  Intrinsic Josephson-junction stacks realized in mesas fabricated out of
high-temperature superconductors may be used as sources of coherent
electromagnetic radiation in the terahertz range. The major challenge is to
synchronize Josephson oscillations in all junctions in the stack to get
significant radiation out of the crystal edge parallel to the c axis. We
suggest a simple way to solve this problem via artificially prepared lateral
modulation of the Josephson critical current identical in all junctions. In
such a stack phase oscillations excite the in-phase Fiske mode when the
Josephson frequency matches the Fiske-resonance frequency which is set by the
stack lateral size. The powerful almost standing electromagnetic wave is
excited inside the crystal in the resonance. This wave is homogeneous across
the layers meaning that the oscillations are synchronized in all junctions in
the stack. We evaluate behavior of the I-V characteristics and radiated power
near the resonance for arbitrary modulation and find exact solutions for
several special cases corresponding to symmetric and asymmetric modulations of
the critical current.
