Related papers: Lens optics and the continuity problems of the ABC…
The beam transfer matrix, often called the $ABCD$ matrix, is a two-by-two matrix with unit determinant, and with three independent parameters. It is noted that this matrix cannot always be diagonalized. It can however be brought by rotation…
We require decomposition methods for the ABCD-matrix formulation in rotationally symmetric paraxial geometric optics when designing a multi-component optical system from a given single paraxial specification (represented by an ABCD matrix)…
It is shown that the one-lens system in para-axial optics can serve as an optical computer for contraction of Wigner's little groups and an analogue computer which transforms analytically computations on a spherical surface to those on a…
With its three independent parameters, the $ABCD$ matrix serves as the beam transfer matrix in optics. If it is transformed to an equi-diagonal form, the matrix has only two independent parameters determined by optical devices. It is shown…
When the gravitational lensing potential can be approximated by that of circularly symmetric system affected by weak perturbations, it is found that the shape of the resulting (tangential) caustics is entirely specified by the local…
Bidirectional transformation, also called lens, has played important roles in maintaining consistency in many fields of applications. A lens is specified by a pair of forward and backward functions which relate to each other in a consistent…
The ABCD matrix is one of the essential mathematical instruments in optics. It is the two-by-two representation of the group Sp(2), which is applicable to many branches of physics, including squeezed states of light, special relativity and…
A purely analytical extension of the flattened Gaussian beams [Opt. Commun. \textbf{107,} 335 (1994)] to any values of the beam order, is here proposed. Due to it, the paraxial propagation problem of axially symmetric, coherent flat-top…
We propose that the height-angle ray vector in matrix optics should be complex, based on a geometric algebra analysis. We also propose that the ray's 2x2 matrix operators should be right-acting, so that the matrix product succession would…
Dual image formation for a two-dimensional object via bimodal propagation through chiral-dispersive thick lens is derived. In this article, first-order frequency-dependent material dispersion of the dielectric permittivity and the lens…
A hidden symmetry of the nonlinear wave equation is exploited to analyse the propagation of paraxial and uniform atom-laser beams in time-independent, quadratic and cylindrical potentials varying smoothly along the propagation axis. The…
We study the conserved quantity associated with the dual symmetry of the Maxwell equations, called the optical helicity, by means of transverse Hertz vectors. In the presence of charges, its evolution yields the integral of…
A persistence lens is a hierarchy of disjoint upper and lower level sets of a continuous luminance image's Reeb graph. The boundary components of a persistence lens's interior components are Jordan curves that serve as a hierarchical…
A novel type of a continuously zoomable telescope is based on two pairs of adjacent toroidal lenses ("saddle lenses") in combination with standard optical components. Its variable magnification is adjusted by a mere rotation of the four…
The leading order monochromatic aberrations are investigated for the optical systems, which obey single-plane symmetry and translational invariance. These aberrations are classified from the symmetry principles for the wave aberration…
The static behavior of orientational glasses is discussed in terms of a replica theory based on the infinite range random bond--random field model. A general version of the model applicable to dipolar and quadrupolar glasses is presented…
Scalar theory of quantum electron beam optics, at the single-particle level, derived from the Dirac equation using a Foldy-Wouthuysen-like transformation technique is considered. Round magnetic electron lenses with Glaser and power law…
Quantum mechanics of bending of a nonrelativistic monoenergetic charged particle beam by a dipole magnet is studied in the paraxial approximation. The transfer map for the position and momentum components of a particle of the beam between…
While modern optics is largely a physics of harmonic oscillators and two-by-two matrices, it is possible to learn about some hidden properties of the two-by-two matrix from optical systems. Since two-by-two matrices can be divided into…
We reconsider the basic properties of ray-transfer matrices for first-order optical systems from a geometrical viewpoint. In the paraxial regime of scalar wave optics, there is a wide family of beams for which the action of a ray-transfer…