Use of Aperiodic Lattices for Integrated Terahertz Quantum Photonics

Abstract

Terahertz (THz) quantum cascade lasers (QCLs) fabricated based on compound semiconductors are compact light sources with high output power, which enable the rapid development of THz technologies. Electrically controlled spectral and spatial emission properties of QCLs are desired for practical applications, but there remain some challenges. The aperiodic lattice (AL), which possesses the user-defined spectral response by defining Fourier resonances in $k$-space, provides one solution to these problems. This thesis investigates the theory and experimental measurements of the properties from a set of previously designed AL QCLs. The theoretical frameworks based on transfer matrix techniques are developed to study the spectral properties of these AL lasers for understanding the controlling mechanism of the integrated AL on laser frequencies. The author starts by studying the emission frequencies of a Y-coupled AL laser. This is achieved by developing a modified transfer matrix method (TMM), which allows the calculation of laser modes for the Y-laser. Results reveal that the lattice still has a remarkable frequency control on the Y-coupled laser despite the influence of optical coupling and Fabry-Perot (FP) facet feedback. In addition, frequency fine-tuning of the AL lasers is analysed by a TMM based numerical model. In this model, the gain dispersion of the QCL is simulated using the Kramers-Kronig (KK) relations. For the AL lasers, frequency tuning behaviour is mode-specific; different modes experience different tuning directions and ranges. Simulations show that the gain dispersion, the lattice dispersion, and FP facet feedback play roles in controlling the fine-tuning behaviour. Furthermore, the author studies nonlinear optical processes (i.e., sum- and difference-frequency generation) in the AL lasers for up-converting THz waves to optical side-bands by developing a nonlinear TMM. Simulations indicate that the spectral response of the AL can control nonlinear optical processes, supporting previously measured experimental results of electrically controlled Terahertz-over-Fibre (ToF) transmission. Most significantly, we show that the directionality of far-field beams can also be defined precisely by the AL - this has been demonstrated experimentally. Because of the multi-band spectral response of the lattice, multiple reciprocal lattice vectors interact with the controllable THz single modes in the AL lasers, producing a set of diffracted far-field beams with precisely defined angles. Based on the modified Bragg condition, diffraction angles of beams are determined by $k$-space detuning between the reciprocal lattice vectors and the THz light wavevectors. The experimental results show that robust directional far-field beams are achieved from the AL lasers with a lattice of strong scattering sites. Finally, the strength of the aperiodic lattice technique is also applied for demonstrating strong coupling in microcavities using a novel theoretical framework for the first time. The numerical model is developed based on the transfer matrix technique for investigating strong coupling of cavity resonances with the exciton implemented in aperiodic lattice microcavities for the on-demand formation of polariton. Specifically, for a pre-defined aperiodic lattice microcavity with four cavity resonances, although only one exciton is embedded in the cavity, strong coupling of cavity resonances with the exciton generates seven polariton states. Overall, the work in this thesis constitutes a step towards developing THz photonic integrated circuits using QCLs.

Date of Award	1 Aug 2022
Original language	English
Awarding Institution	The University of Manchester
Supervisor	Subhasish Chakraborty (Supervisor) & Tim Echtermeyer (Supervisor)