亂數在現今被廣泛應用於資訊安全、人工智慧和不同領域的蒙地卡羅模擬中。其中，亂數可依照不同產生方式，分為偽隨機亂數和物理隨機亂數；不同於偽隨機亂數利用公式計算，物理隨機數利用物理源本身的不可預測特性，如量子力學或非線性機制進行亂數產生。此亂數產生的優點可使亂數本身不具潛在週期性，大幅減少應用上可能的缺點。
本研究選用雷射互注入系統作為亂數產生的熵源。亂數產生速率和系統的頻寬有關，選用此系統的優勢為可產生較寬頻的混沌訊號。並且，由於同時使用兩雷射，因此在亂數產生中，具有雙通道輸出特性，進一步增加亂數產生的速率。但是在具有回饋機制的系統中，混沌動態受到時間延遲特徵(time-delay signature) TDS影響，導致混沌動態具有較高週期顯現性存在。
為了探討TDS對於亂數產生速率的影響。本研究首先討論系統操作在強度對稱注入下，探討不同區域對亂數產生的影響。透過固定失諧頻率在-20、-40、-60、-80和-100 GHz，將耦合強度逐漸增加，觀察對亂數產生的變化。得出當失諧頻率固定於-20、-40和-60 GHz時，系統的熵會因為混沌訊號週期成分增加而下降；而操作在-80和-100 GHz時，系統的熵不隨耦合強度增加而有明顯的下降趨勢，僅有數值上浮動的變化。
同時，本研究也探討互注入系統，在不同延遲時間下對於混沌動態的變化。利用平坦度地圖得知，選取同一操作點下，延遲時間的增加可使該操作點的平坦度略為上升，但不改變亂數產生速率。接著，本研究也針對幾個操作點進行強度非對稱注入，其結果為強度非對稱注入對於亂數產生速率的提升有限。
最後，透過不同條件及參數的模擬下，得出雷射在長延遲互注入系統下，亂數產生速率最高可達1.288 Tbit/s，適合作為超高速亂數產生的應用。

Random numbers are widely used in applications such as information security, artificial intelligence, and Monte Carlo simulations. One approach to generate random numbers is to take advantage of chaos excited in two mutually injected semiconductor lasers. The time series generated by the laser system, however, exhibits a periodic signature, known as time-delay signature (TDS), that results from the inherent nature of a delayed feedback system. It is the purpose of this study to understand how such a periodic signature affects the randomness of numbers generated by the laser system. Because the TDS increases with the coupling strength, this study investigates how entropy changes as the coupling strength increases. The results show that, when the detuning frequency is fixed at −20, −40, and −60 GHz, the entropy decreases with increasing coupling strength because the chaotic time series exhibits more regular patterns. In contrast, when the detuning frequency is fixed at −80 and −100 GHz, the entropy remains nearly unchanged as the coupling strength increases. Finally, the entropy rate and random bit generation rate of this system can reach up to 1.503 Tb/s and 1.288 Tb/s, respectively.

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