Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

IEEE Journal of Quantum Electronics

Diagrammatic analysis of third order nonlinear optical processes

James G. Fujimoto, Ting K. Yee

Published May 1, 1983• 29 citations
Publisher

Abstract

We apply a diagrammatic density matrix perturbation technique to analyze third order nonlinear optical processes. The diagrammatic approach is shown to yield a significant simplification in the computation of both steady state and transient response while including the effects of damping and linewidth. The topology of the diagrams is stressed in identifying and interpreting their associated perturbation terms as well as predicting frequency resonance and transient behavior. We demonstrate the practical utility of the technique by presenting a detailed analysis and discussion of the processes of stimulated Raman scattering, hot luminescence, and pressure induced resonances in four wave mixing.

DOI
10.1109/jqe.1983.1071933

Related papers

Diagrammatic density matrix theory of transient four-wave mixing and the measurement of transient phenomena

James G. Fujimoto, Ting K. Yee

A diagrammatic density matrix perturbation technique is applied to describe transient third-order nonlinear optical processes and their applications to the measurement of transient phenomena. Using this approach, pump probe, parametric scattering, and three-pulse scattering are analyzed in a computationally simple and unified manner. The density matrix allows the description of a wide variety of dynamical processes including population and dephasing relaxation as well as orientational randomization and spatial diffusion. In addition, the diagrams provide a physical interpretation for the density matrix terms that they represent, and the effect of varying experimental parameters for the measurement of transient behavior can often be determined directly from the diagrams. Finally, topological similarities between diagrams provide a unified description of several different transient four-wave mixing measurement techniques.

IEEE Journal of Quantum Electronics•Aug 1, 1986•22 citations

Diagrammatic analysis of the density operator for nonlinear optical calculations: Pulsed and cw responses

Ting K. Yee, T. Kenneth Gustafson

In the present paper a diagrammatic analysis of the density operator for the evaluation of nonlinear optical quantities is considered. The present approach extends earlier diagrammatic analysis by treating the time evolution of both the wave function and its complex conjugate. Time-ordered graphs result, each of which corresponds to a term in the density matrix. Examples involving the third-order susceptibility are discussed for both monochromatic and pulse excitation. In particular coherent rotational transient birefringence is discussed. The diagrams provide a convenient means by which nonlinear optical processes can be precisely defined and the susceptibility readily evaluated.

Physical Review A•Oct 1, 1978•219 citations

Analysis of strong light-matter interaction using a dressed propagator approach

James G. Fujimoto, Ting K. Yee

A diagrammatic density matrix technique is developed and applied to study nonlinear optical processes involving responses from weak probe fields interacting with a system under strong excitation. These diagrams consist of lowest-order double-Feynman diagrams which represent the density matrix perturbation terms describing the system response to the weak probe fields1,2 combined with dressed propagators which represent the density matrix elements of the system under strong excitation. The dressed propagators are described by a set of linear equations which, in most cases, may be derived in inspection. The methodology is similar to the bare-atom approach.2 The advantages of using this diagrammatic technique are that (1) it allows one to select and express analytically the dominant and appropriate density matrix elements (diagrams and dressed propagators); (2) analytical expressions may be constructed directly from the diagrams and thus lengthy calculations needed to obtain closed-form solutions are greatly reduced; (3) it provides a physical interpretation for the density matrix solutions and nonlinear optical processes; and (4) it may be generalized to more complicated, multilevel systems. We demonstrate the application of this technique to describe gain saturation, Stark splitting, and Raman scattering.

Annual Meeting Optical Society of America•Jan 1, 1985•0 citations

Diagrammatical analysis of laser-switched collision processes

Ting K. Yee, M. C. Gower

We have used a diagrammatic approach first developed for nonlinear optical calculations of the density operator to obtain expressions for the transition probability in various laser-switched collision processes. Not only do these diagrams considerably simplify the algebra involved in such calculations, but they also afford a clear visualization of the interaction. In particular, pair absorption, laser-switched Raman scattering, and collisionally enhanced hot luminescence and four-wave mixing processes are considered.

IEEE Journal of Quantum Electronics•Mar 1, 1982•1 citation

Internal photon lines associated with the density matrix operator

T. Kenneth Gustafson

Previous diagrammatic analyses of the density matrix are extended to incorporate quantum-electrodynamic processes fully by inclusion of the photon propagator and its complex conjugate. It is shown that eight fundamental time-ordered diagrams are necessary to describe radiative processes completely. For each of these, inclusion of the photon propagator permits, in addition to polarization, a direct calculation of electric field expectation values. Electric field correlations associated with the fundamental diagrams lead to a diagrammatic (quantum-electrodynamic) interpretation and derivation of the spontaneous emission limited linewidth associated with simulated emission as given by the Townes-Schawlow line narrowing formula. Stimulated Raman scattering, two-wave mixing, and parametric amplification are illustrative of the extension of these diagrammatic techniques to nonlinear optical phenomena.>

IEEE Journal of Quantum Electronics•Jan 1, 1989•1 citation

Theory of Nonlinear Susceptibility

Tatuo Kawasaki

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.

Progress of Theoretical Physics•Feb 1, 1968•6 citations
We apply a diagrammatic density matrix perturbation technique to analyze third order nonlinear optical processes. The diagrammatic approach is shown to yield a significant simplification in the computation of both steady state and transient response while including the effects of damping and linewidth. The topology of the diagrams is stressed in identifying and interpreting their associated perturbation terms as well as predicting frequency resonance and transient behavior. We demonstrate the practical utility of the technique by presenting a detailed analysis and discussion of the processes of stimulated Raman scattering, hot luminescence, and pressure induced resonances in four wave mixing.
A diagrammatic density matrix perturbation technique is applied to describe transient third-order nonlinear optical processes and their applications to the measurement of transient phenomena. Using this approach, pump probe, parametric scattering, and three-pulse scattering are analyzed in a computationally simple and unified manner. The density matrix allows the description of a wide variety of dynamical processes including population and dephasing relaxation as well as orientational randomization and spatial diffusion. In addition, the diagrams provide a physical interpretation for the density matrix terms that they represent, and the effect of varying experimental parameters for the measurement of transient behavior can often be determined directly from the diagrams. Finally, topological similarities between diagrams provide a unified description of several different transient four-wave mixing measurement techniques.
In the present paper a diagrammatic analysis of the density operator for the evaluation of nonlinear optical quantities is considered. The present approach extends earlier diagrammatic analysis by treating the time evolution of both the wave function and its complex conjugate. Time-ordered graphs result, each of which corresponds to a term in the density matrix. Examples involving the third-order susceptibility are discussed for both monochromatic and pulse excitation. In particular coherent rotational transient birefringence is discussed. The diagrams provide a convenient means by which nonlinear optical processes can be precisely defined and the susceptibility readily evaluated.
A diagrammatic density matrix technique is developed and applied to study nonlinear optical processes involving responses from weak probe fields interacting with a system under strong excitation. These diagrams consist of lowest-order double-Feynman diagrams which represent the density matrix perturbation terms describing the system response to the weak probe fields1,2 combined with dressed propagators which represent the density matrix elements of the system under strong excitation. The dressed propagators are described by a set of linear equations which, in most cases, may be derived in inspection. The methodology is similar to the bare-atom approach.2 The advantages of using this diagrammatic technique are that (1) it allows one to select and express analytically the dominant and appropriate density matrix elements (diagrams and dressed propagators); (2) analytical expressions may be constructed directly from the diagrams and thus lengthy calculations needed to obtain closed-form solutions are greatly reduced; (3) it provides a physical interpretation for the density matrix solutions and nonlinear optical processes; and (4) it may be generalized to more complicated, multilevel systems. We demonstrate the application of this technique to describe gain saturation, Stark splitting, and Raman scattering.
We have used a diagrammatic approach first developed for nonlinear optical calculations of the density operator to obtain expressions for the transition probability in various laser-switched collision processes. Not only do these diagrams considerably simplify the algebra involved in such calculations, but they also afford a clear visualization of the interaction. In particular, pair absorption, laser-switched Raman scattering, and collisionally enhanced hot luminescence and four-wave mixing processes are considered.
Previous diagrammatic analyses of the density matrix are extended to incorporate quantum-electrodynamic processes fully by inclusion of the photon propagator and its complex conjugate. It is shown that eight fundamental time-ordered diagrams are necessary to describe radiative processes completely. For each of these, inclusion of the photon propagator permits, in addition to polarization, a direct calculation of electric field expectation values. Electric field correlations associated with the fundamental diagrams lead to a diagrammatic (quantum-electrodynamic) interpretation and derivation of the spontaneous emission limited linewidth associated with simulated emission as given by the Townes-Schawlow line narrowing formula. Stimulated Raman scattering, two-wave mixing, and parametric amplification are illustrative of the extension of these diagrammatic techniques to nonlinear optical phenomena.>
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.