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Oxford University Press eBooks

Transient Optical Response

Stephen Colby Rand

Published Jun 9, 2016• 0 citations
Publisher

Abstract

Abstract Chapter 4 treats the three most important coherent optical transient phenomena using primarily the Bloch vector model. One section is devoted to each effect: nutation, free induction decay, and the photon echo. Through this, the idea that steady-state response to light develops slowly, on a timescale set by inertia in the atom–field interaction, is introduced. Nutation is considered both with and without damping. In the last section, three possible approaches to describing the photon echo are briefly compared to gain perspective on the advantages and disadvantages of algebraic echo analysis, rotation matrix multiplication, or density matrix methodology. By the end of this chapter the reader is prepared for the remaining chapters in which the density matrix approach is used exclusively to calculate the effects of light on a wide variety of systems.

DOI
10.1093/acprof:oso/9780198757450.003.0004

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Transient Optical Response

Stephen Colby Rand

Chapter 4 treats the three most important coherent optical transient phenomena using primarily the Bloch vector model. One section is devoted to each effect: nutation, free induction decay (FID), and photon echo. Through this, the idea that steady‐state response to light develops slowly, on a timescale set by inertia in the atom–field interaction, is introduced. In the last section, three possible approaches to describing the photon echo are briefly compared to gain perspective on the advantages and disadvantages of algebraic, matrix multiplication, or density matrix methodology. By the end of this chapter the reader is prepared for the remaining chapters in which the density matrix approach is used exclusively to calculate the effects of light.

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When an intense and short laser pulse or a fast-switching-on/off laser field interacts with a resonant absorbing medium, several optical coherent transient effects can be observed, including the self-induced transparency effect, photon echo effect, optical nutation effect, and the optical free induction decay effect. The study of these effects enables us to gain a deeper understanding of the coherent transient interaction of an intense pulsed or rapidly switched optical field with the resonant medium, and to measure the magnitude of the dipole-moment matrix elements, relaxation parameters, and spectral broadening mechanisms of the investigated materials. On the other hand, these optical coherent transient effects can also be applied for developing special techniques of optical pulse delay, pulse reshaping, and optical pulse manipulation.

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In Chapter 3 the interaction Hamiltonian which determines the way light interacts with matter is derived. Simple perturbative analysis is applied to see if basic dynamics of atoms can be explained. The partial successes of perturbation theory are compared with predictions of an “exact” method of calculating the occupation probabilities of various atomic states. Even the “exact” method is shown to fail, establishing the need for improved approaches that yield correct results in later chapters. Some elementary results for the transition rates, including Fermi's golden rule are covered. Then the density matrix is introduced as a tool for describing not only the populations of atomic energy levels but coherence that can be created and lost during the dynamic evolution of atoms in time. A vector model based on the Bloch vector is presented as a useful way of picturing coherent atom–field interactions in an optical “spin” space, particularly multiple‐pulse interactions. Mechanisms are described that cause line‐broadening in optical spectroscopy, such as the Doppler effect. The chapter closes by showing that it is usually possible to reduce the complexity of real atoms on an experimental basis to facilitate direct comparisons with theoretical calculations based on simple models with only two or three energy levels.

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Photon echo and free induction decay, i.e., representative coherent optical transients, are described for two level system whose transition frequency is modulated by the Gaussian-Markoffian process. Photon echo signal is shown to decay biexponentially and to be effective in fixing the magnitude and the correlation time of the frequency modulation. Then we present the transition of the free induction decay rate against laser intensity from the Bloch type at the weak laser field into the Redfield one at the strong laser field.

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Pulsed radio-frequency transient phenomena of resonant two-level spins are often described by the Bloch equations where the phenomenological dipole (${T}_{2}$) and population (${T}_{1}$) decay times appear. A similar description has been carried over recently into the microwave and infrared regions as well. At visible-ultraviolet wavelengths, however, a more general solution is required because the transition levels do not constitute an isolated system and also spontaneous emission can no longer be disregarded. As a consequence, the lower (1) and upper (2) transition levels are characterized by vastly different decay rates (${\ensuremath{\gamma}}_{1}\ensuremath{\ne}{\ensuremath{\gamma}}_{2}$) and the lifetime ${T}_{1}$ is no longer a defined quantity. In view of laser-induced coherent transient phenomena now being observed, we present general solutions of the density-matrix equations of motion for an optically resonant two-level system in contact with a multilevel reservoir where ${\ensuremath{\gamma}}_{1}\ensuremath{\ne}{\ensuremath{\gamma}}_{2}$. Particular and perturbative solutions involving intensity-dependent damping and frequency shifts are included with applications to echo and nutation phenomena.

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Coherent transients in molecular gases: comparison of two techniques

Н. Н. Рубцова

Each of three basic coherent transient phenomena (optical nutation, free polarization decay photon echo) can be generated by sufficiently abrupt modulation of the interaction between the matter and radiation. This can be performed by rapid commutation of either radiation parameters, or the parameters of the matter. I present here comparative analysis of these two approaches (the first one, using electro-optical switching of the resonant laser power to create the pulses for the gas excitation and the second one, based on the Stark switching of vibro-rotational levels in a gas, excited by CW laser radiation), used in our experiments in molecular gases, from the point of view of both their capability to generate various coherent transients and their sensitivity to the intensity of laser radiation.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Nov 15, 2001•0 citations
Abstract Chapter 4 treats the three most important coherent optical transient phenomena using primarily the Bloch vector model. One section is devoted to each effect: nutation, free induction decay, and the photon echo. Through this, the idea that steady-state response to light develops slowly, on a timescale set by inertia in the atom–field interaction, is introduced. Nutation is considered both with and without damping. In the last section, three possible approaches to describing the photon echo are briefly compared to gain perspective on the advantages and disadvantages of algebraic echo analysis, rotation matrix multiplication, or density matrix methodology. By the end of this chapter the reader is prepared for the remaining chapters in which the density matrix approach is used exclusively to calculate the effects of light on a wide variety of systems.
Chapter 4 treats the three most important coherent optical transient phenomena using primarily the Bloch vector model. One section is devoted to each effect: nutation, free induction decay (FID), and photon echo. Through this, the idea that steady‐state response to light develops slowly, on a timescale set by inertia in the atom–field interaction, is introduced. In the last section, three possible approaches to describing the photon echo are briefly compared to gain perspective on the advantages and disadvantages of algebraic, matrix multiplication, or density matrix methodology. By the end of this chapter the reader is prepared for the remaining chapters in which the density matrix approach is used exclusively to calculate the effects of light.
When an intense and short laser pulse or a fast-switching-on/off laser field interacts with a resonant absorbing medium, several optical coherent transient effects can be observed, including the self-induced transparency effect, photon echo effect, optical nutation effect, and the optical free induction decay effect. The study of these effects enables us to gain a deeper understanding of the coherent transient interaction of an intense pulsed or rapidly switched optical field with the resonant medium, and to measure the magnitude of the dipole-moment matrix elements, relaxation parameters, and spectral broadening mechanisms of the investigated materials. On the other hand, these optical coherent transient effects can also be applied for developing special techniques of optical pulse delay, pulse reshaping, and optical pulse manipulation.
In Chapter 3 the interaction Hamiltonian which determines the way light interacts with matter is derived. Simple perturbative analysis is applied to see if basic dynamics of atoms can be explained. The partial successes of perturbation theory are compared with predictions of an “exact” method of calculating the occupation probabilities of various atomic states. Even the “exact” method is shown to fail, establishing the need for improved approaches that yield correct results in later chapters. Some elementary results for the transition rates, including Fermi's golden rule are covered. Then the density matrix is introduced as a tool for describing not only the populations of atomic energy levels but coherence that can be created and lost during the dynamic evolution of atoms in time. A vector model based on the Bloch vector is presented as a useful way of picturing coherent atom–field interactions in an optical “spin” space, particularly multiple‐pulse interactions. Mechanisms are described that cause line‐broadening in optical spectroscopy, such as the Doppler effect. The chapter closes by showing that it is usually possible to reduce the complexity of real atoms on an experimental basis to facilitate direct comparisons with theoretical calculations based on simple models with only two or three energy levels.
Photon echo and free induction decay, i.e., representative coherent optical transients, are described for two level system whose transition frequency is modulated by the Gaussian-Markoffian process. Photon echo signal is shown to decay biexponentially and to be effective in fixing the magnitude and the correlation time of the frequency modulation. Then we present the transition of the free induction decay rate against laser intensity from the Bloch type at the weak laser field into the Redfield one at the strong laser field.
Pulsed radio-frequency transient phenomena of resonant two-level spins are often described by the Bloch equations where the phenomenological dipole (T2{T}_{2}T2​) and population (T1{T}_{1}T1​) decay times appear. A similar description has been carried over recently into the microwave and infrared regions as well. At visible-ultraviolet wavelengths, however, a more general solution is required because the transition levels do not constitute an isolated system and also spontaneous emission can no longer be disregarded. As a consequence, the lower (1) and upper (2) transition levels are characterized by vastly different decay rates (${\ensuremath{\gamma}}_{1}\ensuremath{\ne}{\ensuremath{\gamma}}_{2}$) and the lifetime T1{T}_{1}T1​ is no longer a defined quantity. In view of laser-induced coherent transient phenomena now being observed, we present general solutions of the density-matrix equations of motion for an optically resonant two-level system in contact with a multilevel reservoir where ${\ensuremath{\gamma}}_{1}\ensuremath{\ne}{\ensuremath{\gamma}}_{2}$. Particular and perturbative solutions involving intensity-dependent damping and frequency shifts are included with applications to echo and nutation phenomena.
Each of three basic coherent transient phenomena (optical nutation, free polarization decay photon echo) can be generated by sufficiently abrupt modulation of the interaction between the matter and radiation. This can be performed by rapid commutation of either radiation parameters, or the parameters of the matter. I present here comparative analysis of these two approaches (the first one, using electro-optical switching of the resonant laser power to create the pulses for the gas excitation and the second one, based on the Stark switching of vibro-rotational levels in a gas, excited by CW laser radiation), used in our experiments in molecular gases, from the point of view of both their capability to generate various coherent transients and their sensitivity to the intensity of laser radiation.