological insulators, topological states have also been defined for other physical quantities, such as topologically distinct Fermi surfaces and enhanced lattice degrees of freedom in hyperbolic geometry. Here, we investigate a different class of topological states – topological geometry of dynamical state trajectories – in non-Hermitian and nonlinear optical dynamics, revealing topologically protected oscillation quenching mechanisms determined by parity–time (PT) symmetry. For coupled systems composed of nonlinear gain and loss elements, we classify the topology of equilibria separately for unbroken and broken PT symmetry, which result in distinct oscillation quenching mechanisms: amplitude death and oscillation death. We then show that these PT-symmetric quenching mechanisms lead to immunity against temporal perturbations, enabling the applications of topologically protected laser modulation and rectification. The observed connection between the topological geometry of dynamical states, oscillation quenching phenomena in dynamical systems theory, and PT symmetry provides a powerful toolkit for noise-immune signal processing.

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The inverse diffraction problem for acoustic equations

Doklady Mathematics ◽

10.1134/s1064562410020201 ◽

2010 ◽

Vol 81 (2) ◽

pp. 238-240 ◽

Cited By ~ 6

Author(s):

V. G. Romanov

Keyword(s):

Diffraction Problem ◽

Acoustic Equations ◽

Inverse Diffraction

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Development of a Surface Roughness Measurement System in a Narrow Borehole

International Journal of Automation Technology ◽

10.20965/ijat.2016.p0821 ◽

2016 ◽

Vol 10 (5) ◽

pp. 821-826

Author(s):

Eiki Okuyama ◽

◽

Yuichi Suzuki ◽

Masahiro Morikawa ◽

Yuma Suzuki ◽

...

Keyword(s):

Surface Roughness ◽

Conventional Method ◽

Degrees Of Freedom ◽

Optical Signal ◽

Measurement Range ◽

Standard Test ◽

Roughness Measurement ◽

Surface Roughness Measurement ◽

Test Pieces ◽

Large Measurement

In industrial fields, it is frequently necessary to measure surface roughness in confined spaces such as boreholes and grooves in workpieces. However, the surface roughness of a narrow borehole can be measured only up to a few millimeters from its end when using a small stylus. Alternatively, destructive measurements must be performed. We previously proposed a novel surface roughness measurement sensor. To make the sensor sufficiently small, we used a stylus with a cylindrical mirror and a lensed fiber instead of a conventional inductive pick-up. The proposed sensor converts the signal used for measuring the surface roughness of a borehole into an optical signal, which is transferred outside the borehole by an optical fiber. The experimental results demonstrate that this system has a measurement range of 8 μm and a sensitivity of 19 nm. In this paper, we propose a carriage that supports the stylus when measuring the surface roughness in a small borehole. The proposed carriage has two degrees of freedom: displacement along the borehole axis and rotation around the borehole axis. In experiments, the surface roughness of standard test pieces was measured using the proposed method and the conventional method. The measurement results obtained by these methods were found to be very similar. Furthermore, a borehole with 2.4 mm diameter was measured. The measurement result included the characteristic wave that was obtained by the conventional method in places. The experiments also revealed some problems of the proposed system. For example, the setting procedure of the measured surface in the 8 μm measurement range was difficult. Consequently, a large measurement range or a null method is required.

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Approximation of the solution of the inverse diffraction problem by δ-functions and by gaussian distributions

USSR Computational Mathematics and Mathematical Physics ◽

10.1016/0041-5553(87)90089-9 ◽

1987 ◽

Vol 27 (3) ◽

pp. 101-102

Author(s):

D.I. Nikolayev ◽

T.I. Savelova

Keyword(s):

Diffraction Problem ◽

Gaussian Distributions ◽

Inverse Diffraction

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An Inverse Diffraction Problem: Shape Reconstruction

East Asian Journal on Applied Mathematics ◽

10.4208/eajam.310315.250915a ◽

2015 ◽

Vol 5 (4) ◽

pp. 342-360 ◽

Cited By ~ 2

Author(s):

Yanfeng Kong ◽

Zhenping Li ◽

Xiangtuan Xiong

Keyword(s):

Error Estimates ◽

Diffraction Problem ◽

Shape Reconstruction ◽

Numerical Examples ◽

Tikhonov Method ◽

Ill Posed ◽

Tikhonov Regularisation ◽

Slow Evolution ◽

Inverse Diffraction

AbstractAn inverse diffraction problem is considered. Both classical Tikhonov regularisation and a slow-evolution-from-the-continuation-boundary (SECB) method are used to solve the ill-posed problem. Regularisation error estimates for the two methods are compared, and the SECB method is seen to be an improvement on the classical Tikhonov method. Two numerical examples demonstrate their feasibility and efficiency.

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