Nonexistence of exact solutions agreeing with the Gaussian beam on the beam axis or in the focal plane

2018 ◽  
Vol 407 ◽  
pp. 22-26 ◽  
Author(s):  
John Lekner ◽  
Petar Andrejic
Keyword(s):  
Exact Solutions ◽  
Gaussian Beam ◽  
Focal Plane ◽  
Beam Axis

scholarly journals Tight focusing of light beams: a set of exact solutions

2016 ◽  
Vol 472 (2195) ◽  
pp. 20160538 ◽  
Author(s):  
John Lekner
Keyword(s):  
Exact Solutions ◽  
Focal Plane ◽  
Bessel Functions ◽  
Momentum Conservation ◽  
Focal Region ◽  
Beam Direction ◽  
Lommel Functions ◽  
Tight Focusing ◽  
Causal Propagation ◽  
Light Beams

Exact solutions of Maxwell's equations representing light beams are explored. The solutions satisfy all of the physical requirements of causal propagation and of energy, momentum and angular momentum conservation. A set of solutions can be found from a proto-beam by an imaginary translation along the beam direction. The proto-beam is given analytically in terms of the Bessel functions J 0 , J 1 and the Lommel functions U 0 , U 1 , or equivalently in terms of products of the spherical Bessel functions and Legendre polynomials. The complex wavefunction has rings of zeros in the focal plane. Localization of the focal region is to within about one half of the vacuum wavelength.

scholarly journals Comparison of the focused optical vortices produced by high-aperture phase conventional and spiral zone plates

2021 ◽  
Vol 2103 (1) ◽  
pp. 012175
Author(s):  
A A Savelyeva ◽  
E S Kozlova ◽  
V V Kotlyar
Keyword(s):  
Gaussian Beam ◽  
Focal Plane ◽  
Topological Charge ◽  
Focal Spot ◽  
Zone Plate ◽  
Fdtd Simulation ◽  
Optical Vortices ◽  
Phase Zone ◽  
Linearly Polarized ◽  
Sharp Focusing

Abstract Using the FDTD simulation, sharp focusing of a linearly polarized Gaussian beam with an embedded topological charge m = 3 by a phase zone plate and focusing of a Gaussian beam by a phase spiral zone plate with topological charge m = 3 were studied. The obtained results showed that proposed elements formed different patterns of intensity at a focal plane. The spiral zone plate forms a focal spot with three petals. At a distance of 13.5 μm from the focus, the lobe structure of the intensity (and energy flux) is replaced by an annular distribution.

scholarly journals О фокусировке широкополосных терагерцовых импульсов

2019 ◽  
Vol 127 (10) ◽  
pp. 667
Author(s):  
В.Л. Малевич ◽  
Г.В. Синицын ◽  
Н.Н. Розанов
Keyword(s):  
Field Distribution ◽  
Focal Plane ◽  
Amplitude Distribution ◽  
Beam Axis ◽  
Focal Distance ◽  
Spectral Maximum

AbstractThe particular features of the focusing of a broadband THz pulse with a Gaussian transverse amplitude distribution by a lens are investigated theoretically. The expressions for the spatiotemporal field distribution on the beam axis and in the focal plane of the lens are obtained in the quasi-optical approximation. It is shown that, for the focusing to be efficient, it is necessary to use lenses with a focal distance that is much shorter than the characteristic diffraction length at the frequency corresponding to the spectral maximum of the THz pulse.

Axial Observation of X-Ray Spectra from a Beam-Foil Source

1988 ◽  
Vol 102 ◽  
pp. 339-342
Author(s):  
J.M. Laming ◽  
J.D. Silver ◽  
R. Barnsley ◽  
J. Dunn ◽  
K.D. Evans ◽  
...  
Keyword(s):  
Spectral Resolution ◽  
Heavy Ion ◽  
Ion Beams ◽  
Beam Axis ◽  
Doppler Broadening ◽  
X Ray ◽  
Beam Foil

AbstractNew observations of x-ray spectra from foil-excited heavy ion beams are reported. By observing the target in a direction along the beam axis, an improvement in spectral resolution, δλ/λ, by about a factor of two is achieved, due to the reduced Doppler broadening in this geometry.

Tandem scanning reflected light microscopy: How it works and applications

1986 ◽  
Vol 44 ◽  
pp. 84-87
Author(s):  
Alan Boyde ◽  
Milan Hadravský ◽  
Mojmír Petran ◽  
Timothy F. Watson ◽  
Sheila J. Jones ◽  
...  
Keyword(s):  
Light Microscopy ◽  
Focal Plane ◽  
Central Symmetry ◽  
Single Line ◽  
Scanning Microscope ◽  
Reflected Light ◽  
Illuminating Light ◽  
Illuminating Beam

The principles of tandem scanning reflected light microscopy and the design of recent instruments are fully described elsewhere and here only briefly. The illuminating light is intercepted by a rotating aperture disc which lies in the intermediate focal plane of a standard LM objective. This device provides an array of separate scanning beams which light up corresponding patches in the plane of focus more intensely than out of focus layers. Reflected light from these patches is imaged on to a matching array of apertures on the opposite side of the same aperture disc and which are scanning in the focal plane of the eyepiece. An arrangement of mirrors converts the central symmetry of the disc into congruency, so that the array of apertures which chop the illuminating beam is identical with the array on the observation side. Thus both illumination and “detection” are scanned in tandem, giving rise to the name Tandem Scanning Microscope (TSM). The apertures are arranged on Archimedean spirals: each opposed pair scans a single line in the image.

Imaging sub-micron objects with light microscopy: Visualization of the T-4 bacteriophage

1989 ◽  
Vol 47 ◽  
pp. 834-835
Author(s):  
Malcolm Brown ◽  
Reynolds M. Delgado ◽  
Michael J. Fink
Keyword(s):  
Electron Microscopy ◽  
Light Microscopy ◽  
Focal Plane ◽  
Phase Contrast ◽  
Dark Field ◽  
E Coli ◽  
Polystyrene Beads ◽  
Television Camera ◽  
Transmission Electron ◽  
Universal Microscope

While light microscopy has been used to image sub-micron objects, numerous problems with diffraction-limitations often preclude extraction of useful information. Using conventional dark-field and phase contrast light microscopy coupled with image processing, we have studied the following objects: (a) polystyrene beads (88nm, 264nm, and 557mn); (b) frustules of the diatom, Pleurosigma angulatum, and the T-4 bacteriophage attached to its host, E. coli or free in the medium. Equivalent images of the same areas of polystyrene beads and T-4 bacteriophages were produced using transmission electron microscopy.For light microscopy, we used a Zeiss universal microscope. For phase contrast observations a 100X Neofluar objective (N.A.=1.3) was applied. With dark-field, a 100X planachromat objective (N.A.=1.25) in combination with an ultra-condenser (N.A.=1.25) was employed. An intermediate magnifier (Optivar) was available to conveniently give magnification settings of 1.25, 1.6, and 2.0. The image was projected onto the back focal plane of a film or television camera with a Carl Zeiss Jena 18X Compens ocular.

Microspectroscopy Using a Solid Immersion Lens

2001 ◽  
Vol 7 (S2) ◽  
pp. 148-149
Author(s):  
C.D. Poweleit ◽  
J Menéndez
Keyword(s):  
Spatial Resolution ◽  
Focal Plane ◽  
Numerical Aperture ◽  
Normal Incidence ◽  
Spot Size ◽  
Index Of Refraction ◽  
Objective Lens ◽  
Improvement Factor ◽  
Oil Immersion ◽  
Long Time

Oil immersion lenses have been used in optical microscopy for a long time. The light’s wavelength is decreased by the oil’s index of refraction n and this reduces the minimum spot size. Additionally, the oil medium allows a larger collection angle, thereby increasing the numerical aperture. The SIL is based on the same principle, but offers more flexibility because the higher index material is solid. in particular, SILs can be deployed in cryogenic environments. Using a hemispherical glass the spatial resolution is improved by a factor n with respect to the resolution obtained with the microscope’s objective lens alone. The improvement factor is equal to n2 for truncated spheres.As shown in Fig. 1, the hemisphere SIL is in contact with the sample and does not affect the position of the focal plane. The focused rays from the objective strike the lens at normal incidence, so that no refraction takes place.

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