超慢光在重力作用下的偏转
Deflection of ultra slow light under gravity
摘要：
最近几个研究小组在强色散介质中进行的超慢光实验报告了光脉冲的速度减慢到每秒几米的速度，这鼓励我们研究在地球引力下检测超慢光偏转或下降的有趣可能性，即，在实验室长度范围内。在没有一个可用的广义相对论理论的光波传播在这样一个强色散的光学介质中的引力场的存在下，我们提出了一个几何光学为基础的推导，结合{ \it的有效引力折射率}添加与通常的光学色散。它给出了一个偏转，或垂直下降$Δ$为水平遍历$L$为\[ Δ= \frac{L^2}{2}\big(\frac{R_{\oplus G}}{R_\oplus^2}\big) n_g \big(\frac{1}{1+n_g\frac{R_{\oplus G}}{R_\oplus}}\big), \]，其中$R_{\oplus G}/R_\oplus$是地球引力半径（$R_{\oplus G}$）与其几何半径$R_\oplus$的比值，$n_g$是强色散光学介质的群折射率。该表达式基本上是以群速度$v_g=c/n_g$水平投影的物体的牛顿下落的表达式，并且可以通过折射率$n_g$进行折射调谐。对于$L \sim 1 m$和$n_g = c/v_g \sim 10^8$（对应于超慢脉冲速度$\sim few \times 1 ms^{-1}$），我们获得了下降的$Δ\sim 1 μm$，其应该是可测量的$-$，特别是通过其对调谐$n_g$的频率的敏感依赖性。
英文摘要：
Recent experiments on ultra slow light in strongly dispersive media by several research groups reporting slowing down of the optical pulses down to speeds of a few metres per second encourage us to examine the intriguing possibility of detecting a deflection or fall of the ultra slow light under Earth's gravity, i.e., on the laboratory length scale. In the absence of a usable general relativistic theory of light waves propagating in such a strongly dispersive optical medium in the presence of a gravitational field, we present a geometrical optics based derivation that combines {\it the effective gravitational refractive index} additively with the usual optical dispersion. It gives a deflection, or the vertical fall $Δ$ for a horizontal traversal $L$ as \[ Δ= \frac{L^2}{2}\big(\frac{R_{\oplus G}}{R_\oplus^2}\big) n_g \big(\frac{1}{1+n_g\frac{R_{\oplus G}}{R_\oplus}}\big), \] where $R_{\oplus G}/R_\oplus$ is the ratio of the gravitational Earth radius($R_{\oplus G}$) to its geometrical radius $R_\oplus$, and $n_g$ is the group refractive index of the strongly dispersive optical medium. The expression is essentailly that for the Newtonian fall of an object projected horizontally with the group speed $v_g=c/n_g$, and is tunable refractively through the index $n_g$. For $L \sim 1 m$ and $n_g = c/v_g \sim 10^8$ (corresponding to the ultra-slow pulse speed $\sim few \times 1 ms^{-1}$), we obtain a fall $Δ\sim 1 μm$, that should be measurable $-$ in particular through its sensitive dependence on the frequency that tunes $n_g$.
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