- Email: [email protected]
Photon-echo profile in the ultrashort time region for pentacene molecules in crystals
Volume 44, number 6
OPTICS COMMUNICATIONS
15 February 1983
PHOTON-ECHO PROFILE IN THE ULTRASHORT TIME REGION FOR PENTACENE MOLECULES IN CRYSTALS Arao NAKAMURA ‘), Yuzo YOSHIKUNI 2, , Yuzo ISHIDA, Shigeo SHIONOYA and Ma&i 7’heInstitue for Solid State Physics, The University of Tokyo, Roppongi, Minato-ku, Tokyo 106, Japan
AIHARA *
Received 8 November 1982
Photon-echo behavior in the ultrashort time region is studied for pentacene molecules in p-terphenyl crystals at 1.7 K by means-of the accumulated three-pulse echo. We show highly resolved echo spectra with a parameter of time separation and also time behavior of echo intensity as a function of pulse separation measured at various frequencies near the peak position of the absorption line of the So-S1 transition. We demonstrate various features of echo profile in both time and frequency domains, which are dependent on the time region of observation.
1. Introduction Coherent phenomena associated with optical transitions in inhomogeneously broadened systems have recently attracted much attention. Recent advances of laser technology have enabled us to study various kinds of coherent transient phenomena in various materials. In particular, a number of workers have performed photon-echo experiments for atomic or molecular gas [l] and various impurity centers in solids, i.e. impurity ions in inorganic crystals [2,3] and impurity molecules in organic crystals [4]. Although photon echo is theoretically treated on the assumption that the inhomogeneous spectral width is much narrower than the reciprocal of excitation pulse width (short-pulse excitation limit), most experiments have been done in systems where the inhomogeneous line broadening is much larger than the reciprocal of pulse width. Nevertheless, observed echo behavior, for example, exponential time decay of echo intensity, was well explained on the basis of this assumption. This was believed to be due to the ‘1 Present address: Department of Applied Physics, Faculty of Engineering, Tohoku University, Aramaki, Sendai 980, Japan. ‘1 Present address: Musashino Electrical Communication Laboratory, NTT, Musashino-shi, Tokyo 180, Japan. * Department of Physics, Faculty of Liberal Arts, Yamaguchi University, Yamaguchi 753, Japan.
0 030-4018/83/0000-0000/$03.00
0 1983 North-Holland
existence of many modes in the excitation pulse, which smoothed out fine structure in the echo generated by each mode. However, observation of echo behavior in the ideal situation, i.e. in the short-pulse excitation limit, is still interesting, especially in the ultrashort time region, f12 < A”,‘, where t12 is the time separation between the first and second pulses and AVi is the inhomogeneous width (full width at the half maximum). The temporal profile of echo for t12 9 Au,’ is a gaussian shape with a width of the order of Au?’ and a peak at the time of 2t12 from the first pulse in the two-pulse echo, but in the ultrashort time region the rising edge of the gaussian profile will disappear in the time region before the time of the second pulse. Then, the echo spectrum will be broadened compared with that in the long time region, because it is related to the temporal profile through the Fourier transform. Such a deformation of echo profile will be expected from the reason why there occurs no echo before the second pulse because of the time causality of echo-pulse sequence. Furthermore, if the experimental time resolution were comparable to the thermal-reservoir correlation time, TV,a new phenomenon related with the non-markovian process would be observed [5]. Very recently, Hesselink et al. [3] have done picosecond photon-echo experiments for pentacene 431
Volume
44, number
15 February
OPTICS COMMUNICATIONS
6
molecules in p-terphenyl and naphthalene crystals in the short-pulse excitation limit. Moreover, they used a new configuration, called accumulated threepulse echo configuration, by using a pulse train with high repetition rate generated by a synchronously pumped dye laser. In the accumulated three-pulse echo, echo signals are caused by scattering from a population grating of the triplet state of pentacene molecules in the frequency domain. In spite of the low population of the excited singlet state, a large echo signal can be observed because of the accumulation effect in the triplet state which acts as a bottleneck in the relaxation path of the excited states. Since the quasi-continuous echo signal allows us to use lock-in detection technique, signal-to-noise ratio improves by a factor of about ten. Thus, by means of the accumulated echo we can perform highly resolved spectroscopy in both the spectral region and time region. The latter is determined by the excitation pulse width. In this paper, we report experiments of highly resolved spectroscopy of photon echo in the ultrashort time region by means of the accumulated three-pulse echo. We show highly resolved echo spectra with a parameter of pulse separation cl2 and time behavior of echo intensity as a function of pulse separation measured at various frequencies near the peak position of the absorption line. Various features of echo profile are shown, which are dependent on the time region of pulse separation, i.e. t12 > Av,’ or cl2 < Avi’. We mention observation of the deformation of time variation of echo intensity in samples of
Rapid Scan Autocorrelator
high optical density, and propose a method of observation of correct time variation in such samples. We also discuss the possibility of observation of the non-markovian behavior.
2. Experimental Pentacene-doped p-terphenyl crystals were grown by using the Bridgman technique. Crystals were cleaved in parallel to the ab cleavage plane. The concentration of pentacene molecules was 8 X lop6 mol/mol. For the Z&-S, transition of pentacene molecules, there exist four zero-phonon lines 0,) O,, 0, and 0, originating from different sites [6]. We performed photon-echo measurements for the O3 and 0, levels, which are located at 17006 and 17065 cm-l respectively, and inhomogeneously broadened with the width, aVi of 1.2 cm-l. In accumulated three-pulse echo experiments, we used a rhodamine 6G dye laser with a mixed dye solution of a gain medium and a saturable absorber (DODCI), which was synchronously pumped by an actively mode-locked argon ion laser [7]. This hybrid dye laser system can yield easily a shorter pulse width and a pulse profile without substructure corresponding to imperfect mode-locking. The characteristics of pulses were duration of 1.5 ps and peak power of about 25 W. The laser beams were focused on the sample with a diameter of about 100 pm. This gives an excitation density corresponding to the pulse area of about n/ 100. As shown in fig. 1, the laser beam was split into
JAperture
w 1.;
Variable
Fig. 1. Experimental
432
arrangement
for accumulated
1983
three-pulse
echo in the configuration
of k, = 2kz - k 1.
Volume 44, number 6
OPTICS COMMUNICATIONS
15 February 1983
two beams, one of which was modulated with a chopper at 300 Hz and the other was delayed by a variable optical delay. The two beams were parallel but non-collinear, and were focused on the sample at an angle of about 1.2”. A part of the laser beam was fed into a rapid-scan autocorrelator [8] for monitoring the pulse width during the measurement. Two different configurations for observing the echo are possible depending on the direction of observation; the echo can be detected in the direction of (1) k, = 2k, - k, (k2 = k3) or (2) k, = k2 (k, = kg). In this paper, we are concerned mostly with the results for the configuration (1). The echo signal was fed into a Jarrel-Ash double monochromator and detected by a lock-in amplifier. Highly resolved spectra were taken with the resolution of 0.25 cm-l under the condition where the whole absorption band with the inhomogeneous broadening of the So-S, transition was excited by the broad band pulses (-20 cm-‘).
3. Results and discussion Fig. 2(a) shows time behavior of echo intensity versus the pulse separation at 1.7 K, when the whole echo spectrum is detected with low resolution of 6 cm-‘. The decay time of echo in this sample is known to be about 3 ns from our ordinary two-pulse echo experiments [9,10] at this temperature. A slight decrease of echo intensity was observed, although the decay of echo intensity with the time constant of 3 ns should be quite small in this short time region. In fig. 2(b)-(f) we show time behavior of echo intensities observed by fixing the wavelength of the monochromator with high resolution of 0.25 cm-I at several frequencies in the vicinity of the peak POsition of the absorption line, vo. In the case where V-Vu- - 0, the echo grows with the rise time of about 25 ps which is nearly equal to Avi’, and shows no decay in the time region concerned. On the other hand, when the monochromator is tuned at the wave number +l .l cm-’ above the center frequency vo, a rapid rise and fall are seen in the time range from -10 ps to 25 ps followed by long decay. In the case where v - v. = +2.0 cm-‘, such a rise and fall become more rapid. The same behavior is observed for the case where v - v. < 0. These results indicate that the
Fig. 2. Time behavior of echo intensity as a function of the pulse separations for various frequencies. (a): the whole spectrum detected, (b) - (0: spectrally resolved time behavior. v: observed frequency, vo: the center frequency of the absorption line.
spectral components for v f v. rapidly grow and fall in the short time region, tJ2 < Au;‘; where the total echo signal for the whole spectrum would monotonously increase. In fig. 3 we show highly resolved echo spectra with a parameter of pulse separations t12. For t12 = 26.0 ps, the sharp spectrum with a small dip is seen. A rough estimate of the line width is about 1 cm-‘. Since the echo profile should be gaussian in inhomogeneously broadened systems [2,11], this observed spectrum is reasonable as an echo spectrum in such systems except the small dip. As this small dip is located exactly at the absorption peak, it may have arisen from the reabsorption of the echo signal. Such a reabsorption effect is quite large even in the sample whose optical density is about 0.5. In general, for a highly absorbing sample we must take into account effects of the echo pulse propagation through the sample [ 121. However, when the pulse area is much smaller than n/2 as in our case, we may neglect such effects. When the pulse separation is reduced in fig. 3, spectra become broadened depending on the magnitude of the pulse separation. 433
Volume
44, number
OPTICS
6
I
17ooa
WAVE
Fig. 3. Highly separation.
resolved
NUMBER
echo spectra
17010 (cm-‘)
with a parameter
of pulse
Both the frequency-dependent time behavior of echo intensity and the t12-dependent echo spectra will be explained by considering behavior of the temporal profile of the echo in the ultrashort time region where t12 5 Avi’ . In fig. 4 we illustrate schematically time sequence of the echo in the configuration of k, = 2kZ - k, of the accumulated three-pulse echo. The radiation intensity of echo in an inhomogeneously broadened system as a function of time after the first pulse is written as follows [ 111 I(t) a {exp[(-Awf/4)(t X exp[-(t
Fig. 4. Schematic the configuration pulse echo.
434
- 2t,, - t23)2]
- t23)/T2112,
15 February
COMMUNICATIONS
(1)
illustration for the time sequence of echo in of k, = 2kz - k 1 of the accumulated three-
1983
where an inhomogeneous spectrum g(w) = exp(-w2/ 4Aoz) and Awi = nAvi/2(ln 2)lj2. An echo with a gaussian shape is expected to be seen at the time of 2t12 t t23. In the case where t12 9 Avi’, we can see a full gaussian profile of the echo, because the time separation between the echo and the third pulse is large enough compared with the echo width. For t12 < - Av;’ , in contrast, the gaussian profile with the peak at the time of t12 from the third pulse become incomplete, since there exists no echo before the third pulse because of the time causality. If we take into account such disappearance of the rising edge of gaussian profile in the time region before the third pulse, the broadening of the echo spectrum will be expected, because the spectrum and the temporal profile are related to each other through the Fourier transform. From the Fourier transform of eq. (1) the echo spectrum is written as follows
dt exp(-iwt)
ze(0) a J t1z+i13
X exp[(-Awf/4)(t
- 2t,2 - t23)2] 2
X exp L-0
-
t23>/T21 .
(2)
When t12 B Au,‘, the radiation intensity of echo becomes almost zero at the time of t12 t t23 and has a peak at 2t,, t t23. Then, from the relation of the Fourier transform the echo spectrum has a gaussian shape with the width of 2(2 In 2)V2Awi (fwhm). When t12 -< Au,‘, the echo with the same gaussian width has a finite intensity at the time of t12 + t23 and before this time there is no echo, so that the echo spectrum will be broadened. These features are shown in fig. 5, which were calculated with the parameter of t12. This result explains well the observed spectra in the configuration of k, = 2k2 - k, , which are dependent on the pulse separation. We find that the broadened spectrum of echo reflects the temporal profile of echo in the ultrashort time region. From the same argument we can show the time behavior of the echo intensity as a function of pulse separation. The behavior is dependent on the frequency at which it is measured. As we can calculate echo spectra with the parameter of t12 as shown in fig. 5, the echo intensity can be plotted as a function of t12
I
-1
15 February 1983
OPTICS COMMUNICATIONS
Volume 44. number 6
I
0
WAVE NUMBER
I
+t (cm-l)
Fig. 5. Calculated echo spectra with a parameter of pulse separation. for different frequencies. Fig. 6 shows the results. We find that the behavior is consistent with the experimental one. Quantitative agreement between experimental curves and calculated ones is not so good.
This seems to be due to the fact that the excitation pulses used in this work are not completely transformlimited. From these calculated curves, we find that the variation of echo intensity with the pulse separation in case where v - v. = 0 is exactly the same as that which is seen when the total echo signal for the whole spectrum is detected. For v # vo, however, the rapid rise and fall appear even in the time region where if we observe the whole spectral components, no decay is seen. If the component at the center frequency is somewhat depressed because of the reabsorption effect of the echo at the absorption peak, quite different time behavior is observed in the ultrashort time region t12 < AUF’, although the whole spectral components are detected. We note that we must be careful for such an effect even in the sample with rather low optical density (OD - 0.5). Nevertheless, if we make observation at the center frequency even in the ultrashort time region, we can obtain intrinsic time behavior of dephasing of the system, in which the large oscillator strength makes it difficult to use a sample with very low optical density. We briefly mention the results which were observed in the configuration of k, = k2 (/cl = k3). The echo spectra for various pulse separations, r12, showed \l oscillatory structure with the period of tii cm . The spectrally resolved time behavior of echo intensity also showed the oscillatory structure with the period of (v - vo)-l s. In this configuration, the echo is detected as the interference in the sample between a probe pulse and the echo polarization. In order to interpret such oscillations we will need to consider the Bloch and Maxwell equations simultaneously [12,13].
4. Summary and concluding
PULSE SEPARATION ( ps 1 Fig. 6. Calculated time behavior of echo intensity as a function of pulse separation for various frequencies.
remarks
We have performed highly resolved spectroscopy of photon echo in the ultrashort time region. It is found that when t12 < AVi-‘, the echo spectra are broadened because of the deformation of the gaussian profile of echo at the time of the third pulse. We showed that in the ultrashort time region the component at the center frequency (v = vo) behaves in the same manner as the total echo signal for the whole spectrum, although the spectral components for v # v. have rapid time variation. We note that in the 435
Volume
44, number
6
OPTICS
COMMUNICATIONS
sample with high optical density observed time behavior for the whole echo spectrum does not provide a correct rise and fall of echo because of the reabsorption effect of the component at the center frequency. When the dephasing time is comparable to Avi’, we also note that the disappearance of the rising edge of echo profile must be taken into account in order to obtain the correct dephasing time. Furthermore, if we take into consideration the non-markovian process in the inhomogeneously broadened system, the echo profile in the ultrashort time region should be expected to show various features [14]. When t12 - Av[’ > ~c, the echo appears at the instance of the second pulse (in the two-pulse echo configuration) and forms a gaussian profile with the peak at the time of 2t12 from the first pulse. We note that this is similar to the behavior which is expected when the markovian process is taking place. When t12 -rc
436
15 February
1983
References [II J.P. Gordon,C.H.
Wang,C.K.N. Pate], R.E. Slusher and W.J. Thomlinson, Phys. Rev. 179 (1969) 294. PI I.D. Abella, N.A. Kurnit and S.R. Hartmann, Phys. Rev. 141 (1966) 391. [31 S. Chandra, N. Takeuchi and S.R. Hartmann, Phys. Lett. 41A (1972) 91. [41 W.H. Hesselink and D.A. Wiersma, J. Chem. Phys. 73 (1980) 648; and references therein. I51 M. Aihara, Phys. Rev. B25 (1982) 53. 161 R.W. Olson and N.D. Fayer, J. Phys. Chem. 84 (1980) 2001. [71 Y. Ishida, T. Yajima and K. Naganuma, Jpn. J. Appl. Phys. 19 (1980) L717.
PI Y. Ishida, Y. Yajima and Y. Tanaka, [91 1101 [Ill [I21 (131 [I41
Jpn. J. Appl. Phys. 19 (1980) L289. Y. Yoshikuni, A. Nakamura and S. Shionoya, Bull. Chem. Sot. Jpn. 55 (1982) 2749. Y. Yoshikuni, A. Nakamura, S. Shionoya and M. Aihara, J. Phys. Sot. Jpn. 51 (1982) 2604. N. Takeuchi, IEEE J. Quant. Electron. QEll (1975) 230. S.L. McCall and F.L. Hahn, Phys. Rev. 183 (1969) 457. W.H. Hessebnk and D.A. Wiersma, J. Chem. Phys. 75 (1981) 4192. M. Aihara, to be published.
OPTICS COMMUNICATIONS
15 February 1983
PHOTON-ECHO PROFILE IN THE ULTRASHORT TIME REGION FOR PENTACENE MOLECULES IN CRYSTALS Arao NAKAMURA ‘), Yuzo YOSHIKUNI 2, , Yuzo ISHIDA, Shigeo SHIONOYA and Ma&i 7’heInstitue for Solid State Physics, The University of Tokyo, Roppongi, Minato-ku, Tokyo 106, Japan
AIHARA *
Received 8 November 1982
Photon-echo behavior in the ultrashort time region is studied for pentacene molecules in p-terphenyl crystals at 1.7 K by means-of the accumulated three-pulse echo. We show highly resolved echo spectra with a parameter of time separation and also time behavior of echo intensity as a function of pulse separation measured at various frequencies near the peak position of the absorption line of the So-S1 transition. We demonstrate various features of echo profile in both time and frequency domains, which are dependent on the time region of observation.
1. Introduction Coherent phenomena associated with optical transitions in inhomogeneously broadened systems have recently attracted much attention. Recent advances of laser technology have enabled us to study various kinds of coherent transient phenomena in various materials. In particular, a number of workers have performed photon-echo experiments for atomic or molecular gas [l] and various impurity centers in solids, i.e. impurity ions in inorganic crystals [2,3] and impurity molecules in organic crystals [4]. Although photon echo is theoretically treated on the assumption that the inhomogeneous spectral width is much narrower than the reciprocal of excitation pulse width (short-pulse excitation limit), most experiments have been done in systems where the inhomogeneous line broadening is much larger than the reciprocal of pulse width. Nevertheless, observed echo behavior, for example, exponential time decay of echo intensity, was well explained on the basis of this assumption. This was believed to be due to the ‘1 Present address: Department of Applied Physics, Faculty of Engineering, Tohoku University, Aramaki, Sendai 980, Japan. ‘1 Present address: Musashino Electrical Communication Laboratory, NTT, Musashino-shi, Tokyo 180, Japan. * Department of Physics, Faculty of Liberal Arts, Yamaguchi University, Yamaguchi 753, Japan.
0 030-4018/83/0000-0000/$03.00
0 1983 North-Holland
existence of many modes in the excitation pulse, which smoothed out fine structure in the echo generated by each mode. However, observation of echo behavior in the ideal situation, i.e. in the short-pulse excitation limit, is still interesting, especially in the ultrashort time region, f12 < A”,‘, where t12 is the time separation between the first and second pulses and AVi is the inhomogeneous width (full width at the half maximum). The temporal profile of echo for t12 9 Au,’ is a gaussian shape with a width of the order of Au?’ and a peak at the time of 2t12 from the first pulse in the two-pulse echo, but in the ultrashort time region the rising edge of the gaussian profile will disappear in the time region before the time of the second pulse. Then, the echo spectrum will be broadened compared with that in the long time region, because it is related to the temporal profile through the Fourier transform. Such a deformation of echo profile will be expected from the reason why there occurs no echo before the second pulse because of the time causality of echo-pulse sequence. Furthermore, if the experimental time resolution were comparable to the thermal-reservoir correlation time, TV,a new phenomenon related with the non-markovian process would be observed [5]. Very recently, Hesselink et al. [3] have done picosecond photon-echo experiments for pentacene 431
Volume
44, number
15 February
OPTICS COMMUNICATIONS
6
molecules in p-terphenyl and naphthalene crystals in the short-pulse excitation limit. Moreover, they used a new configuration, called accumulated threepulse echo configuration, by using a pulse train with high repetition rate generated by a synchronously pumped dye laser. In the accumulated three-pulse echo, echo signals are caused by scattering from a population grating of the triplet state of pentacene molecules in the frequency domain. In spite of the low population of the excited singlet state, a large echo signal can be observed because of the accumulation effect in the triplet state which acts as a bottleneck in the relaxation path of the excited states. Since the quasi-continuous echo signal allows us to use lock-in detection technique, signal-to-noise ratio improves by a factor of about ten. Thus, by means of the accumulated echo we can perform highly resolved spectroscopy in both the spectral region and time region. The latter is determined by the excitation pulse width. In this paper, we report experiments of highly resolved spectroscopy of photon echo in the ultrashort time region by means of the accumulated three-pulse echo. We show highly resolved echo spectra with a parameter of pulse separation cl2 and time behavior of echo intensity as a function of pulse separation measured at various frequencies near the peak position of the absorption line. Various features of echo profile are shown, which are dependent on the time region of pulse separation, i.e. t12 > Av,’ or cl2 < Avi’. We mention observation of the deformation of time variation of echo intensity in samples of
Rapid Scan Autocorrelator
high optical density, and propose a method of observation of correct time variation in such samples. We also discuss the possibility of observation of the non-markovian behavior.
2. Experimental Pentacene-doped p-terphenyl crystals were grown by using the Bridgman technique. Crystals were cleaved in parallel to the ab cleavage plane. The concentration of pentacene molecules was 8 X lop6 mol/mol. For the Z&-S, transition of pentacene molecules, there exist four zero-phonon lines 0,) O,, 0, and 0, originating from different sites [6]. We performed photon-echo measurements for the O3 and 0, levels, which are located at 17006 and 17065 cm-l respectively, and inhomogeneously broadened with the width, aVi of 1.2 cm-l. In accumulated three-pulse echo experiments, we used a rhodamine 6G dye laser with a mixed dye solution of a gain medium and a saturable absorber (DODCI), which was synchronously pumped by an actively mode-locked argon ion laser [7]. This hybrid dye laser system can yield easily a shorter pulse width and a pulse profile without substructure corresponding to imperfect mode-locking. The characteristics of pulses were duration of 1.5 ps and peak power of about 25 W. The laser beams were focused on the sample with a diameter of about 100 pm. This gives an excitation density corresponding to the pulse area of about n/ 100. As shown in fig. 1, the laser beam was split into
JAperture
w 1.;
Variable
Fig. 1. Experimental
432
arrangement
for accumulated
1983
three-pulse
echo in the configuration
of k, = 2kz - k 1.
Volume 44, number 6
OPTICS COMMUNICATIONS
15 February 1983
two beams, one of which was modulated with a chopper at 300 Hz and the other was delayed by a variable optical delay. The two beams were parallel but non-collinear, and were focused on the sample at an angle of about 1.2”. A part of the laser beam was fed into a rapid-scan autocorrelator [8] for monitoring the pulse width during the measurement. Two different configurations for observing the echo are possible depending on the direction of observation; the echo can be detected in the direction of (1) k, = 2k, - k, (k2 = k3) or (2) k, = k2 (k, = kg). In this paper, we are concerned mostly with the results for the configuration (1). The echo signal was fed into a Jarrel-Ash double monochromator and detected by a lock-in amplifier. Highly resolved spectra were taken with the resolution of 0.25 cm-l under the condition where the whole absorption band with the inhomogeneous broadening of the So-S, transition was excited by the broad band pulses (-20 cm-‘).
3. Results and discussion Fig. 2(a) shows time behavior of echo intensity versus the pulse separation at 1.7 K, when the whole echo spectrum is detected with low resolution of 6 cm-‘. The decay time of echo in this sample is known to be about 3 ns from our ordinary two-pulse echo experiments [9,10] at this temperature. A slight decrease of echo intensity was observed, although the decay of echo intensity with the time constant of 3 ns should be quite small in this short time region. In fig. 2(b)-(f) we show time behavior of echo intensities observed by fixing the wavelength of the monochromator with high resolution of 0.25 cm-I at several frequencies in the vicinity of the peak POsition of the absorption line, vo. In the case where V-Vu- - 0, the echo grows with the rise time of about 25 ps which is nearly equal to Avi’, and shows no decay in the time region concerned. On the other hand, when the monochromator is tuned at the wave number +l .l cm-’ above the center frequency vo, a rapid rise and fall are seen in the time range from -10 ps to 25 ps followed by long decay. In the case where v - v. = +2.0 cm-‘, such a rise and fall become more rapid. The same behavior is observed for the case where v - v. < 0. These results indicate that the
Fig. 2. Time behavior of echo intensity as a function of the pulse separations for various frequencies. (a): the whole spectrum detected, (b) - (0: spectrally resolved time behavior. v: observed frequency, vo: the center frequency of the absorption line.
spectral components for v f v. rapidly grow and fall in the short time region, tJ2 < Au;‘; where the total echo signal for the whole spectrum would monotonously increase. In fig. 3 we show highly resolved echo spectra with a parameter of pulse separations t12. For t12 = 26.0 ps, the sharp spectrum with a small dip is seen. A rough estimate of the line width is about 1 cm-‘. Since the echo profile should be gaussian in inhomogeneously broadened systems [2,11], this observed spectrum is reasonable as an echo spectrum in such systems except the small dip. As this small dip is located exactly at the absorption peak, it may have arisen from the reabsorption of the echo signal. Such a reabsorption effect is quite large even in the sample whose optical density is about 0.5. In general, for a highly absorbing sample we must take into account effects of the echo pulse propagation through the sample [ 121. However, when the pulse area is much smaller than n/2 as in our case, we may neglect such effects. When the pulse separation is reduced in fig. 3, spectra become broadened depending on the magnitude of the pulse separation. 433
Volume
44, number
OPTICS
6
I
17ooa
WAVE
Fig. 3. Highly separation.
resolved
NUMBER
echo spectra
17010 (cm-‘)
with a parameter
of pulse
Both the frequency-dependent time behavior of echo intensity and the t12-dependent echo spectra will be explained by considering behavior of the temporal profile of the echo in the ultrashort time region where t12 5 Avi’ . In fig. 4 we illustrate schematically time sequence of the echo in the configuration of k, = 2kZ - k, of the accumulated three-pulse echo. The radiation intensity of echo in an inhomogeneously broadened system as a function of time after the first pulse is written as follows [ 111 I(t) a {exp[(-Awf/4)(t X exp[-(t
Fig. 4. Schematic the configuration pulse echo.
434
- 2t,, - t23)2]
- t23)/T2112,
15 February
COMMUNICATIONS
(1)
illustration for the time sequence of echo in of k, = 2kz - k 1 of the accumulated three-
1983
where an inhomogeneous spectrum g(w) = exp(-w2/ 4Aoz) and Awi = nAvi/2(ln 2)lj2. An echo with a gaussian shape is expected to be seen at the time of 2t12 t t23. In the case where t12 9 Avi’, we can see a full gaussian profile of the echo, because the time separation between the echo and the third pulse is large enough compared with the echo width. For t12 < - Av;’ , in contrast, the gaussian profile with the peak at the time of t12 from the third pulse become incomplete, since there exists no echo before the third pulse because of the time causality. If we take into account such disappearance of the rising edge of gaussian profile in the time region before the third pulse, the broadening of the echo spectrum will be expected, because the spectrum and the temporal profile are related to each other through the Fourier transform. From the Fourier transform of eq. (1) the echo spectrum is written as follows
dt exp(-iwt)
ze(0) a J t1z+i13
X exp[(-Awf/4)(t
- 2t,2 - t23)2] 2
X exp L-0
-
t23>/T21 .
(2)
When t12 B Au,‘, the radiation intensity of echo becomes almost zero at the time of t12 t t23 and has a peak at 2t,, t t23. Then, from the relation of the Fourier transform the echo spectrum has a gaussian shape with the width of 2(2 In 2)V2Awi (fwhm). When t12 -< Au,‘, the echo with the same gaussian width has a finite intensity at the time of t12 + t23 and before this time there is no echo, so that the echo spectrum will be broadened. These features are shown in fig. 5, which were calculated with the parameter of t12. This result explains well the observed spectra in the configuration of k, = 2k2 - k, , which are dependent on the pulse separation. We find that the broadened spectrum of echo reflects the temporal profile of echo in the ultrashort time region. From the same argument we can show the time behavior of the echo intensity as a function of pulse separation. The behavior is dependent on the frequency at which it is measured. As we can calculate echo spectra with the parameter of t12 as shown in fig. 5, the echo intensity can be plotted as a function of t12
I
-1
15 February 1983
OPTICS COMMUNICATIONS
Volume 44. number 6
I
0
WAVE NUMBER
I
+t (cm-l)
Fig. 5. Calculated echo spectra with a parameter of pulse separation. for different frequencies. Fig. 6 shows the results. We find that the behavior is consistent with the experimental one. Quantitative agreement between experimental curves and calculated ones is not so good.
This seems to be due to the fact that the excitation pulses used in this work are not completely transformlimited. From these calculated curves, we find that the variation of echo intensity with the pulse separation in case where v - v. = 0 is exactly the same as that which is seen when the total echo signal for the whole spectrum is detected. For v # vo, however, the rapid rise and fall appear even in the time region where if we observe the whole spectral components, no decay is seen. If the component at the center frequency is somewhat depressed because of the reabsorption effect of the echo at the absorption peak, quite different time behavior is observed in the ultrashort time region t12 < AUF’, although the whole spectral components are detected. We note that we must be careful for such an effect even in the sample with rather low optical density (OD - 0.5). Nevertheless, if we make observation at the center frequency even in the ultrashort time region, we can obtain intrinsic time behavior of dephasing of the system, in which the large oscillator strength makes it difficult to use a sample with very low optical density. We briefly mention the results which were observed in the configuration of k, = k2 (/cl = k3). The echo spectra for various pulse separations, r12, showed \l oscillatory structure with the period of tii cm . The spectrally resolved time behavior of echo intensity also showed the oscillatory structure with the period of (v - vo)-l s. In this configuration, the echo is detected as the interference in the sample between a probe pulse and the echo polarization. In order to interpret such oscillations we will need to consider the Bloch and Maxwell equations simultaneously [12,13].
4. Summary and concluding
PULSE SEPARATION ( ps 1 Fig. 6. Calculated time behavior of echo intensity as a function of pulse separation for various frequencies.
remarks
We have performed highly resolved spectroscopy of photon echo in the ultrashort time region. It is found that when t12 < AVi-‘, the echo spectra are broadened because of the deformation of the gaussian profile of echo at the time of the third pulse. We showed that in the ultrashort time region the component at the center frequency (v = vo) behaves in the same manner as the total echo signal for the whole spectrum, although the spectral components for v # v. have rapid time variation. We note that in the 435
Volume
44, number
6
OPTICS
COMMUNICATIONS
sample with high optical density observed time behavior for the whole echo spectrum does not provide a correct rise and fall of echo because of the reabsorption effect of the component at the center frequency. When the dephasing time is comparable to Avi’, we also note that the disappearance of the rising edge of echo profile must be taken into account in order to obtain the correct dephasing time. Furthermore, if we take into consideration the non-markovian process in the inhomogeneously broadened system, the echo profile in the ultrashort time region should be expected to show various features [14]. When t12 - Av[’ > ~c, the echo appears at the instance of the second pulse (in the two-pulse echo configuration) and forms a gaussian profile with the peak at the time of 2t12 from the first pulse. We note that this is similar to the behavior which is expected when the markovian process is taking place. When t12 -rc
436
15 February
1983
References [II J.P. Gordon,C.H.
Wang,C.K.N. Pate], R.E. Slusher and W.J. Thomlinson, Phys. Rev. 179 (1969) 294. PI I.D. Abella, N.A. Kurnit and S.R. Hartmann, Phys. Rev. 141 (1966) 391. [31 S. Chandra, N. Takeuchi and S.R. Hartmann, Phys. Lett. 41A (1972) 91. [41 W.H. Hesselink and D.A. Wiersma, J. Chem. Phys. 73 (1980) 648; and references therein. I51 M. Aihara, Phys. Rev. B25 (1982) 53. 161 R.W. Olson and N.D. Fayer, J. Phys. Chem. 84 (1980) 2001. [71 Y. Ishida, T. Yajima and K. Naganuma, Jpn. J. Appl. Phys. 19 (1980) L717.
PI Y. Ishida, Y. Yajima and Y. Tanaka, [91 1101 [Ill [I21 (131 [I41
Jpn. J. Appl. Phys. 19 (1980) L289. Y. Yoshikuni, A. Nakamura and S. Shionoya, Bull. Chem. Sot. Jpn. 55 (1982) 2749. Y. Yoshikuni, A. Nakamura, S. Shionoya and M. Aihara, J. Phys. Sot. Jpn. 51 (1982) 2604. N. Takeuchi, IEEE J. Quant. Electron. QEll (1975) 230. S.L. McCall and F.L. Hahn, Phys. Rev. 183 (1969) 457. W.H. Hessebnk and D.A. Wiersma, J. Chem. Phys. 75 (1981) 4192. M. Aihara, to be published.