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![Page 1: Time-dependent Simulations of Electromagnetically Induced Transparency with Intense Ultra-short Pulses Wei-Chih Liu 劉威志 Department of Physics National.](https://reader036.fdocument.pub/reader036/viewer/2022081506/56649f4f5503460f94c71c4c/html5/thumbnails/1.jpg)
Time-dependent Simulations of Electromagnetically Induced Transparency
with Intense Ultra-short Pulses
Wei-Chih Liu 劉威志Department of Physics
National Taiwan Normal University
2011.12.19@NTHU
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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
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Electromagnetically Induced Transparency
![Page 4: Time-dependent Simulations of Electromagnetically Induced Transparency with Intense Ultra-short Pulses Wei-Chih Liu 劉威志 Department of Physics National.](https://reader036.fdocument.pub/reader036/viewer/2022081506/56649f4f5503460f94c71c4c/html5/thumbnails/4.jpg)
Simulation model
1.8 GHz
1 1 2 F1 = 3 S ,F = , M = - 1 2 1 2 F2 = 3 S ,F = 2 , M = -
3 3 2 F= 3 P ,F = 2 , M = - 2
pE t cE t
cE t
pE t
Na atom
Probe field =589 nmCoupling field
1-D EM wave and 1-D atomic array
![Page 5: Time-dependent Simulations of Electromagnetically Induced Transparency with Intense Ultra-short Pulses Wei-Chih Liu 劉威志 Department of Physics National.](https://reader036.fdocument.pub/reader036/viewer/2022081506/56649f4f5503460f94c71c4c/html5/thumbnails/5.jpg)
Numerical simulation methods
The electromagnetic fields are solved by discretizing Maxwell equation and propagating the electromagnetic waves by finite-difference method.
2
2
022
2
22
2 11
t
P
ct
E
cx
E
With one-directional radiation boundary condition
![Page 6: Time-dependent Simulations of Electromagnetically Induced Transparency with Intense Ultra-short Pulses Wei-Chih Liu 劉威志 Department of Physics National.](https://reader036.fdocument.pub/reader036/viewer/2022081506/56649f4f5503460f94c71c4c/html5/thumbnails/6.jpg)
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
![Page 7: Time-dependent Simulations of Electromagnetically Induced Transparency with Intense Ultra-short Pulses Wei-Chih Liu 劉威志 Department of Physics National.](https://reader036.fdocument.pub/reader036/viewer/2022081506/56649f4f5503460f94c71c4c/html5/thumbnails/7.jpg)
At Resonance - Absorption
Position (x/λ)
Am
plit
ude
-- Probe Field No coupling field
![Page 8: Time-dependent Simulations of Electromagnetically Induced Transparency with Intense Ultra-short Pulses Wei-Chih Liu 劉威志 Department of Physics National.](https://reader036.fdocument.pub/reader036/viewer/2022081506/56649f4f5503460f94c71c4c/html5/thumbnails/8.jpg)
EIT – Transparency
Position (x/λ)
Am
plit
ude
-- Probe Field with coupling field
![Page 9: Time-dependent Simulations of Electromagnetically Induced Transparency with Intense Ultra-short Pulses Wei-Chih Liu 劉威志 Department of Physics National.](https://reader036.fdocument.pub/reader036/viewer/2022081506/56649f4f5503460f94c71c4c/html5/thumbnails/9.jpg)
EIT from purterbation theory
K.-J. Boller, A. Imamoglu, and S. E. Harris, Phys. Rev. Lett. 66, 2593 (1991).
![Page 10: Time-dependent Simulations of Electromagnetically Induced Transparency with Intense Ultra-short Pulses Wei-Chih Liu 劉威志 Department of Physics National.](https://reader036.fdocument.pub/reader036/viewer/2022081506/56649f4f5503460f94c71c4c/html5/thumbnails/10.jpg)
Energy level shift from simulations
Total waveProbe fieldScattering field
Frequency(ω/ω31)
coupling field power = 3×104 mW cm-2
![Page 11: Time-dependent Simulations of Electromagnetically Induced Transparency with Intense Ultra-short Pulses Wei-Chih Liu 劉威志 Department of Physics National.](https://reader036.fdocument.pub/reader036/viewer/2022081506/56649f4f5503460f94c71c4c/html5/thumbnails/11.jpg)
Energy level shift from simulations
Total waveProbe fieldScattering field
Frequency(ω/ω31)
Ωc/2
coupling field power = 3×107 mW cm-2
![Page 12: Time-dependent Simulations of Electromagnetically Induced Transparency with Intense Ultra-short Pulses Wei-Chih Liu 劉威志 Department of Physics National.](https://reader036.fdocument.pub/reader036/viewer/2022081506/56649f4f5503460f94c71c4c/html5/thumbnails/12.jpg)
Total waveProbe fieldScattering field
Frequency(ω/ω31)
Large Energy level shift - Transparencycoupling field power = 1.2×108 mW cm-2
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Mode coupling and energy level shift in EIT
1 2
3
cE t
1
2 3 2 3
• Ec » Ep
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Single atom in intense, ultra-short pulses
E12 = 1 a.u.E13 = 0.95 a.u.
Decay rate = 2 π / 1000
Density-matrix simulation
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Polarization with various coupling filed intensity
coupling field FWHM=256 T/2πprobe field FWHM=16 T/2π Ωp=0.01
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Polarization with various coupling filed intensity
coupling field FWHM=256 T/2πprobe field FWHM=16 T/2π Ωc=0.1
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Polarization with various coupling filed intensity
coupling field FWHM=256 T/2πprobe field FWHM=16 T/2π Ωp=1.0
![Page 18: Time-dependent Simulations of Electromagnetically Induced Transparency with Intense Ultra-short Pulses Wei-Chih Liu 劉威志 Department of Physics National.](https://reader036.fdocument.pub/reader036/viewer/2022081506/56649f4f5503460f94c71c4c/html5/thumbnails/18.jpg)
Polarization with various coupling filed intensity
coupling field FWHM=256 T/2πprobe field FWHM=16 T/2π Ωp=10.0
![Page 19: Time-dependent Simulations of Electromagnetically Induced Transparency with Intense Ultra-short Pulses Wei-Chih Liu 劉威志 Department of Physics National.](https://reader036.fdocument.pub/reader036/viewer/2022081506/56649f4f5503460f94c71c4c/html5/thumbnails/19.jpg)
Time-dependent polarization behavior
coupling field FWHM =256 T/2π Ωp=10.0probe field FWHM =16 T/2π Ωc=0.0
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Time-dependent polarization behavior
coupling field FWHM =256 T/2π Ωp=10.0probe field FWHM =16 T/2π Ωc=10.0
![Page 21: Time-dependent Simulations of Electromagnetically Induced Transparency with Intense Ultra-short Pulses Wei-Chih Liu 劉威志 Department of Physics National.](https://reader036.fdocument.pub/reader036/viewer/2022081506/56649f4f5503460f94c71c4c/html5/thumbnails/21.jpg)
Time-dependent polarization behavior
coupling field FWHM =256 T/2π Ωp=10.0probe field FWHM =16 T/2π Ωc=100.0
![Page 22: Time-dependent Simulations of Electromagnetically Induced Transparency with Intense Ultra-short Pulses Wei-Chih Liu 劉威志 Department of Physics National.](https://reader036.fdocument.pub/reader036/viewer/2022081506/56649f4f5503460f94c71c4c/html5/thumbnails/22.jpg)
Time-dependent polarization behavior
coupling field FWHM =256 T/2π Ωp=10.0probe field FWHM =16 T/2π Ωc=400.0
![Page 23: Time-dependent Simulations of Electromagnetically Induced Transparency with Intense Ultra-short Pulses Wei-Chih Liu 劉威志 Department of Physics National.](https://reader036.fdocument.pub/reader036/viewer/2022081506/56649f4f5503460f94c71c4c/html5/thumbnails/23.jpg)
Interaction between light and polarization wave
Coupling field turned off by a Gaussian profile
0)/exp(
0122
ttprofile
tprofile
1
2
3
cE t
![Page 24: Time-dependent Simulations of Electromagnetically Induced Transparency with Intense Ultra-short Pulses Wei-Chih Liu 劉威志 Department of Physics National.](https://reader036.fdocument.pub/reader036/viewer/2022081506/56649f4f5503460f94c71c4c/html5/thumbnails/24.jpg)
Coupling field turn-off – = 50 fs
Position (x/λ)
Am
plit
ude
-- Probe Field -- Polarization between 1-2 level
![Page 25: Time-dependent Simulations of Electromagnetically Induced Transparency with Intense Ultra-short Pulses Wei-Chih Liu 劉威志 Department of Physics National.](https://reader036.fdocument.pub/reader036/viewer/2022081506/56649f4f5503460f94c71c4c/html5/thumbnails/25.jpg)
Position (x/λ)
Am
plit
ude
-- Polarization between 1-2 level
Coupling field turn-off – = 20 fs
-- Probe Field
![Page 26: Time-dependent Simulations of Electromagnetically Induced Transparency with Intense Ultra-short Pulses Wei-Chih Liu 劉威志 Department of Physics National.](https://reader036.fdocument.pub/reader036/viewer/2022081506/56649f4f5503460f94c71c4c/html5/thumbnails/26.jpg)
Position (x/λ)
Am
plit
ude
-- Polarization between 1-2 level
Coupling field turn-off – = 10 fs
-- Probe Field
![Page 27: Time-dependent Simulations of Electromagnetically Induced Transparency with Intense Ultra-short Pulses Wei-Chih Liu 劉威志 Department of Physics National.](https://reader036.fdocument.pub/reader036/viewer/2022081506/56649f4f5503460f94c71c4c/html5/thumbnails/27.jpg)
Position (x/λ)
Am
plit
ude
-- Polarization between 1-2 level
Coupling field turn-off – = 5 fs
-- Probe Field
![Page 28: Time-dependent Simulations of Electromagnetically Induced Transparency with Intense Ultra-short Pulses Wei-Chih Liu 劉威志 Department of Physics National.](https://reader036.fdocument.pub/reader036/viewer/2022081506/56649f4f5503460f94c71c4c/html5/thumbnails/28.jpg)
Coupling field turn-off – = 1 fs
Position (x/λ)
Am
plit
ude
-- Polarization between 1-2 level-- Probe Field
![Page 29: Time-dependent Simulations of Electromagnetically Induced Transparency with Intense Ultra-short Pulses Wei-Chih Liu 劉威志 Department of Physics National.](https://reader036.fdocument.pub/reader036/viewer/2022081506/56649f4f5503460f94c71c4c/html5/thumbnails/29.jpg)
Coupling field turn-off – = 1 fs (zoom in)
Position (x/λ)
Am
plit
ude
-- Polarization between 1-2 level-- Probe Field
![Page 30: Time-dependent Simulations of Electromagnetically Induced Transparency with Intense Ultra-short Pulses Wei-Chih Liu 劉威志 Department of Physics National.](https://reader036.fdocument.pub/reader036/viewer/2022081506/56649f4f5503460f94c71c4c/html5/thumbnails/30.jpg)
Analyze polarization wave from one atom in the array
The polarization between |1> and |2> 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
1
2
3
cE t
![Page 31: Time-dependent Simulations of Electromagnetically Induced Transparency with Intense Ultra-short Pulses Wei-Chih Liu 劉威志 Department of Physics National.](https://reader036.fdocument.pub/reader036/viewer/2022081506/56649f4f5503460f94c71c4c/html5/thumbnails/31.jpg)
Atomic Dynamics - Coupling field = 3×107 mW cm-2
Time (t/T)
Am
plit
ude
-- Polarization between 1-2 level-- Probe Field
![Page 32: Time-dependent Simulations of Electromagnetically Induced Transparency with Intense Ultra-short Pulses Wei-Chih Liu 劉威志 Department of Physics National.](https://reader036.fdocument.pub/reader036/viewer/2022081506/56649f4f5503460f94c71c4c/html5/thumbnails/32.jpg)
Atomic Dynamics - Coupling field = 6×107 mW cm-2
Time (t/T)
Am
plit
ude
-- Polarization between 1-2 level-- Probe Field
![Page 33: Time-dependent Simulations of Electromagnetically Induced Transparency with Intense Ultra-short Pulses Wei-Chih Liu 劉威志 Department of Physics National.](https://reader036.fdocument.pub/reader036/viewer/2022081506/56649f4f5503460f94c71c4c/html5/thumbnails/33.jpg)
Atomic Dynamics - Coupling field = 1.2×108 mW cm-2
Time (t/T)
Am
plit
ude
-- Polarization between 1-2 level-- Probe Field
![Page 34: Time-dependent Simulations of Electromagnetically Induced Transparency with Intense Ultra-short Pulses Wei-Chih Liu 劉威志 Department of Physics National.](https://reader036.fdocument.pub/reader036/viewer/2022081506/56649f4f5503460f94c71c4c/html5/thumbnails/34.jpg)
C1*C2e-i12t component with different
coupling light turn-off rate
perturbation theory, single atom
without atom-atom interaction
with atom-atom interaction
![Page 35: Time-dependent Simulations of Electromagnetically Induced Transparency with Intense Ultra-short Pulses Wei-Chih Liu 劉威志 Department of Physics National.](https://reader036.fdocument.pub/reader036/viewer/2022081506/56649f4f5503460f94c71c4c/html5/thumbnails/35.jpg)
Coupling field turn-off and on off = 25 period
Position (x/λ)
Am
plit
ude
- Probe Field -- Polarization between 1-2 level
![Page 36: Time-dependent Simulations of Electromagnetically Induced Transparency with Intense Ultra-short Pulses Wei-Chih Liu 劉威志 Department of Physics National.](https://reader036.fdocument.pub/reader036/viewer/2022081506/56649f4f5503460f94c71c4c/html5/thumbnails/36.jpg)
Coupling field turn-off and on off = 50 period
Position (x/λ)
Am
plit
ude
- Probe Field -- Polarization between 1-2 level
![Page 37: Time-dependent Simulations of Electromagnetically Induced Transparency with Intense Ultra-short Pulses Wei-Chih Liu 劉威志 Department of Physics National.](https://reader036.fdocument.pub/reader036/viewer/2022081506/56649f4f5503460f94c71c4c/html5/thumbnails/37.jpg)
Coupling field turn-off and on off = 75 period
Position (x/λ)
Am
plit
ude
- Probe Field -- Polarization between 1-2 level
![Page 38: Time-dependent Simulations of Electromagnetically Induced Transparency with Intense Ultra-short Pulses Wei-Chih Liu 劉威志 Department of Physics National.](https://reader036.fdocument.pub/reader036/viewer/2022081506/56649f4f5503460f94c71c4c/html5/thumbnails/38.jpg)
Coupling field turn-off and on off = 100 period
Position (x/λ)
Am
plit
ude
- Probe Field -- Polarization between 1-2 level
![Page 39: Time-dependent Simulations of Electromagnetically Induced Transparency with Intense Ultra-short Pulses Wei-Chih Liu 劉威志 Department of Physics National.](https://reader036.fdocument.pub/reader036/viewer/2022081506/56649f4f5503460f94c71c4c/html5/thumbnails/39.jpg)
Probe pulse reading efficiency vs coupling light turn-off duration
atomic density 1×1018cm-3
decay rate Γ3=ω31/20π
rati
o
![Page 40: Time-dependent Simulations of Electromagnetically Induced Transparency with Intense Ultra-short Pulses Wei-Chih Liu 劉威志 Department of Physics National.](https://reader036.fdocument.pub/reader036/viewer/2022081506/56649f4f5503460f94c71c4c/html5/thumbnails/40.jpg)
Probe pulse reading efficiency vs atomic density
coupling light turn-off duration τc=τp
decay rate Γ3=ω31/20π
rati
o
![Page 41: Time-dependent Simulations of Electromagnetically Induced Transparency with Intense Ultra-short Pulses Wei-Chih Liu 劉威志 Department of Physics National.](https://reader036.fdocument.pub/reader036/viewer/2022081506/56649f4f5503460f94c71c4c/html5/thumbnails/41.jpg)
Probe pulse reading efficiency vs decay rate
coupling light turn-off duration τc=τp
atomic density 4×1017cm-3
rati
o
![Page 42: Time-dependent Simulations of Electromagnetically Induced Transparency with Intense Ultra-short Pulses Wei-Chih Liu 劉威志 Department of Physics National.](https://reader036.fdocument.pub/reader036/viewer/2022081506/56649f4f5503460f94c71c4c/html5/thumbnails/42.jpg)
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
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Epsilon-negative (ENG) medium
Classification of Metamaterials
Re[ ]
Re[ ]
DPSk
DNGk
ENG
k MNG
k
RegularDielectricsDPS
Double positive (DPS) medium
Mu-negative (MNG) mediumDouble-negative (DNG) medium
![Page 44: Time-dependent Simulations of Electromagnetically Induced Transparency with Intense Ultra-short Pulses Wei-Chih Liu 劉威志 Department of Physics National.](https://reader036.fdocument.pub/reader036/viewer/2022081506/56649f4f5503460f94c71c4c/html5/thumbnails/44.jpg)
Realization of DNG Metamaterials
44R. A. Shelby, D. R. Smith, and S. Schultz, Science 292, 77 (2001).2001
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Subwavelength Focusing
Perfect lens
(Pendry, 2000)
45
n=1
n=-1
y = 2d
y = -2d
![Page 46: Time-dependent Simulations of Electromagnetically Induced Transparency with Intense Ultra-short Pulses Wei-Chih Liu 劉威志 Department of Physics National.](https://reader036.fdocument.pub/reader036/viewer/2022081506/56649f4f5503460f94c71c4c/html5/thumbnails/46.jpg)
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.
![Page 47: Time-dependent Simulations of Electromagnetically Induced Transparency with Intense Ultra-short Pulses Wei-Chih Liu 劉威志 Department of Physics National.](https://reader036.fdocument.pub/reader036/viewer/2022081506/56649f4f5503460f94c71c4c/html5/thumbnails/47.jpg)
Induced transparency in metamaterials by symmetry breaking
Papasimakis and Zheludev, Optics & Photonics News, p22 (Oct 2009)
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Active metamaterial for loss-compensated pulse delays
Loss-compensated slow-light device: metamaterial array with EIT-like dispersion placed on a gain substrate (=9.5+035i). At the wavelength of 1.7 µm, it shows single-pass amplification and simultaneously sharp normal dispersion.
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Metamaterial mimicking EIT
N. Papasimakis, et al. Appl. Phys. Lett. 94, 211902 (2009)
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Acknowledgements
Dar-Yeong Ju (朱達勇 )at NIU and NTNU
Meng-Chang Wu (吳孟昌 ) (currently at IAMS, AS)
Supported by NSC