SUPERRADIANCE OF POLARITONS - CROSSOVER FROM 2-DIMENSIONAL TO 3-DIMENSIONAL CRYSTALS

Ln spite of the relative simplicity of the structure of Frenkel excito ns in molecular crystals some questions concerning the theory of polar itons in such crystals remain controversial-especially those concernin g the crossover from the two-dimensional to the three-dimensional case . In the present work a detailed microscopic study of Frenkel exciton- polaritons in crystal slabs of arbitrary thickness is performed for th e states with the tangential wave vector k(parallel to)=0. Starting fr om the microscopic quantum theory we have obtained two basic equations . One of them relates the complex energy of a polariton E to the quant ity q, which in the limiting case of bulk crystal comes to the normal component of the wave vector. When the number N of the monolayers in t he pile is large, N much greater than 1, this equation is reduced to t he dispersion equation of the macroscopic electrodynamics which uses t he dielectric function epsilon(omega). The other equation of our micro scopic theory has the meaning of Ewald's extinction rule and for N muc h greater than 1 is reduced to Maxwell's boundary conditions. Using th e equations obtained we found the complete set of polariton terms for the arbitrary N from N=1 to N-->infinity. We have traced the rise and evolution of two branches of polariton terms with increasing N. Specia l attention was paid to the study of polariton superradisnce-enormous radiative damping or very short corresponding lifetimes for some state s. At small N much less than lambda/a, with lambda being the light wav elength and a the lattice constant, the superradiant linewidth is prop ortional to N(lambda/a)T-2((0)), where Gamma((0)) is the molecular rad iative width. After further increasing the thickness this linewidth is monotonously decreased to zero. We also show that for the macroscopic slabs the radiative broadening may be obtained as a result of taking into account multiple reflections of the polariton from the surfaces o f the crystal. illustrative calculations were performed using paramete rs of the anthracene crystal. (C) 1997 American Institute of Physics.