Time-dependent Simulations of Electromagnetically Induced Transparency with Intense Ultra-short Pulses

1
Time-dependent Simulations of Electromagnetically
Induced Transparency with Intense Ultra-short
Pulses

• Wei-Chih Liu ???
• Department of Physics
• National Taiwan Normal University

2011.12.19_at_NTHU
2
Outline

• Introduction to Electromagnetically Induced
  Transparency (EIT) and time-dependent simulation
  approach.
• Single atom response with intense, ultra-short
  pulses
• 1D atomic array response with intense,
  ultra-short pulses with pulse turn-off and
  turn-on
• Metamaterials and EIT

3
Electromagnetically Induced Transparency
4
Simulation model
1-D EM wave and 1-D atomic array
Coupling field
Probe field l 589 nm
Na atom
5
Numerical simulation methods
The electromagnetic fields are solved by
discretizing Maxwell equation and propagating the
electromagnetic waves by finite-difference method.
With one-directional radiation boundary condition
6
Numerical simulation methods

• The atomic states and atomic polarization P is
  simulated by solving time-dependent Schrödinger
  equation by Runge-Kutta 4th-order method.
• Using simple cj or density-matrix approach
• Without rotating wave approximation.
• No spontaneous emission yet!
• explicit or implicit method

7
At Resonance - Absorption
No coupling field
-- Probe Field
Amplitude
Position (x/?)
8
EIT Transparency
with coupling field
-- Probe Field
Amplitude
Position (x/?)
9
EIT from purterbation theory
K.-J. Boller, A. Imamoglu, and S. E. Harris,
Phys. Rev. Lett. 66, 2593 (1991).
10
Energy level shift from simulations
coupling field power 3104 mW cm-2
11
Energy level shift from simulations
coupling field power 3107 mW cm-2
12
Large Energy level shift - Transparency
coupling field power 1.2108 mW cm-2
Frequency(?/?31)
13
Mode coupling and energy level shift in EIT

• Ec Ep

14
Single atom in intense, ultra-short pulses
Density-matrix simulation
E12 1 a.u.
E13 0.95 a.u.
Decay rate 2 p / 1000
15
Polarization with various coupling filed intensity
coupling field FWHM256 T/2p probe field
FWHM16 T/2p Op0.01
16
Polarization with various coupling filed intensity
coupling field FWHM256 T/2p probe field
FWHM16 T/2p Oc0.1
17
Polarization with various coupling filed intensity
coupling field FWHM256 T/2p probe field
FWHM16 T/2p Op1.0
18
Polarization with various coupling filed intensity
coupling field FWHM256 T/2p probe field
FWHM16 T/2p Op10.0
19
Time-dependent polarization behavior
coupling field FWHM 256 T/2p
Op10.0 probe field FWHM 16 T/2p Oc0.0
20
Time-dependent polarization behavior
coupling field FWHM 256 T/2p
Op10.0 probe field FWHM 16 T/2p Oc10.0
21
Time-dependent polarization behavior
coupling field FWHM 256 T/2p
Op10.0 probe field FWHM 16 T/2p Oc100.0
22
Time-dependent polarization behavior
coupling field FWHM 256 T/2p
Op10.0 probe field FWHM 16 T/2p Oc400.0
23
Interaction between light and polarization wave
Coupling field turned off by a Gaussian profile
24
Coupling field turn-off t 50 fs
-- Probe Field
-- Polarization between 1-2 level
Amplitude
Position (x/?)
25
Coupling field turn-off t 20 fs
-- Polarization between 1-2 level
-- Probe Field
Amplitude
Position (x/?)
26
Coupling field turn-off t 10 fs
-- Polarization between 1-2 level
-- Probe Field
Amplitude
Position (x/?)
27
Coupling field turn-off t 5 fs
-- Polarization between 1-2 level
-- Probe Field
Amplitude
Position (x/?)
28
Coupling field turn-off t 1 fs
-- Polarization between 1-2 level
-- Probe Field
Amplitude
Position (x/?)
29
Coupling field turn-off t 1 fs (zoom in)
-- Polarization between 1-2 level
-- Probe Field
Amplitude
Position (x/?)
30
Analyze polarization wave from one atom in the
array
The polarization between 1gt and 2gt of one atom
in the atomic array under constant coupling field
is analyzed.The polarization becomes similar to
the envelope of the probe field, while the
intensity of the coupling field is large enough
31
Atomic Dynamics - Coupling field 3107 mW cm-2
-- Polarization between 1-2 level
-- Probe Field
Amplitude
Time (t/T)
32
Atomic Dynamics - Coupling field 6107 mW cm-2
-- Polarization between 1-2 level
-- Probe Field
Amplitude
Time (t/T)
33
Atomic Dynamics - Coupling field 1.2108 mW
cm-2
-- Polarization between 1-2 level
-- Probe Field
Amplitude
Time (t/T)
34
C1C2e-iw12t component with different coupling
light turn-off rate
perturbation theory, single atom
without atom-atom interaction
with atom-atom interaction
35
Coupling field turn-off and on toff 25 period
- Probe Field
-- Polarization between 1-2 level
Amplitude
Position (x/?)
36
Coupling field turn-off and on toff 50 period
- Probe Field
-- Polarization between 1-2 level
Amplitude
Position (x/?)
37
Coupling field turn-off and on toff 75 period
- Probe Field
-- Polarization between 1-2 level
Amplitude
Position (x/?)
38
Coupling field turn-off and on toff 100 period
- Probe Field
-- Polarization between 1-2 level
Amplitude
Position (x/?)
39
Probe pulse reading efficiency vs coupling light
turn-off duration
atomic density 11018cm-3 decay rate G3?31/20p
ratio
40
Probe pulse reading efficiency vs atomic density
coupling light turn-off duration tctp decay rate
G3?31/20p
ratio
41
Probe pulse reading efficiency vs decay rate
ratio
coupling light turn-off duration tctp atomic
density 41017cm-3
42
Metamaterial
Metamaterials are artificially structured
materials that can have profoundly unique
electromagnetic or optical properties. - D. R.
Smith
Metamaterials are artificial materials engineered
to have properties that may not be found in
nature. Metamaterials usually gain their
properties from structure rather than
composition, using small inhomogeneities to
create effective macroscopic behavior. -
Wikipedia
43
Classification of Metamaterials
Epsilon-negative (ENG) medium
Double positive (DPS) medium
Double-negative (DNG) medium
Mu-negative (MNG) medium
44
Realization of DNG Metamaterials
R. A. Shelby, D. R. Smith, and S. Schultz,
Science 292, 77 (2001).2001
44
45
Subwavelength Focusing
Perfect lens (Pendry, 2000)
45
46
Cloaking and Transformation Optics

• Is it possible to smoothly bend light around an
  object?
• No backscatter, no shadow effectively
  invisible.
• Can there really be such an interesting solution
  still lurking in classical electromagnetics?
  Pendry et al. Science, 2006 showed how it can
  be done.
• Key realization coordinate transformations on
  electromagnetic fields are completely equivalent
  to a nonuniform permittivity and permeability.

47
Induced transparency in metamaterials by symmetry
breaking
Papasimakis and Zheludev, Optics Photonics
News, p22 (Oct 2009)
48
Active metamaterial for loss-compensated pulse
delays
Loss-compensated slow-light device metamaterial
array with EIT-like dispersion placed on a gain
substrate (e9.5035i). At the wavelength of 1.7
µm, it shows single-pass amplification and
simultaneously sharp normal dispersion.
49
Metamaterial mimicking EIT
N. Papasimakis, et al. Appl. Phys. Lett. 94,
211902 (2009)
50
Acknowledgements

• Dar-Yeong Ju (???)at NIU and NTNU
• Meng-Chang Wu (???) (currently at IAMS, AS)
• Supported by NSC