綠色雜訊的行為可用一組聯立的微分方程加以描述，從中我們可知雜訊產生的原因來自於共振腔內不同模態之間的耦合，所以對單模操作而言不會有雜訊的出現，且在進入穩態時會有一短暫的鬆弛振盪現象，至於多模操作下的雜訊行為則可以分為Q-Switching脈衝和CW加以分析；在文中我們計算共振腔的瓊斯矩陣，以及所對應的特徵向量，藉此得知光子進入倍頻晶體前的兩個電場偏振方向，在後續的推導中可發現，對Type II相位匹配而言，光子耦合的效率會因極化方向不同而有g和(1-g)的差別，對Type I相位匹配而言，耦合效率會因極化方向的不同而有 、 以及 的差別，為了將這些差異性考慮在內，我們可將Rate Equation推廣，並發現在某些條件下可以消除模態間的耦合而使雜訊消除，所以我們對g的行為作了一系列的探討，以期能找出適合的腔體結構，使雜訊降低。
除了從腔體結構上著手消除雜訊外，我們也嘗試著從增益調變的方式著手，在數學模擬上我們從β著手，並發現當β為時變時，雜訊確實有所改善且調變頻率愈快雜訊愈小，所以我們認為有機會以干擾增益競爭的方式，來達到削減雜訊目的。

The Green Noise can be described by a set of coupled ODEs, and we come to realize that the noise comes from the coupling between different modes inside the cavity. After obtaining the polarization of the photons by calculating the eigenvector of Jones matrix of the cavity, we discovered that the coupling coefficient between modes could be g or (1-g). Previous papers had proposed different structures to reduce the noise by controlling the g factor. Here, by varying the saturation parameter β with time, we discovered that it is possible to reduce the noise mathematically. Therefore we believe it is possible to eliminate the noise by disturbing the gain competition.

1. W. P. Risk , T. R. Gosnell , A. V. Nurmikko , “Compact blue-green lasers”, chapter 1 , Cambridge University press 2003
2. Bahaa E. A. Saleh , Malvin Carl Teich , “Fundamentals of photonics” , John Wiley & Sons , Ch6 (1991)
3. Pochi Yeh , Claire Gu , “Optics of Liquid Crystal Displays” , John Wiley & Sons , Ch3 (1999)
4. Robert W. Boyd “Nonlinear Optics” , Academic Press , Ch1,Ch2 (1992)
5. Amnon Yariv , Pochi Yeh , “Optical waves in crystals” , John Wiley & Sons , Ch3,Ch4,Ch12 (2003)
6. V.D Dmitriev , G.G. Gurzadyan , D.N. Nikogosuan , “Handbook of Nonlinear Optical Crystals” , Spinger (1999)
7. K. Asaumi “Approximate effective nonlinear coefficient of second-harmonic generation in KTiOPO4” , Applied optics Vol.32 No.30 page 5983 (1993)
8. T. Baer ,”Large-amplitude fluctuation due to longitudinal mode coupling in diode-pumped intracavity-doubled Nd:YAG lasers”, J. Opt. Soc. Am. B3,1175~1180(1986)
9. M. Oka and S. Kubota ,”Stable intracavity doubling of orthogonal linearly polarized modes in diode-pumped Nd:YAG lasers”, Opt. Lett. 13 ,805~807 (1988)
10. G.E. James, E.M. Harrell II,”Intermittency and chaos in intracavity doubled lasers” , R. Roy, Phys. Rev. A41,2778~2790 (1990)
11. G.E. James, E.M. Harrell II, C. bracikowski, K. Wiesenfeld ,R. Roy,”Elimination of chaos in an intracavity-doubled Nd:YAG lasers”, Opt. Lett. 15 1141~1143(1990)
12. R. Roy , C. bracikowski , G.E. James ,”Dynamics of multimode laser with nonlinear birefringent intracavity elements”, in Recent Developments in Quantum Optics , edited by R. Inguva (Plenum Press , New York ) page 309 (1993)
13. Volker Gaebler , Baining Liu , Hans J. Eichler , Zhiguo Zhang , Panming Fu , F Peuker , “Stable diode-pumped microlaser with two crossed intracavity frequency doublers” , Digest of Conference on Lasers and Electro-Optics (Optical Society of America , Washington , D.C.) , CFD3 (1999)
14. Volker Gaebler , Baining Liu , Han Joachim Eichler , Zhiguo Zhang , Dezhong Shen , “Efficient blue cw Nd:YAG microchip laser with two intracavity frequency doublers” , Opt. Lett. 25 1343-1345 (2000)
15. Dehua Li , Changhong Zhu , Volker Gaebler , Baining Liu , Han Joachim Eichler , Zhiguo Zhang , Ying Wang , Zhenjia Li , Junlin Qiu , “ Theoretical and experimental studies of noise suppression for intracavity frequency doublers lasers with phase matching type I or II ” , Opt. Commun. 189 357-364 (2001)