Observation of a Push Force on the End Face of a Nanometer Silica Filament Exerted by Outgoing Light

There are two different proposals for the momentum of light in a transparent dielectric of refractive index $n$: Minkowski’s version $nE/c$ and Abraham’s version $E/(nc)$, where $E$ and $c$ are the energy and vacuum speed of light, respectively. Despite many tests and debates over nearly a century, momentum of light in a transparent dielectric remains controversial. In this Letter, we report a direct observation of the inward push force on the free end face of a nanometer silica filament exerted by the outgoing light. Our results suggest that Abraham’s momentum is correct.

Figure 1

The stationary micrograph of the tip of the SF, showing that the diameter of the SF tip is about 450 nm. The inset is the enlarged profile of a weak red light beam outgoing from the SF end face.

Figure 2

The video frames of the moving SF as the result of the optical force for the SF in air, where (a), (b), (c), and (d) are the images of SF at 0, $1/15$, $2/15$, and $3/15\mathrm{s}$, respectively, after a laser pulse arrives, and (e), (f), (g), and (h) correspond to the next laser pulse. Figures (i) and (j) show the effect of asymmetric refraction related, respectively, to Abraham momentum ${\mathbf{K}}_{\mathbf{0}}/n$ and Minkowski momentum $n{\mathbf{K}}_{\mathbf{0}}$, where ${\mathbf{K}}_{\mathbf{0}}$ is the vacuum momentum of light and $\Delta \mathbf{K}$ ($-\Delta \mathbf{K}$) is the momentum change of light (SF end). Pink solid and dashed lines in (i) and (j) indicate two different states of the SF.

Figure 3

(a) The measurements for the transmission of SF $P_T$, the transmission plus scattering of SF $P_{T\&S}$, and the transmission of a cut bare single-mode fiber $P_{\mathrm{Fib}}$. (b),(c) The experiment of thermal effect of the SF: A colophony filament with $3\mu \mathrm{m}$ diameter is adhered on the SF tip. The overlap of the colophony filament and SF is between two bright spots. The coupled-in power of cw 650 nm light is 6.5 mW. The time intervals for (b) and (c) are, respectively, 1 and 60 minutes after turning on the laser. The room temperature is $27°\mathrm{C}$.

Figure 4

The video frames of the moving SF as the result of the optical force for the SF in a vacuum of $2\times {10}^{-5}\mathrm{Torr}$ at $20°\mathrm{C}$ with an electrostatic shield. The SF is driven by a power-tunable, unpolarized cw 980 nm light and highlighted by a 0.1 mW cw 650 nm light. (a) No 980 nm light is coupled in; (b) the coupled-in power of 980 nm is 17.8 mW; (c)–(e) the power is increased further to 19.5 mW in a time of 1.9 s; (f) the micrograph of the SF tip. Figures (A) and (B) are the results of the numerical simulations, with (A) corresponding to the initial state (a) and (B) corresponding to (b). The white vertical lines are for displacement reference.