以有限差分時域法分析非線性光子晶體

Abstract

在這篇論文，我們使用了有限差分時域法討論了非線性光子晶體共振腔的穿透率變化。光子晶體的特性與折射率有關，改變光子晶體共振腔的折射率將改變共振頻率。另一方面，在非線性效應中，電場強度可以改變物質的介電係數，所以只要從光子晶體外面輸入不同功率的電磁波，就可以改變光子晶體的共振腔頻率。由於光子晶體共振腔能夠蓄積電磁能，將使所需要入射功率大大減少。在波導和共振腔直接耦合方面，入射頻率越接近共振頻率，穿透率越大。 入射一個電磁波，其頻率低於非線性效應不顯著時候的共振頻率，之後改變入射功率使共振頻率下降，結果顯示二維或三維平板結構輸出功率都具有雙穩態。在共振腔置於波導旁的結構中，在接近共振頻率時，穿透幾乎是零。經由同樣的方法模擬二維結構，也有雙穩態，並且有極高的輸出對比。更近一步的，利用不同功率的控制光，改變共振腔的特性，控制使特定頻率的信號光穿透與否，達到了由光控制光的效果，實現光開關器的作用。

In the thesis, we study the power transmission in the nonlinear photonic crystal cavities with the finite-difference time-domain method.The refractive index of photonic crystal cavities changes with the field intensity, which results in the change of resonant frequency.Therefore, we can launch different input power to control the resonant frequency.Because the field intensity can be very high in the photonic crystal cavities, the incident power level can be lowered dramatically. In the direct-coupled resonator geometry, the transmission increases as the frequency gets closer to the resonant frequency.With the input frequency lower than the resonant one in a linear limit and the input power varied, the result exhibits optical bistability of the transmission in two-dimensional structures and three-dimensional slab structures.In the side-coupled resonator geometry, the input wave is completely reflected at the resonant frequency.Using the similar procedure, the result exhibits optical bistability and high contrast in the power transmission in two-dimensional structures.Furthermore, using a control input changes the resonant frequency of the signal input,then the transmission of the signal input can be controlled by the control input.This provides an all-optical switch.