Phonon polariton

One of the applications of TRXRD is to study complex systems where electric fields couple to multiple degrees of freedom. Though femtosecond laser pulses can generate THz radiation from ferroelectric LiTa03, the corresponding lattice motion remained undetected by optical measurements. Cavalleri and coworkers demonstrated the coherent modulation of the X-ray intensity at 1.5 THz [10], and assigned it as phonon-polariton mode of A symmetry (Fig. 3.3). Nakamura and coworkers detected the coherent LO phonon of CdTe... 

The elementary excitations mentioned so far are not related in any special way to the solid state and will therefore not be treated in this article. We will discuss here the following low-lying quantized excitations or quasi-particles which have been investigated by Raman spectroscopic methods phonons, polaritons, plasmons and coupled plasmon-phonon states, plasmaritons, mag-nons, and Landau levels. Finally, phase transitions were also studied by light scattering experiments however, they cannot be dealt with in this article. 

The use of lasers for the excitation of Raman spectra of solids has led to the detection of many new elementary excitations of crystals and to the observation of nonlinear effects. In this review we have tried to lead the reader to a basic understanding of these elementary excitations or quasi-particles, namely, phonons, polaritons, plasmons, plasmaritons, Landau levels, and magnons. Particular emphasis was placed upon linear and stimulated Raman scattering at polaritons, because the authors are most familiar with this part of the field and because it facilitates understanding of the other quasi-particles. 

A phonon-polariton is a boson quasi-particle that couples an infrared photon with an optical phonon. 

Figure 1 Phonon-polariton dispersion in LiTa03. The solid lines describe the dispersion of the upper and lower branches of the polariton, the dashed line describes the dispersion of light at frequencies below the phonon resonance, and the dotted line describes the dispersion of light at frequencies above the phonon resonance.

A variably delayed probe pulse can be used to monitor the time-dependent vibrational oscillations and decay through coherent scattering ( diffraction ), yielding data like that shown in the simulation in Fig. 3a. In this simulation, the excitation and probe regions are overlapped spatially, and the decay of signal is due to damping and dephasing of the phonon-polariton response. From data of this form, the polariton frequency co and... 

Figure 3 Simulation of ISRS diffraction data from propagating phonon-polaritons. Use of (a) large (1 mm) and (b) small (250 pm) excitation and probe spot sizes gives rise to large differences in apparent damping kinetics for these 1 THz polari-tons propagating at a velocity of 50 pm/ps.

The electromagnetic fields of the right- and left-propagating polaritons, respectively, follow the wave equations with the speeds and damping rates of the different frequency components dispersed according to the frequency- and wavevector-dependent complex refractive index n = v/e(k, oj). A typical example of the dispersion of these modes is shown in Fig. 1 for the case of a real permittivity e. The term Ao(r,t) represents the envelope of the wavepacket on the phonon-polariton coordinate A. Note that this phonon-polariton coordinate is a linear combination of ionic and electromagnetic displacements, which both contribute to the polarization... 

Fixed spatial phase in the grating pattern also facilitates experiments with multiple excitation pulses (20). A second, delayed pulse incident on the diffractive optic is split in the same manner as the first and results in a second excitation pattern with the same peak and null positions. Thus, multiple excitation gratings, delayed temporally and shifted spatially if desired, can be used for excitation of phonon-polaritons whose coherent superposition is well controlled. A preliminary experiment of this type has been reported (21). 

Now we turn to methods for phonon-polariton detection. The signal intensity in a grating measurement like that illustrated in Fig. 2 is given by the... 

Figure 8 Images of propagating phonon-polaritons in LiTa03 produced by impulsive grating excitation with spatial preriod 30 pm. To improve the quality of the images, 11 scans taken well before time t = 0 were averaged and subtracted from the raw data. Image dimensions 2050 pm tall x 895 pm wide. (From Ref. 16.)...

Figure 9 Images from propagating phonon polaritons produced by a single beam focused to a round spot. Background data have been subtracted as in Fig. 8. The splotch in the center that obscures some data near time t = 0 is due to intense scattered pump light, which could not be completely filtered from the imaging setup. Image dimensions 1020 pm tall x 860 pm wide. (From Ref. 16.)...

APPENDIX PHONON-POLARITON EXCITATION EQUATIONS OF MOTION... 

The dielectric is often assumed to be isotropic in order to simplify Eq. (8) by assuming transverse phonon-polaritons the extension to anisotropic media is straightforward (31). In the limit of very short pulse duration compared to the phonon-polariton oscillation period, the time-dependence of the excitation field can be treated as a delta function, and the phonon-polariton response is given by the impulse response function for the spatial excitation pattern used. If crossed excitation pulses are used, then it is simplest to describe the excitation and response in terms of the excitation wavevector or wavevector range. 

Romero-Rochin V, Koehl RM, Brennani CJ, Nelson KA. Theory of anharmonic phonon-polariton excitation in LiTaOj by ISRS and detection by wavevector overtone spectroscopy. J Chem Phys 1999 111(8) 3559—3571. 

The coupled phonon-polariton oscillations can be detected by measurement of oscillatory birefringence with a variably delayed probe pulse. (The transit time and the spectral content of the probe pulse also should show oscillatory time dependences.) As in forward ISRS, this pulse surfs along a crest or null of the polariton wave. Since the polariton radiates outward from the excitation beam, the probe pulse need not be overlapped spatially with the excitation pulse. By varying the spatial separation between the two parallel-propagating beams, the polariton group velocity and dispersion can be determined. Phonon-polariton dynamics in LiTaOj crystals were determined in this manner [36, 59]. An example of data is shown in Figure 9. 

Figure 9. Oscillations of phonon-polariton mode in lithium tantalate crystal excited through inverse electro-optic effect and impulsive stimulated polariton scattering. Time-dependent birefringence measured with probe pulse, which propagated parallel to but not collinear with excitation pulse. (Reprinted with permission from ref. 36.)...

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