Theory of harmonic generation using antiferromagnets in the far-infrared

This paper considers the usefulness of antiferromagnetic materials as second-harmonic generators. Using molecular field theory and a 2-sublattice model, the second-order susceptibility of an antiferromagnetic structure is derived. The resulting nonlinear electromagnetic wave equations are then solved using a particular set of boundary conditions for the case in which the input radiation is at the material´s antiferromagnetic resonance frequency. The strong absorption of the fundamental radiation at this frequency is taken into account. A method of matching the impedance of the material to that of the environment is described, wherein one face of the material is impedance matched at the frequency of the entering primary radiation, and the opposite face is impedance matched at the harmonic frequency of the emerging radiation. The theoretical results are applied to the particular case of FeF2. Using published results for the anisotropy, resonance frequency, and bandwidth of FeF2, its efficiency as a second-harmonic generator is found. This result is compared to the efficiency of KDP, a non-linear dielectric used as an harmonic generator in the optical band. It is concluded that, in the far-infrared waveband, FeF2, used at its resonant frequency, should be 10⁶to 10⁶times as efficient as KDP. In conclusion, a summary of the relative advantages and disadvantages of magnetic and dielectric materials as harmonic generators in the far-infrared is given.