1、Lecture 12,Chapter VIII Second-Harmonic Generation and Parametric Oscillation,Highlights,1. Nonlinear Optics,3. Parametric Oscillation,2. Second-Harmonic Generation,Nonlinear polarization,4. Frequency Up-Conversion,Wave propagation in nonlinear media,参考书：光电子学基础，李家泽，阎吉祥著，北京理工大学出版社,Phase-Matching,SHG
2、inside Resonator,8.0 Introduction to Nonlinear Optics,非线性光学是专门研究强相干光与物质相互作用机理、现象和应用的光学分支。,光的电磁理论认为，光和物质相互作用的微观机理是光波电场引起介质极化，从而使介质中的原子（分子、离子）成为电偶极子，由于光波电场是时间的周期函数，所以各个偶极子将随时间作周期振动，这种受迫振动的频率与光波场的频率相同。并且这些振动的偶极子是一种场源，也要辐射电磁波，这就是通常所说的次波发射。,线性光学：,非线性光学：,线性极化,非线性极化,8.0 Introduction to Nonlinear Optics,以二阶
3、极化为例：,单色平面电磁波：,极化波作为一个场源，不仅有基频光分量，还有直流分量和倍频分量。如果有多波作用，还会出现和频分量和差频分量。,需要指出的是，实际中一般并不容易同时观察到基频、倍频等光波，究竟哪一种频率的光波占主导作用，还要受到具体实验条件的限制。,1961年Franken的倍频实验标志着非线性光学的诞生。该领域的权威著作有 N. Bloembergen 的 “Nonlinear Optics”和 Y.R. Shen 的 “The Principles of Nonlinear Optics”。,8.1 On The Physical Origin of Nonlinear Pola
4、rization,(1) 线性振子模型和线性极化率,(2) 非线性振子模型,8.1 On The Physical Origin of Nonlinear Polarization,A. In a Symmetric Crystal,B. In a Asymmetric Crystal,Just consider the first two terms of restoring force, at D0, a positive displacement (x0) results in a larger force, than that of opposite direction.,Indica
5、te at the same E, electron moves shorter length in positive direction,The above result means, at the same E, positive direction has smaller P,No second order polarization exists,8.1 On The Physical Origin of Nonlinear Polarization,Fourier Analysis,8.1 On The Physical Origin of Nonlinear Polarization
6、,单色平面电磁波：,Assume the solution for x in the form,与线性振子模型一致,First order:,8.1 On The Physical Origin of Nonlinear Polarization,Second order:,or,C. Nonlinear Optical Coefficients and Symmetry of Crystals,8.1 On The Physical Origin of Nonlinear Polarization,Centro-symmetric crystals:,No SHG occurs,Noncen
7、tro-symmetric crystals:,Depends on crystals conditions,8.2 Formalism of Wave Propagation in Nonlinear Media,耦合波方程 (coupling wave functions),Consider three plane wave propagating along z direction with frequency,8.2 Formalism of Wave Propagation in Nonlinear Media,Nonlinear polarization contains:,or,
8、These oscillate at the new frequencies, will not be able to drive the oscillation at , , or , unless,Thus, we will have a power flow from the field and into that at,8.2 Formalism of Wave Propagation in Nonlinear Media,Assume:,振幅慢变化近似,耦合波方程,8.3 Optical Second-Harmonic Generation,Franken的倍频实验：,No depl
9、eted input,Output intensity is proportional to:,(1) Conversion Efficiency,8.3 Optical Second-Harmonic Generation,Conversion efficiency of SHG,(2) Phase-Matching in SHG,To increase the conversion efficiency:,Increase the fundamental frequency optical intensityb. Phase-matching factor gets maximum,or,
10、Coherence length,8.3 Optical Second-Harmonic Generation,Calculate the coherence length,Coherence length is the maximum crystal length that is useful in producing the second-harmonic power,How to achieve phase-matching requirement,In isotropic media impossible,Birefringence effect, different wave typ
11、es,In anisotropic media same wave type also impossible,8.3 Optical Second-Harmonic Generation,Index ellipsoid,Normal Surface,Positive uniaxial crystal,Negative uniaxial crystal,8.3 Optical Second-Harmonic Generation,In a negative uniaxial crystal,8.3 Optical Second-Harmonic Generation,Numerical Exam
12、ple: Second-Harmonic Generation,KDP crystal:,Calculate:,Plot the index surface for illustration,(3) Experimental Verification of Phase-Matching,8.3 Optical Second-Harmonic Generation,No phase-matching:,Fig. 8-9 to see experimental results,(4) SHG with Focused Gaussian Beams,8.3 Optical Second-Harmonic Generation,For,8.3 Optical Second-Harmonic Generation,For,Example,(5) SHG with a Depleted Input,8.3 Optical Second-Harmonic Generation,8.3 Optical Second-Harmonic Generation,Manley-Rowe Relations,Assume,
