هذه صفحة لقطة ثنائية اللغة تم حفظها بواسطة المستخدم في 2025-5-8 2:02 لـ https://app.immersivetranslate.com/pdf-pro/4876fd42-71d8-4cb0-a4de-da4bcc823464/?isTrial=true، مقدمة بدعم ثنائي اللغة من قبل الترجمة الغامرة. تعلم كيفية الحفظ؟

CHAPTER 6 Retry    Reason

Optics of Solids Retry    Reason

6.1 General Remarks Retry    Reason

The study of the propagation of light through matter, particularly solid matter, comprises one of the important and interesting branches of optics. The many and varied optical phenomena exhibited by solids include such things as selective absorption, dispersion, double refraction, polarization effects, and electro-optical and magneto-optical effects. Many of the optical properties of solids can be understood on the basis of classical electromagnetic theory. The present chapter applies the macroscopic Maxwell theory to the propagation of light through solids. The microscopic origin of the optical properties of solids will be treated classically, since the quantum-theoretical treatment is beyond the scope of this book. But the way in which the phenomena are described by the classical theory gives considerable physical insight and helps to provide a fundamental background for later study. Retry    Reason

6.2 Macroscopic Fields and Maxwell's Equations Retry    Reason

The electromagnetic state of matter at a given point is described by four quantities: Retry    Reason
  1. The volume density of electric charge ρ ρ rho\rho Retry    Reason
  2. The volume density of electric dipoles, called the polarization P P P\mathbf{P} Retry    Reason
  3. The volume density of magnetic dipoles, called the magnetization M M M\mathbf{M} Retry    Reason
  4. The electric current per unit area, called the current density J J J\mathbf{J} Retry    Reason
All of these quantities are considered to be macroscopically averaged in order to smooth out the microscopic variations due to the atomic makeup of all matter. They are related to the macroscopically averaged fields E E E\mathbf{E} and H H H\mathbf{H} by the following Maxwell equations: Retry    Reason
∇ × E = − μ 0 ∂ H ∂ t − μ 0 ∂ M ∂ t ∇ × E = − μ 0 ∂ H ∂ t − μ 0 ∂ M ∂ t grad xxE=-mu_(0)(delH)/(del t)-mu_(0)(delM)/(del t)\nabla \times \mathbf{E}=-\mu_{0} \frac{\partial \mathbf{H}}{\partial t}-\mu_{0} \frac{\partial \mathbf{M}}{\partial t}
∇ × H = ϵ 0 ∂ E ∂ t + ∂ P ∂ t + J ∇ × H = ϵ 0 ∂ E ∂ t + ∂ P ∂ t + J grad xxH=epsilon_(0)(delE)/(del t)+(delP)/(del t)+J\boldsymbol{\nabla} \times \mathbf{H}=\epsilon_{0} \frac{\partial \mathbf{E}}{\partial t}+\frac{\partial \mathbf{P}}{\partial t}+\mathbf{J}
∇ ⋅ E = − 1 ϵ 0 ∇ ⋅ P + ρ ϵ 0 ∇ ⋅ E = − 1 ϵ 0 ∇ ⋅ P + ρ ϵ 0 grad*E=-(1)/(epsilon_(0))grad*P+(rho)/(epsilon_(0))\boldsymbol{\nabla} \cdot \mathbf{E}=-\frac{1}{\epsilon_{0}} \boldsymbol{\nabla} \cdot \mathbf{P}+\frac{\rho}{\epsilon_{0}}
∇ ⋅ H = − ∇ ⋅ M ∇ ⋅ H = − ∇ ⋅ M grad*H=-grad*M\boldsymbol{\nabla} \cdot \mathbf{H}=-\boldsymbol{\nabla} \cdot \mathbf{M}
If one introduces the abbreviation D D D\mathbf{D} for the quantity ϵ 0 E + P ϵ 0 E + P epsilon_(0)E+P\epsilon_{0} \mathbf{E}+\mathbf{P}, known as the electric displacement, and the abbreviation B B B\mathbf{B} for μ 0 ( H + M ) μ 0 ( H + M ) mu_(0)(H+M)\mu_{0}(\mathbf{H}+\mathbf{M}), called the magnetic induction, then Maxwell’s equations assume the more compact forms: Retry    Reason
∇ × E = − ∂ B ∂ t ∇ × E = − ∂ B ∂ t grad xxE=-(delB)/(del t)\boldsymbol{\nabla} \times \mathbf{E}=-\frac{\partial \mathbf{B}}{\partial t}
∇ × H = ∂ D ∂ t + J ∇ × H = ∂ D ∂ t + J grad xxH=(delD)/(del t)+J\nabla \times \mathbf{H}=\frac{\partial \mathbf{D}}{\partial t}+\mathbf{J}
∇ ⋅ D = ρ ∇ ⋅ D = ρ grad*D=rho\boldsymbol{\nabla} \cdot \mathbf{D}=\rho
∇ ⋅ B = 0 ∇ ⋅ B = 0 grad*B=0\boldsymbol{\nabla} \cdot \mathbf{B}=0
The response of the conduction electrons to the electric field is given by the current equation (Ohm’s law) Retry    Reason
J = σ E J = σ E J=sigmaE\mathbf{J}=\sigma \mathbf{E}
where σ σ sigma\sigma is the conductivity. The constitutive relation Retry    Reason
D = ϵ E D = ϵ E D=epsilonE\mathbf{D}=\epsilon \mathbf{E}
describes the aggregate response of the bound charges to the electric field. The Retry    Reason