Physical review. B, Condensed matter

Optical-density effect in heterodyne-detected accumulated photon echo

S. Saikan, H. Miyamoto, Y. Tosaki, Atsushi Fujiwara

Published Sep 15, 1987• 37 citations

Abstract

The effect of optical density on the heterodyne-detected accumulated photon echo is investigated both experimentally and theoretically. The cause of the distortion of the echo temporal behavior observed in the $^{4}G_{\frac{5}{2}}$ manifold of Nd:YAG (where YAG is yttrium aluminum garnet) is attributed to the optical-density effect, which is closely related to the change of the field correlation function as the excitation pulse propagates through the sample.

DOI: 10.1103/physrevb.36.5074

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Detailed Investigation of temporal behavior in accumulated photon echo

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A detailed parametric study of accumulated photon echo and hole-burning spectroscopy was performed on three kinds of sample including Nd:YAG, Nd:glass, and dye-doped polymers to clarify the causes of spiking behavior which appears frequently in the echo signal masking longer relaxation behavior. Accumulated photon echo was detected by the high-frequency modulated heterodyne method. Transient or persistent hole-burning spectra were obtained in Nd:glass and dye- doped polymers.

Apr 26, 19870 citations

Subpicosecond Accumulated Photon Echo with Incoherent Light

修治浅香, Hiroki Nakatsuka, Masahiro Fujiwara +1 more

An analytic theory and experimental studies of the accumulated photon echo is presented. We define a temporal correlation function $\tilde{G}$ of the excitation field E ( t ) as $\tilde{G}(\tau,t)=(1/T_{1})\int_{0}^{\infty}\mathrm{d}t'E(t-t')E(t-t'-\tau)\cdot\exp(-t'/T_{1})$, where T 1 is the population relaxation time of the sample, and call the width of $\tilde{G}$ with respect to τ a temporal correlation time $\tilde{\tau}_{\text{c}}(t)$. It is proved that the echo intensity is written by the temporal correlation functions when (1) T 1 and the duration of the excitation light τ p are much longer than $\tilde{\tau}_{\text{c}}(t)$ in order to make the function $\tilde{G}((\tau,t)$ well-defined, (2) T 1 and τ p are much longer than the homogeneous dephasing time T 2 , and (3) one can find a time interval Δ t such that $\tilde{G}(\tau,t)$ does not change much between t and t + Δ t , where $\varDelta t{\gg}\tilde{\tau}_{\text{c}}$. Then we can show that the time resolution of the accumulated photon echo is determined by the averaged $\tilde{\tau}_{\text{c}}(t)$ over an interval of the integration of the echo signal. This discussion is valid for any excitation source if the above conditions are satisfied, and applies to almost all cases of the practical accumulated photon echo experiment. A discussion is also made on the spurious spike on the echo decay curve near zero delay time that appeared in an experiment with a high time resolution in Nd 3+ -doped silicate glass. It is shown that the most probable cause for this spike is uncorrelated inhomogeneous broadenings of the resonant lines of neodymium ions.

Journal of the Physical Society of JapanJun 15, 198715 citations

Non-Markovian behavior in stimulated photon echoes: Waiting-time dependence

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Physical Review ADec 1, 199210 citations

High-Frequency Heterodyned Detection of Picosecond Accumulated Photon Echoes

S. Saikan, Atsushi Fujiwara, Takashi Kushida +1 more

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Japanese Journal of Applied PhysicsJun 1, 198714 citations

Intensity-dependent photon-echo relaxation in rare-earth-doped crystals

Stefan Kröll, E. Y. Xu, M. K. Kim +2 more

Physical review. B, Condensed matterJun 1, 199033 citations

Phase matching memory effect in optical coherent transient effects

José Soto M.

Annual Meeting Optical Society of AmericaJan 1, 19890 citations

Physical review. B, Condensed matter

Optical-density effect in heterodyne-detected accumulated photon echo

S. Saikan, H. Miyamoto, Y. Tosaki, Atsushi Fujiwara

Published Sep 15, 1987• 37 citations

Publisher

Abstract

^{4}G_{\frac{5}{2}}

manifold of Nd:YAG (where YAG is yttrium aluminum garnet) is attributed to the optical-density effect, which is closely related to the change of the field correlation function as the excitation pulse propagates through the sample.

DOI: 10.1103/physrevb.36.5074

Related papers

Detailed Investigation of temporal behavior in accumulated photon echo

S. Saikan

Apr 26, 19870 citations

Subpicosecond Accumulated Photon Echo with Incoherent Light

修治浅香, Hiroki Nakatsuka, Masahiro Fujiwara +1 more

An analytic theory and experimental studies of the accumulated photon echo is presented. We define a temporal correlation function $\tilde{G}$ of the excitation field E ( t ) as $\tilde{G}(\tau,t)=(1/T_{1})\int_{0}^{\infty}\mathrm{d}t'E(t-t')E(t-t'-\tau)\cdot\exp(-t'/T_{1})$ , where T 1 is the population relaxation time of the sample, and call the width of $\tilde{G}$ with respect to τ a temporal correlation time $\tilde{\tau}_{\text{c}}(t)$ . It is proved that the echo intensity is written by the temporal correlation functions when (1) T 1 and the duration of the excitation light τ p are much longer than $\tilde{\tau}_{\text{c}}(t)$ in order to make the function $\tilde{G}((\tau,t)$ well-defined, (2) T 1 and τ p are much longer than the homogeneous dephasing time T 2 , and (3) one can find a time interval Δ t such that $\tilde{G}(\tau,t)$ does not change much between t and t + Δ t , where $\varDelta t{\gg}\tilde{\tau}_{\text{c}}$ . Then we can show that the time resolution of the accumulated photon echo is determined by the averaged $\tilde{\tau}_{\text{c}}(t)$ over an interval of the integration of the echo signal. This discussion is valid for any excitation source if the above conditions are satisfied, and applies to almost all cases of the practical accumulated photon echo experiment. A discussion is also made on the spurious spike on the echo decay curve near zero delay time that appeared in an experiment with a high time resolution in Nd 3+ -doped silicate glass. It is shown that the most probable cause for this spike is uncorrelated inhomogeneous broadenings of the resonant lines of neodymium ions.An analytic theory and experimental studies of the accumulated photon echo is presented. We define a temporal correlation function $\tilde{G}$ of the excitation field E ( t ) as $\tilde{G}(\tau,t)=(1/T_{1})\int_{0}^{\infty}\mathrm{d}t'E(t-t')E(t-t'-\tau)\cdot\exp(-t'/T_{1})$, where T 1 is the population relaxation time of the sample, and call the width of $\tilde{G}$ with respect to τ a temporal correlation time $\tilde{\tau}_{\text{c}}(t)$. It is proved that the echo intensity is written by the temporal correlation functions when (1) T 1 and the duration of the excitation light τ p are much longer than $\tilde{\tau}_{\text{c}}(t)$ in order to make the function $\tilde{G}((\tau,t)$ well-defined, (2) T 1 and τ p are much longer than the homogeneous dephasing time T 2 , and (3) one can find a time interval Δ t such that $\tilde{G}(\tau,t)$ does not change much between t and t + Δ t , where $\varDelta t{\gg}\tilde{\tau}_{\text{c}}$. Then we can show that the time resolution of the accumulated photon echo is determined by the averaged $\tilde{\tau}_{\text{c}}(t)$ over an interval of the integration of the echo signal. This discussion is valid for any excitation source if the above conditions are satisfied, and applies to almost all cases of the practical accumulated photon echo experiment. A discussion is also made on the spurious spike on the echo decay curve near zero delay time that appeared in an experiment with a high time resolution in Nd 3+ -doped silicate glass. It is shown that the most probable cause for this spike is uncorrelated inhomogeneous broadenings of the resonant lines of neodymium ions.

Journal of the Physical Society of JapanJun 15, 198715 citations

Non-Markovian behavior in stimulated photon echoes: Waiting-time dependence

S. Saikan, J. W-I. Lin, H. Nemoto

By using stochastic theory, we analyze the non-Markovian temporal behavior in four types of photon echoes, including the two-pulse echo, stimulated echo, accumulated echo, and heterodyne-detected accumulated echo. In particular, the origin of the exp(- ${\mathit{ct}}^{3}$ ) dependence of the two-pulse echo in the limit of slow modulation is discussed in detail. It is also pointed out that, at the slow-modulation limit, the temporal behavior of the stimulated echo changes from exp(- ${\mathit{ct}}^{3}$ ) dependence to exp(- ${\mathit{ct}}^{2}$ ) dependence as the waiting time (the time interval between the second and the third excitation pulses) is varied.By using stochastic theory, we analyze the non-Markovian temporal behavior in four types of photon echoes, including the two-pulse echo, stimulated echo, accumulated echo, and heterodyne-detected accumulated echo. In particular, the origin of the exp(-${\mathit{ct}}^{3}$) dependence of the two-pulse echo in the limit of slow modulation is discussed in detail. It is also pointed out that, at the slow-modulation limit, the temporal behavior of the stimulated echo changes from exp(-${\mathit{ct}}^{3}$) dependence to exp(-${\mathit{ct}}^{2}$) dependence as the waiting time (the time interval between the second and the third excitation pulses) is varied.

Physical Review ADec 1, 199210 citations

High-Frequency Heterodyned Detection of Picosecond Accumulated Photon Echoes

S. Saikan, Atsushi Fujiwara, Takashi Kushida +1 more

Japanese Journal of Applied PhysicsJun 1, 198714 citations

Intensity-dependent photon-echo relaxation in rare-earth-doped crystals

Stefan Kröll, E. Y. Xu, M. K. Kim +2 more

Photon-echo-relaxation measurements made on the $^{3}\mathrm{H}_{4}$ ${\mathrm{\ensuremath{-}}}^{3}$ ${\mathrm{P}}_{0}$ transition of 0.01 at. % ${\mathrm{Pr}}^{3+}$ :YAG (where YAG represents yttrium aluminum garnet), $^{3}\mathrm{H}_{4}$ ${\mathrm{\ensuremath{-}}}^{1}$ ${\mathrm{D}}_{2}$ transition in 0.1 at. % ${\mathrm{Pr}}^{3+}$ : ${\mathrm{YAlO}}_{3}$ , and $^{7}\mathrm{F}_{0}$ ${\mathrm{\ensuremath{-}}}^{5}$ ${\mathrm{D}}_{0}$ transition in 0.25 at. % ${\mathrm{Eu}}^{3+}$ : ${\mathrm{YAlO}}_{3}$ show that the photon-echo relaxation rate increases when the intensities of the excitation pulses are increased. Although a part of the relaxation-rate increase in ${\mathrm{Pr}}^{3+}$ :YAG may be attributed to an instantaneous spectral diffusion (ISD) in which the presence of excited neighboring ${\mathrm{Pr}}^{3+}$ ions change the local field and the absorption frequency of the rare-earth ions, our data deviate significantly from the ISD-model predictions. An additional intensity-dependent relaxation mechanism is required to explain the results.Photon-echo-relaxation measurements made on the $^{3}\mathrm{H}_{4}$${\mathrm{\ensuremath{-}}}^{3}$${\mathrm{P}}_{0}$ transition of 0.01 at. % ${\mathrm{Pr}}^{3+}$:YAG (where YAG represents yttrium aluminum garnet), $^{3}\mathrm{H}_{4}$${\mathrm{\ensuremath{-}}}^{1}$${\mathrm{D}}_{2}$ transition in 0.1 at. % ${\mathrm{Pr}}^{3+}$:${\mathrm{YAlO}}_{3}$, and $^{7}\mathrm{F}_{0}$${\mathrm{\ensuremath{-}}}^{5}$${\mathrm{D}}_{0}$ transition in 0.25 at. % ${\mathrm{Eu}}^{3+}$:${\mathrm{YAlO}}_{3}$ show that the photon-echo relaxation rate increases when the intensities of the excitation pulses are increased. Although a part of the relaxation-rate increase in ${\mathrm{Pr}}^{3+}$:YAG may be attributed to an instantaneous spectral diffusion (ISD) in which the presence of excited neighboring ${\mathrm{Pr}}^{3+}$ ions change the local field and the absorption frequency of the rare-earth ions, our data deviate significantly from the ISD-model predictions. An additional intensity-dependent relaxation mechanism is required to explain the results.

Physical review. B, Condensed matterJun 1, 199033 citations

Phase matching memory effect in optical coherent transient effects

José Soto M.

It has been generally accepted that the off-resonance heterodyne optical field in Stark-switching and frequency-switching techniques does not have any measurable influence in photon echo and other related experiments. In this work we present theoretical and experimental evidence that through a previously unknown memory effect the heterodyne field produces important undulations in the decay curves of photon echo. This effect appears to be also responsible for other experimental anomalies observed in optical coherent transient effects.1It has been generally accepted that the off-resonance heterodyne optical field in Stark-switching and frequency-switching techniques does not have any measurable influence in photon echo and other related experiments. In this work we present theoretical and experimental evidence that through a previously unknown memory effect the heterodyne field produces important undulations in the decay curves of photon echo. This effect appears to be also responsible for other experimental anomalies observed in optical coherent transient effects.1

Annual Meeting Optical Society of AmericaJan 1, 19890 citations

^{4}G_{\frac{5}{2}}

An analytic theory and experimental studies of the accumulated photon echo is presented. We define a temporal correlation function

\tilde{G}

of the excitation field E ( t ) as

\tilde{G}(\tau,t)=(1/T_{1})\int_{0}^{\infty}\mathrm{d}t'E(t-t')E(t-t'-\tau)\cdot\exp(-t'/T_{1})

, where T 1 is the population relaxation time of the sample, and call the width of

\tilde{G}

with respect to τ a temporal correlation time

\tilde{\tau}_{\text{c}}(t)

. It is proved that the echo intensity is written by the temporal correlation functions when (1) T 1 and the duration of the excitation light τ p are much longer than

\tilde{\tau}_{\text{c}}(t)

in order to make the function

\tilde{G}((\tau,t)

well-defined, (2) T 1 and τ p are much longer than the homogeneous dephasing time T 2 , and (3) one can find a time interval Δ t such that

\tilde{G}(\tau,t)

does not change much between t and t + Δ t , where

\varDelta t{\gg}\tilde{\tau}_{\text{c}}

. Then we can show that the time resolution of the accumulated photon echo is determined by the averaged

\tilde{\tau}_{\text{c}}(t)

over an interval of the integration of the echo signal. This discussion is valid for any excitation source if the above conditions are satisfied, and applies to almost all cases of the practical accumulated photon echo experiment. A discussion is also made on the spurious spike on the echo decay curve near zero delay time that appeared in an experiment with a high time resolution in Nd 3+ -doped silicate glass. It is shown that the most probable cause for this spike is uncorrelated inhomogeneous broadenings of the resonant lines of neodymium ions.

{\mathit{ct}}^{3}

) dependence of the two-pulse echo in the limit of slow modulation is discussed in detail. It is also pointed out that, at the slow-modulation limit, the temporal behavior of the stimulated echo changes from exp(-

{\mathit{ct}}^{3}

) dependence to exp(-

{\mathit{ct}}^{2}

) dependence as the waiting time (the time interval between the second and the third excitation pulses) is varied.

Photon-echo-relaxation measurements made on the

^{3}\mathrm{H}_{4}

${\mathrm{\ensuremath{-}}}^{3}$

{\mathrm{P}}_{0}

transition of 0.01 at. %

{\mathrm{Pr}}^{3+}

:YAG (where YAG represents yttrium aluminum garnet),

^{3}\mathrm{H}_{4}

${\mathrm{\ensuremath{-}}}^{1}$

{\mathrm{D}}_{2}

transition in 0.1 at. %

{\mathrm{Pr}}^{3+}

{\mathrm{YAlO}}_{3}

, and

^{7}\mathrm{F}_{0}

${\mathrm{\ensuremath{-}}}^{5}$

{\mathrm{D}}_{0}

transition in 0.25 at. %

{\mathrm{Eu}}^{3+}

{\mathrm{YAlO}}_{3}

show that the photon-echo relaxation rate increases when the intensities of the excitation pulses are increased. Although a part of the relaxation-rate increase in

{\mathrm{Pr}}^{3+}

:YAG may be attributed to an instantaneous spectral diffusion (ISD) in which the presence of excited neighboring

{\mathrm{Pr}}^{3+}

ions change the local field and the absorption frequency of the rare-earth ions, our data deviate significantly from the ISD-model predictions. An additional intensity-dependent relaxation mechanism is required to explain the results.