I arrived at KAUST on Jan 16th and have been here for more than one month. During this month, it’s the peaceful environment in KAUST that touches my heart. The Red Sea is near our academic buildings. The fresh air, blue sky, warm sunshine, and the sound of water flow make up the campus. The culture here is very different with the culture in my country, China. But it is an interesting thing to experience a different life. I like to go swimming and play bowling after work. I am trying to study swimming now with my friends’ help. I am also not good at bowling, but after practicing many times, I do better now.
As for the study life, I have attended some conferences, workshops, and seminars. And I gave a presentation about self-introduction and my previous work at JCM on Feb. 20th. Because electrical engineering is a brand new field for me, I have many things to learn. In this month, I learned basic physics knowledge of the quantum well laser, from Fermi's Golden Rule to the theoretical formula for the gain spectrum of the quantum well laser. Fermi’s Golden Rule gives the formula to calculate the transition rate from state m to state n. We can use time-dependent perturbation theory to get the Fermi’s Golden Rule. With Fermi’s Golden Rule, we can calculate the absorption spectrum and the gain spectrum in the general situation by summing all of the possible states. Quantum well laser is a kind of laser whose active layer is quantum well structure. Quantum well structure’s energy band in real space is step-like and its density of the state is also step-like. We can get the mathematical expressions of energy bands by applying Kane’s model and there are conduction band, heavy hole band, light hole band and spin-orbit split-off band in Kane’s model. Considering the Fermi-Dirac distribution of electrons and quasi-Fermi level in the quantum well structure, we can write down its gain spectrum, which is one of the most significant parameters.
I also learned about FDTD simulations, a useful method to simulate the mode file and optical confinement of a laser. FDTD is the abbreviation of “Finite-Difference Time-Domain”. The general idea of the FDTD method is to rewrite the differential equation into the sum of finite terms by using the thought of linear interpolation. Then we can rewrite Maxwell’s equation and each E(electrical field) and H(magnetic field) in each time can be expressed by the sum of finite terms we have known. There is a software doing FDTD simulations. So we can use this software to simulate our model easily. Figure One is an example of FDTD simulation. I simulated a simple three-layer structure: AlN substrate on the bottom – AlN graded down layer (from 100% to 80%) – active layer (72%) – AlN graded up layer (from 80% to 100%). In the future, I will spend much time doing FDTD simulations and will use FDTD method to simulate deep UV LED, nanowire laser emitting green light and red light, and finally to simulate deep UV nanowire laser.
Fig.1: An example of FDTD simulation, a three-layer structure. Left figure is electrical field distribution in y-z plane. Right figure is refractive index and electrical field in y direction.