Slow Light Structures
Slow light: group delay τ = n_gL/c, group velocity and delay-bandwidth product from a group index, or from a Lorentzian resonance (Brillouin gain, EIT window) whose delay is G/Γ.
Group Index n_g
10
slowdown n_g/n₀ = 6.667
Group Velocity c/n_g
29980000 m/s
10 % of c
Group Delay τ
33.36 ps
33.36 ps per mm
Excess Delay over n₀
28.35 ps
background alone: 5.003 ps
Signal Bandwidth Δν
124.8 GHz
Δλ = 1 nm at 1550 nm
Delay × Bandwidth τΔν
4.162
excess Δτ·Δν = 3.538 (≈ bits stored beyond plain propagation)
Model
τ = n_g L/c, v_g = c/n_g, Δν = c/(λ − Δλ/2) − c/(λ + Δλ/2)
τ_res(Δ) = (G/2)·γ(γ² − Δ²)/(γ² + Δ²)², τ_res(0) = G/Γ, γ = Γ/2 = π·FWHM
The group index sets the delay over the structure; the delay-bandwidth product counts how many bits (or pulses) the structure holds at once, which is what limits slow-light buffers. A Lorentzian resonance of power gain G (power e-folds, e^G) has the causal phase (G/2)γΔ/(γ² + Δ²), whose slope is the delay: gain lines and transparency windows slow light, absorption lines (negative gain) speed it up. Its delay times its width is fixed at G/2π, so a narrow line gives long delay over a small bandwidth. Lossless background, one isolated line, signal narrower than the line.
Model and references
Textbook approximation. A standard approximation from the literature (for example paraxial, plane-wave or Gaussian-beam), valid within the range the page states. About the tiers
τ = n_gL/c and v_g = c/n_g are exact. The resonance is one isolated Lorentzian line with a causal (Kramers–Kronig) phase, a lossless background and a signal narrower than the line; pulse distortion, saturation and the background's own dispersion are not modelled.
- Okawachi Y., Bigelow M. S., Sharping J. E. et al. (2005). Tunable all-optical delays via Brillouin slow light in an optical fiber. Phys. Rev. Lett. 94, 153902. doi:10.1103/PhysRevLett.94.153902
- Tucker R. S., Ku P.-C., Chang-Hasnain C. J. (2005). Slow-light optical buffers: capabilities and fundamental limitations. J. Lightwave Technol. 23, 4046–4066. doi:10.1109/JLT.2005.853125
- Hau L. V., Harris S. E., Dutton Z., Behroozi C. H. (1999). Light speed reduction to 17 metres per second in an ultracold atomic gas. Nature 397, 594–598. doi:10.1038/17561
- Baba T. (2008). Slow light in photonic crystals. Nat. Photonics 2, 465–473. doi:10.1038/nphoton.2008.146