Slow, Fast, and Backwards Light: Fundamentals and Applications Robert W. Boyd

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1 Slow, Fast, and Backwards Light: Fundamentals and Applications Robert W. Boyd Institute of Optics and Department of Physics and Astronomy University of Rochester with George Gehring, Giovanni Piredda, Paul Narum, Aaron Schweinsberg, Zhimin Shi, Heedeuk Shin, Joseph Vornehm, Petros Zerom, and many others Presented at the OSA Topical Meeting on Slow Light, July 9-11, 2007

2 Slow Light and Optical Buffers All-Optical Switch input ports switch output ports Use Optical Buffering to Resolve Data-Packet Contention controllable slow-light medium But what happens if two data packets arrive simultaneously? Controllable slow light for optical buffering can dramatically increase system performance. Daniel Blumenthal, UC Santa Barbara; Alexander Gaeta, Cornell University; Daniel Gauthier, Duke University; Alan Willner, University of Southern California; Robert Boyd, John Howell, University of Rochester

3 Slow-Light Telecom Buffer / Regeneration System Optical Buffering Need many pulse-widths of delay Use the conversion / dispersion method of Gaeta and others FWM wavelength conversion dispersive delay D(λ) FWM wavelength conversion ΔT Regeneration of Pulse Timing Single pulse-width of delay adequate, but need precise control Use true slow light (SBS?) pump off pump on time slot

4 Slow and Fast Light and Optical Resonances Pulses propagate at the group velocity given by v g = c n g n g = n + dn d Want large dispersion to obtain extreme group velocities Sharp spectral features produce large dispersion. The group index can be large and positive (slow light). positive and much less than unity (fast light) or negative (backwards light).

5 How to Create Slow and Fast Light I Use Isolated Gain or Absorption Resonance α absorption resonance g gain resonance 0 0 n n ng slow light ng slow light fast light fast light

6 How to Create Slow and Fast Light II Use Dip in Gain or Absorption Feature g n dip in gain feature 0 0 α n dip in absorption feature ng slow light ng slow light fast light fast light Narrow dips in gain and absorption lines can be created by various nonlinear optical effects, such as electromagnetically induced transparency (EIT), coherent population oscillations (CPO), and conventional saturation.

7 Challenge / Goal (2003) Slow light in a room-temperature, solid-state material. Our solution: Slow light via coherent population oscillations (CPO), a quantum coherence effect related to EIT but which is less sensitive to dephasing processes.

8 Slow Light via Coherent Population Oscillations E 3, + δ E 1, saturable medium + δ measure absorption 2γ ba = 2 T 2 b Γ ba = 1 T 1 a absorption profile 1/T 1 Ground state population oscillates at beat frequency δ (for δ < 1/T 1 ). Population oscillations lead to decreased probe absorption (by explicit calculation), even though broadening is homogeneous. Rapid spectral variation of refractive index associated with spectral hole leads to large group index. Ultra-slow light (ng > 10 6 ) observed in ruby and ultra-fast light (n g = 4 x 10 5 ) observed in alexandrite by this process. Slow and fast light effects occur at room temperature! PRL 90,113903(2003); Science, 301, 200 (2003)

9 Advantages of Coherent Population Oscillations for Slow Light Works in solids Works at room temperature Insensitive of dephasing processes Laser need not be frequency stabilized Works with single beam (self-delayed) Delay can be controlled through input intensity

10 Slow Light via Coherent Population Oscillations Ultra-slow light (ng > 10 6 ) observed in ruby and ultra-fast light (n g = 4 x 10 5 ) observed in alexandrite at room temperature. Slow and fast light in an EDFA 0.15 Slow light in a SC optical amplifier Fractional Advancement mw mw mw mw mw - 0 mw Slow light in PbS quantum dots Modulation Frequency (Hz) 3 ps

11 Numerical Modeling of Pulse Propagation through Slow and Fast-Light Media Numerically integrate the reduced wave equation A z 1 v g A t = 0 and plot A(z,t) versus distance z. Assume an input pulse with a Gaussian temporal profile. Study three cases: Slow light v g = 0.5 c Fast light v g = 5 c and v g = -2 c CAUTION: This is a very simplistic model. It ignores GVD and spectral reshaping.

12 Pulse Propagation through a Fast-Light Medium (n g =.2, v g = 5 c)

13 Pulse Propagation through a Backwards- Light Medium (n g = -.5, v g = -2 c)

14 Slow and Fast Light in an Erbium Doped Fiber Amplifier Fiber geometry allows long propagation length Saturable gain or loss possible depending on pump intensity Output Advance = 0.32 ms Input FWHM = 1.8 ms 0.15 Time 6 ms Fractional Advancement mw mw mw mw mw - 0 mw out in Modulation Frequency (Hz) Schweinsberg, Lepeshkin, Bigelow, Boyd, and Jarabo, Europhysics Letters, 73, 218 (2006).

15 Observation of Backward Pulse Propagation in an Erbium-Doped-Fiber Optical Amplifier 1550 nm laser ISO 980 nm laser or 80/20 coupler Ref WDM EDF Signal WDM We time-resolve the propagation of the pulse as a function of position along the erbiumdoped fiber. Procedure cutback method couplers embedded in fiber normalized intensity pulse is placed on a cw background to minimize pulse distortion out in G. M. Gehring, A. Schweinsberg, C. Barsi, N. Kostinski, R. W. Boyd, Science 312, time (ms)

16 Experimental Results: Backward Propagation in Erbium-Doped Fiber Normalized: (Amplification removed numerically)

17 Observation of Backwards Pulse Propagation - conceptual prediction - laboratory results A strongly counterintuitive phenomenon But entirely consistent with established physics Δt = 0 Δt = 3 G. M. Gehring, A. Schweinsberg, C. Barsi, N. Kostinski, and R. W. Boyd, Science 312, Δt = 6 Δt = 9 Δt = 12 Δt = x10 Normalized length n g Z (m) 5

18 Observation of Backward Pulse Propagation in an Erbium-Doped-Fiber Optical Amplifier Summary: Backwards propagation is a realizable physical effect. (Of course, many other workers have measured negative time delays. Our contribution was to measure the pulse evolution within the material medium.)

19 Causality and Superluminal Signal Transmission Ann. Phys. (Leipzig) 11, 2002.

20 Propagation of a Truncated Pulse through Alexandrite as a Fast-Light Medium normalized intensity output pulse input pulse time (ms) Smooth part of pulse propagates at group velocity Discontinuity propagates at phase velocity Information resides in points of discontinuity Bigelow, Lepeshkin, Shin, and Boyd, J. Phys: Condensed Matter, 3117, See also Stenner, Gauthier, and Neifeld, Nature, 425, 695, 2003.

21 How to Reconcile Superluminality with Causality emitted waveform pulse front transmitter receiver vacuum propagation transmitter receiver fast-light propagation transmitter receiver Gauthier and Boyd, Photonics Spectra, p. 82 January 2007.

22 Information Velocity Tentative Conclusions In principle, the information velocity is equal to c for both slow- and fast-light situations. So why is slow and fast light even useful? Because in many practical situations, we can perform reliable meaurements of the information content only near the peak of the pulse. In this sense, useful information often propagates at the group velocity. In a real communication system it would be really stupid to transmit pulses containing so much energy that one can reliably detect the very early leading edge of the pulse. which gives better S/N? front

23 Fundamental Limits on Slow and Fast Light Slow Light: There appear to be no fundamental limits on how much one can delay a pulse of light (although there are very serious practical problems).* Fast Light: But there do seem to be essentially fundamental limits to how much one can advance a pulse of light. Why are the two cases so different?** * Boyd, Gauthier, Gaeta, and Willner, PRA 2005 ** We cannot get around this problem simply by invoking causality, first because we are dealing with group velocity (not information velocity), and second because the relevant equations superficially appear to be symmetric between the slow- and fast-light cases.

24 Why is there no limit to the amount of pulse delay? At the bottom of the dip in the absorpton, the absorption can in principle be made to vanish. There is then no limit on how long a propagation distance can be used. This trick works only for slow light. α n ng dip in absorption feature 0 infinite propagation distance slow light fast light

25 Influence of Spectral Reshaping (Line-Center Operation, Dip in Gain or Absorption Feature) input pulse output pulse slow-light output pulse fast-light T( ) G( ) for still longer propagation distances, the pulse breaks up spectrally and temporally spectrally narrowed pulse spectrally broadened pulse double-humped pulse

26 Numerical Results: Propagation through a Linear Dispersive Medium Full (causal) model solve wave equation with P = χe where ( ) = A 0 i Fast light: Lorentzian absorption line T = exp(-32) vary line width to control advance Slow light: Lorentzian gain line T = exp(+32) vary line width to control delay Slow Light 1 pulse-width delay 2 pulse-widths delay 4 pulsewidth delay Fast Light 1 pulse-width advance 2 pulse-widths advance vacuum 4 pulse-widths advance Same Gaussian input pulse in all cases vacuum 6 pulsewidth delay 6 pulse-widths advance time time

27 Propagation of Full and Truncated Pulse Trains Slow Fast Fast - truncated

28 Propagation of Truncated Pulse Trains Through a Fast-Light Medium z z time z z Second output pulse is generated out of nothing.

29 Interferometry and Slow Light Under certain (but not all) circumstances, the sensitivity of an interferomter is increased by the group index of the material within the interferometer! Sensitivity of a spectroscopic interferometer is increased Typical interferometer: Beam Splitter #1 Slow Light Medium We use CdS x Se 1-x as our slow-light medium Beam expander L 0 Tunable Laser L Detector Beam Splitter #2 Tunable laser z θ y Slow-light medium Imaging lens P C Here is why it works: d φ d = d d Shih et al, Opt. Lett nl c = L c dn (n + d ) = Ln g c Our experimental results Fringe movement rate (period/nm) experimental data theory for a slow-light medium theory for a non-dispersive medium wavelength (nm) n g

30 High-Resolution Slow-Light Fourier Transform Interferometer Conventional FT Interferometer detector beam splitter input field moving arm 0.5L max 0.5δL fixed arm Slow-light FT Interferometer detector beam splitter input field tunable slowlight medium fixed arms 5 2 P 3/2 5 2 S 1/2 Energy Levels 87 Rb F =2> F =1> 85 Rb F ' > 5 2 P 3/2 F ' > Results 5 2 S 1/2 F =3> F =2> transmission n 1 n g GHz Theoretical Model GHz 2.48 GHz frequency range of measurement detuning (GHz) output intensity relative intensity delay τ g (ns) experiment simulation actual input Shi, Boyd, Camacho, Setu, and Howell detuning (GHz)

31 Tunable Delays of up to 80 Pulse Widths in Atomic Cesium Vapor There is no delay-bandwidth product limitation on slow light! Pulse intensity signal optional optical pumping fields group index approximately 10 to 100 coarse tuning: temperature Air 275 ps pulses increasing temperature tra nsmission n x n signal detuning (GHz) pump off 1.0 ns spectrum (275 ps pulse) fine tuning: optical pumping 275 ps pulses v g pump on 0.1 v g / c time (ns) Camacho, Peck, Howell, Schweinsberg, Boyd, PRL 98, (2007) time (ns)

32 Summary Progress in Slow-Light Research 30 PMT signal (mv) T = 450 nk τ Delay = 7.05 ± 0.05 μs L = 229 ± 3 μm v g = 32.5 ± 0.5 m s 1 Pulse intensity Air 275 ps pulses increasing temperature Time (μs) time (ns) Delay of 3 pulse widths (1999) Results of Hau, L Delay of 80 pulse widths (2007) Results of Howell

33 Thank you for your attention!

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