Far-infrared radiation (λ ≈ 60 μm) by difference frequency generation in coupled quantum wells

The generation of coherent far infrared radiation in quantum semiconductor structures has recently attracted considerable attention. Different physical means of generating far ir have been explored such as sequential resonant tunneling, coherent charge oscillations in coupled wells and Bloch oscillations in superlattices. In this paper we report the first observation of far-infrared radiation (λ approx. 60 μm) by difference frequency generation associated with intersubband transitions in coupled quantum wells. The conduction band diagram of one period of the structure is shown in Fig. 1. The sample grown by MBE on a semi-insulating GaAs substrate, comprises fifty modulation doped coupled quantum wells. Each period consists of two GaAs wells, respectively 60 angstrom and 70 angstrom thick, separated by a 20 angstrom Al_0.33Ga_0.67As barrier. The coupled well periods are separated by a 950 angstrom Al_0.33Ga_0.67As space layer. To supply the electron charge in the wells, a δ-doped Si layer (1 × 10¹²/cm²) is inserted in the spacer layers. At the cryogenic temperatures of our experiment (approx.10 K), only the lowest state is populated. Far-infrared generation (ℏω-ir$/) arises from the nonlinear mixing between two CO₂ lasers of frequencies ω-1$/ and ω-2$/ in near resonance with the intersubband transition (ℏω-1$/ - ℏω-2$/ = E₂ - E₁). The corresponding nonlinear susceptibility χ⁽²⁾ is greatly enhanced by resonant denominators corresponding to the 1 → 3 and the 2 → 1 transitions and the large matrix elements (z₁₂ = 27 angstrom, z₁₃ = 8 angstrom, z₂₃ = 22 angstrom), similar to other nonlinear coefficients associated with intersubband transitions. To observe the ir generation, it is crucial to minimize the broadening of the transitions using modulation doping and low temperatures. Using FTIR absorption measurements we were able to clearly resolve the 1 → 3 and 1 → 2 transitions with FWHM of 3 meV and 1.5 meV, respectively. For the experiment the sample was processed in a trapezoidal 2-pass waveguide corresponding to a nonlinear interaction length of 1.3 μm. The power of the CO₂ laser beams is concentrated on a 100 μm diameter spot size. The ir signal was detected via a bolometer and phase sensitive techniques. Figure 2 shows the measured ir power as a function of the product of the powers of the two CO₂ laser beams. The expected linear dependence is verified.