Superluminal Group Velocities (a.k.a. Fast Light) Dan Gauthier Duke University Department of Physics, The Fitzpatrick Center for Photonics and Communication Systems SCUWP January 17, 2010

Information on Optical Pulses

Where is the information on the waveform? How fast does it travel? Modern Optical Telecommunication Systems: Transmitting information encoded on optical fields http://www.picosecond.com/objects/AN-12.pdf 1 0 1 1 0 RZ data clock Where is the information on the waveform? How fast does it travel?

Slow Light Controllably adjust the speed of an optical pulse propagating through a dispersive optical material Slow light: Slow-light medium control

Motivation for Using “Slow” Light Optical buffers and all-optical tunable delays for routers and data synchronization. data packets router router

Outline Introduction to “Slow" and "Fast" Light Fast and backward light Reconcile with the Special Theory of Relativity

Pulse Propagation in Dispersive Materials

Propagation through glass

Propagation Through Dispersive Materials Q: How fast does a pulse of light propagate through a a dispersive material? A: There is no single velocity that describes how light propagates through a dispersive material dispersive media A pulse disperses (becomes distorted) upon propagation An infinite number of velocities!

Propagating Electromagnetic Waves: Phase Velocity monochromatic plane wave E z phase velocity Points of constant phase move a distance Dz in a time Dt phase Dispersive Material: n = n(w)

Linear Pulse Propagation: Group Velocity Lowest-order statement of propagation without distortion group velocity Control group velocity: metamaterials, highly dispersive materials different

Variation in vg with dispersion slow light fast light

Pulse Propagation: Slow Light (Group velocity approximation)

Achieving Slow Light Boyd and Gauthier, in Progress of Optics 43, 497-530 (2002) Boyd and Gauthier, Science 306, 1074 (2009)

When is the dispersion large? Absorption coefficient absorption 2-level system |2> Index of refraction laser field n - 1 |1> Group index ng - 1 frequency (a.u.)

Electromagnetically-Induced Transparency (EIT) Absorption coefficient absorption 3-level system |2> control field Index of refraction laser field n - 1 |3> |1> Group index ng - 1 frequency (a.u.) S. Harris, etc.

EIT: Slowlight Group velocities as low as 17 m/s observed! Hau, Harris, Dutton, and Behroozi, Nature 397, 594 (1999) Group velocities as low as 17 m/s observed!

Fast-Light Fast light theory, Gaussian pulses: C. G. B. Garrett, D. E. McCumber, Phys. Rev. A 1, 305 (1970). Fast light experiments, resonant absorbers: S. Chu, S. Wong, Phys. Rev. Lett. 48, 738 (1982). B. Ségard and B. Macke, Phys. Lett. 109, 213 (1985). A. M. Akulshin, A. Cimmino, G. I. Opat, Quantum Electron. 32, 567 (2002). M. S. Bigelow, N. N. Lepeshkin, R. W. Boyd, Science 301, 200 (2003)

Pulse Propagation: Fast Light (Group velocity approximation)

Fast-light via a gain doublet Steingberg and Chiao, PRA 49, 2071 (1994) (Wang, Kuzmich, and Dogariu, Nature 406, 277 (2000))

Achieve a gain doublet using stimulated Raman scattering with a bichromatic pump field Wang, Kuzmich, and Dogariu, Nature 406, 277 (2000)

Fast light in a laser driven potassium vapor large anomalous dispersion

Observation of large pulse advancement tp = 263 ns A = 10.4% vg = -0.051c ng = -19.6 M.D. Stenner, D.J. Gauthier, and M.A. Neifeld, Nature 425, 695 (2003).

Reconcile with the Special Theory of Relativity

Problems with superluminal information transfer Light cone

Minimum requirements of the optical field L. Brillouin, Wave Propagation and Group Velocity, (Academic, New York, 1960). (compendium of work by A. Sommerfeld and L. Brillouin from 1907-1914) A. Sommerfeld A "signal" is an electromagnetic wave that is zero initially. front http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Sommerfeld.html

Primary Finding of Sommerfeld (assumes a Lorentz-model dielectric with a single resonance) The front travels at c regardless of the details of the dielectric Physical interpretation: it takes a finite time for the polarization of the medium to build up; the first part of the field passes straight through!

Generalization of Sommerfeld and Brillouin's work point of non-analyticity P t knowledge of the leading part of the pulse cannot be used to infer knowledge after the point of non-analyticity new information is available because of the "surprise" Chiao and Steinberg find point of non-analyticity travels at c. Therefore, they associate it with the information velocity.

Implications for fast-light vacuum transmitter receiver transmitter receiver with dispersive material transmitter receiver information still available at c!

Send the symbols through our fast-light medium

Fast light, backward light and the light cone The pulse peak can do weird things, but can't go beyond the pulse front (outside the light cone)

Summary Slow and fast light allows control of the speed of optical pulses Amazing results using atomic systems Transition research to applications using existing telecommunications technologies Fast light gives rise to unusual behavior Interesting problem in E&M to reconcile with the special theory of relativity

Collaborators http://www.phy.duke.edu/ Duke U of Arizona UCSC UCSB D. Blumenthal U of Arizona M. Neifeld Rochester R. Boyd, J. Howell Cornell A. Gaeta UCSC A. Willner http://www.phy.duke.edu/

A beam with two frequencies: The group velocity Sir Hamilton 1839 J.S. Russell 1844 G.G. Stokes 1876 Lord Rayleigh 1877 A beam with two frequencies: The group velocity Photos from: http://www-gap.dcs.st-and.ac.uk/~history/l

Speed of the envelope in dispersive materials