面射型雷射光性之模擬

Abstract

本論文將介紹一個有效率的計算垂直共振腔面射型雷射之臨界增益與發光波長的光性計算模型。本模型是基於馬克斯威爾方程式的向量分析，亦導入了人工吸收層的概念，且使用了可避免程式計算上的數值不穩定的散射矩陣演算法。最後模擬結果將著重在氧化物孔徑的大小與結構，造成垂直共振腔面射型雷射之臨界增益與發光波長的影響。 我們發現隨著氧化物孔徑變小，則雷射發光波長有藍移的現象，而臨界增益也會變大。雙氧化物孔徑的垂直共振腔面射型雷射結構會有較單氧化物孔徑結構低的臨界增益，而單氧化物孔徑之垂直共振腔面射型雷射結構的波長偏移較雙氧化物孔徑結構小。當主動層的增益與上層氧化物孔徑相關時，變動上下層孔徑的相對大小對光性不會有明顯影響，但固定上層氧化物孔徑大小時可以穩定臨界增益。一旦藍移的波長偏移DBR所設計的波長過多時，鏡面漏失會急劇增加。需要加一層覆蓋層作為與金屬接觸時，以介質中的四分之一波長為厚度會有最小的臨界增益。

We present an efficient numerical optical model for computing threshold material gain and lasing wavelength in vertical-cavity surface-emitting lasers. It is based on a vectorial solution of Maxwell’s equations with an artificial optical boundary outside the VCSEL structure, and a scattering matrix algorithm to prevent the numerical instability during the computation. Results are given concerning the influence of oxided-aperture radius and the structure of oxide-confined devices on threshold gain and lasing wavelength. We notice that the lasing wavelength blue-shifts and the threshold gain increases as the aperture radius becoming small. The VCSEL with double oxided-aperture has lower threshold gain than the one with single oxided-aperture, and on the contrary, the VCSEL with single oxided-aperture blue-shifts less than the one with double oxided-aperture. As the gain region related to the size of the upper aperture, there is no obvious influence on wavelength shifting with the relative size changing of the upper and lower aperture. Otherwise, fixing the radius of upper aperture will get more stable threshold gain than fixing the radius of lower one. As the blue-shifted wavelength being far away from the one designed for DBR, the mirror loss will affect the threshold gain strongly. And the thickness of the metal contact cap layer would be a quarter wavelength in the dielectric with the lowest threshold gain.