Abstract
We develop a coupled mode theory (CMT) model of the behavior of a polarization source in a general photonic structure, and obtain an analytical expression for the resulting generated electric field; loss, gain and/or nonlinearities can also be modeled. Based on this treatment, we investigate the criteria needed to achieve an enhancement in various nonlinear effects, and to produce efficient sources of terahertz radiation, in particular. Our results agree well with exact finite-difference time-domain (FDTD) results. Therefore, this approach can also in certain circumstances be used as a potential substitute for the more numerically intensive FDTD method.
Highlights
Since the emergence of nonlinear optics[1] in 1961, and the major breakthroughs[4, 3, 2, 5, 6, 7] that subsequently marked its growth, the field of nonlinear optics has been producing continuous scientific excitement: Numerous nonlinear optical phenomena have been discovered, and have significantly impacted scientific progress in many respects[9, 12, 10, 11, 8]
A light source embedded in a photonic structure is known to emit faster when the local density of photonic states (LDOS) at the source frequency is larger, and this applies for light sources originating from nonlinear polarization as well
We theoretically investigate sending an optical beam into an appropriately designed 2D nonlinear photonic crystal, and we use our coupled mode theory (CMT)-based result to calculate the total energy radiated at terahertz frequencies
Summary
Since the emergence of nonlinear optics[1] in 1961, and the major breakthroughs[4, 3, 2, 5, 6, 7] that subsequently marked its growth, the field of nonlinear optics has been producing continuous scientific excitement: Numerous nonlinear optical phenomena have been discovered, and have significantly impacted scientific progress in many respects[9, 12, 10, 11, 8]. Given the current challenge of making high-power terahertz sources, we illustrate our general approach, by proposing, for the first time, a method for efficient generation of terahertz waves by optical rectification in a two-dimensional (2D) photonic crystal For this purpose, we theoretically investigate sending an optical beam into an appropriately designed 2D nonlinear photonic crystal, and we use our CMT-based result to calculate the total energy radiated at terahertz frequencies. A specific example of such cases is the generation of terahertz radiation by optical rectification, where a proper FDTD calculation should involve simultaneously wavelengths in both the optical and terahertz regimes, resulting in a computational burden that could go beyond the capabilities of currently available computers Such complications, are not present if one uses our CMT formalism, instead. IV, we apply our work to the specific problem of THz generation and compare our results with FDTD results
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