Intrinsic localized modes in the bulk and at the surface of anharmonic diatomic chains

Intrinsic localized vibrational modes in a diatomic anharmonic chain are discussed in detail. We consider a finite (even or odd) number of particles interacting with nearest-neighbor harmonic and cubic and quartic anharmonic potentials. For suitable values of the potential parameters we find two odd parity modes localized about light and heavy atoms, respectively, with frequencies above the top of the optical branch. In the gap there are localized modes arising from the top of the acoustic branch with odd parity if they are centered on a heavy atom and even parity if centered on a light atom. There are also two localized modes originating from the bottom of the optical branch. The odd parity mode is centered on a light atom, while the even parity mode is centered on a heavy atom. In addition, we have found two types of surface modes. One is the anharmonic version of the surface mode occurring in a finite diatomic harmonic chain with frequency in the gap, and the other is entirely due to the anharmonicity. The latter mode has its frequency above the top of the optical branch. A comparison with other work is given.