Wave theory of light leading to the generalized vectorial laws of reflection and refraction

This paper deals with the application of Huygens’ wave theory of light for the derivation of the generalized vectorial laws of reflection and refraction discovered by the author in 2005. The long-running literature falls short of such a theoretical proof of the generalized vectorial laws of reflection and refraction on the basis of wave theory. As such the present work is novel and original. At the same time it also enhances the theoretical foundation of the discovery of the generalized vectorial laws of reflection and refraction there by proving the efficiency and increasing the range of applicability of the wave theory of light as well.     

Exhaustive study of reflection and refraction at spherical surfaces on the basis of the newly discovered generalized vectorial laws of reflection and refraction

This paper deals with the application of the newly discovered generalized vectorial laws of reflection and refraction for making an extensive analysis of reflection and refraction at spherical surfaces. Various cases of image formation have been considered. It has been observed that, direct application of the generalized vectorial laws of reflection and refraction leads to the appropriate formula of ray optics for each of the cases considered. The analysis of the results are ultimately summed up to give birth to the generalized mirror formula as well as the generalized formula for refraction at spherical surfaces. Also by using the results obtained for refraction at spherical surfaces, the Lens makers’ formulae have been finally offered.     

Discovering the generalized vectorial laws of multiple reflection and refraction

This paper reports on the discovery of the generalized vectorial laws of multiple reflection and refraction as an extension of the earlier discovery of the generalized vectorial laws of reflection and refraction reported in 2005. The present discovery is novel and original and interesting from academic point of view. It will enrich the field of optics.     

Addressing some issues of Ray Optics on the basis of the newly discovered generalized vectorial laws of reflection and refraction

This paper addresses a few issues concerning Ray Optics on the basis of the newly discovered generalized vectorial laws of reflection and refraction. Along with confirming the validity of the principle of reversibility of light, the present study confirms the existing relationship between object distance and image distance in case of reflection by a plane mirror. General novel relations between real distance and apparent distance in case of image formation due to refraction also resulted from the present study. Finally novel treatment has been offered to deal with the problem of refraction through a parallel-sided slab of a refracting material on the basis of the aforesaid generalized vectorial law of refraction.     

Vectorial approach of determining the wave propagation at metasurfaces

Vector approach often benefits optical engineers and physicists, and a vector formulation of the laws of reflection and refraction has been studied (Tkaczyk, 2012). However, the conventional reflection and refraction laws may be violated in the presence of a metasurface, and reflection and refraction at the metasurface obey generalized laws of reflection and refraction (Yu et al., 2011). In this letter, the vectorial laws of reflection and refraction at the metasurface were derived, and the matrix formulation of these vectorial laws are also obtained. These results enable highly efficient and unambiguous computations in ray-tracing problems that involve a metasurface.     

The generalized vectorial laws of reflection and refraction applied to the rotation problems in ray optics

This paper deals with the mirror rotation problem and the problem of rotation of refracting surface in ray optics. These two problems of rotation in ray optics have been dealt with on the basis of the generalized vectorial laws of reflection and refraction discovered by the author in 2005. In addition to the development of many interesting physical insights to the aforesaid rotation problems in ray optics, the most remarkable fact that has been discovered in the present study is that the proposition ‘Velocity of light is unattainable’ is not correct. Rather, it is possible to have velocity exceeding the velocity of light - a result not in agreement with the special theory of relativity.     

hcp结构的Co磁性膜表面和界面的非线性克尔旋转及SHG的研究

本文基于对称性理论、磁性表面的菲涅耳反射和折射定律,研究了hcp(密排六方体)Co结构的χ⁽²⁾、SHG(二次谐波振荡)信号强度和非线性磁光克尔旋转角Φ_k,α⁽²⁾与入射角、偏振角及光子能量的关系.结果表明,Φ_k,α⁽²⁾比线性克尔角有巨大的增强;当接近垂直入射时,Φ_k,α⁽²⁾接近90°;Φ_k,α⁽²⁾灵敏地依赖于M的影响,从而可以通过Φ_k,α⁽²⁾来决定薄膜中的晶轴方向和磁化强度的取向.     

The wave flow effect on a plane boundary between vacuum and an optical medium with a quasi-zero refractive index

A boundary problem in which a plane electromagnetic wave is reflected and refracted at a plane boundary of a semi-infinite optical medium with a quasi-zero refractive index has been solved. Such a medium has a random refractive index taking values in an interval from zero to some finite value less than unity. It means that the concept of a sharp interface between two media loses its meaning, the boundary of the medium becomes inhomogeneous, and laws of reflection and refraction of light become non-Fresnelian. Formulas for non-Fresnelian amplitudes of reflection and refraction have been derived. It is shown that a surface wave arises near the boundary of a medium with a quasi-zero refractive index. The wave propagates both on the inside and outside of the boundary.     

用于相位突变界面的广义的反射定律和折射定律

考虑到位于两物质界面上的Metasurface对光线传播行为的影响, 从费马原理和边界条件连续两种角度出发, 推导了可用于相位突变界面的广义反射与折射定律. 该定律在界面对光波的相位改变量为零的情况下, 回归为通常的反射定律和折射定律. 利用广义的折射定律和反射定律讨论了介质折射率、界面上的相位梯度等因素对光传播行为的影响, 发现利用广义的折射定律和反射定律很容易实现反常反射和反常折射行为, 并给出了出现反常反射和反常折射的条件, 以此为基础可以实现对光波的随意控制. 依据广义的折射定律和反射定律分析了一维相位掩模板对光场传播行为的影响. 关键词： 超材料 相位突变界面 反射定律 折射定律     

利用对称性原理推导几何光学三定律

从对称性的角度,分析了光波在无限大均匀介质中、两种媒质的分界面上传播必须遵从的时间和空间平移不变性,推导出光的直线传播、反射以及折射定律,揭示了支配几何光学三定律的更为深刻而底层的对称性原因,这种视角对于光学部分的教学将产生深刻的影响.     

电磁波方程及折射、反射定律的一些思考

本文由电磁波的麦克斯韦方程组出发,介绍导出折射定律和反射定律的一种证明方法.其证明方法,使用了空间微元近似,然后推广至全空间传播的方法,从而简化了麦克斯韦方程组求解的烦琐过程,提出了一种可教学推广的实用性方法.通过使用微元法,求解得到麦克斯韦方程的行波解形式,即得出电磁场是一种行波.由电磁场的向量形式推导空间中电磁波的折射、反射定律,得到折射、反射定律的证明并不需要电磁波的解析形式,在连续函数的情形下是普遍成立的.求解过程中加深对麦克斯韦方程组的理解,体现了电磁过程的深刻物理图像,也为由几何光学向波动光学过渡提供一种思想上的指导.     

电磁波在运动介质中及表面处的传播特性

论述了运动介质对电磁波频率、速度和传播方向的影响及在运动介质表面的反射定律和折射定律。     

Formulation of the Snell–Descartes Laws in Terms of Geometric Algebra

Russian Physics Journal - A formulation of the laws of reflection and refraction of optical rays by the interface of two isotropic media using the mathematical apparatus of geometric algebra is...     

Vectorial laws of refraction and reflection using the cross product and dot product

We demonstrate that published vectorial laws of reflection and refraction of light based solely on the cross product do not, in general, uniquely determine the direction of the reflected and refracted waves without additional information. This is because the cross product does not have a unique inverse operation, which is explained in this Letter in linear algebra terms. However, a vector is in fact uniquely determined if both the cross product (vector product) and dot product (scalar product) with a known vector are specified, which can be written as a single equation with a left-invertible matrix. It is thus possible to amend the vectorial laws of reflection and refraction to incorporate both the cross and dot products for a complete specification with unique solution. This enables highly efficient, unambiguous computation of reflected and refracted wave vectors from the incident wave and surface normal.     

规范不变系统量子水平的变换性质及应用

按Faddeev-Popov路径积分量子化方法,给出规范不变系统在位形空间中的生成泛函,导出了系统位形空间中量子水平的变换性质.讨论了该系统量子水平的守恒律问题,且给出了Poincar群变换下电磁场在介质分界面附近量子水平的变换性质,在量子水平上说明了电磁波反射和折射时能量中心的“横移”现象. 关键词： 规范理论 位形空间 路径积分 “横移”效应     

用于液晶电光特性计算的无奇异点2×2矩阵研究

Berreman的矩阵法是研究和计算液晶光学特性的通用方法.为了减少计算量,近年来许多学者致力于简化其方法以提高计算速度,本文根据各向异性介质中光传播的电磁场理论以及光学折反射定律,在保证其准确性的同时,推出了新的矩阵方法.这种2×2矩阵公式表示相当简单.理论研究结果表明,该方法减少了以往的计算量,快速简洁,结果准确.     

Photon recoil momentum in dispersive media

A systematic shift of the photon recoil momentum due to the index of refraction of a dilute gas of atoms has been observed. The recoil frequency was determined with a two-pulse light grating interferometer using near-resonant laser light. The results show that the recoil momentum of atoms caused by the absorption of a photon is n variant Planck's k, where n is the index of refraction of the gas and k is the vacuum wave vector of the photon. This systematic effect must be accounted for in high-precision atom interferometry with light gratings.     

反射后激光(光子)螺旋性改变的量子论解释和信息论意义

基于近年来王顺金提出的处理螺旋光纤中激光(光子)传播时的螺旋性变化的理论方法和所得结果,分析了激光(光子)在反射后螺旋性(左旋与右旋)互换这一实验事实,发现激光(光子)反射的瞬息过程会产生一个极高的激光束回转频率,它与激光园偏振(光子自旋)发生科式惯性力耦合,进而改变激光(光子)的螺旋性.还发现当激光束回转频率达到极大时,将发生激光(光子)螺旋性(左旋与右旋)互换.讨论了激光反射后螺旋性互换的信息论含义及其应用.     

热Fock态下量子效应对介观左手传输线负折射系数的影响

基于热场动力学理论研究了热Fock态下量子效应对介观左手传输线微波段负折射系数的影响.结果表明:负折射系数随电流涨落的增加表现出线性递增的特点,而随温度的升高、频率的增大表现出锐减特性;负折射系数的变化幅度受光子数调控.该结论可对基于左手传输线开发的微波器件的微型化、集成化研究提供参考.     

On the mechanism of the volume reflection of relativistic particles

The mechanisms of the volume reflection of positively and negatively charged relativistic particles in a bent crystal have been analyzed. It has been shown that the empty core effect is significant for the reflection of the negatively charged particles. The average reflection angle of the negatively charged particles has been determined and the conditions for the observation of the reflection and refraction are discussed.