Deflection of ultra slow light under gravity

TL;DR

This paper proposes a theoretical framework to detect gravitational deflection of ultra slow light in laboratory conditions, predicting a measurable vertical fall of about 1 micron over 1 meter.

Contribution

It introduces a geometrical optics approach combining effective gravitational refractive index with optical dispersion to estimate ultra slow light deflection under Earth's gravity.

Findings

Predicted vertical fall of about 1 micron for 1 meter traversal with ultra slow light.

Derived a formula relating fall to group refractive index and Earth's gravitational parameters.

Suggests the effect is measurable and tunable via optical dispersion properties.

Abstract

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 $\Delta$ for a horizontal traversal $L$ as \[ \Delta = \frac{L^2}{2}\big(\frac{R_{\oplus G}}{R_\oplus^2}\big) n_g \big(\frac{1}{1+n_g\frac{R_{\oplus G}}{R_\oplus}}\big), \] 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 $\Delta \sim 1 \mu m$, that should be measurable $-$ in particular through its sensitive dependence on the frequency that tunes $n_g$.