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The use of laser pulse sequences to drive the cascaded difference frequencygeneration of high energy, high peak-power and multi-cycle terahertz pulses incryogenically cooled periodically poled lithium niobate is proposed. Detailedsimulations considering the coupled nonlinear interaction of terahertz andoptical waves show that unprecedented optical-to-terahertz energy conversionefficiencies > 5%, peak electric fields of hundred(s) of Mega volts/meter atterahertz pulse durations of hundred(s) of picoseconds can be achieved. Theproposed methods are shown to circumvent laser-induced damage at Joule-levelpumping by 1$\mu$m lasers to enable multi-cycle terahertz sources with pulseenergies >> 10 milli-joules. Various pulse sequence formats are proposed andanalyzed. Numerical calculations for periodically poled structures accountingfor cascaded difference frequency generation, self-phase-modulation, cascadedsecond harmonic generation and laser induced damage are introduced.Unprecedented studies of the physics governing terahertz generation in thishigh conversion efficiency regime, limitations and practical considerations arediscussed. Varying the poling period along the crystal length and furtherreduction of absorption is shown to lead to even higher energy conversionefficiencies >>10%. An analytic formulation valid for arbitrary pulse formatsand closed-form expressions for important cases are presented. Parametersoptimizing conversion efficiency in the 0.1-1 THz range, the corresponding peakelectric fields, crystal lengths and terahertz pulse properties are furnished.

Pulse Sequences for Efficient Multi-Cycle Terahertz Generation in Periodically Poled Lithium Niobate