1、,补充材料,1、复杂系统光线追踪请用ABCD光线传输矩阵，高斯光束的传播请用ABCD定律。,2、FP腔的有关概念：,补充材料,Lecture 6,Chapter IV Interaction of Radiation and Atomic Systems,Highlights,1. Blackbody Radiation and Einstein Coefficients,2. Homogeneous and Inhomogeneous Broadening,3. The Properties and Significance of ,4. Rate Equations,5. Gain Sat
2、uration,The Theories of Interaction of Radiation and Atoms,I、经典理论,原子系统和电磁场都作经典处理，麦克斯韦方程组描述电磁场，原子为经典振子,成功解释吸收和色散，定性说明自发辐射及其谱线宽度,II、半经典理论（兰姆理论）,麦克斯韦方程组描述电磁场，原子则用量子力学描述,成功解释强度特性、增益饱和、多模耦合和竞争、相位锁定、频率牵引等大部分现象,III、量子理论,数学处理比较简单,数学处理比较繁杂,原子系统和电磁场都作量子化处理，并将二者作为一个统一物理体系加以描述,只有在需要严格确定相干性和噪声等特性时才是必要的,理论深奥,IV、速
3、率方程理论,量子理论的简化形式,只能给出强度特性，定性描述烧孔效应、兰姆凹陷、多模竞争等现象,形式简明,4.0 Blackbody Radiation and Concept of Transitions,What is blackbody?,完全吸收任何波长的电磁辐射的物质,What is blackbody radiation?,黑体除了吸收电磁辐射外，还会发出电磁辐射（热辐射）。当吸收的辐射能量等于发出的辐射能量，黑体处于某一温度T的热平衡。这种平衡必然使空腔内存在完全确定的辐射场。这种辐射场称为黑体辐射或平衡辐射。,Spectral Energy Density (Plancks Fo
4、rmula)：,Average energy per mode:,Mode number per volume:,Plancks Formula,1）Spontaneous Emission（自发辐射）,4.0 Blackbody Radiation and Concept of Transitions,Three interactions exist between radiation field and atomic system,tsp: Average lifetime in upper level,Einstein SP coefficients:,Atom Transition u
5、nder Radiation Filed,2）Stimulated Absorption（受激吸收）,Einstein SA coefficients:,4.0 Blackbody Radiation and Concept of Transitions,3）Stimulated Radiation（受激辐射）,Einstein SR coefficients:,4.1 The Relation Between Einstein Coefficients,1）存在热平衡黑体辐射,2）原子数按能级分布服从玻尔兹曼分布,f1 , f2: 统计权重,3）在热平衡下，n1 (或 n2) 应保持不变,W
6、hen T infinite, above equation should still be valid:,and,4.1 The Relation Between Einstein Coefficients,When f1 = f2,and,4.2 Lineshape Function - Broadening,Radiation from level 2 to 1 is not strictly monochromatic, but occupies a finite frequency bandwidth. The function describing the distribution
7、 of emitted intensity versus the frequency is referred as the lineshape function g(n).,I. Lineshape Function,II. Homogeneous Broadening,Considering a damped oscillator and decay time is t:,4.2 Lineshape Function - Broadening,(atoms are subjected to indistinguishable interaction),1）自然加宽：,Finite lifet
8、ime on the excited state,4.2 Lineshape Function - Broadening,Lorentzian lineshape,(The response of damped resonant system),2）碰撞加宽：,Collisions causes wave phase change abruptly,Linewidth:,3）晶格振动加宽：,High T causes energy bandwidth enlarge,4.2 Lineshape Function - Broadening,Pressure and temperature dep
9、endence:,Collision between two species,Collision between one species,Collision between atom and container wall,Inelastic collision causes lifetime of excited state being shorter,4.2 Lineshape Function - Broadening,III. Inhomogeneous Broadening,(atoms are subjected to distinguishable interaction),1）多
10、普勒加宽：,Due to the Doppler shift from the moving atoms,Maxwell velocity distribution function,4.2 Lineshape Function - Broadening,Assume atom only moves along x direction,and,Gaussian lineshape,Linewidth:,2）晶格缺陷加宽：,Impurities and imperfections in solid state matter,4.2 Lineshape Function - Broadening,
11、Exercise: The Doppler Linewidth of Ne,Calculate:,4.3 Absorption and Amplification,Recall:,and,When N2 N1 (population invert): intensity grows exponentially,When N2 N1 : intensity is attenuated,4.3 Absorption and Amplification,When atomic system is at thermal equilibrium:,( f1 = f2 ),Obviously, to ob
12、tain the amplification, we need population invert, which need external excitation.,4.3 Absorption and Amplification,Recall:,(1.2-20),(1.3-36),or,This is a key result and it will be used on numerous occasions,4.3 Absorption and Amplification,Exercise: The Exponential Gain Constant in a Ruby Laser, 300K,Calculate:,
