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Wei-Chih Liu 劉威志 Department of Physics National Taiwan Normal University

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.

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Wei-Chih Liu 劉威志 Department of Physics National Taiwan Normal University

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  1. 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

  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. 1.8 GHz 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/λ)

  8. EIT – Transparency with coupling field -- Probe Field Amplitude Position (x/λ)

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

  10. Total wave Probe field Scattering field Energy level shift from simulations coupling field power = 3×104 mW cm-2 Frequency(ω/ω31)

  11. Total wave Probe field Scattering field Energy level shift from simulations coupling field power = 3×107 mW cm-2 Ωc/2 Frequency(ω/ω31)

  12. Total wave Probe field Scattering field Large Energy level shift - Transparency coupling field power = 1.2×108 mW cm-2 Frequency(ω/ω31)

  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 π / 1000

  15. Polarization with various coupling filed intensity coupling field FWHM=256 T/2π probe field FWHM=16 T/2π Ωp=0.01

  16. Polarization with various coupling filed intensity coupling field FWHM=256 T/2π probe field FWHM=16 T/2π Ωc=0.1

  17. Polarization with various coupling filed intensity coupling field FWHM=256 T/2π probe field FWHM=16 T/2π Ωp=1.0

  18. Polarization with various coupling filed intensity coupling field FWHM=256 T/2π probe field FWHM=16 T/2π Ωp=10.0

  19. Time-dependent polarization behavior coupling field FWHM =256 T/2π Ωp=10.0 probe field FWHM =16 T/2π Ωc=0.0

  20. Time-dependent polarization behavior coupling field FWHM =256 T/2π Ωp=10.0 probe field FWHM =16 T/2π Ωc=10.0

  21. Time-dependent polarization behavior coupling field FWHM =256 T/2π Ωp=10.0 probe field FWHM =16 T/2π Ωc=100.0

  22. Time-dependent polarization behavior coupling field FWHM =256 T/2π Ωp=10.0 probe field FWHM =16 T/2π Ωc=400.0

  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/λ)

  25. Coupling field turn-off – t = 20 fs -- Probe Field -- Polarization between 1-2 level Amplitude Position (x/λ)

  26. Coupling field turn-off – t = 10 fs -- Probe Field -- Polarization between 1-2 level Amplitude Position (x/λ)

  27. Coupling field turn-off – t = 5 fs -- Probe Field -- Polarization between 1-2 level Amplitude Position (x/λ)

  28. Coupling field turn-off – t = 1 fs -- Probe Field -- Polarization between 1-2 level Amplitude Position (x/λ)

  29. Coupling field turn-off – t = 1 fs (zoom in) -- Probe Field -- Polarization between 1-2 level Amplitude Position (x/λ)

  30. 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

  31. Atomic Dynamics - Coupling field = 3×107 mW cm-2 -- Probe Field -- Polarization between 1-2 level Amplitude Time (t/T)

  32. Atomic Dynamics - Coupling field = 6×107 mW cm-2 -- Probe Field -- Polarization between 1-2 level Amplitude Time (t/T)

  33. Atomic Dynamics - Coupling field = 1.2×108 mW cm-2 -- Probe Field -- Polarization between 1-2 level Amplitude Time (t/T)

  34. C1*C2e-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/λ)

  36. Coupling field turn-off and on toff = 50 period － Probe Field -- Polarization between 1-2 level Amplitude Position (x/λ)

  37. Coupling field turn-off and on toff = 75 period － Probe Field -- Polarization between 1-2 level Amplitude Position (x/λ)

  38. Coupling field turn-off and on toff = 100 period － Probe Field -- Polarization between 1-2 level Amplitude Position (x/λ)

  39. Probe pulse reading efficiency vs coupling light turn-off duration atomic density 1×1018cm-3 decay rate Γ3=ω31/20π ratio

  40. Probe pulse reading efficiency vs atomic density coupling light turn-off duration τc=τp decay rate Γ3=ω31/20π ratio

  41. Probe pulse reading efficiency vs decay rate ratio coupling light turn-off duration τc=τp atomic density 4×1017cm-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 DPS ENG DPS Regular Dielectrics DNG MNG • Double-negative (DNG) medium • Mu-negative (MNG) medium

  44. Realization of DNG Metamaterials R. A. Shelby, D. R. Smith, and S. Schultz, Science292, 77 (2001).2001 44

  45. Subwavelength Focusing Perfect lens (Pendry, 2000) y = 2d n=1 n=-1 y = -2d 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 (e=9.5+035i). 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 (朱達勇)at NIU and NTNU • Meng-Chang Wu(吳孟昌) (currently at IAMS, AS) • Supported by NSC

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