Variational analysis of SPM- and IPM-based interactions in cubic non-local nonlinear media

SPATIAL SOLITARY WAVES IN GENERALIZED NON-LOCAL NONLINEAR MEDIA

Journal of Nonlinear Optical Physics & Materials ◽

10.1142/s0218863510005170 ◽

2010 ◽

Vol 19 (02) ◽

pp. 311-317 ◽

Cited By ~ 1

Author(s):

WEI-PING ZHONG ◽

ZHENG-PING YANG

Keyword(s):

Solitary Wave ◽

Solitary Waves ◽

Initial Conditions ◽

Soliton Solutions ◽

Solitary Wave Solutions ◽

Cylindrical Coordinates ◽

Intensity Pattern ◽

Nonlinear Media ◽

Wave Solutions ◽

Non Local

We introduce a very general self-trapped beam solution to the generalized non-local nonlinear Schrödinger equation in cylindrical coordinates, by combining superpositions of the known single accessible soliton solutions. Specific values of soliton parameters are selected as initial conditions and superpositions of the single soliton solutions in the highly non-local regime are launched into the non-local nonlinear medium with Gaussian response function, to obtain novel numerical solitary wave solutions. Novel solitary waves have been constructed that exhibit unique features whose intensity pattern is formed by various figures.

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Optical beams in sub-strongly non-local nonlinear media: A variational solution

Optics Communications ◽

10.1016/j.optcom.2005.08.067 ◽

2006 ◽

Vol 259 (1) ◽

pp. 336-341 ◽

Cited By ~ 28

Author(s):

Qi Guo ◽

Boren Luo ◽

Sien Chi

Keyword(s):

Variational Solution ◽

Nonlinear Media ◽

Non Local ◽

Optical Beams

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Interaction between spacial optical solitons in sub-strongly non-local nonlinear media

Acta Physica Sinica ◽

10.7498/aps.57.6365 ◽

2008 ◽

Vol 57 (10) ◽

pp. 6365

Author(s):

Cao Long-Gui ◽

Lu Da-Quan ◽

Hu Wei ◽

Yang Ping-Bao ◽

Zhu Ye-Qing ◽

...

Keyword(s):

Optical Solitons ◽

Nonlinear Media ◽

Non Local

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Toward High-Resolution Low-Voltage SEM

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100103152 ◽

1988 ◽

Vol 46 ◽

pp. 218-219

Author(s):

Zhifeng Shao

Keyword(s):

Low Voltage ◽

Spherical Aberration ◽

Chromatic Aberration ◽

Limiting Factor ◽

Operating Voltage ◽

Probe Radius ◽

Non Local ◽

Electron Microscopes ◽

Image Position ◽

Scanning Electron Microscopes

Recently, low voltage (≤5kV) scanning electron microscopes have become popular because of their unprecedented advantages, such as minimized charging effects and smaller specimen damage, etc. Perhaps the most important advantage of LVSEM is that they may be able to provide ultrahigh resolution since the interaction volume decreases when electron energy is reduced. It is obvious that no matter how low the operating voltage is, the resolution is always poorer than the probe radius. To achieve 10Å resolution at 5kV (including non-local effects), we would require a probe radius of 5∽6 Å. At low voltages, we can no longer ignore the effects of chromatic aberration because of the increased ratio δV/V. The 3rd order spherical aberration is another major limiting factor. The optimized aperture should be calculated as

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Chromatic aberration and low-voltage SEM

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100127293 ◽

1987 ◽

Vol 45 ◽

pp. 546-547

Author(s):

Zhifeng Shao ◽

A.V. Crewe

Keyword(s):

Electron Energy ◽

Low Voltage ◽

Spherical Aberration ◽

Chromatic Aberration ◽

Primary Electron ◽

Probe Size ◽

Non Local ◽

Optical Treatment ◽

Electron Microscopes ◽

Scanning Electron Microscopes

For scanning electron microscopes, it is plausible that by lowering the primary electron energy, one can decrease the volume of interaction and improve resolution. As shown by Crewe /1/, at V0 =5kV a 10Å resolution (including non-local effects) is possible. To achieve this, we would need a probe size about 5Å. However, at low voltages, the chromatic aberration becomes the major concern even for field emission sources. In this case, δV/V = 0.1 V/5kV = 2x10-5. As a rough estimate, it has been shown that /2/ the chromatic aberration δC should be less than ⅓ of δ0 the probe size determined by diffraction and spherical aberration in order to neglect its effect. But this did not take into account the distribution of electron energy. We will show that by using a wave optical treatment, the tolerance on the chromatic aberration is much larger than we expected.

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