- Email: [email protected]
Real-space and real-time imaging of polariton wavepackets
Journal of Luminescence 87}89 (2000) 840}843
Real-space and real-time imaging of polariton wavepackets Satoru Adachi *, Richard M. Koehl, Keith A. Nelson Department of Material Science, Himeji Institute of Technology, 3-2-1 Koto, Kamigori, Ako-gun, Hyogo 678-1297, Japan Department of Chemistry, Massachusetts Institute of Technology, Cambridge 01239, USA
Abstract Coherent optic phonon}polaritons generated through impulsive stimulated Raman scattering in a ferroelectric crystal are imaged with 5-lm spatial resolution and 35-fs time resolution. This imaging spectroscopy allows us to perform direct measurement of space- and time-dependent response function induced by the propagating phonon-polaritons. The method will also permit direct examination of nonlinear lattice dynamics and will provide feedback in coherent control system. 2000 Elsevier Science B.V. All rights reserved. PACS: 42.30Va; 77.84; 78.47 Keywords: Phonon}polariton; Imaging; Ultrashort pulses
The recent time-resolved observations of phonon} polaritons has been conducted on time scales that are not only shorter than vibrational lifetimes, but also shorter than individual vibrational oscillation periods [1]. Although these works have provided new insights into the dynamical behavior including structural rearrangements of various systems, the probing has been "xed to temporal domain mainly. If we extend the probing of vibrations to two-dimensional, time and space [2], the vast information of polaritons will be obtained. We report here a novel technique for the pseudo-real-time monitoring of propagating polaritons in a lithium tantalate crystal using optical femtosecond pulses. This method allows the real-time study of the entire collective spatio-temporal response of polaritons in a crystal. Because the polaritons are the way far-infrared THz-radiation propagates in ferroelectrics, it is of interest also as real-time imaging of THzwavepackets by light-scattering compared with the T-ray imaging [3]. The imaging spectroscopy consists of two processes; generation of coherent phonon}polaritons and reading-out
* Corresponding author. Fax: #81-791-58-0137. E-mail address: adachi}[email protected] (S. Adachi)
of the polariton response as an image. The experiment is based on an arrangement of a typical impulsive stimulated Raman spectroscopy (ISRS), but the probe beam has much larger cross section than in usual, and the probe is imaged in transmission geometry. In the experiments, we use a mode-locked Ti : sapphire oscillator and ampli"er system (pulse width 35 fs, repetition rate 1 kHz) as a source of pump and probe pulses and a LiTaO crystal (4;1;2 mm) as a sample. Coher ent phonon}polaritons can be generated by impulsive optical excitation in various conditions. Some possible excitation conditions are (1) a single pump pulse focused to round spot (point excitation in Fig. 1) or to a narrow line on the sample (wedge excitation in Fig. 1), (2) crossed pulses forming an optical interference pattern (grating excitation in Fig. 1), (3) a simple or complex pulse sequence formed by a pulse shaping device [4]. The reading-out of the polariton response, which manifests through its in#uence on the complex refractive index n(k, t) at laser wavelength, is carried out with a time-delayed probe pulse whose spot size is large enough to cover the entire sample region of interest. The transmitted probe light that includes the zero-order and higher-order components that are di!racted by polariton wavepackets is imaged onto a CCD camera using a two-lens telescope. Various imaging con"gurations can be used. In one, as much as possible of
0022-2313/00/$ - see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 2 3 1 3 ( 9 9 ) 0 0 4 3 4 - 2
S. Adachi et al. / Journal of Luminescence 87}89 (2000) 840}843
Fig. 1. The obtained images of the propagating polariton wavepackets in (a) point excitation, (b) wedge excitation, and (c) grating excitation. In (a), the splotch in the center is due to intense scattered pump light. In (c), the center wave vector of excited phonon}polaritons is about 2100 cm\. The horizontal image sizes are 860, 400, and 500 lm in (a), (b) and (c), respectively.
the transmitted probe light is collected and the CCD is placed slightly out of the image plane of the sample. In this case, when CCD is precisely in the focal plane the image disappears, since the polaritons modulate the
841
n(k, t) and the formed one is an image of phase object. In other con"gurations, part of the transmitted probe light is blocked after the "rst lens in the telescope. In this type of phase-contrast imaging, since all the di!racted light components are not recombined at the image plane, a spatial structure of the polariton wavepacket can be observed even when the CCD is in focus. In a straightforward manner, this method permits `moviesa of temporal and spatial evolution of polariton wavepackets. Fig. 1 show the two `framesa from the movies of polariton wavepacket motion. The time 0 ps is the moment when the pump and probe pulses overlap temporally on the sample. As shown in the "gure, the imaging method allows us to examine the entire spatial structure clearly. The pump and probe polarizations are parallel to the c-axis of the crystal. In point excitation (Fig. 1(a)), no propagation along c-axis happens and the response is anisotropic because there is no polariton mode with electric "eld perpendicular to the c-axis. It is possible to excite phonons in wide wavevector region from&0 cm\ by focusing laser beam to a small spot in (a) and (b) since the spatial position and wave vector are bound to the uncertainty principle. On the other hand, the grating excitation (c) selects the center wave vector of phonon distribution by adjusting the crossing angle between two pump beams. In all conditions, the generated polariton propagates slower than the laser pulse(s) and forms the shock wave front like Cherenkov radiation [5] because of the coupling of low-frequency phonon mode to the laser "eld. The shape of the shock wave front is a cone in (a) and a wedge in (b) and (c). Fig. 2 shows the position-time plot in grating excitation. The "gure was made simply by sequential arranging one line pro"le along x-axis of images. This "gure shows clearly the temporal evolution of the propagating polariton with grating structure. The amplitude waveforms of at 0.5, 2.5 and 4.5 ps after the excitation are also indicated in the "gure. The signal is linearly proportional to the polariton response function, as in earlier heterodyne measurement of polariton responses. From the slope of the grating structure motion, the group velocity of the wavepacket is &16% of light speed in vacuum. The data in Fig. 2 can be converted by discrete Fourier transformation (DFT) to other physical parameter region. Fig. 3(a) shows the wave-vector-dependence of the squared response "n(k, t)", and yields the wave-vector region of excited polaritons and their temporal evolution. It is clear from this "gure that the apparent damping of the fringes in Fig. 2 is due to primarily to dephasing of the di!erent wave-vector components in the coherently excited wavepacket because the di!erent wave-vector components have di!erent velocity according to the dispersive nature. The polariton shows oscillatory behavior during the propagation while the electronic response that
842
S. Adachi et al. / Journal of Luminescence 87}89 (2000) 840}843
Fig. 2. The image representation of the signal amplitude in position-time region S(x, t) for the data in Fig. 1(c). Two polariton wavepackets with grating structures were generated at t"0 ps and propagate in opposite direction with each other. The white lines indicate the amplitude of the wavepackets at t"0.5, 2.5 and 4.5 ps.
occurs at &0 ps and &0 cm\ does not propagate. The slice at a given wave-vector in this "gure can be compared directly with the usual time-resolved results in ISRS experiment. Fig. 3(b) shows the cross section at 2030 cm\. It is noted that the temporal pro"le I(k, t) in Fig. 3(b) is the absolute squared amplitude of the signal S(k, t)(Jn(k, t));
Fig. 3. "S(k, t)" for the image data in Fig. 1(c). The color axis is logarithmic and is calculated with arbitrary units. (b) The signal amplitude at 2030 cm\ that is a slice at the wave-vector in Fig. 3(a).
I(k, t)""S(k, t)"J"Ae\AR sin(ut# )" ""A"e\AR+1!cos(2ut#2 ),,
(1)
where A and c is k-dependent amplitude and damping rate, respectively. A "tting result by Eq. (1) is also indicated by a thin solid line. Unlike usual ISRS signal [1,6] with a little damping coe$cient, which #ops at twice polariton frequency 2u, the observed signal (dotted line) is seen at u. Therefore, it should be noted that the obtained signal is proportional to the dielectric response itself, which oscillates at u. The deduced u"53.6 cm\ and c"1.36 cm\ agree with those in our previous work [6]. Finally, it is possible to convert the signal S(k, t) into S(k, u) by applying the DFT along the time-axis to each wave-vector component (Fig. 4). Because we focused two 35-fs pulses to a small spot size, phonon}polaritons are produced over a part of the dispersion curve,
Fig. 4. S(k, u) for the image data in Fig. 1(c). The excited polaritons spread at around 2000 cm\. The contour "gure shows complex material response, where the ridge of the contour shows a part of the frequency dispersion (thick solid line) and the width indicates the damping rate.
S. Adachi et al. / Journal of Luminescence 87}89 (2000) 840}843
not with single wave-vector that is selected out by the di!raction grating. The observed signal density localization in Fig. 4 agrees well with a part of the calculated lower-branch polariton dispersion curve (thick solid line). The ridge and width re#ect the frequency dispersion and damping rate, respectively since the signal S(k, u) is proportional to the complex refractive index n(k, u). In summary, we have demonstrated the direct measurement of the spatio-temporal response function in LiTaO through imaging a wide transmitted probe onto a CCD. We pointed that the developed imaging spectroscopy has some advantageous features against usual ISRS spectroscopy. Prospects for space- and time-dependent studies of anharmonic response and manipulation
843
of the energy and coherence of polaritons in crystals are encouraging.
References [1] L. Dhar, J.A. Rogers, K.A. Nelson, Chem Rev. 94 (1994) 157 and references therein. [2] F. ValleH e, C. Flytzanis, Phys. Rev. B 46 (1992) 13799. [3] B.B. Hu, M.C. Nuss, Opt. Lett. 20 (1995) 1716. [4] A.M. Weiner, Prog. Quant. Electr. 19 (1995) 161 and references therein. [5] D.H. Auston, K.P. Cheung, J.A. Valdmanis, S.A. Kleinman, Phys. Rev. Lett. 53 (1984) 1555. [6] G.P. Widerrecht, T.P. Dougherty, L. Dhar, K.A. Nelson, D.E. Leaird, A.M. Weiner, Phys. Rev. B 51 (1995) 916.
Real-space and real-time imaging of polariton wavepackets Satoru Adachi *, Richard M. Koehl, Keith A. Nelson Department of Material Science, Himeji Institute of Technology, 3-2-1 Koto, Kamigori, Ako-gun, Hyogo 678-1297, Japan Department of Chemistry, Massachusetts Institute of Technology, Cambridge 01239, USA
Abstract Coherent optic phonon}polaritons generated through impulsive stimulated Raman scattering in a ferroelectric crystal are imaged with 5-lm spatial resolution and 35-fs time resolution. This imaging spectroscopy allows us to perform direct measurement of space- and time-dependent response function induced by the propagating phonon-polaritons. The method will also permit direct examination of nonlinear lattice dynamics and will provide feedback in coherent control system. 2000 Elsevier Science B.V. All rights reserved. PACS: 42.30Va; 77.84; 78.47 Keywords: Phonon}polariton; Imaging; Ultrashort pulses
The recent time-resolved observations of phonon} polaritons has been conducted on time scales that are not only shorter than vibrational lifetimes, but also shorter than individual vibrational oscillation periods [1]. Although these works have provided new insights into the dynamical behavior including structural rearrangements of various systems, the probing has been "xed to temporal domain mainly. If we extend the probing of vibrations to two-dimensional, time and space [2], the vast information of polaritons will be obtained. We report here a novel technique for the pseudo-real-time monitoring of propagating polaritons in a lithium tantalate crystal using optical femtosecond pulses. This method allows the real-time study of the entire collective spatio-temporal response of polaritons in a crystal. Because the polaritons are the way far-infrared THz-radiation propagates in ferroelectrics, it is of interest also as real-time imaging of THzwavepackets by light-scattering compared with the T-ray imaging [3]. The imaging spectroscopy consists of two processes; generation of coherent phonon}polaritons and reading-out
* Corresponding author. Fax: #81-791-58-0137. E-mail address: adachi}[email protected] (S. Adachi)
of the polariton response as an image. The experiment is based on an arrangement of a typical impulsive stimulated Raman spectroscopy (ISRS), but the probe beam has much larger cross section than in usual, and the probe is imaged in transmission geometry. In the experiments, we use a mode-locked Ti : sapphire oscillator and ampli"er system (pulse width 35 fs, repetition rate 1 kHz) as a source of pump and probe pulses and a LiTaO crystal (4;1;2 mm) as a sample. Coher ent phonon}polaritons can be generated by impulsive optical excitation in various conditions. Some possible excitation conditions are (1) a single pump pulse focused to round spot (point excitation in Fig. 1) or to a narrow line on the sample (wedge excitation in Fig. 1), (2) crossed pulses forming an optical interference pattern (grating excitation in Fig. 1), (3) a simple or complex pulse sequence formed by a pulse shaping device [4]. The reading-out of the polariton response, which manifests through its in#uence on the complex refractive index n(k, t) at laser wavelength, is carried out with a time-delayed probe pulse whose spot size is large enough to cover the entire sample region of interest. The transmitted probe light that includes the zero-order and higher-order components that are di!racted by polariton wavepackets is imaged onto a CCD camera using a two-lens telescope. Various imaging con"gurations can be used. In one, as much as possible of
0022-2313/00/$ - see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 2 3 1 3 ( 9 9 ) 0 0 4 3 4 - 2
S. Adachi et al. / Journal of Luminescence 87}89 (2000) 840}843
Fig. 1. The obtained images of the propagating polariton wavepackets in (a) point excitation, (b) wedge excitation, and (c) grating excitation. In (a), the splotch in the center is due to intense scattered pump light. In (c), the center wave vector of excited phonon}polaritons is about 2100 cm\. The horizontal image sizes are 860, 400, and 500 lm in (a), (b) and (c), respectively.
the transmitted probe light is collected and the CCD is placed slightly out of the image plane of the sample. In this case, when CCD is precisely in the focal plane the image disappears, since the polaritons modulate the
841
n(k, t) and the formed one is an image of phase object. In other con"gurations, part of the transmitted probe light is blocked after the "rst lens in the telescope. In this type of phase-contrast imaging, since all the di!racted light components are not recombined at the image plane, a spatial structure of the polariton wavepacket can be observed even when the CCD is in focus. In a straightforward manner, this method permits `moviesa of temporal and spatial evolution of polariton wavepackets. Fig. 1 show the two `framesa from the movies of polariton wavepacket motion. The time 0 ps is the moment when the pump and probe pulses overlap temporally on the sample. As shown in the "gure, the imaging method allows us to examine the entire spatial structure clearly. The pump and probe polarizations are parallel to the c-axis of the crystal. In point excitation (Fig. 1(a)), no propagation along c-axis happens and the response is anisotropic because there is no polariton mode with electric "eld perpendicular to the c-axis. It is possible to excite phonons in wide wavevector region from&0 cm\ by focusing laser beam to a small spot in (a) and (b) since the spatial position and wave vector are bound to the uncertainty principle. On the other hand, the grating excitation (c) selects the center wave vector of phonon distribution by adjusting the crossing angle between two pump beams. In all conditions, the generated polariton propagates slower than the laser pulse(s) and forms the shock wave front like Cherenkov radiation [5] because of the coupling of low-frequency phonon mode to the laser "eld. The shape of the shock wave front is a cone in (a) and a wedge in (b) and (c). Fig. 2 shows the position-time plot in grating excitation. The "gure was made simply by sequential arranging one line pro"le along x-axis of images. This "gure shows clearly the temporal evolution of the propagating polariton with grating structure. The amplitude waveforms of at 0.5, 2.5 and 4.5 ps after the excitation are also indicated in the "gure. The signal is linearly proportional to the polariton response function, as in earlier heterodyne measurement of polariton responses. From the slope of the grating structure motion, the group velocity of the wavepacket is &16% of light speed in vacuum. The data in Fig. 2 can be converted by discrete Fourier transformation (DFT) to other physical parameter region. Fig. 3(a) shows the wave-vector-dependence of the squared response "n(k, t)", and yields the wave-vector region of excited polaritons and their temporal evolution. It is clear from this "gure that the apparent damping of the fringes in Fig. 2 is due to primarily to dephasing of the di!erent wave-vector components in the coherently excited wavepacket because the di!erent wave-vector components have di!erent velocity according to the dispersive nature. The polariton shows oscillatory behavior during the propagation while the electronic response that
842
S. Adachi et al. / Journal of Luminescence 87}89 (2000) 840}843
Fig. 2. The image representation of the signal amplitude in position-time region S(x, t) for the data in Fig. 1(c). Two polariton wavepackets with grating structures were generated at t"0 ps and propagate in opposite direction with each other. The white lines indicate the amplitude of the wavepackets at t"0.5, 2.5 and 4.5 ps.
occurs at &0 ps and &0 cm\ does not propagate. The slice at a given wave-vector in this "gure can be compared directly with the usual time-resolved results in ISRS experiment. Fig. 3(b) shows the cross section at 2030 cm\. It is noted that the temporal pro"le I(k, t) in Fig. 3(b) is the absolute squared amplitude of the signal S(k, t)(Jn(k, t));
Fig. 3. "S(k, t)" for the image data in Fig. 1(c). The color axis is logarithmic and is calculated with arbitrary units. (b) The signal amplitude at 2030 cm\ that is a slice at the wave-vector in Fig. 3(a).
I(k, t)""S(k, t)"J"Ae\AR sin(ut# )" ""A"e\AR+1!cos(2ut#2 ),,
(1)
where A and c is k-dependent amplitude and damping rate, respectively. A "tting result by Eq. (1) is also indicated by a thin solid line. Unlike usual ISRS signal [1,6] with a little damping coe$cient, which #ops at twice polariton frequency 2u, the observed signal (dotted line) is seen at u. Therefore, it should be noted that the obtained signal is proportional to the dielectric response itself, which oscillates at u. The deduced u"53.6 cm\ and c"1.36 cm\ agree with those in our previous work [6]. Finally, it is possible to convert the signal S(k, t) into S(k, u) by applying the DFT along the time-axis to each wave-vector component (Fig. 4). Because we focused two 35-fs pulses to a small spot size, phonon}polaritons are produced over a part of the dispersion curve,
Fig. 4. S(k, u) for the image data in Fig. 1(c). The excited polaritons spread at around 2000 cm\. The contour "gure shows complex material response, where the ridge of the contour shows a part of the frequency dispersion (thick solid line) and the width indicates the damping rate.
S. Adachi et al. / Journal of Luminescence 87}89 (2000) 840}843
not with single wave-vector that is selected out by the di!raction grating. The observed signal density localization in Fig. 4 agrees well with a part of the calculated lower-branch polariton dispersion curve (thick solid line). The ridge and width re#ect the frequency dispersion and damping rate, respectively since the signal S(k, u) is proportional to the complex refractive index n(k, u). In summary, we have demonstrated the direct measurement of the spatio-temporal response function in LiTaO through imaging a wide transmitted probe onto a CCD. We pointed that the developed imaging spectroscopy has some advantageous features against usual ISRS spectroscopy. Prospects for space- and time-dependent studies of anharmonic response and manipulation
843
of the energy and coherence of polaritons in crystals are encouraging.
References [1] L. Dhar, J.A. Rogers, K.A. Nelson, Chem Rev. 94 (1994) 157 and references therein. [2] F. ValleH e, C. Flytzanis, Phys. Rev. B 46 (1992) 13799. [3] B.B. Hu, M.C. Nuss, Opt. Lett. 20 (1995) 1716. [4] A.M. Weiner, Prog. Quant. Electr. 19 (1995) 161 and references therein. [5] D.H. Auston, K.P. Cheung, J.A. Valdmanis, S.A. Kleinman, Phys. Rev. Lett. 53 (1984) 1555. [6] G.P. Widerrecht, T.P. Dougherty, L. Dhar, K.A. Nelson, D.E. Leaird, A.M. Weiner, Phys. Rev. B 51 (1995) 916.