Cherenkov radiation 带电粒子在介质中运动产生诱导电流，当粒子速度超过介质内光速时， Cherenkov1934,Frank &Tam 1937 1958 Nobel prize 真空中匀速直线运动带电粒子不辐射？ 带电粒子在介质中运动产生诱导电流，当粒子速度超过介质内光速时， 激发次波与原粒子电磁场干涉，可以形成辐射场。 方向性好:

介质中运动电荷产生的场可用推迟势（介质光速）表示

特定频率分量 讨论

Angular distribution 单位频率间隔 单位路程辐射能量 由典型的色散曲线（show）知 Cherenkov 辐射只包括某一频段

Dispersion (p309) 当电磁波入射到介质内时，由束缚电子散射的次波会叠加成介质内传播的电磁波。宏观电磁现象由极化强度 P 和 磁化强度 M 决定。 束缚电子（谐振子）散射 散射波

平均能流密度 散射截面

稀薄气体近似：忽略分子间相互作用， 单位体积电子数N，利用束缚电子散射结果 通常测定的折射率即为实部 n

考虑到多个固有频率（激发态），分支为 fi

Scattering and Diffraction Involved scales: Wavelength and size of target Lowest order induced EM multipoles oscillate and radiate energy Need more systematic treatment with multipoles Semi-geometric methods

The incident fields are Induced dipole moments (p and m) radiate energy in all directions. The scattered (radiated) fields (in the direction n) are (9.19,10.2)

The differential cross section = power radiated per unit solid angle, per unit incident flux Rayleigh’s law: universal characteristic of the of the long wave length scattering by any finite system

Scattering by a small dielectric sphere of radius a The electric dipole moment is (4.56) at p158) So the differential cross section

The incident wave is unpolarized the parallel and perpendicular components are The polarization, differential and total scattering cross section are (see Fig 10.2 at p459)

Scattering by a small perfectly conducting sphere of radius a The electric dipole moment is (see section 2.5 at p62) So the differential cross section

The differential cross section and polarization The cross section has a strong backward peaking caused by electric dipole -- magnetic dipole interference. The polarization reaches 1 at 60 degrees and is positive through the whole angular range.

Perturbation theory- the medium is supposed to have small changes in its response to applied fields The wave equation for D With harmonic time variation, the above equation becomes A formal solution is

The scattering amplitude The differential cross section (a formal solution)

Born approximation The unperturbed fields so Suppose that the scattering region is a uniform dielectric sphere of radius a, is constant inside a sphere and vanishes outside

Perform the integral At low frequencies or in the forward direction

Blue sky If individual molecules are assumed to possess dipole moments where is molecular polarizability (p161) The effective variation in dielectric constant is The differential cross section is

The total cross section For dilute gases The total cross section In traversing a thickness dx of the gases, the fractional loss of flux is so the beam intensity is with absorption or attenuation coefficient

Discussion Light received away from the incident beam is more heavily weighted in high-frequency (blue) components than the spectral distribution of the incident beam Transmitted beam becomes increasingly red in its spectral composition, as well as diminishing in overall intensity The blueness of the sky, the redness of the sunset, the waneness of the winter sun, and the ease of sunburning at midday in summer Relative intensities: Zenith Sunrise-Sunset Red (6500A) 0.96 0.21 Green (5200A) 0.90 0.024 Violet (4100A) 0.76 0.000065