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Oxford University Press eBooks

Optical Coherent Transient Effects

Guang S. He

Published Oct 30, 2014• 0 citations
Publisher

Abstract

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.

DOI
10.1093/acprof:oso/9780198702764.003.0010

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MODULATION OF COHERENT TRANSIENT EFFECTS BY HETERODYNE FIELDS IN STARK AND FREQUENCY SWITCHING.

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Coherent transient effects are the optical analogs of the many transient phenomena seen in pulsed nuclear magnetic resonance experiments on spin systems. For example, photon-echo and optical nutation are the respective optical equivalents of spin echo and transient nutation of nuclear magnetic resonance. In Stark-switching and frequency-switching techniques the laser field and the molecules are brought into resonance in a sequence of pulses, the rest of the time they remain well off-resonance. So far it has been assumed that the off-resonance field does not have any measureable influence on the experimental results and is utilized to implement a very efficient detection scheme. This work discusses how the off-resonance field affects the coherent transient effects. It is shown here how this field, by inducing changes in the index of refraction as small as 10⁻⁶ produces easily observable effects in photon echo and delayed optical nutation.

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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.

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Optical coherent transients by laser frequency switching

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A simple method for observing coherent optical-transient phenomena is described. Effects such as photon echoes and free induction decay (FID) should allow studies of the dynamic properties of atoms, molecules, and solids on a time scale ranging from milliseconds to \ensuremath{\sim} 50 ps. The frequency of a cw dye laser is switched with an intracavity electro-optic modulator, producing in an external sample coherent transients which are detected in the forward beam. Measurements of long dephasing times are possible, as in FID, because the laser can oscillate indefinitely at the new frequency following a step-function switching pulse. Measurements of short decay times are also practical because the switching time is not restricted by the laser gain or cavity ringing time. In addition, the dye's dephasing time of a few picoseconds or less is too rapid to interfere with these observations. Since the pulse sequence can be preselected, the entire class of coherent optical transients is accessible. The method thus incorporates all of the advantages inherent in Stark switching, including heterodyne detection and high sensitivity, without being restricted to Stark-tunable systems. Laser frequency switching is discussed also in terms of a theoretical model which exposes the time-dependent properties of a phase-modulated cavity mode. Dephasing studies have been carried out thus far in atomic and molecular gases and low-temperature solids containing inorganic impurity ions or large organic molecules. The utility of the FID effect is emphasized where precise dephasing times are obtained from time-frequency Fourier transformation of FID signals using a digital computer. The first quantitative and detailed test of FID theory is provided by these experimental techniques.

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Reversible absorption of weak fields revealed in coherent transients

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It is shown that the absorbtion of a weak field in a thick resonant absorber is a reversible process even in the case of the homogeneous broadening of the absorption line. As an example, the propagation of a long rectangular pulse with sharp edges in an optically dense resonant medium is studied theoretically in the linear response approximation. Transient nutation (TN), free induction decay (FID), and transients, induced by the phase switch of the incident pulse, are considered. It is shown that in exact resonance the amplitude of FID increases with the length of the medium. FID arises due to the scattered radiation field (dipoles ringing). In a thick medium the scattered field is almost of the same amplitude but opposite in phase with the incident radiation field. Both fields interfere destructively to produce what is seen as radiation damping at the output of the medium. The scattered field needs time to develop. Therefore, the leading edge of the pulse is not absorbed, demonstrating temporal transparency followed by TN. Phase shift (180${}^{\ensuremath{\circ}}$) of the pulse brings the incident pulse in phase with the scattered radiation. Constructive interference of the pulse with the scattered radiation field produces a short pulse with an amplitude that is two times larger than the amplitude of the incident pulse. If the input pulse is detuned from resonance, for a particular detuning and optical thickness of the medium the amplitude of the transient pulse, induced by the phase shift, is nearly three times larger than the amplitude of the incident pulse. This is explained by the interference of the scattered field, the phase-shifted input field, and the slowly propagating part of the pulse, developed before the phase shift.

Physical Review A•Feb 21, 2012•13 citations

Transient Optical Response

Stephen Colby Rand

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.

Oxford University Press eBooks•Jun 9, 2016•0 citations
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.
Coherent transient effects are the optical analogs of the many transient phenomena seen in pulsed nuclear magnetic resonance experiments on spin systems. For example, photon-echo and optical nutation are the respective optical equivalents of spin echo and transient nutation of nuclear magnetic resonance. In Stark-switching and frequency-switching techniques the laser field and the molecules are brought into resonance in a sequence of pulses, the rest of the time they remain well off-resonance. So far it has been assumed that the off-resonance field does not have any measureable influence on the experimental results and is utilized to implement a very efficient detection scheme. This work discusses how the off-resonance field affects the coherent transient effects. It is shown here how this field, by inducing changes in the index of refraction as small as 10⁻⁶ produces easily observable effects in photon echo and delayed optical nutation.
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.
For pt.I see ibid., vol.8, no.3, 339 (1975). The transient behaviour of two short optical pulses in two-photon coherent propagation is obtained by calculating numerically the coherent propagation equations which couple the two electromagnetic pulses and the atomic system in self-consistent fashion. The coherent interaction of the two different frequency pulses gives rise to lossless propagation in the absorptive medium. This description is characterized by a two-photon area theorem. Novel coherent propagation effects of peak amplification and multiple pulse breakup are found. These effects are ascribed to two-photon self-induced transparency analogous to that of a one-photon transition in a two-level system. A difference of input intensity between the two different frequency pulses yields curious modulation effects involving sharp peak amplification and marked pulse breakup for the low-intensity input. In contrast, the high-intensity input pulse displays a smooth variation with distance and time. Low-loss pulse transmission above threshold, and pulse advance and delay are found for the present case in contrast to that for one-photon self-induced transparency.
A simple method for observing coherent optical-transient phenomena is described. Effects such as photon echoes and free induction decay (FID) should allow studies of the dynamic properties of atoms, molecules, and solids on a time scale ranging from milliseconds to \ensuremath{\sim} 50 ps. The frequency of a cw dye laser is switched with an intracavity electro-optic modulator, producing in an external sample coherent transients which are detected in the forward beam. Measurements of long dephasing times are possible, as in FID, because the laser can oscillate indefinitely at the new frequency following a step-function switching pulse. Measurements of short decay times are also practical because the switching time is not restricted by the laser gain or cavity ringing time. In addition, the dye's dephasing time of a few picoseconds or less is too rapid to interfere with these observations. Since the pulse sequence can be preselected, the entire class of coherent optical transients is accessible. The method thus incorporates all of the advantages inherent in Stark switching, including heterodyne detection and high sensitivity, without being restricted to Stark-tunable systems. Laser frequency switching is discussed also in terms of a theoretical model which exposes the time-dependent properties of a phase-modulated cavity mode. Dephasing studies have been carried out thus far in atomic and molecular gases and low-temperature solids containing inorganic impurity ions or large organic molecules. The utility of the FID effect is emphasized where precise dephasing times are obtained from time-frequency Fourier transformation of FID signals using a digital computer. The first quantitative and detailed test of FID theory is provided by these experimental techniques.
It is shown that the absorbtion of a weak field in a thick resonant absorber is a reversible process even in the case of the homogeneous broadening of the absorption line. As an example, the propagation of a long rectangular pulse with sharp edges in an optically dense resonant medium is studied theoretically in the linear response approximation. Transient nutation (TN), free induction decay (FID), and transients, induced by the phase switch of the incident pulse, are considered. It is shown that in exact resonance the amplitude of FID increases with the length of the medium. FID arises due to the scattered radiation field (dipoles ringing). In a thick medium the scattered field is almost of the same amplitude but opposite in phase with the incident radiation field. Both fields interfere destructively to produce what is seen as radiation damping at the output of the medium. The scattered field needs time to develop. Therefore, the leading edge of the pulse is not absorbed, demonstrating temporal transparency followed by TN. Phase shift (180${}^{\ensuremath{\circ}}$) of the pulse brings the incident pulse in phase with the scattered radiation. Constructive interference of the pulse with the scattered radiation field produces a short pulse with an amplitude that is two times larger than the amplitude of the incident pulse. If the input pulse is detuned from resonance, for a particular detuning and optical thickness of the medium the amplitude of the transient pulse, induced by the phase shift, is nearly three times larger than the amplitude of the incident pulse. This is explained by the interference of the scattered field, the phase-shifted input field, and the slowly propagating part of the pulse, developed before the phase shift.
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.