: For distance well beyond the Rayleigh range ftheradius then increases again as R(z)~z, i.e., thegaussian beam becomes essentially like aspherical wave centered at the beam waist. Whatthis means in physical terms is that the center ofcurvature of the wavefront starts out at -oo for awavefront right at the beam waist, and thenmoves monotonically inward toward the waist, asthe wavefront itself moves outward toward z-> oo
• For distance well beyond the Rayleigh range f the radius then increases again as R(z)z, i.e., the gaussian beam becomes essentially like a spherical wave centered at the beam waist. What this means in physical terms is that the center of curvature of the wavefront starts out at – for a wavefront right at the beam waist, and then moves monotonically inward toward the waist, as the wavefront itself moves outward toward z→
·高斯光束在其传输轴线附近可近似看作是一种非均匀球面波，其曲率中心随着传输过程而不断改变，但其振幅和强度在横截面内始终保持高斯分布特性，且其等相位面始终保持为球面
• 高斯光束在其传输轴线附近可近似看 作是一种非均匀球面波，其曲率中心 随着传输过程而不断改变，但其振幅 和强度在横截面内始终保持高斯分布 特性，且其等相位面始终保持为球面
三、基模高斯光束的特征参数用参数の。（或f）及束腰位置表征高斯光束用参数(z)和R(z)表征高斯光束如果知道了某给定位置处的α(z)和R(z)，可决定高斯光束腰斑的大小の.和位置2高斯光束的q参数
用参数0（或f）及束腰位置表征高斯光束 用参数(z)和R(z)表征高斯光束 如果知道了某给定位置处的(z)和R(z)，可决 定高斯光束腰斑的大小0和位置z 高斯光束的q参数 三、基模高斯光束的特征参数
CVoo(x, y,z)Lkzarctg2 R(2)(z)0重新整理2Cexp[-i(kz -arctg Voo(x,y,zR(2)2w(z)元引入一个新的参数q()定义为π0(2)R(z)q(z)
) ]} 2 ( ) ]exp{ [ ( ( ) exp[ ( ) ( , , ) 2 2 2 0 0 f z arctg R z r i k z z r z c x y z = − − + − ]}exp[ ( )] ( ) ( ) 1 [ 2 exp{ ( ) ( , , ) 2 2 0 0 f z i k z arctg z i R z r ik z c x y z = − − − − ( ) ( ) 1 ( ) 1 2 z i q z R z = − 引入一个新的参数q(z)， 定义为 重新整理
·参数q将(z)和R(z)统一在一个表达式中，知道了高斯光束在某位置处的q参数值，可由下式求出该位置处α(z)和R(z)的数值ReR(2)gz1元元Im(z)2元0(0)R(O)q(0)q(zqo元0用o=(O)表示z=0处ifqo的参数值，得出qo is purelyimaginary
• 参数q将(z)和R(z)统一在一个表达式中，知 道了高斯光束在某位置处的q参数值，可由下 式求出该位置处(z)和R(z)的数值 ] ( ) 1 Im[ ( ) 1 ] ( ) 1 Re[ ( ) 1 2 z q z R z q z = − = q i if i q q R = = = = − 2 0 0 2 0 (0) (0) 1 (0) 1 1 用q0=q(0)表示z=0处 的参数值，得出 q0 is purely imaginary