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
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
(a) Incident image
(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.
(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 ( email@example.com), 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.
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).
4. O. Firstenberg et al. Phys. Rev. Lett. 102, 043601 (2009).
5. O. Firstenberg et al. Nature Physics. Published online:
doi: 10.1038/nphys1358 (2009).