Using the molecular strong-field approximation, we investigate high-order harmonic generation by heteronuclear diatomic molecules exposed to an orthogonally polarized two-color laser field, which consists of two mutually orthogonal linearly polarized fields with frequencies $$r\omega $$ and $$s\omega $$ . Here, r and s are integers and $$\omega $$ is the fundamental frequency. The harmonic emission rate and the harmonic ellipticity can be controlled using the laser-field parameters, in particular the relative phase and the intensity ratio of the laser-field components. The value of the relative phase, for which the emission rate is optimal, and the position of the cutoff can be estimated using a classical model. Also, we analyze the harmonic emission rate and the harmonic ellipticity as functions of the molecular orientation, which can also be used as a control parameter. Two types of minima are present in the spectra, depending on r and s. For $$r+s$$ even, interference minima are present in the spectra of the T-matrix component either parallel or perpendicular to the internuclear axis. Using quantum-orbit theory and the saddle-point method, we derive a condition for the interference minima, which relates the molecular orientation angle $$\theta _L$$ and the harmonic order n. The corresponding curves in the ( $$\theta _L$$ , n) plane well reproduce the minima of the numerically calculated spectra. For $$r+s$$ odd, minima are present in the spectra for a particular molecular orientation angle. These minima are explained using the explicit form of the T-matrix element. A heteronuclear as opposed to a homonuclear molecule affords a larger region in the parameter space where both the harmonic ellipticity and the harmonic intensity vary smoothly and both are large.
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