Model of generating either odd or even optical harmonics by varying the coupling parameters between source quantum dots

We show that the high harmonics generation (HHG) in quantum dot structures can be changed from only odd orders to both odd and even orders by controlling the coupling parameters. We find that even harmonics cannot be generated in a multilevel system if the electronic levels can be classified into groups by the parity of oscillation modes (the Fourier components of Floquet states) and the radiative transitions within same group are forbidden. Otherwise both odd and even harmonics are possible. According to the two distinct dynamic behaviors of HHG, we obtain a straightforward judgement of HHG in any multilevel systems.