We present a theory of frequency-dependent optical dephasing as measured by narrow-band photon-echo experiments. We consider a substitutionally disordered crystal with inhomogeneous broadening (diagonal disorder) and electronic interactions between occupied sites. We include the possibility of site-energy correlations. We find that the frequency dependence of the dephasing rate 1/ ${T}_{2}$ is very sensitive to the ratio \ensuremath{\xi}/a, where \ensuremath{\xi} is the correlation length and a is the lattice spacing. When \ensuremath{\xi}/a\ensuremath{\rightarrow}\ensuremath{\infty}, and there are macroscopic domains of resonant ions, 1/ ${T}_{2}$ becomes frequency independent. In the other limit when \ensuremath{\xi}/a\ensuremath{\rightarrow}0, and the site energies are uncorrelated (microscopic broadening), 1/ ${T}_{2}$ is proportional to the inhomogeneous line shape. We have compared our results to experiments by Macfarlane and Shelby on ${\mathrm{Y}}_{2}$ ${\mathrm{O}}_{3}$ : ${\mathrm{Eu}}^{3+}$ (2 at. %) and ${\mathrm{EuP}}_{5}$ ${\mathrm{O}}_{14}$ . We find reasonable agreement with experiment when \ensuremath{\xi} is less than a few lattice sites. Thus, for these systems the model of microscopic broadening is more appropriate than that of macroscopic broadening.We present a theory of frequency-dependent optical dephasing as measured by narrow-band photon-echo experiments. We consider a substitutionally disordered crystal with inhomogeneous broadening (diagonal disorder) and electronic interactions between occupied sites. We include the possibility of site-energy correlations. We find that the frequency dependence of the dephasing rate 1/${T}_{2}$ is very sensitive to the ratio \ensuremath{\xi}/a, where \ensuremath{\xi} is the correlation length and a is the lattice spacing. When \ensuremath{\xi}/a\ensuremath{\rightarrow}\ensuremath{\infty}, and there are macroscopic domains of resonant ions, 1/${T}_{2}$ becomes frequency independent. In the other limit when \ensuremath{\xi}/a\ensuremath{\rightarrow}0, and the site energies are uncorrelated (microscopic broadening), 1/${T}_{2}$ is proportional to the inhomogeneous line shape. We have compared our results to experiments by Macfarlane and Shelby on ${\mathrm{Y}}_{2}$${\mathrm{O}}_{3}$:${\mathrm{Eu}}^{3+}$ (2 at. %) and ${\mathrm{EuP}}_{5}$${\mathrm{O}}_{14}$. We find reasonable agreement with experiment when \ensuremath{\xi} is less than a few lattice sites. Thus, for these systems the model of microscopic broadening is more appropriate than that of macroscopic broadening.

Physical review. B, Condensed matterSep 15, 198525 citations

Optical dephasing and photon echoes from energetically and substitutionally disordered crystals

Leslie J. Root, James L. Skinner

For a crystal with both diagonal disorder (inhomogeneous broadening) and substitutional disorder we have calculated the contribution to the photon echo decay due to purely electronic intersite interactions. We have considered the two important limiting cases of macroscopic and microscopic inhomogeneous broadening. In the case of macroscopic broadening we find that the optical dephasing rate constant 1/T2∼f J, where f is the fractional concentration of impurities and J is the nearest-neighbor intersite interaction in frequency units. This result is valid for f≪1. In the opposite limit of microscopic inhomogeneous broadening, we find that 1/T2∼f J2/δ̄, where δ̄ is the width in frequency units of the inhomogeneous distribution. This result is valid for arbitrary f, including f=1, and for J≪δ̄. In the case that f≪1 and J≪δ̄, 1/T2 is much smaller for microscopic broadening than for macroscopic broadening. We discuss our results in relation to several experiments on mixed molecular crystals and to an experiment on the stoichiometric material EuP5O14.For a crystal with both diagonal disorder (inhomogeneous broadening) and substitutional disorder we have calculated the contribution to the photon echo decay due to purely electronic intersite interactions. We have considered the two important limiting cases of macroscopic and microscopic inhomogeneous broadening. In the case of macroscopic broadening we find that the optical dephasing rate constant 1/T2∼f J, where f is the fractional concentration of impurities and J is the nearest-neighbor intersite interaction in frequency units. This result is valid for f≪1. In the opposite limit of microscopic inhomogeneous broadening, we find that 1/T2∼f J2/δ̄, where δ̄ is the width in frequency units of the inhomogeneous distribution. This result is valid for arbitrary f, including f=1, and for J≪δ̄. In the case that f≪1 and J≪δ̄, 1/T2 is much smaller for microscopic broadening than for macroscopic broadening. We discuss our results in relation to several experiments on mixed molecular crystals and to an experiment on the stoichiometric material EuP5O14.

The Journal of Chemical PhysicsDec 15, 198436 citations

Disorder effect induced by electron-electron interaction

Jialin Zhu, R. Riklund, K. A. Chao

Physics Letters AMar 1, 19861 citation

Electron-electron interaction in a disordered electron gas in non-equilibrium

Heiner Linke, P. Omling, H. Xu +1 more

Jan 1, 19970 citations

Manybody-effects in nonlinear optics of semiconductors

Wilfried Schäfer

Many-body Coulomb interactions dominate nonlinear optical properties of semiconductor structures in many respects. Resulting effects show up most distinct in the temporal evolution of transient four-wave mixing signals. The simplest example in systems with homogeneously broadened absorption is the static exchange interaction, which prevents the occurrence of pure free polarization decay and gives rise to an additional interaction induced signal. For inhomogeneous broadening one obtains photon echo-like behaviour. The temporal duration of the signal, however, is not determined by the width of the inhomogeneous broadening, as is predicted by theory if interaction effects are neglected, but is much smaller due to exciton-exciton interaction. Additional to the static interaction effects electron-electron correlations give rise to laser induced renormalization and dephasing processes which depend sensitively on the polarizations of the driving fields. These effects are analyzed on the basis of quantum-kinetic equations, which allow to describe the temporal evolution of the nonlinear polarizations. Numerical results are presented for various excitation conditions and material systems.Many-body Coulomb interactions dominate nonlinear optical properties of semiconductor structures in many respects. Resulting effects show up most distinct in the temporal evolution of transient four-wave mixing signals. The simplest example in systems with homogeneously broadened absorption is the static exchange interaction, which prevents the occurrence of pure free polarization decay and gives rise to an additional interaction induced signal. For inhomogeneous broadening one obtains photon echo-like behaviour. The temporal duration of the signal, however, is not determined by the width of the inhomogeneous broadening, as is predicted by theory if interaction effects are neglected, but is much smaller due to exciton-exciton interaction. Additional to the static interaction effects electron-electron correlations give rise to laser induced renormalization and dephasing processes which depend sensitively on the polarizations of the driving fields. These effects are analyzed on the basis of quantum-kinetic equations, which allow to describe the temporal evolution of the nonlinear polarizations. Numerical results are presented for various excitation conditions and material systems.

Physica ScriptaJan 1, 19941 citation

{T}_{2}

is very sensitive to the ratio \ensuremath{\xi}/a, where \ensuremath{\xi} is the correlation length and a is the lattice spacing. When \ensuremath{\xi}/a\ensuremath{\rightarrow}\ensuremath{\infty}, and there are macroscopic domains of resonant ions, 1/

{T}_{2}

becomes frequency independent. In the other limit when \ensuremath{\xi}/a\ensuremath{\rightarrow}0, and the site energies are uncorrelated (microscopic broadening), 1/

{T}_{2}

is proportional to the inhomogeneous line shape. We have compared our results to experiments by Macfarlane and Shelby on

{\mathrm{Y}}_{2}

{\mathrm{O}}_{3}

{\mathrm{Eu}}^{3+}

(2 at. %) and

{\mathrm{EuP}}_{5}

{\mathrm{O}}_{14}

. We find reasonable agreement with experiment when \ensuremath{\xi} is less than a few lattice sites. Thus, for these systems the model of microscopic broadening is more appropriate than that of macroscopic broadening.