Rigorous electromagnetic field mask modeling and related lithographic effects in the low k1 and ultrahigh numerical aperture regime

2007 ◽  
Vol 6 (3) ◽  
pp. 031002 ◽  
Author(s):  
Andreas Erdmann
Keyword(s):  
Electromagnetic Field ◽  
Numerical Aperture

scholarly journals Electromagnetic Mode Matching in a Wilson Basis --- Optical Fiber Connections with a Gap

2021 ◽  
Author(s):  
Sander J. Floris ◽  
Bastiaan P. de Hon ◽  
Martijn C. van Beurden ◽  
Ton Bolhaar
Keyword(s):  
Electromagnetic Field ◽  
Power Distribution ◽  
Numerical Aperture ◽  
Basis Functions ◽  
Physical Contact ◽  
Interface Problem ◽  
Destructive Interference ◽  
Mode Matching ◽  
Core Diameter ◽  
Multi Mode

Abstract On the basis of two optical fibers with an optional lateral and longitudinal displacement in a homogeneous background medium, we describe a general full-vectorial Wilson-basis discretized mode-matching method that evaluates the converged electromagnetic fields after all resonances in the possible gap cavity have settled. Wilson basis functions feature strong localization in both the spatial and the spectral domain, which allows for efficient modal electromagnetic field expansions, adequate truncation of field propagation operators, and sparse translation operators, which in turn allow to make ad hoc electromagnetic field-matching operators. For physical contact connections between single-mode fibers with a mode-field diameter mismatch, we obtain attenuation curves that are right between those obtained from approximation methods that either effectively match the electric field or the magnetic field under the assumption of a vanishing reflection. For fibers separated by a growing gap, constructive and destructive interference patterns in the cavity are computed by the successive application of Love's equivalence principle and the propagation operator. By leveraging the physical width of the Wilson basis functions and the stepsize of the propagation operator, the initial operators may be reused in solving the interface problem for other wavelengths. For multi-mode fiber connections, we provide attenuation curves on a modal electromagnetic field level, as well as for overfilled and core-confined target encircled-flux compliant launches. A comparison to geometrical-optics based approaches shows attenuation differences in the order of several hundredth of a dB, and although that is small, it is significant for modern connection attenuation specifications. In the final example of connections between regular and trench-assisted multi-mode fibers, we notice that the relative change in the cumulative near-field power distribution can be significant, despite a marginally small attenuation. The influence of a core diameter and/or numerical aperture mismatch can be examined with a deliberate lateral misalignment.

Video-Enhanced Microscopy--Better Visibility of Plant Cell Structures

1982 ◽  
Vol 40 ◽  
pp. 182-185
Author(s):  
N.S. Allen ◽  
R.D. Allen
Keyword(s):  
Diffraction Pattern ◽  
Theoretical Basis ◽  
Numerical Aperture ◽  
Gain Control ◽  
Control Unit ◽  
Camera Control ◽  
Variable Gain ◽  
Contrast Method ◽  
Fine Detail ◽  
Cell Structures

Various methods of video-enhanced microscopy combine TV cameras with light microscopes creating images with improved resolution, contrast and visibility of fine detail, which can be recorded rapidly and relatively inexpensively. The AVEC (Allen Video-enhanced Contrast) method avoids polarizing rectifiers, since the microscope is operated at retardations of λ/9- λ/4, where no anomaly is seen in the Airy diffraction pattern. The iris diaphram is opened fully to match the numerical aperture of the condenser to that of the objective. Under these conditions, no image can be realized either by eye or photographically. Yet the image becomes visible using the Hamamatsu C-1000-01 binary camera, if the camera control unit is equipped with variable gain control and an offset knob (which sets a clamp voltage of a D.C. restoration circuit). The theoretical basis for these improvements has been described.

On resolving fine periodic microstructures in the optical microscope

1989 ◽  
Vol 47 ◽  
pp. 364-365
Author(s):  
W.S. Putnam ◽  
C. Viney
Keyword(s):  
Liquid Crystalline ◽  
Numerical Aperture ◽  
Polarized Light ◽  
Normal Incidence ◽  
Optical Microscope ◽  
Angle Of Incidence ◽  
Resolution Limit ◽  
Crystalline Materials ◽  
Periodic Microstructures ◽  
Liquid Crystalline Materials

Many sheared liquid crystalline materials (fibers, films and moldings) exhibit a fine banded microstructure when observed in the polarized light microscope. In some cases, for example Kevlar® fiber, the periodicity is close to the resolution limit of even the highest numerical aperture objectives. The periodic microstructure reflects a non-uniform alignment of the constituent molecules, and consequently is an indication that the mechanical properties will be less than optimal. Thus it is necessary to obtain quality micrographs for characterization, which in turn requires that fine detail should contribute significantly to image formation.It is textbook knowledge that the resolution achievable with a given microscope objective (numerical aperture NA) and a given wavelength of light (λ) increases as the angle of incidence of light at the specimen surface is increased. Stated in terms of the Abbe resolution criterion, resolution improves from λ/NA to λ/2NA with increasing departure from normal incidence.

Performance Evaluation of a Novel Type of Low-Energy Electron Microscope

1990 ◽  
Vol 48 (1) ◽  
pp. 354-355
Author(s):  
Bertholdand Senftinger ◽  
Helmut Liebl
Keyword(s):  
Electron Microscope ◽  
High Resolution ◽  
Field Strength ◽  
Numerical Aperture ◽  
Low Energy ◽  
Energy Electron ◽  
High Resolution Imaging ◽  
Lens System ◽  
Resolution Imaging ◽  
Low Energy Electron

During the last few years the investigation of clean and adsorbate-covered solid surfaces as well as thin-film growth and molecular dynamics have given rise to a constant demand for high-resolution imaging microscopy with reflected and diffracted low energy electrons as well as photo-electrons. A recent successful implementation of a UHV low-energy electron microscope by Bauer and Telieps encouraged us to construct such a low energy electron microscope (LEEM) for high-resolution imaging incorporating several novel design features, which is described more detailed elsewhere.The constraint of high field strength at the surface required to keep the aberrations caused by the accelerating field small and high UV photon intensity to get an improved signal-to-noise ratio for photoemission led to the design of a tetrode emission lens system capable of also focusing the UV light at the surface through an integrated Schwarzschild-type objective. Fig. 1 shows an axial section of the emission lens in the LEEM with sample (28) and part of the sample holder (29). The integrated mirror objective (50a, 50b) is used for visual in situ microscopic observation of the sample as well as for UV illumination. The electron optical components and the sample with accelerating field followed by an einzel lens form a tetrode system. In order to keep the field strength high, the sample is separated from the first element of the einzel lens by only 1.6 mm. With a numerical aperture of 0.5 for the Schwarzschild objective the orifice in the first element of the einzel lens has to be about 3.0 mm in diameter. Considering the much smaller distance to the sample one can expect intense distortions of the accelerating field in front of the sample. Because the achievable lateral resolution depends mainly on the quality of the first imaging step, careful investigation of the aberrations caused by the emission lens system had to be done in order to avoid sacrificing high lateral resolution for larger numerical aperture.

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.

Comparison of high- and low-frequency electromagnetic field analysis

1993 ◽  
Vol 3 (3) ◽  
pp. 363-371 ◽  
Author(s):  
A. Konrad ◽  
I. A. Tsukerman
Keyword(s):  
Electromagnetic Field ◽  
Low Frequency ◽  
Field Analysis
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