  The use of laser pulse sequences to drive the cascaded difference frequency
generation of high energy, high peak-power and multi-cycle terahertz pulses in
cryogenically cooled periodically poled lithium niobate is proposed. Detailed
simulations considering the coupled nonlinear interaction of terahertz and
optical waves show that unprecedented optical-to-terahertz energy conversion
efficiencies > 5%, peak electric fields of hundred(s) of Mega volts/meter at
terahertz pulse durations of hundred(s) of picoseconds can be achieved. The
proposed methods are shown to circumvent laser-induced damage at Joule-level
pumping by 1$\mu$m lasers to enable multi-cycle terahertz sources with pulse
energies >> 10 milli-joules. Various pulse sequence formats are proposed and
analyzed. Numerical calculations for periodically poled structures accounting
for cascaded difference frequency generation, self-phase-modulation, cascaded
second harmonic generation and laser induced damage are introduced.
Unprecedented studies of the physics governing terahertz generation in this
high conversion efficiency regime, limitations and practical considerations are
discussed. Varying the poling period along the crystal length and further
reduction of absorption is shown to lead to even higher energy conversion
efficiencies >>10%. An analytic formulation valid for arbitrary pulse formats
and closed-form expressions for important cases are presented. Parameters
optimizing conversion efficiency in the 0.1-1 THz range, the corresponding peak
electric fields, crystal lengths and terahertz pulse properties are furnished.
