Modeling and design of lossy waveguide structures for generation of broadband terahertz pulses through difference frequency mixing

We present an integral coupled mode theory (CMT), suited to account for high optical losses, to model ultra-broadband terahertz (THz) waveguide emitters (0.1- 20 THz) based on difference frequency generation (DFG) pumped by femtosecond infrared (IR) optical pulses. This integral model works even in the situation where the DFG occurs between several IR and THz modes. We also present a simplified CMT approximation that reproduces the results of the rigorous integral CMT for situations where the THz generation is mediated through single-IR-mode to single-THz-mode interactions. Using the simplified approach we derive a new expression that incorporates loss effects into the coherence length for optical rectification (OR). The expression that we derived for the coherence length can be adapted to describe other second order nonlinear processes such as second harmonic generation.;We apply both models to study waveguide emitters whose nonlinear cores are composed of poled guest-host electro-optic (EO) polymer composites, which belong to the 1mm symmetry class and have high nonlinearities. We apply the models to a generic, symmetric, five-layer, metal/cladding/core waveguide structure and provide design strategies for efficient ultra-broadband THz emitters. Two different design strategies are analyzed, one in which the waveguides are designed to have a single-IR-mode and a single-THz-mode guided within the structure, and other where the waveguide is made with a single-THz-mode but admits several IR guided modes. In both strategies the waveguide geometric parameters are optimized to obtain the highest THz conversion efficiencies and broader output bandwidth.;The simplified CMT approach is much faster to implement than the integral CMT. Thus, we use the simplified approach to perform a parametric study for different waveguide parameters and pumping wavelengths, in the telecom and short wavelength infrared region, to establish under what conditions the five-layered structure yields its highest conversion efficiencies. Coupling conditions are also optimized to guarantee that most of the incident pump power (∼ 80%) is utilized in the interaction. We find conversion efficiencies as high as 35 x 10-4 W-1 and bandwidths up to 20 THz for a structure with a core made of EO polymer AJTB203, polystyrene cladding layers and Al metal-capping layers, when pumped at 1900 nm. We found that for an optimized structure there must be a perfect balance between both modal phase-matching and mode losses effects. Also, we observed that low-loss-cladding layers enhance the efficiency for phase-matched structures, increase the interaction length, and improve the stability of the efficiency with respect to variations in waveguide parameters.;Finally, we identified under what conditions the simplified CMT approximation fails to describe broadband THz generation. For five-layered structures with thin cladding layers (∼ 200 nm thick) both the fundamental and first excited IR modes are involved in the DFG interaction and both must be accounted for to completely describe THz DFG. This is necessary since the fundamental TM-IR mode of structure hybridizes into a plasmon mode as the cladding layers are thinned and THz generation occurs also through OR of the first excited even TM IR mode. The first excited even TM IR mode acts as a quasi-fundamental mode in the absence of cladding layers. In this case the full integral CMT formulation with must be used to correctly model the THz generation.