User:Kshs95

Physical origin

While relativity holds that the speed of light in a vacuum is a universal constant (c), the speed at which light propagates in a material may be significantly less than c. For example, the speed of the propagation of light in water is only 0.75c. Matter can be accelerated beyond this speed during nuclear reactions and in particle accelerators. Čerenkov radiation results when a charged particle, most commonly an electron, exceeds the speed at which light is propagating in a dielectric (electrically insulating) medium through which it passes.

Moreover, the velocity that must be exceeded is the phase velocity rather than the group velocity. The phase velocity can be altered dramatically by employing a periodic medium, and in that case one can even achieve Čerenkov radiation with no minimum particle velocity — a phenomenon known as the Smith-Purcell effect. In a more complex periodic medium, such as a photonic crystal, one can also obtain a variety of other anomalous Čerenkov effects, such as radiation in a backwards direction (whereas ordinary Čerenkov radiation forms an acute angle with the particle velocity).

As a charged particle travels, it disrupts the local electromagnetic field (EM) in its medium. Electrons in the atoms of the medium will be displaced and polarized by the passing EM field of a charged particle. Photons are emitted as an insulator's electrons restore themselves to equilibrium after the disruption has passed. (In a conductor, the EM disruption can be restored without emitting a photon.) In normal circumstances, these photons destructively interfere with each other and no radiation is detected. However, when a disruption which travels faster than light is propagating through the medium, the photons constructively interfere and intensify the observed radiation.

It is important to note, however, that the speed at which the photons travel is always the same. That is, the speed of light, commonly designated as c, does not change. The light appears to travel more slowly while traversing a medium due to the frequent interactions of the photons with matter. This is similar to a train that, while moving, travels at a constant velocity. If such a train were to travel on a set of tracks with many stops it would appear to be moving more slowly overall; i.e., have a lower average velocity, despite having a constant higher velocity while moving.

The geometry of the Čerenkov radiation.

A common analogy is the sonic boom of a supersonic aircraft or bullet. The sound waves generated by the supersonic body do not move fast enough to get out of the way of the body itself. Hence, the waves "stack up" and form a shock front.

In a similar way, a charged particle can generate a photonic shock wave as it travels through an insulator.

In the figure, the particle (red arrow) travels in a medium with speed $v_{p}$ and we define the ratio between the speed of the particle and the speed of light as $\beta =v_{p}/c$ where $c$ is speed of light. n is the refractive index of the medium and so the emitted photons (blue arrows) travel at speed $v_{em}=c/n$.

The left corner of the triangle represents the location of the superluminal particle at some initial moment (t=0). The right corner of the triangle is the location of the particle at some later time t. In the given time t, the particle travels the distance

$x_{p}=v_{p}t=\beta \,ct$

whereas the emitted electromagnetic waves are constricted to travel the distance

$x_{em}=v_{em}t={\frac {c}{n}}t$

So:

$\cos \theta ={\frac {1}{n\beta }}$

Note that since this ratio is independent of time, one can take arbitrary times and achieve similar triangles. The angle stays same, meaning that subsequent waves generated between the initial time t=0 and final time t will form similar triangles with coinciding right endpoints to the one shown.

物理學解釋

根據狹義相對論，具有靜質量的物體運動速度不可能超過真空中的光速c，而光在介質中的傳播速度（群速度）是小於c的，例如在水中（折射率n為1.33）光僅以0.75c的速度在傳播。物體可以被加速到超過介電質中的光速，加速的來源可以是核反應或者是粒子加速器。當超過介電質中光速的粒子是帶電時（通常是電子）並通過這樣的介質時，切侖可夫輻射即會產生。

此外，要超過的光速是光的相速度而非群速度。透過採用週期性介質(periodic medium)的方法，光的相速度可以被大幅改變，甚至可以讓切侖可夫輻射沒有最小粒子速度的限制——此現象稱為史密斯-柏塞爾效應(Smith-Purcell effect)。在更複雜的週期性介質中，例如光子晶體，可以得到各式各樣的異常切侖可夫效應(anomalous Cherenkov effects)，例如反向傳播的輻射（在尋常切侖可夫輻射中，輻射和粒子速度呈一銳角）。

切侖可夫輻射的幾何關係。

和切侖可夫輻射相類比的是超音速飛行器或子彈的音爆現象。由超音速物體產生的音波速度無法快到足以離開物體，因此波「堆積」了起來，形成了一個震波波前。類似的情形，快船超過水波速度時也會在水面上產生很大的弓形震波(bow shock)。

相同地，當一個帶電的超光速粒子行經絕緣體，會產生光子震波。

右圖中，c是真空光速，n是介質折射率，v是粒子速度(紅色箭頭)，β是v/c。藍色箭頭則是發出的光子。幾何上，此二方向之角度關係為：

$\cos \theta ={\frac {1}{n\beta }}$。

特性

切侖可夫輻射的總強度與入射帶電粒子的速度成比例關係，另外粒子數量越多總強度也越強。與螢光或受激放射的電磁頻譜具有特定頻率的峰值的情形相異，切侖可夫輻射的頻譜是呈連續性的。一個頻率下的相對強度與該頻率呈正比，也就是說在切侖可夫輻射，高頻率（短波長）會有較強的強度。這解釋了為何可見光波段部分的切侖可夫輻射看起來呈亮藍色。實際上，多數切侖可夫輻射是在紫外線波段——當帶電粒子被更充足地加速後，才會使可見光波段變得明顯而得見；人眼感光最敏銳的波段是綠色光(平均為555奈米)，對於藍色光到紫色光的感應度則相當低。

如同音爆的情形一般，震波椎的角度與波源速度呈反比，在切侖可夫輻射也是如此。因此，觀測到的入射角可以用來計算產生切侖可夫輻射的帶電粒子的方向及速度。