Second harmonic generation from metamaterials strongly coupled to intersubband transitions in quantum wells

We theoretically analyze the second harmonic generation capacity of two-dimensional periodic metamaterials comprising sub-wavelength resonators strongly coupled to intersubband transitions in quantum wells (QWs) at mid-infrared frequencies. The metamaterial is designed to support a fundamental resonance at ∼30THz and an orthogonally polarized resonance at the second harmonic frequency (∼60THz), while the asymmetric quantum well structure is designed to provide a large second order susceptibility. Upon continuous wave illumination at the fundamental frequency we observe second harmonic signals in both the forward and backward directions, with the forward efficiency being larger. We calculate the overall second harmonic conversion efficiency of the forward wave to be ∼1.3×10^-2 W/W² - a remarkably large value, given the deep sub-wavelength dimensions of the QW structure (about 1/15th of the free space wavelength of 10μm). The results shown in this Letter provide a strategy for designing easily fabricated sources across the entire infrared spectrum through proper choice of QW and resonator designs.