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Physical Review Letters

Coherent Transients by Optical Phase Switching: Dephasing in La Cl3 : Pr3+

Azriel Z. Genack, David A. Weitz, R. M. Macfarlane, Robert M. Shelby, Axel Schenzle

Published Aug 11, 1980• 31 citations
Publisher

Abstract

A novel coherent transient effect is observed following a rapid shift in the relative phase of an exciting laser and sample polarization. An analytical expression is derived for the signal which is a sum of exponentially decaying terms with characteristic times involving both ${T}_{1}$ and ${T}_{2}$. Phase switching is a powerful approach to the study of optical relaxation and is applied here to measure dephasing in La${\mathrm{Cl}}_{3}$: ${\mathrm{Pr}}^{3+}$.

DOI
10.1103/physrevlett.45.438

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Coherent Transients by Optical Phase Switching: Dephasing in La Cl3 : Pr3+

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We show that the optical dephasing time ${T}_{2}$ can be obtained from a measurement of the time delay ${T}_{0}$ between two shifts of $\ifmmode\pm\else\textpm\fi{}\frac{\ensuremath{\pi}}{2}$ in the phase of the exciting laser for which a null occurs in the jump in the nonlinear transmission through a sample. The phase shift is imposed upon a single-mode cw laser by applying a rectangular voltage pulse to an electro-optic phase modulator placed in the laser beam. The time delay at which the null occurs is proportional to ${T}_{2}$, which is given by the expression ${T}_{2}=(\frac{2}{\mathrm{ln}2}){T}_{0}$. The method is demonstrated in atomic sodium and iodine vapor and the separation of third-order optical transients from linear transients induced by the phase shift is discussed. An analytic expression for the jump in the nonlinear transmission, induced by the second phase shift, as well as for the transient in transmission following a single phase shift of a laser which weakly saturates an optically thin sample is derived. It is also shown that optical dephasing rates may be inferred from the variation of the integral of the transmitted light in a double-phase-switching experiment.

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Coherent Transients by Laser-Acoustical Diffraction Spectroscopy

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Recently we have reported[1] on the measurements of electronic dephasing (T_2) and radiationless decay (T_1) in molecules using emission spectroscopy as a probe for the detection of the photon echo. This right-angle photon echo utilizes a single mode of a narrow-band (~MHz) cw dye laser and an intracavity electro-optical (EO) element that modulates the frequency of the laser.[2] Applying voltage pulses into the EO crystal switches the laser frequency from ω_0 (the peak frequency of the transition resonance) into another frequency ω. This switching procedure introduced by Brewer et al. for the observation of transients in the forward direction of the laser allows one to observe coherent transients in gases,[1,2] solids[3-5] and molecular beams.[6] Typically, the dispersion of the nonlinear EO crystal (e.g., AD*P) gives a 60 MHz frequency shift within the inhomogeneous resonance of the optical transition (width ~GHz or larger). Therefore, to switch the laser frequency further, one must use high-voltage signals that are usually hard to obtain especially for multiple-pulse experiments. Secondly, there is a limit on the frequency shift which is conditioned by the mode spacing of the cavity. Thirdly, because the laser is switched into a new group of molecules some complications may arise in interpreting the transient spectra especially in large molecules. This is because in large molecules the density of excited states is high and thus the buildup of transients of w molecules (which could be complex) will be superimposed on the decay of ω_0 molecules. Finally, off-resonance effects (e.g., beats) between the molecules at frequency ω and ω_0 cannot be avoided.

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Journal of Experimental and Theoretical Physics Letters•Jul 1, 2006•0 citations
A novel coherent transient effect is observed following a rapid shift in the relative phase of an exciting laser and sample polarization. An analytical expression is derived for the signal which is a sum of exponentially decaying terms with characteristic times involving both T1{T}_{1}T1​ and T2{T}_{2}T2​. Phase switching is a powerful approach to the study of optical relaxation and is applied here to measure dephasing in LaCl3{\mathrm{Cl}}_{3}Cl3​: Pr3+{\mathrm{Pr}}^{3+}Pr3+.
We show that the optical dephasing time T2{T}_{2}T2​ can be obtained from a measurement of the time delay T0{T}_{0}T0​ between two shifts of $\ifmmode\pm\else\textpm\fi{}\frac{\ensuremath{\pi}}{2}$ in the phase of the exciting laser for which a null occurs in the jump in the nonlinear transmission through a sample. The phase shift is imposed upon a single-mode cw laser by applying a rectangular voltage pulse to an electro-optic phase modulator placed in the laser beam. The time delay at which the null occurs is proportional to T2{T}_{2}T2​, which is given by the expression T2=(2ln2)T0{T}_{2}=(\frac{2}{\mathrm{ln}2}){T}_{0}T2​=(ln22​)T0​. The method is demonstrated in atomic sodium and iodine vapor and the separation of third-order optical transients from linear transients induced by the phase shift is discussed. An analytic expression for the jump in the nonlinear transmission, induced by the second phase shift, as well as for the transient in transmission following a single phase shift of a laser which weakly saturates an optically thin sample is derived. It is also shown that optical dephasing rates may be inferred from the variation of the integral of the transmitted light in a double-phase-switching experiment.
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.
Recently we have reported[1] on the measurements of electronic dephasing (T_2) and radiationless decay (T_1) in molecules using emission spectroscopy as a probe for the detection of the photon echo. This right-angle photon echo utilizes a single mode of a narrow-band (~MHz) cw dye laser and an intracavity electro-optical (EO) element that modulates the frequency of the laser.[2] Applying voltage pulses into the EO crystal switches the laser frequency from ω_0 (the peak frequency of the transition resonance) into another frequency ω. This switching procedure introduced by Brewer et al. for the observation of transients in the forward direction of the laser allows one to observe coherent transients in gases,[1,2] solids[3-5] and molecular beams.[6] Typically, the dispersion of the nonlinear EO crystal (e.g., AD*P) gives a 60 MHz frequency shift within the inhomogeneous resonance of the optical transition (width ~GHz or larger). Therefore, to switch the laser frequency further, one must use high-voltage signals that are usually hard to obtain especially for multiple-pulse experiments. Secondly, there is a limit on the frequency shift which is conditioned by the mode spacing of the cavity. Thirdly, because the laser is switched into a new group of molecules some complications may arise in interpreting the transient spectra especially in large molecules. This is because in large molecules the density of excited states is high and thus the buildup of transients of w molecules (which could be complex) will be superimposed on the decay of ω_0 molecules. Finally, off-resonance effects (e.g., beats) between the molecules at frequency ω and ω_0 cannot be avoided.
By extending the laser-frequency-switching technique to a 100-psec time scale, we have observed for the Na D1{D}_{1}D1​ line the first-order free-induction decay, its inhomogeneous dephasing time T2∗{{T}_{2}}^{*}T2​∗, its interference with the nonlinear free-induction decay, and a 1.8-GHz interference beat of the ground-state hfs. Detailed theoretical predictions of these new coherence effects are faithfully observed.