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Quantum Electronics and Laser Science Conference

Cascade-like nonlinearity caused by local-field effects: Extending bloembergen's result

Ksenia Dolgaleva, Robert W. Boyd, John E. Sipe

Published May 1, 2007• 0 citations
Publisher

Abstract

We treated the saturation effect in a dense medium up to the fifth order of nonlinearity, and discovered that the expression for the local-field-corrected fifth-order susceptibility disagrees with what was understood to be Bloembergen's prediction.
DOI
10.1109/qels.2007.4431712

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Contributions to the fifth-order nonlinear optical susceptibility ${\ensuremath{\chi}}^{(5)}$ of a collection of homogeneously broadened two-level atoms that scale as ${N}^{2}{({\ensuremath{\gamma}}_{\mathrm{at}}^{(3)})}^{2}$ and ${N}^{2}{\ensuremath{\mid}{\ensuremath{\gamma}}_{\mathrm{at}}^{(3)}\ensuremath{\mid}}^{2}$, where ${\ensuremath{\gamma}}_{\mathrm{at}}^{(3)}$ is the lower-order atomic hyperpolarizability and NNN is the atomic number density, are predicted theoretically. These ``cascaded'' contributions are a consequence of local-field effects. We determine them from a fifth-order solution of the Lorentz-Maxwell-Bloch equations. They are missing from a straightforward generalization of Bloembergen's result for the local field correction to the second order nonlinearity, but are recovered by a careful application of his general approach. We find that at high atomic densities $(N>{10}^{15}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3})$ the value of the cascaded third-order contribution can be as large as the ``direct'' fifth-order term in the expression for the fifth-order susceptibility.
The semi-classical theory of a single-mode gas laser has been extended to include higher-order terms by a simpler method than previous ones. The present theory takes not only the lifetimes of the two states but also the effect of phase-perturbing collisions into consideration by using three phenomenological decay constants in the two-level system. Explicit expressions in the general case of nonlinear susceptibility of the laser medium or the saturable absorber are presented for the fifth and seventh orders, while the ninth-order expression is shown for a special case of a very long longitudinal relaxation time.
A diagrammatic approach to the theory of nonlinear susceptiblities is developed. Including damping, the steady state nonlinear response functions to several simultaneously applied monochromatic electromagnetic fields are obtained in terms of linear response functions in the weak coupling system. Saturation phenomena in microwave resonance and in parametric processes can be understood as lower order responses in the system with higher spin temperature. The condition for the Raman emission is discussed in some details. Results are compared with previous theories, in particular with that of Bloembergen and Shen. The theory is extended to the case where the spacially inhomogeneous perturbation is imposed.