Optics & Photonics News - December 2009

SLOW LIGHT ’09
Diffraction Elimination: Dragging Slow-Light
with Diffusing Atoms

Ofer Firstenberg, Paz London, Moshe Shuker, Amiram Ron and Nir Davidson

Optical di;raction, a fundamental phenomenon that dominates the propagation of light in free space, has stimulated research for centuries. Its understanding and manipulation are the cornerstones of optical technology. Diffraction elimination of a single optical mode can be obtained, as in an optical fiber or a waveguide, by patterning the index of refraction in the real transverse plane. However, within these waveguides, a multi-mode pattern is not maintained, and arbitrary images rapidly blur. Here, we present a medium with novel optical properties, in which the paraxial diffraction is manipulated in its natural wave-vector basis. We demonstrate several realizations of optical control over the magnitude and orientation of di;raction—non-di;ractive propagation of arbitrary images, negative-di;raction lensing and optically induced deflection.

We recently showed that images imprinted on a laser pulse can be dramatically slowed when traversing an alkali vapor medium via electromagnetically induced transparency (EIT). 1 Delayed images in vapor have also been performed with weak coherent pulses2 and have demonstrated the preservation of quantum coherence and entanglement. 3 At a typical group velocity of 1,000 m/s, the propagation of slow light is strongly a;ected by the thermal motion of the room-temperature atoms. Introducing an inert bu;er-gas attenuates the ballistic motion and reduces it to the di;usion regime, but nevertheless the di;usion length of the alkalis is still comparable to the slow-light spreading along its propagation.

In an equivalent spectral interpretation, the frequent collision with the buffer gas atoms cause Dicke narrowing of the Doppler spectrum, and the complex susceptibility becomes quadratic in the transverse momentum space. 4 ;us, on

(b)

(a) Incident image

Free-space diffraction

EIT, ∆=0

EIT, ∆<0

Free-space diffraction

(a) After 50 mm of free-space diffraction, the 100-;m features in the image are substantially distorted. When EIT takes place (∆=0), the diffracting image is slowed, dragged by the moving atoms, and exhibits diffusion. At ∆<0, however, both the diffraction and the diffusion are eliminated. (b) In an analogy to the Doppler trapping of atoms with negative detuning, outwards-confronting light components couple more ef;ciently to inwards moving atoms, counterbalancing the natural diffraction. (c) The digit ‘ 2,’ otherwise diffracting substantially, is imaged using a negative-diffraction medium in a slab-lens con;guration. Rays entering the cell refract to the opposite angle and refract back upon exiting.

Incident image

Transmitted image

(c) Negative diffraction

top of the free-space di;raction, slowed images are partially dragged by the atoms and undergo di;usion and additional induced paraxial-di;raction, the magnitude of which is determined by the EIT frequency detuning, ∆.

In such a medium, the optical di;raction of slow images can be eliminated completely. 5 By setting an appropriate detuning (∆<0) and carefully tuning the EIT parameters, we found that the induced di;raction completely counterbalances the paraxial free-space di;raction. Somewhat surprisingly, the di;usion can also be canceled in this regime, resulting in a non-di;ractive non-di;usive propagation or arbitrary images. ;e random thermal motion of the atoms is exploited to “Doppler trap” the light in the plane perpendicular to the propagation direction, regardless of its location. No other vapor medium exists that eliminates the optical di;raction of arbitrary images

and for any distance throughout their propagation. ;e sign, magnitude and direction of the induced di;raction can be optically controlled by varying the EIT parameters. For example, we have demonstrated a regime in which the di;raction occurs twice as fast and the possibility of inflicting a directional bias on a di;racting light beam. Most intriguing, we have realized a medium with a negative di;raction, in which the di;raction behaves as in a negative-index material. 

Ofer Firstenberg ( oferfir@tx.technion.ac.il), Paz London, Moshe Shuker and Amiram Ron are with the physics department of the Technion-Israel Institute of Technology. Nir Davidson is with the department of physics of complex systems in the Weizmann Institute of Science in Israel.

References

1. M. Shuker et al. Phys. Rev. Lett. 100, 223601 (2008). 2. R. M. Camacho et al. Phys. Rev. Lett. 98, 043902 (2007). 3. A.M. Marino et al. Nature 457, 859-62 (2009).