Self-consistent Maxwell-Bloch theory of quantum-dot-population switching in photonic crystals

Journal Article · Sun May 15 00:00:00 EDT 2011 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.83.053811· OSTI ID:21546860

Takeda, Hiroyuki; John, Sajeev ^[1]

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1. Department of Physics, University of Toronto, 60 St. George Street, Toronto, Ontario M5S 1A7 (Canada) and International Center for Young Scientists, National Institute for Materials Science, 1-2-1 Sengen, Tsukuba, Ibaraki, 305-0047 (Japan)

We theoretically demonstrate the population switching of quantum dots (QD's), modeled as two-level atoms in idealized one-dimensional (1D) and two-dimensional (2D) photonic crystals (PC's) by self-consistent solution of the Maxwell-Bloch equations. In our semiclassical theory, energy states of the electron are quantized, and electron dynamics is described by the atomic Bloch equation, while electromagnetic waves satisfy the classical Maxwell equations. Near a waveguide cutoff in a photonic band gap, the local electromagnetic density of states (LDOS) and spontaneous emission rates exhibit abrupt changes with frequency, enabling large QD population inversion driven by both continuous and pulsed optical fields. We recapture and generalize this ultrafast population switching using the Maxwell-Bloch equations. Radiative emission from the QD is obtained directly from the surrounding PC geometry using finite-difference time-domain simulation of the electromagnetic field. The atomic Bloch equations provide a source term for the electromagnetic field. The total electromagnetic field, consisting of the external input and radiated field, drives the polarization components of the atomic Bloch vector. We also include a microscopic model for phonon dephasing of the atomic polarization and nonradiative decay caused by damped phonons. Our self-consistent theory captures stimulated emission and coherent feedback effects of the atomic Mollow sidebands, neglected in earlier treatments. This leads to remarkable high-contrast QD-population switching with relatively modest (factor of 10) jump discontinuities in the electromagnetic LDOS. Switching is demonstrated in three separate models of QD's placed (i) in the vicinity of a band edge of a 1D PC, (ii) near a cutoff frequency in a bimodal waveguide channel of a 2D PC, and (iii) in the vicinity of a localized defect mode side coupled to a single-mode waveguide channel in a 2D PC.

• OSTI ID: 21546860
• Journal Information: Physical Review. A, Vol. 83, Issue 5; Other Information: DOI: 10.1103/PhysRevA.83.053811; (c) 2011 American Institute of Physics; ISSN 1050-2947
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
ATOMS
BLOCH EQUATIONS
BLOCH THEORY
CRYSTALS
ELECTROMAGNETIC FIELDS
ELECTROMAGNETIC RADIATION
ELECTRONS
MATHEMATICAL SOLUTIONS
MAXWELL EQUATIONS
ONE-DIMENSIONAL CALCULATIONS
PHONONS
PHOTONS
POLARIZATION
POPULATION INVERSION
QUANTUM DOTS
SEMICLASSICAL APPROXIMATION
STIMULATED EMISSION
TWO-DIMENSIONAL CALCULATIONS
WAVEGUIDES
APPROXIMATIONS
BOSONS
CALCULATION METHODS
DIFFERENTIAL EQUATIONS
ELEMENTARY PARTICLES
EMISSION
ENERGY-LEVEL TRANSITIONS
EQUATIONS
FERMIONS
LEPTONS
MASSLESS PARTICLES
NANOSTRUCTURES
PARTIAL DIFFERENTIAL EQUATIONS
QUASI PARTICLES
RADIATIONS