| For over 100 years, the problem of how a wave travels through a dispersive material is one that has been studied in great detail. Recent interest in this problem has been sparked by the discovery of systems that have high dispersion, yet allow a pulse to propagate relatively undistorted. Electromagnetically induced transparency, which can reduce absorption while retaining strong dispersion, has attracted more interests. In this thesis, we first propose Phonon Induced Transparency concept. Due to strong phonon-exciton interaction, transparency effect can occur in quantum dot system. This is different from normal there-level system. If there is no phonon interaction, there would be no transparency. We can also get giant Kerr effect which is larger than normal system. We theoretically study the double quantum dot systems, which also existing giant Kerr effect. We use voltage instead of light field to manipulate tunneling, and Kerr effect could change from positive value to negative value with voltages changing. So we have investigated mature QD system, including single QD and double QDs. We also propose to use magnetic field to decrease decay rate of spin-orbit interaction. We are sure our theoretical theory would shed light on how to efficiently suppress decoherence and distanglement. In this thesis, we have made a deep investigation on the optical effect in polymers. With strong pump field and weak probe field, we first investigate superluminal light in polymers. Because polymers are easy to prepare, we hope our work could provide some help for future experiment.(1) We study slow light effect in quantum dot systems where exciton behaves as a two-level system. It is shown that due to strong exciton–phonon coupling, slow light effect can occur in such a quantum dot system and signal light can propagate without absorption. The nonlinear optical absorption and Kerr coefficient based are also calculated. The numerical results show that giant nonlinear optical effects can be obtained while the frequency of the signal field differs only by an amount of LO phonon frequency from the exciton frequency in quantum dot systems.(2)We study theoretically the influence of local field effects on phonon-induced transparency (PIT) in quantum-dot systems embedded in a semiconductor matrix. As compared with our previous work without local field effects, we present analytical and numerical results from solution of the generalized optical Bloch equations including the local field effects. It is shown that the local field effects broaden the transparency window due to PIT and reduce the group velocity of light. For some specific parameters of the light and quantum dots, fast light can be obtained in such systems. The results also demonstrate that Kerr nonlinearity is enhanced greatly due to the local field effects.(3) We study Kerr nonlinearity in an asymmetric double quantum-dot systems coupling with voltage. It is found that, by proper tuning of two light beams and tunneling via a bias voltage, the Kerr nonlinearity can be enhanced and varied from positive value to negative value.(4) The effect of direct spin-phonon interactions on spin-orbit-driven coherent oscillations in a single quantum dot which proposed by Debald and Emary is investigated theoretically in terms of the perturbation treatment based on a unitary transformation. It is shown that the decoherence rate induced by acoustic phonons strongly depends on the spin-orbit coupling strength, the magnetic field strength and quantum dot size. By increasing the magnetic field, the decay rate can be reduced to zero. Numerical results show that if quantum dot size is large enough, decay rate would be suppressed.(5) We consider the linear optical property in charge-transfer excitons systems where light pulse would not be absorbed but be amplified. We calculate the linear susceptibility and obtain an abnormal slope in refractive curve which means superluminal propagation can exist in this system.
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