Related papers: Orthonormalization of phase-only basis functions
Control of orbital angular momentum (OAM) in optical fields has seen tremendous growth of late, with a myriad of tools existing for their creation and detection. What has been lacking is the ability to arbitrarily modify the OAM spectrum of…
Nonclassical phenomena can be enhanced by introducing $q$-deformation in optomechanical systems. This motivates investigation of the optical response in a $q$-deformed linearly coupled optomechanical system. The system consists of two…
Numerical optimization is used to construct new orthonormal compactly supported wavelets with Sobolev regularity exponent as high as possible among those mother wavelets with a fixed support length and a fixed number of vanishing moments.…
This paper presents a new family of localized orthonormal bases - sinlets - which are well suited for both signal and image processing and analysis. One-dimensional sinlets are related to specific solutions of the time-dependent harmonic…
In this paper we develop a plane wave type method for discretization of homogeneous Helmholtz equations with variable wave numbers. In the proposed method, local basis functions (on each element) are constructed by the geometric optics…
At Integrable Optics Test Accelerator it is possible to create a nonlinear focusing optics with one invariant of motion using just conventional magnets. 6D simulations show that this will allow to achieve a tune spread of 0.05 without…
We provide an algorithm for the construction of orthonormal multivariate polynomials that are symmetric with respect to the interchange of any two coordinates on the unit hypercube and are constrained to the hyperplane where the sum of the…
In astronomy or biological imaging, refractive index inhomogeneities of e.g. atmosphere or tissues induce optical aberrations which degrade the desired information hidden behind the medium. A standard approach consists in measuring these…
Wavelet systems on the generalized Vilenkin groups are considered. An algorithmic method for the construction of orthogonal wavelet bases is presented. These bases consist of compactly supported test functions (i.e. functions whose Fourier…
Sets of orthogonal basis functions over two-dimensional circular areas--most often representing pupils in optical applications--are known in the literature for the full circle (Zernike or Jacobi polynomials) and the annulus. This work…
The decomposition of an image into a linear combination of digitised basis functions is an everyday task in astronomy. A general method is presented for performing such a decomposition optimally into an arbitrary set of digitised basis…
We combine lossless, phase-only transformations with fully-transmitting linear-optical scatterers to define the principle of linear-optical phase amplification. This enables a physical phase shift $\phi$ to be nonlinearly mapped to a new…
Quantum optomechanics uses optical means to generate and manipulate quantum states of motion of mechanical resonators. This provides an intriguing platform for the study of fundamental physics and the development of novel quantum devices.…
The promise of innovative applications has triggered the development of many modern technologies capable of exploiting quantum effects. But in addition to future applications, such quantum technologies have already provided us with the…
This paper presents two novel regularization methods motivated in part by the geometric significance of biorthogonal bases in signal processing applications. These methods, in particular, draw upon the structural relevance of orthogonality…
In this paper, we propose a novel approach to the problem of augmenting distance-based formation controllers with a secondary constraint for the purpose of preventing 3D formation ambiguities. Specifically, we introduce three controlled…
Vector beams are often regarded as non-separable superpositions of spatial and polarization degrees of freedom that satisfy the wave equation. This interpretation ties their polarization structure to their spatial shape. Here, we introduce…
Light scattering is the main limitation for optical imaging. However, light can be focused through or inside turbid media by spatially shaping the incident wavefront. Wavefront shaping is ultimately limited by the available photon budget.…
Optical phase conjugation (OPC) is a nonlinear technique used for counteracting wavefront distortions, with various applications ranging from imaging to beam focusing. Here, we present the design of a diffractive wavefront processor to…
Structured optical waveforms are emerging as powerful control fields for the next generation of complex photonic and electromagnetic systems, where the temporal structure of light can determine the ultimate performance of scientific…