Slow, Fast, and Backwards Light: Fundamental Aspects Robert W. Boyd University of Rochester Paul Narum Norwegian Defence Research Establishment with George Gehring, Giovanni Piredda, Aaron Schweinsberg, Katie Schwertz, Zhimin Shi, Heedeuk Shin, Joseph Vornehm, Petros Zerom. Presented at PQE, January 6, 2007.
Interest in Slow Light Intrigue: Can (group) refractive index really be 10 6? Fundamentals of optical physics Optical delay lines, optical storage, optical memories Implications for quantum information What about fast light (v > c) and backwards light (v negative)? Boyd and Gauthier, Slow and Fast Light, in Progress in Optics, 43, 2002.
Slow Light and Optical Buffers All-Optical Switch input ports switch output ports Use Optical Buffering to Resolve Data-Packet Contention 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
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).
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
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.
How to Create Slow and Fast Light III Dispersion Management gain coefficient g () double gain line single gain line flattened gain profile contributions to double gain line (n 1) 0 extended region of linear dependence single gain line double gain line 8 6 4 2 0 2 4 6 8 frequency ( 0 )/γ M. D. Stenner, M. A. Neifeld, Z. Zhu, A. M. C. Dawes, and D. J. Gauthier, Optics Express 13, 9995 (2005).
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.
Pulse Propagation through a Slow-Light Medium (n g = 2, v g = 0.5 c)
Pulse Propagation through a Fast-Light Medium (n g =.2, v g = 5 c)
Pulse Propagation through a Fast-Light Medium (n g = -.5, v g = -2 c)
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 0.1 0.05 0-0.05-97.5 mw - 49.0 mw - 24.5 mw - 9.0 mw - 6.0 mw - 0 mw out in -0.1 10 100 10 3 10 4 10 5 Modulation Frequency (Hz) Schweinsberg, Lepeshkin, Bigelow, Boyd, and Jarabo, Europhysics Letters, 73, 218 (2006).
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 1550 980 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 3 2 1 0 out in G. M. Gehring, A. Schweinsberg, C. Barsi, N. Kostinski, R. W. Boyd, Science 312, 985 2006. 0 2 4 6 time (ms)
Experimental Results: Backward Propagation in Erbium-Doped Fiber Normalized: (Amplification removed numerically)
Experimental Results: Backward Propagation in Erbium-Doped Fiber Un-Normalized
Observation of Backward Pulse Propagation in an Erbium-Doped-Fiber Optical Amplifier Δt=0 0.04 ms pulse amplitude (arb units) 0.06 ms 0.08 ms 0.12 ms 0.14 ms -25 0 25 normalized distance n g z (m)
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.)
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.
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
Why can one delay (but not advance) a pulse by an arbitrarily large amount? Two crucial differences between slow and fast light (1) First, note that we cannot use gains greater than approximately exp(16) at any frequency to avoid ASE. And we cannot have absorption larger than T = exp(-16) at the signal frequency, so signal can be measured. (Of course, the argument does not hinge on the value 16.) When examined quantitatively, these constraints impose a limit of at most two pulse-widths of delay or advancement. One can overcome these constraints by using a deep hole in an absorption feature, but this trick works only for slow light, as we have just seen. (2) Spectral reshaping of the pulse is the dominant competing effect in most slow/fast light systems. This also behaves differently for slow and fast-light systems, as we shall now see.
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
Numerical Results: Propagation through a Linear Dispersive Medium Fast light: single Lorentzian absorption line T = exp(-16) vary absorption line width to control advance Slow light: single Lorentzian gain line T = exp(+16) vary absorption line width to control delay Same Gaussian input pulse in all cases 1 pulse-width delay Slow Light Results 2 pulsewidth advance Fast Light Results note pulse compression and break-up 2 pulse-width delay (expanded time axis) 1 pulse-width advance vacuum propagation 4 pulse-width delay (expanded time axis) note pulse broadening time time
Tunable Delays of up to 80 Pulse Widths in Atomic Cesium Vapor signal optional optical pumping fields tra nsmission n-1 1.0 0.5 0 1 x 10-3 n 0 spectrum (275 ps pulse) 0.1 v g / c v g coarse tuning: temperature -1-5 0 5 signal detuning (GHz) 0 Pulse intensity Air 275 ps pulses increasing temperature fine tuning: optical pumping 275 ps pulses pump off 1.0 ns pump on 0 2 4 6 8 time (ns) Camacho, Peck, Howell, Schweinsberg, Boyd 4 6 8 time (ns)
Tunable Delays of up to 80 Pulse Widths in Atomic Cesium Vapor Comment: In EIT based slow light, spectral reshaping is the dominant limitation. But far off resonance, this effect is negligible. Group velocity dispersion becomes important. Longer input pulses lead to reduced gvd distortion and longer fractional delays Results for 740 ps pulses intensity 0.6 0.4 0.2 Air x1/2 X 10 X 500 0 0 10 20 30 40 50 60 70 time (ns) fractional broadening 0.6 0.4 740 ps pulses 0.2 0 0 20 40 60 80 100 fractional delay Camacho, Peck, Howell, Schweinsberg, Boyd
How to Prevent Pulse Distortion (Which Can Limit Data Rates) Two primary mechanisms for pulse distortion in EDFA Spectral broadening, leading to temporal compression CPO gain dip causes spectral components in the wings to be amplified more than central components Temporal gain recovery, leading to temporal broadening Leading edge of signal pulse saturates gain, but for long pulses, the trailing edge can experience recovered gain To minimize second effect, add a cw background to reduce the influence of gain recovery P sig For the proper choice of background power, the two effects exactly cancel! P bg
Minimizing Pulse Distortion Laboratory Results 980 nm laser 1550 nm laser EOM ISO splitter WDM function generator Polarizer EDF P sig Pbg 980 1550 WDM broadening compression Pulse width ratio (Tout / Tin) 1.6 1.4 1.2 1 2 ms 5 ms 10 ms 40 ms 0.8 0 0.5 1 1.5 2 2.5 power ratio (P bg / P sig )
Summary Slow-light techniques hold great promise for applications in telecommunications Good progress being made in devloping new slow-light techniques and applications Backwards and superluminal propagation are strongly counterintuitive, but are fully explained by standard physics.