The two‐state linear curve crossing problems revisited. II. Analytical approximations for the Stokes constant and scattering matrix: The Landau–Zener case

1992 ◽  
Vol 97 (11) ◽  
pp. 8497-8514 ◽  
Author(s):  
Chaoyuan Zhu ◽  
Hiroki Nakamura
Keyword(s):  
Scattering Matrix ◽  
Analytical Approximations ◽  
Stokes Constant ◽  
Curve Crossing

scholarly journals Exceptional points in composite structures consisting of two dielectric diffraction gratings with Lorentzian line shape

2021 ◽  
Vol 2015 (1) ◽  
pp. 012049
Author(s):  
Nikita Golovastikov ◽  
Dmitry Bykov ◽  
Leonid Doskolovich
Keyword(s):  
Composite Structure ◽  
Composite Structures ◽  
Diffraction Gratings ◽  
Scattering Matrix ◽  
Matrix Formalism ◽  
Exceptional Points ◽  
Lorentzian Line ◽  
Analytical Approximations ◽  
Lorentzian Profile ◽  
Analytical Expressions

Abstract Using scattering matrix formalism we derive analytical expressions for the eigenmodes of a composite structure consisting of two dielectric diffraction gratings with Lorentzian profile in reflection. Analyzing these expressions we prove formation of two distinct pairs of exceptional points, provide analytical approximations for their coordinates and by rigorous simulation demonstrate eigenmodes interchange as a result of encircling said exceptional points.

“Preparation of Single Crystalline Gold Films for ED Studies”

1972 ◽  
Vol 30 ◽  
pp. 634-635
Author(s):  
Joseph D. C. Peng
Keyword(s):  
Crystal Morphology ◽  
Diffraction Theory ◽  
Scattering Matrix ◽  
Vacuum Evaporation ◽  
Gold Films ◽  
Matrix Formulation ◽  
Silver Films ◽  
Single Crystalline ◽  
Grating Pattern ◽  
Stacking Disorder

The relative intensities of the ED spots in a cross-grating pattern can be calculated using N-beam electron diffraction theory. The scattering matrix formulation of N-beam ED theory has been previously applied to imperfect microcrystals of gold containing stacking disorder (coherent twinning) in the (111) crystal plane. In the present experiment an effort has been made to grow single-crystalline, defect-free (111) gold films of a uniform and accurately know thickness using vacuum evaporation techniques. These represent stringent conditions to be met experimentally; however, if a meaningful comparison is to be made between theory and experiment, these factors must be carefully controlled. It is well-known that crystal morphology, perfection, and orientation each have pronounced effects on relative intensities in single crystals.The double evaporation method first suggested by Pashley was employed with some modifications. Oriented silver films of a thickness of about 1500Å were first grown by vacuum evaporation on freshly cleaved mica, with the substrate temperature at 285° C during evaporation with the deposition rate at 500-800Å/sec.

Reduction of the scattering matrix array

2015 ◽  
Vol 185 (9) ◽  
pp. 941-945 ◽  
Author(s):  
Ivan A. Sadovskyy
Keyword(s):  
Scattering Matrix ◽  
Matrix Array

Scattering Matrix in the DKP Theory. Barrier Potential Case

2014 ◽  
Vol 59 (6) ◽  
pp. 565-568 ◽  
Author(s):  
Boutabia-Chéraitia B. Boutabia-Chéraitia B. ◽  
◽  
Boudjedaa T. Boudjedaa T. ◽  
Keyword(s):  
Scattering Matrix ◽  
Barrier Potential ◽  
Potential Case
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