The Slow-Light Effect
First year talk
Mark Zentile
Project Members
Lee Weller
08/04/2015
Charles Adams
1st year talk, Mark Zentile
Ifan Hughes
Outline
• Slow-light:
– What is slow-light? What conditions are needed to
see it? What are the applications?
– Phase shift and absorption from the electric
susceptibility.
– Transmission spectra to extract key parameters for
the model.
– Using the our model for the electric susceptibility
with Fourier analysis to model pulse propagation.
– Experimental method and examples of data with
theoretical predictions.
08/04/2015
1st year talk Mark Zentile
Outline
• Future outlook:
– Introduce the Faraday effect.
– Use a Faraday signal to make a tuneable laser lock
over ± 20 GHz detuning.
– Harness the slow-light Faraday effect to make an
optical switch.
08/04/2015
1st year talk Mark Zentile
What is ‘Slow-Light’?
08/04/2015
1st year talk Mark Zentile
What is ‘Slow-Light’?
08/04/2015
1st year talk Mark Zentile
Slow-light with EIT
08/04/2015
1st year talk Mark Zentile
Better interferometers
08/04/2015
1st year talk Mark Zentile
Image rotation  Image coding
08/04/2015
1st year talk Mark Zentile
Optical Delay Line
08/04/2015
1st year talk Mark Zentile
Optical Switch
08/04/2015
1st year talk Mark Zentile
Outline
• Slow-light:
– What is slow-light? What conditions are needed to
see it? What are the applications?
– Phase shift and absorption from the electric
susceptibility.
– Transmission spectra to extract key parameters for
the model.
– Using the our model for the electric susceptibility
with Fourier analysis to model pulse propagation.
– Experimental method and examples of data with
theoretical predictions.
08/04/2015
1st year talk Mark Zentile
Complex refractive index
ABSORPTION
08/04/2015
DISPERSION
1st year talk Mark Zentile
Transmission Spectra
08/04/2015
1st year talk Mark Zentile
The model for the electric susceptibility
• Our model has been developed over many years:
Result of solving the optical
Bloch equations for a two
level atom.
• Accurate up to ~ 120oC
• Includes:
 absolute linestrengths
 Doppler broadening
 Temperature
dependent number
density.
Siddons et al. J. Phys. B: At. Mol. Opt. Phys. 41 (2008) 155004
08/04/2015
1st year talk Mark Zentile
The model for the electric susceptibility
• Inclusion of self-broadening:
• Accurate up to ~ 360oC
• Includes:
 absolute linestrengths
 Doppler broadening
 Temperature
dependent number
density.
 Self-broadening for
binary-collision
approximation
Weller et al. J. Phys. B: At. Mol. Opt. Phys. 44 (2011) 195006
08/04/2015
1st year talk Mark Zentile
The model for the electric susceptibility
• Inclusion of magnetic field:
• Tested up to 0.6 T
• Includes:
 absolute linestrengths
 Doppler broadening
 Temperature
dependent number
density.
 Self-broadening for
binary-collision
approximation
 Magnetic energy
level shift.
Weller et al. J. Phys. B: At. Mol. Opt. Phys. 45 (2012) 055001
08/04/2015
1st year talk Mark Zentile
Outline
• Slow-light:
– What is slow-light? What conditions are needed to
see it? What are the applications?
– Phase shift and absorption from the electric
susceptibility.
– Transmission spectra to extract key parameters for
the model.
– Using the our model for the electric susceptibility
with Fourier analysis to model pulse propagation.
– Experimental method and examples of data with
theoretical predictions.
08/04/2015
1st year talk Mark Zentile
Transmission: Extracting parameters
• We want to use transmission spectra to measure
experimental parameters.
– Transmission  χ(ω)  dispersion  slow-light theory.
• Why model transmission spectra? Can’t we just use
Kramers-Kronig?
– Yes, but...
08/04/2015
1st year talk Mark Zentile
Transmission: Extracting parameters
• Rubidium 75 mm long cell, room temperature.
Excellent agreement.
One fit parameter:
Temp = (20.70 ± 0.13) oC
08/04/2015
1st year talk Mark Zentile
Transmission: Extracting parameters
• 2 mm long 98.2% 87Rb cell:
3 fit parameters:
Temp = (90.2 ± 0.1)oC
Lorentzian FWHM = 2π ∙ (165 ± 1) MHz
Very large! => Buffer gas.
Ratio of 87Rb to 85Rb = 0.982 ± 0.009
08/04/2015
1st year talk Mark Zentile
Transmission: Extracting parameters
• 2 mm long 87Rb cell (high temp):
2 fit parameters:
Temp = (182.1 ± 0.4)oC
Lorentzian FWHM = 2π ∙ (170 ± 4) MHz
Very large! => Buffer gas.
08/04/2015
1st year talk Mark Zentile
Outline
• Slow-light:
– What is slow-light? What conditions are needed to
see it? What are the applications?
– Phase shift and absorption from the electric
susceptibility.
– Transmission spectra to extract key parameters for
the model.
– Using the our model for the electric susceptibility
with Fourier analysis to model pulse propagation.
– Experimental method and examples of data with
theoretical predictions.
08/04/2015
1st year talk Mark Zentile
Fourier Method for pulse propagation
• Electric susceptibility model is designed for
monochromatic continuous wave light.
• Pulses are clearly not monochromatic
continuous wave light!
• Solution: Use a Fourier transform to write the
pulse in terms of continuous wave light.
08/04/2015
1st year talk Mark Zentile
Fourier Method for pulse propagation
• Fourier decomposition:
08/04/2015
1st year talk Mark Zentile
Good conditions for slow-light?
Rubidium at natural abundance
08/04/2015
1st year talk Mark Zentile
98.2% 87Rb
Fast-Light
08/04/2015
1st year talk Mark Zentile
Outline
• Slow-light:
– What is slow-light? What conditions are needed to
see it? What are the applications?
– Phase shift and absorption from the electric
susceptibility.
– Transmission spectra to extract key parameters for
the model.
– Using the our model for the electric susceptibility
with Fourier analysis to model pulse propagation.
– Experimental method and examples of data with
theoretical predictions.
08/04/2015
1st year talk Mark Zentile
Experimental Setup
08/04/2015
1st year talk Mark Zentile
Advantages/disadvantages of FPD
• Works over one shot
• Slow rise time => poor resolution
• Need relatively intense pulses
=> may not be weak probe.
08/04/2015
1st year talk Mark Zentile
Picture from
http://www.eotech.com/product/14/
2GHz_Amplified/
Advantages/disadvantages of SPCM
• Slightly better timing resolution.
• Works for much less
Intense pulses.
• Must build a pulse profile
over many repetitions.
Picture from
http://excelitas.com/downloads/
DTS_SPCM_AQRH.pdf
08/04/2015
1st year talk Mark Zentile
Preliminary experimental data (FPD)
Group refractive
index of ~1000
08/04/2015
1st year talk Mark Zentile
Experimental data with theory (FPD)
Reference
• 87Rb cell.
•Laser locked by polarization spectroscopy.
• Carrier frequency on resonant with 85Rb
D1 Fg=2  Fe=2,3 transition frequency.
Pink = Measured output
Red Dashed = Theory
08/04/2015
1st year talk Mark Zentile
Experimental data with theory (SPCM)
Reference
• Rb natural abundance cell.
•Counted over a relatively short time
Red = Measured output
Black Dashed = Theory
08/04/2015
1st year talk Mark Zentile
Outline
• Future outlook:
– Introduce the Faraday effect.
– Use a Faraday signal to make a tuneable laser lock
over ± 20 GHz detuning.
– Harness the slow-light Faraday effect to make an
optical switch.
08/04/2015
1st year talk Mark Zentile
The Faraday Effect
• Linearly polarized light can be constructed
from a circularly polarized basis.
08/04/2015
1st year talk Mark Zentile
The Faraday Effect
• A magnetic field breaks the degeneracy for
right and left circular components
08/04/2015
1st year talk Mark Zentile
The Faraday Effect
• Have already seen that the model can accurately predict
Faraday rotation:
Weller et al. J. Phys. B: At. Mol. Opt.
Phys. 45 (2012) 055001
08/04/2015
1st year talk Mark Zentile
A Faraday signal as a laser lock
• Take inspiration from this paper. Locking offresonance
Marchant, A. L., Händel, S.,
Wiles, T. P., Hopkins, S. A.,
Adams, C. S., & Cornish, S. L.
(2011). Optics letters, 36, 64-6.
08/04/2015
1st year talk Mark Zentile
A Faraday signal as a laser lock
• Can use our 1 mm long cell placed in a permanent
magnet to achieve high magnetic fields
• We will be able to lock on-resonance as well as off.
08/04/2015
1st year talk Mark Zentile
Outline
• Future outlook:
– Introduce the Faraday effect.
– Use a Faraday signal to make a tuneable laser lock
over ± 20 GHz detuning.
– Harness the slow-light Faraday effect to make an
optical switch.
08/04/2015
1st year talk Mark Zentile
The Slow-light Faraday effect
Large rotation with
little absorption
Siddons, P., Bell, N., Cai, Y., Adams, C. S., & Hughes, I. G. (2009).
Nature Photonics, 3, 225
08/04/2015
1st year talk Mark Zentile
Use optical pumping to control rotation
• Can also cause a rotation by having an
unbalanced distribution in the populations of the
Zeeman sub-levels.
08/04/2015
1st year talk Mark Zentile
Use optical pumping to control rotation
08/04/2015
1st year talk Mark Zentile
Summary
– Seen what slow-light is and what its applications
are.
– Phase shift and absorption from the electric
susceptibility.
– How we use transmission spectra to measure
parameters for the model.
– Seen how to model pulse propagation with the
Fourier analysis, once χ in known.
– Experimental method and examples of data with
theoretical predictions.
08/04/2015
1st year talk Mark Zentile
Summary
– Explained the Faraday effect.
– Want to use a Faraday signal to make a tuneable
laser lock.
– Harness the slow-light Faraday effect to make an
optical switch.
08/04/2015
1st year talk Mark Zentile
End
Thanks for listening.
08/04/2015
1st year talk Mark Zentile
Fit with magnetic field
08/04/2015
1st year talk Mark Zentile
Controlled Faraday rotation
Siddons, P., Adams, C. S., & Hughes, I. G. (2010). Physical Review A, 81, 043838
08/04/2015
1st year talk Mark Zentile
Pump-Probe energy level diagram
08/04/2015
1st year talk Mark Zentile
Jitter in arrival time
• FPD shows a ‘jitter’ in the arrival time and
peak height.
• This will broaden a
photon counted pulse!
08/04/2015
1st year talk Mark Zentile
Simulating photon counting pulses
08/04/2015
1st year talk Mark Zentile