| The study of coherent control of optical properties and optical courses is one of the most important and active research front fields in international optics nowadays. The study of coherent control has not only an important theoretical value, but also wide application prospects in many fields, such as quantum optics, nonlinear optics, quantum information and optical communication, etc. In addition, atomic coherence and quantum interference effects have multiple potential applications in many aspects. Among numerous phenomena of atomic coherence and quantum interference, lasing without inversion (LWI) has received tremendous attention. As a new mechanism of producing laser, LWI can obtain laser light spectral domains, e.g. the x-ray evenγ-ray range, where conventional methods based on population inversion are not available or are difficult to implement, so the study of LWI has not only an important theoretical value, but also wide application prospects.Based on the work of the former people, we mainly studied the coherent control of optical properties in aΛ-type three-level system of lasing without inversion. This paper consists of four chapters.In Chapter 1, we explained the significance for studying coherent control and LWI, showed the basic principle of producing LWI, and introduced simply the current research state of coherent control and LWI, and the main contents for the important study subject at present.In Chapter 2, we studied the effect of propagation of fields on lasing without inversion and the modulation role of spontaneously generated coherence on this effect in a closedΛ-type three-level system with or without the Doppler effect, respectively. Ignoring the Doppler effect, we discussed the effects of the propagation of fields on the LWI gain, Rabi frequencies of the driving and probe fields, the population difference for different values ofθ. We also studied the relationship between the LWI gain at the specific distance and the Rabi frequency of the driving field at the entrance of the medium for different values ofθ. Considering the Doppler effect, we analyzed the effects of the propagation of fields on the LWI gain, Rabi frequencies of the driving and probe fields, the population difference for different values ofθwhen the probe and driving fields and atomic motion are co-propagating. We also studied the relationships between the LWI gain at the specific distance and the Rabi frequency of the driving field at the entrance of the medium, Doppler broadening width whenθtakes different values. It is shown that: regardless of the existence of the Doppler effect, LWI gain increases first and decreases afterwards, Rabi frequency of the probe field increases and the Rabi frequency of the driving field decreases with the distance increasing. At a specific distance, LWI gain increases first and decreases afterwards with the Rabi frequency of the driving field at the entrance of the medium increasing. Considering the Doppler effect, the LWI gain decreases monotonously with the Doppler broadening width increasing.In Chapter 3, based on the work of chapter 2, we investigated the control role of the relative phase (Φ) between the probe and driving fields on the LWI gain, Rabi frequencies of the driving and probe fields, the population difference during the propagation process in a closedΛ-type system with spontaneously generated coherence (SGC). WhenΦ=0, i.e. when only SGC is considered, LWI gain can be obtained, but the LWI gain is less; whenΦ=π/4andΦ=π/2, larger LWI gain can be obtained. We also studied the relationships between the LWI gain at a specific distance and the Rabi frequency of the driving field at the entrance of the medium, Doppler broadening width when the relative phase takes different values.In Chapter 4, we studied the effects of the relative phase,Φ, between the probe and driving fields on the transient evolution rule of the atomic response in an openΛ-type inversionless lasing system with spontaneously generated coherence by numerical results. We found that: when the incoherent pumping is absent, electromagnetically induced transparency (EIT) can occur. Specially, varying the atomic exit rate and ratio of the atomic injection rates can remarkably modulate the transient evolution rule of the phase–dependent gain. It is also shown that under the same conditions, the values of the LWI gain with incoherent pumping are evidently larger than those without incoherent pumping exceptΦ=0(π) and the time reaching the steady state is shorter; varying the initial condition doesn't change the stationary value of the LWI gain but can remarkably affect the transient evolution process of the LWI gain.
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