Starting from Hopfield's theory of the excitonic polariton, the energies and momenta of the particles involved in a two-photon Raman scattering process may be calculated self-consistently from the direction of the exciting photons, their energy, and the direction of the scattered light. Attributing to the calculated momenta the measured energies of the emitted photons, one obtains the dispersion relation of the excitonic polaritons with a high accuracy in a semiexperimental way.Because of the strong coupling between the electromagnetic radiation field and the polarization in the crystal, eigenstates of the coupled excitonphoton system have been shown to be mixed states of excitons and photons. 1 ' 2 In CuCl, the eigenvalues of these states-so-called polaritons-give rise to a nonlinear dispersion relation in the region where the photon dispersion crosses the r 5 exciton band. In addition, the threefold degeneracy of the T 5 exciton band is partly lifted by this interaction and one obtains one longitudinal exciton band and two twofold degenerate-upper and lower-polariton branches. The usual equation describing the polariton dispersion relation E(p) reads 1
E (5)For the transverse exciton band, in the effectivemass approximation, this equation depends on four parameters: the high-energy dielectric constant €oo, the effective exciton mass m*, and the energies E L of the longitudinal exciton and E T of the transverse exciton at a momentum p = 0.The longitudinal exciton band, given byand the upper polariton branch E 2 (p) [following from Eq. (1)] were first directly observed by nonresonant two-photon absorption. 3 In this study, the momentum p of the excited quasiparticles was tuned by changing the angle between the two photon beams. Information on the lower polariton branch E x (p) [following from Eq. (1)], however, could not be obtained because of the conservation of energy and momentum in the two-photon absorption process. We will show in this work that a combined absorption and emission process, like resonant twophoton Raman scattering via biexcitons, gives the possibility of performing spectroscopy in momentum space of the lower polariton branch, too.Biexcitons in their ground state can be excited resonantly by two-photon absorption in CuCl when the energy of the exciting photons is equal to half the biexciton energy E B /2, as shown unambiguously. 4 When the energy of the exciting photons is detuned from this resonance, biexcitons are created only virtually, with a momentum equal to two times the momentum q, of the exciting polaritons. These virtual biexcitons recombine, emitting a lower polariton of energy E x {q), and leaving in the crystal a lower polariton E l (Jz) > an upper polariton E 2 (k), or a longitudinal exciton E L (k) 5 These processes conserve energy and momentum of the different particles involved; namely, and 2Hu> l =E 1 (q)+E 1 (k),In the experiment, the crystal is excited with a laser beam making an angle of incidence a on the sample. The photon energy of the laser is fooj. The photons emitte...