Short pitch structures in smectics with interactions over more than two layers

Phenomenological model of chiral polar smectics is introduced with interact ions up to the fourth neighboring layers. The minimization of the free ener gy gives three stable structures: the ferroelectric Sm C* phase, the antife rroelectric Sm C-A* phase and the hellicoidally modulated structure of the Sm C-H* phase. The Sm C-H* phase can be recognized as the Sm C-alpha*, phas e below Sm A phase and as the Sm C-FI2* phase or as the Sm C-FI1* phase whe n appearing between the Sm C* phase and the Sm C-A* phase. Stability of the se phases is analyzed and the phase diagram in the space of model parameter s is presented.