scholarly journals Corrected coupled-wave theory for non-slanted reflection gratings

2011 ◽  
Author(s):  
L. Alberto Estepa ◽  
Cristian Neipp ◽  
Jorge Francés ◽  
Andrés Márquez ◽  
Sergio Bleda ◽  
...  
Keyword(s):  
Wave Theory ◽  
Reflection Gratings ◽  
Coupled Wave

scholarly journals Beta Value Coupled Wave Theory for Nonslanted Reflection Gratings

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Cristian Neipp ◽  
Jorge Francés ◽  
Sergi Gallego ◽  
Sergio Bleda ◽  
Francisco Javier Martínez ◽  
...  
Keyword(s):  
Boundary Conditions ◽  
Exact Solutions ◽  
Matrix Method ◽  
Diffraction Gratings ◽  
Wave Theory ◽  
Refractive Indices ◽  
Mathieu Functions ◽  
Reflection Gratings ◽  
Coupled Wave

We present a modified coupled wave theory to describe the properties of nonslanted reflection volume diffraction gratings. The method is based on the beta value coupled wave theory, which will be corrected by using appropriate boundary conditions. The use of this correction allows predicting the efficiency of the reflected order for nonslanted reflection gratings embedded in two media with different refractive indices. The results obtained by using this method will be compared to those obtained using a matrix method, which gives exact solutions in terms of Mathieu functions, and also to Kogelnik’s coupled wave theory. As will be demonstrated, the technique presented in this paper means a significant improvement over Kogelnik’s coupled wave theory.

Coupled-wave theory for birefringent photonic quasicrystal structures

2012 ◽  
Vol 29 (3) ◽  
pp. 382 ◽  
Author(s):  
I-Lin Ho ◽  
Ming-Tsung Lee ◽  
Yia-Chung Chang
Keyword(s):  
Wave Theory ◽  
Photonic Quasicrystal ◽  
Coupled Wave

Study on Natural Vibration Characteristics Based on the Coupled Wave Theory of Spring Supported Elastic Pipes and Fluids

2020 ◽  
Author(s):  
Takeshi Tokunaga ◽  
Koji Mori ◽  
Hiroko Kadowaki ◽  
Takashi Saito
Keyword(s):  
Boundary Condition ◽  
Blood Vessel ◽  
Flow Velocity ◽  
Blood Vessels ◽  
Natural Vibration ◽  
Wave Theory ◽  
Vibration Characteristics ◽  
Elastic Pipes ◽  
Coupled Wave ◽  
Natural Vibration Characteristics

Abstract A gradient of a blood flow velocity on the surface of a blood vessel is one of the clinical medicine concerns from the view point of prevention of the arteriosclerosis. In previous study, we formulated a relationship between the pressure and a flow velocity based on the coupled wave theory of elastic pipes and Newtonian fluids [1]. In addition, a flow velocity distribution and a wall shear stress are estimated by using the blood pressure data, which are non-invasively obtained by the tonometry method. This method is quasi-analytical method to apply the coupled wave theory for industrial flow field inside steel pipes proposed by Urata [4] to blood vessel, and has the advantage of systematic estimator compared with the numerical calculation. However, the coupled wave theory has applied to the elastic pipes that were assumed to be infinitely long. In addition, a single wave was assumed to be dominant within the elastic pipes and the Newtonian fluids. Therefore, in order to apply various length vessels in clinical field, the boundary of the blood vessels that varies from site to site, and the natural vibration characteristics that depend on the boundary conditions, could not be reflected in the wall shear stress estimation. In general, in order to solve the forced vibration with the boundary condition, it is necessary to clarify natural frequency and natural mode as natural vibration characteristics of structure. In this study, we introduce the spring supported elastic pipes to the coupled wave theory and formulated a relationship between the natural vibration characteristics and the boundary conditions. In this proposed method, the spring-supported elastic pipe has a feature that can be treated as an arbitrary boundary condition of an artery by giving an appropriate spring coefficients. Therefore, it is easy to apply to various types of blood vessels clinically. By investigating the natural vibration characteristics of blood vessels that varies from site to site, it may be possible to clarify fluctuations of blood flow in response to blood pressure with some frequency-bands. In addition, natural angular frequencies and natural modes of the spring supported elastic pipes and the Newtonian fluids were estimated for general blood vessel based on the coupled wave theory. In the result, the natural angular frequencies and the natural modes that reflect the clinical vibration characteristics to some extent can be estimated. On the other hand, particular modes may not reflect boundary condition, and further examination of the relationship between natural vibration characteristics and boundary condition is needed.

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