time-dependent simulations of electromagnetically induced transparency with intense ultra-short...

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

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

Electromagnetically Induced Transparency

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

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

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

At Resonance - Absorption

Position (x/λ)

Am

plit

ude

-- Probe Field No coupling field

EIT – Transparency

Position (x/λ)

Am

plit

ude

-- Probe Field with coupling field

EIT from purterbation theory

K.-J. Boller, A. Imamoglu, and S. E. Harris, Phys. Rev. Lett. 66, 2593 (1991).

Energy level shift from simulations

Total waveProbe fieldScattering field

Frequency(ω/ω31)

coupling field power = 3×104 mW cm-2

Energy level shift from simulations


Frequency(ω/ω31)

Ωc/2

coupling field power = 3×107 mW cm-2


Frequency(ω/ω31)

Large Energy level shift - Transparencycoupling field power = 1.2×108 mW cm-2

Mode coupling and energy level shift in EIT

1 2

3

cE t

1

2 3 2 3

• Ec » Ep

Single atom in intense, ultra-short pulses

E12 = 1 a.u.E13 = 0.95 a.u.

Decay rate = 2 π / 1000

Density-matrix simulation

Polarization with various coupling filed intensity

coupling field FWHM=256 T/2πprobe field FWHM=16 T/2π Ωp=0.01


coupling field FWHM=256 T/2πprobe field FWHM=16 T/2π Ωc=0.1

Time-dependent polarization behavior

coupling field FWHM =256 T/2π Ωp=10.0probe field FWHM =16 T/2π Ωc=0.0

Interaction between light and polarization wave

Coupling field turned off by a Gaussian profile

0)/exp(

0122

ttprofile

tprofile

1

2

3

cE t

Coupling field turn-off – = 50 fs

Position (x/λ)

Am

plit

ude

-- Probe Field -- Polarization between 1-2 level

Position (x/λ)

Am

plit

ude

-- Polarization between 1-2 level


-- Probe Field

Position (x/λ)

Am

plit

ude



-- Probe Field


Position (x/λ)

Am

plit

ude

-- Polarization between 1-2 level-- Probe Field

Coupling field turn-off – = 1 fs (zoom in)

Position (x/λ)

Am

plit

ude


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

Atomic Dynamics - Coupling field = 3×107 mW cm-2

Time (t/T)

Am

plit

ude


Atomic Dynamics - Coupling field = 6×107 mW cm-2

Time (t/T)

Am

plit

ude


Atomic Dynamics - Coupling field = 1.2×108 mW cm-2

Time (t/T)

Am

plit

ude


C1*C2e-i12t component with different

coupling light turn-off rate

perturbation theory, single atom

without atom-atom interaction

with atom-atom interaction

Coupling field turn-off and on off = 25 period

Position (x/λ)

Am

plit

ude

－ Probe Field -- Polarization between 1-2 level


Position (x/λ)

Am

plit

ude


Probe pulse reading efficiency vs coupling light turn-off duration

atomic density 1×1018cm-3

decay rate Γ3=ω31/20π

rati

o

Probe pulse reading efficiency vs atomic density

coupling light turn-off duration τc=τp

decay rate Γ3=ω31/20π

rati

o

Probe pulse reading efficiency vs decay rate

coupling light turn-off duration τc=τp

atomic density 4×1017cm-3

rati

o

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

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

Realization of DNG Metamaterials

44R. A. Shelby, D. R. Smith, and S. Schultz, Science 292, 77 (2001).2001

Subwavelength Focusing

Perfect lens

(Pendry, 2000)

45

n=1

n=-1

y = 2d

y = -2d

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.

Induced transparency in metamaterials by symmetry breaking

Papasimakis and Zheludev, Optics & Photonics News, p22 (Oct 2009)

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.

Metamaterial mimicking EIT

N. Papasimakis, et al. Appl. Phys. Lett. 94, 211902 (2009)

Acknowledgements

Dar-Yeong Ju (朱達勇 )at NIU and NTNU

Meng-Chang Wu (吳孟昌 ) (currently at IAMS, AS)

Supported by NSC

time-dependent simulations of electromagnetically induced transparency with intense ultra-short...

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