Theoretical investigation on intrinsic linewidth of quantum cascade lasers

• Main Author: Liu, Tao
• Other Authors: Wang Qijie
• Format: Theses and Dissertations
• Language: English
• Published: 2014
• Subjects: DRNTU::Science::Physics::Optics and light
• Online Access: https://hdl.handle.net/10356/59550
• Institution: Nanyang Technological University

Quantum cascade lasers (QCLs) are unipolar laser sources relying on intersubband transitions in coupled multiple quantum well systems. The light emission can be tuned across the mid-infrared (mid-IR, from 3 to 20 micrometer) and Terahertz (THz, from 1.2 to 5 THz, or 60 to 250 micrometer) ranges of the electromagnetic spectrum. Since their invention in 1994 for mid-IR QCLs and in 2002 for THz QCLs, respectively, these lasers have undergone tremendous improvement, and have become probably the most prominent coherent light sources in the mid-IR and THz spectral ranges. However, many important applications of mid-IR and THz coherent light sources, e.g. spectroscopy and high-speed free-space data communication, are greatly influenced by intrinsic laser fluctuations and noises. Although intrinsic linewidth and noise in semiconductor diode lasers have been widely investigated, theoretical and experimental studies in noise dynamics and linewidth of QCLs have only attracted interests recently. This field is still in its infancy. Since the operational principle of QCLs is totally different from that of semiconductor diode lasers (resonant tunneling effect and coherent interactions in QCLs are unique owing to the intersubband transitions), models on noise and linewidth investigations of diode lasers cannot be directly applied to QCLs. New physical models must be developed on both noise dynamics and linewidth for QCLs. This thesis discusses many aspects of intrinsic linewidth and noises of QCLs, and it is divided into three main parts. Since optical gain spectrum can greatly influence the intrinsic linewidth of lasers, in the first part, we report the study on optical gain of QCLs. The optical gain of QCLs is investigated based on a developed microscopic density-matrix (DM) model. Intersubband semiconductor-Bloch equations are established by incorporating many-body Coulomb interaction, non-parabolicity and coherence of resonant-tunneling transport effects in a quantitative way. The calculations demonstrate the importance of many-body interaction, non-parabolicity and resonant-tunneling transport on optical gain spectrum of mid-IR and THz QCLs. The results show that the gain peak in frequency calculated by the developed microscopic DM model is closer to the experimentally measured lasing frequency compared with the existing macroscopic DM model. In addition, the dependence of optical gain of THz and mid-IR QCLs on device parameters such as the injection and extraction coupling strengths, energy detuning and doping density are also systematically studied in details. This model provides a comprehensive picture of optical properties of THz and mid-IR QCLs and potentially enables a more accurate and faster prediction of the device performance e.g. the laser linewidth enhancement factor and current characteristics. In the second part of the thesis, we report the intrinsic linewidth of QCLs caused by the spontaneous emission, thermal photon and fundamental thermodynamic fluctuation. The linewidth induced by spontaneous emission and thermal photon is analytically derived on the basis of the quantum mechanical Langevin equation. It differs from the traditional rate equation model for the laser linewidth calculation of diode lasers in that the dynamics of coherent interaction and resonant-tunneling effects are considered. Results show that the coupling strength and the dephasing rate associated with resonant tunneling strongly affect the linewidth of THz QCLs in the incoherent resonant-tunneling transport regime but only induce little influence in the coherent regime. The dynamics of coherent interaction and resonant-tunneling transport show negligible effects on the linewidth calculation of mid-IR QCLs due to strong coupling in resonant tunneling. The fundamental thermodynamic noise and linewidth broadening is investigated based on the Green function analysis and the Van Vliet-Fassett theory. The results show that the fundamental frequency noise caused by intrinsic temperature fluctuations is prominent in the low frequency range (below a few kHz) and is sensitive to the temperature, heat conductivity and the thickness of the active region/substrate. Specifically, for THz QCLs, considering only the refractive index variation caused by the current-induced device self-heating, we calculate the linewidth broadening to be only around 1 Hz, which is comparable to the predicted value of 3 Hz caused by spontaneous emission and thermal photon in high power THz QCLs. For mid-infrared QCLs, this frequency noise leads to a linewidth broadening from 14.74 Hz to 62.02 Hz as the temperature increases from 200 K to 400 K. When the microscopic features of the refractive index variations associated with the intersubband gain transition, the self-heating-induced thermal expansion and energy level broadening in mid-IR QCLs are considered, an estimation shows that the linewidth broadening increases greatly by a factor of more than 4 times. In the final part, microscopic density matrix analysis on the linewidth enhancement factor (LEF) of QCLs is reported by taking into account of the many body Coulomb interactions, coherence of resonant-tunneling transport and non-parabolicity. A non-zero LEF at the gain peak is obtained due to these combined microscopic effects. The results show that, for mid-IR QCLs, both the many body Coulomb interaction and non-parabolicity contribute to the non-zero LEF. In contrast, for THz QCLs, both the many body Coulomb interactions and the resonant-tunneling effects greatly influence the LEF which deviates from the zero value at the gain peak. This microscopic model can not only partially explain the non-zero LEF of QCLs at the gain peak, which existed in the field for a while but cannot be explicitly explained, but also be employed to improve the active region designs so as to reduce the LEF by optimizing the corresponding parameters.