激光原理-谐振腔-1

1、激光原理与技术激光原理与技术(2014年秋季学期)张春峰南京大学物理学院谐振腔，高斯光束2014-9-26Cavity Laser modesParaxial wave equation222210EEct22(x,y,z)(x,y,z)0Ek E/kcz0( , , )ikrEE x y zer22222222( 1 ()/)z2xyrxyzzxyzz 22(xy )/2z0( , , ) ikzikEE x y zeez球面波近轴近似( , , ) (x,y,z)eikzE x y zHelmholtz equation( , , ) (x,y,z)eikzE x y z22(x,y,z)

2、(x,y,z)0Ek E22222222(e)()eikzikzikzikzikzeikek exyzzz22zz2222()0ikxyzSlow varying envelope approximation(SVEA)222222,zxyParaxial approximationFundamental mode2222()0ikxyz22(z)(xy )2 (z)(x,y,z) ekiq (z)Complex phase difference(z)qComplex radius of curvature2222(z)(xy )(1)2k()0(z)(z)kdqdiqdzdzq2222(z)

3、(xy )(1)2k()0(z)(z)kdqdiqdzdzq0(z)()(z)0(z)qLnqiqeeq 22(z)(xy )2 (z)(x,y,z) ekiq 22 (z)0( , , ) (x,y,z)e(z)ikrikzikzqqE x y zeq222rxyimaginary222122222()tan(z/z )2(zz )2(zz )22( , , ) (x,y,z)e1e(1+z / z )RRRRRikrikzz izikzRRkz rkzriiikzRizE x y zezizeee20( )1 (z/ z )Rz22222( )2(zz )/ kz(1 (z/ z ) )R

4、RRRzzk002/ k/RRzzn22( )z(1)RzR zzRayleigh length222(z)/(z)/(z)1( , , ) (z)ikziikrRrE x y zeeeePropagation factorGuoy phase shift Spherical wave factor“Gaussian” factor222/(z)21(x,y,z) (z)rIe22( )z(1)RzR zzHigh-order modes22(z)(xy )2 (z)(x,y,z) ekiq 22(z)(xy )2 (z)(x,y,z) g() ()ekiqxyhww 22(z)(xy )2

5、(z)(x,y,z) ()h()ekiqrgw Rectangular Cartesian coordinates systemCircular resonator symmetryHermite-Gaussian modesLaguerre-Gaussian modesFundamental modeABCD matrix(r, )ABCD matrixFree space propagationThin lensABCD matrix均匀介质ABCD matrix曲率半径ABCD law for Gaussian beamHomework121AqBqCqDFocusThin lens w

6、ith focal length f121AqBqCqD2211RffzCavityABCD121AqBqCqDAqBqCqD2(D A)q B0Cq 2/(A)/q C0B qD2(D A)(A D)412BCqB211(z)(z)(z)iqR2(A D)40BC1ADBC2(A D)41(A D)/ 21 Stable cavity2/(A)/q C0B qD2(D A)(A D)412BCqB211(z)(z)(z)iqR2DARB2212(A D)4BBCResonant frequency222(z)/(z)/(z)1( , , ) (z)ikziikrRrE x y zeeee(z)kz(z)2121(z)k()( (z )(z )nzz211(arctan()arctan()2nRRzzcndzz121arccos()2ncng gdResonator cavityLongit