We investigate the photon emission in coupled quantum dots based on symmetry considerations. With the help of a new theorem we proved, we reveal the origin of the various emission patterns, which is the combinative symmetry in the time domain and spectrum domain. We are able to tailor the emission patterns and obtain emission spectra with odd harmonics only, even harmonics only, both odd and even harmonic components, or even the quenching of all components. These interesting emission patterns can be obtained in experiments by careful design of the nanostructures, which are of many applications in optical-electric nanodevices.

Based on spatial-temporal symmetry breaking mechanism, we propose a novel scheme for terahertz (THz) wave generation from hyper-Raman lines associated with the 0th harmonic (a particular even harmonic) in a two-level quantum system driven by two-color laser fields. With the help of analysis of quasi-energy, the frequency of THz wave can be tuned by changing the field amplitude of the driving laser. By optimizing the parameters of the laser fields, we are able to obtain arbitrary frequency radiation in the THz regime with appreciable strength (as strong as the typical harmonics). Our proposal can be realized in experiment in view of the recent experimental progress of even-harmonics generation by two-color laser fields.PACS numbers: 42.65. Ky, 42.50.Hz, 78.20.Bh Introduction Terahertz (THz) radiation, electromagnetic radiation with typical frequency from 0.1 THz to 10 THz-lying in the spectrum gap between the infrared and microwaves, has varieties of applications in information and communication technology, biology and medical sciences, homeland security, and global environmental monitoring etc.1 . The generation of THz wave is a challenge problem due to the lack of appropriate materials with small bandgaps in the usual optical approach. Great effort has been made to the design of THz sources 2-15 . THz wave can be obtained by both electronic and optical methods. The uni-travelling-carrier photodiode 6 and the quantum cascade laser 9-13 are two examples. The electronic approach is limited in the low frequency end of the THz regime, and the optical approach usually focuses on the cases of small energy gap. Technological innovation in photonics and nanotechnology has provided us more new ways for THz radiation generation. Recently an interesting approach based on semiconductor nanostructure driven by acoustic wave was suggested 16 , and electrically pumped photonic-crystal THz laser was developed 17 . THz wave generation by up conversion method through high-order harmonics generation(HHG) in semiconductor quantum dot(QD) was also suggested in our previous work 18 .

Based on coupled quantum dots, we present an interesting optical effect in a four-level loop coupled system. Both the two upper levels and the two lower levels are designed to be almost degenerate, which induces a considerable dipole moment. The terahertz wave is obtained from the low-frequency component of the photon emission spectrum. The frequency of the terahertz wave can be controlled by tuning the energy levels via designing the nanostructure appropriately or tuning the driving laser field. A terahertz wave with adjustable frequency and considerable intensity (100 times higher than that of the Rayleigh line) can be obtained. It provides an effective scheme for a terahertz source.

Using the spatial-temporal symmetry principle we developed recently, we propose an effective scheme for even-harmonics generation in coupled quantum dots. The relative intensity of odd and even harmonic components in the emission spectrum can be controlled by tuning the dipole couplings among the dots, which can be realized in experiments by careful design of the nanostructures. In particular, pure 2nth harmonics and (2n + 1)th harmonics (where n is an integer) can be generated simultaneously with polarizations in two mutual perpendicular directions in our systems. An experimental design of the coupled dots system is presented.

We develop a theory of original quantum mechanism for finding strong optical activity quantum optical system in three-level non-chiral nanostructures, where symmetrical incidence (the propagation of the incident light is vertical to the plane of nanostructures) is considered. The theory is validated via both analytical and numerical analysis of specifically designed non-chiral coupled quantum dots models. In particular, by proper designing of the incidence, tunable terahertz wave polarized even in the opposite direction of the incidence is obtained. The effect could be explored for developing novel highly efficient terahertz polarization rotator and modulators, and may lead to the appearance of a new class of negative index terahertz nanostructures.