Infrared Generation by Coherent Excitation of Polaritons

The work presents a transient theory of the propagation in a cubic crystal of a polariton wave excited by a three-wave nonlinear parametric interaction. The coupling coefficient of the mixing process is calculated using a quantum-mechanical perturbation approach in the second-quantization formulation and including explicitly in the theory the phase and momentum mismatches of the interaction. The solution of the partial differential equations describing the evolution of the driving optical pulses leads to a complete formulation of the transient problem for the polariton pulse propagation. The transient problem is fully solved in the case in which the duration of the driving pulse $f(z,t)\mathrm{}$ of the polariton wave is larger than the damping parameter ${\Gamma }^{-1\mathrm{}}$: a case of general physical relevance including the optical behavior of short pulses generated by mode-locked lasers. In particular the solution of the problem leads to the definition of a characteristic interaction length and time depending on the initial conditions and affecting in a critical way the efficiency of the "coherent excitation" process. The Raman mixing process is briefly discussed as a particular case of the polariton process. The process of infrared generation is then taken into account on a semiclassical basis, with particular emphasis on the discussion of the propagation effects of the boundary conditions. In particular, the inhomogeneous character of the free solutions of the propagation equations is discussed. The theory is further extended to a brief discussion of the nonlinear optical behavior of the reststrahl band, leading to the consideration of an infinite nonlinear backward reflectivity at $\omega ={\omega }_{\mathrm{LO}}$. An experiment is then described in which the coherent infrared generation in a crystal of gallium phosphide is applied to a series of accurate measurements of the linear and nonlinear optical parameters in the polariton region. The angular distribution of the emitted infrared intensity at wavelengths $\lambda =29.2, 29.9, \mathrm{and} 34.6$ μ and the spatial evolution of the polariton field in the quasicollinear kinematical configuration lead to the determination of the index of refraction of the crystal at these wavelengths and to the first direct measurement of the absorption coefficient in the zone of large polariton dispersion. On the basis of our results, we could verify the correctness of the multiple-oscillator theoretical model proposed by Barker in order to describe the lattice oscillation in GaP. Finally, the infrared intensity at the various frequencies leads to the determination of the dispersion of the modulus of the nonlinear optical susceptibility $\mathrm{}\left|d\right|\mathrm{}$ of the crystal. Assuming in first approximation a single-oscillator model for the lattice in the nonlinear regime, we could measure the characteristic nonlinear parameter $C=S\left(\frac{d_Q^{\prime }}{d_E^{\prime }}\right)$. We found $C=-0.48\mathrm{}\pm 0.01$. The experimental methods described in the present work are of general interest for the nonlinear spectroscopy of solids in the optical and infrared range of frequencies.