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We consider the Bose-Einstein condensate in a parabolic trap as a macroscopic quantum oscillator and describe, analytically and numerically, its collective modes - a nonlinear generalisation of the (symmetric and antisymmetric)…
We demonstrate that a triangular cavity can operate as an efficient discriminator for Hermite-Gaussian optical modes. The process is applied to distinct fields produced by a Spatial Light Modulator, decomposing the generated paraxial field…
Light's spatial degree of freedom is emerging as a potential resource for a myriad of applications, in both classical and quantum domains, including secure communication, sensing and imaging. However, it has been repeatedly shown that a…
Physical mechanism for the geometric phase in terms of angular momentum exchange is elucidated. It is argued that the geometric phase arising out of the cyclic changes in the tranverse mode space of the Gaussian light beams is a…
Time-resolved illumination provides rich spatio-temporal information for applications such as accurate depth sensing or hidden geometry reconstruction, becoming a useful asset for prototyping and as input for data-driven approaches.…
Parameter identification problems in partial differential equations (PDEs) consist in determining one or more functional coefficient in a PDE. In this article, the Bayesian nonparametric approach to such problems is considered. Focusing on…
Solving the Gross--Pitaevskii (GP) equation describing a Bose--Einstein condensate (BEC) immersed in an optical lattice potential can be a numerically demanding task. We present a variational technique for providing fast, accurate solutions…
This contribution discusses isocurvature modes, in particular the non-Gaussianities of local type generated by these modes. Since the isocurvature transfer functions differ from the adiabatic one, the coexistence of a primordial…
For partially coherent light fields with random fluctuations, the intensity distributions and statistics have been proven to be more propagation robust compared with coherent light. However, its full potential in practical applications has…
In this paper, we consider several geometric inverse problems for linear elliptic systems. We prove uniqueness and stability results. In particular, we show the way that the observation depends on the perturbations of the domain. In some…
We develop a non-perturbative formulation based on the Green-function quantization method, that can describe spontaneous parametric down-conversion in the high-gain regime in nonlinear optical structures with arbitrary amount of loss and…
A new kind of tridimensional scalar optical beams is introduced. These beams are called Lorentz beams because the form of their transverse pattern in the source plane is the product of two independent Lorentz functions. Closed-form…
We describe power-dependent dynamics of conversion of the guided modes of various guiding structures due to nearly resonant longitudinal modulation of the nonlinear coefficient of the medium. It is shown that the control of the energy…
We investigate the propagation of Gaussian beams through optical waveguide lattices characterized by correlated non-Hermitian disorder. In the framework of coupled mode theory, we demonstrate how the imaginary part of the refractive index…
The theory of noncommutative geometry provides an interesting mathematical background for developing new physical models. In particular, it allows one to describe the classical Standard Model coupled to Euclidean gravity. However,…
A class of elliptic-hyperbolic equations is placed in the context of a geometric variational theory, in which the change of type is viewed as a change in the character of an underlying metric. A fundamental example of a metric which changes…
A rigorous and powerful theoretical framework is proposed to obtain systems of orthogonal functions (or shape modes) to represent optical surfaces. The method is general so it can be applied to different initial shapes and different…
Recently, we showed experimentally that light carrying orbital angular momentum experiences a slight subluminality under free-space propagation [1]. We thank Saari [2] for pointing out an apparent discrepancy between our theoretical results…
Following up on previous studies on parity-time-symmetric gain-loss bi-layers, and inspired by formal analogies with plasmonic waveguides, we study non-Hermiticity-induced wave confinement and guiding phenomena that can occur in…
We prove the convergence of (solid) ellipsoids to a Gaussian space in Gromov's concentration/weak topology as the dimension diverges to infinity. This gives the first discovered example of an irreducible nontrivial convergent sequence in…