§8.4 SHG Inside the Laser Resonator To improve SHG conversion efficiency, high intensity of fundamental frequency laser is need. However, this situation is changed when SHG inside the laser resonator. When R approaches 1, the SHG conversion efficiency will be very large. We may expect 100% conversion efficiency. Optimum power coupling

§8.4 SHG Inside the Laser Resonator Total loss per pass of fundamental beam Pe is the total power emitted from stimulated emission The same as the power expression of fundamental frequency as before and

§8.4 SHG Inside the Laser Resonator Nonlinear coupling constant Independent of the g0 Numerical Example: Internal SHG

§8.5 Photon Model of SHG Output flux at Nonlinear Crystal Input flux at Output flux at +

§8.6 Parametric Amplification 当频率为 的较强光束（泵浦光）与频率为 的较弱光束（信号光）在二阶非线性介质中相互作用时，泵浦光能量会转移给信号光，并产生频率为 的光波（闲置光）。这一过程称为光学参量放大。 where if Degenerate parametric amplification Consider a classical nondriven oscillator: Solution: Consider another oscillator which energy storage parameter is modulated at a frequency

§8.6 Parametric Amplification Suppose a solution:

§8.6 Parametric Amplification Steady-state oscillation conditions: , In such way, the circuit will break into spontaneous oscillation at frequency Threshold condition

§8.6 Parametric Amplification Capacitance variation at frequency Capacitance change by pulling and pushing the parallel plate separation Charge has an eigen oscillation frequency Voltage increases twice in each eigen Oscillation cycle Same phase: energy fed into system Invert phase: system loss energy

§8.6 Parametric Amplification 耦合波方程

§8.6 Parametric Amplification At the conditions: Initial conditions: Solutions:

§8.6 Parametric Amplification : Signal light : Idler light For Numerical Example

§8.7 Phase-Matching in Parametric Amplification Phase-matching condition: In the general cases: Suppose the solutions like:

§8.7 Phase-Matching in Parametric Amplification Exponential coefficient is a function of The signal and idler are no longer sustained growth, but oscillate as functions of distance z Phase-Matching realization:

§8.8 Parametric Oscillation Optic axis of crystal Laser medium Nonlinear crystal Motivation: convert pump laser power to signal and idler light, with their frequencies can be tuned continuously over larger ranges. Steady-state

§8.8 Parametric Oscillation Threshold condition for parametric oscillation Threshold condition as a function of quality factor Threshold condition as a function of mirror reflectivity

§8.9 Frequency Tuning in Parametric Oscillation Phase-Matching condition: Frequency Crystal orientation (E beam) Indices of refraction: Electric field (EO crystals) Temperature Causes frequency change Assume at: we have After crystal orientation changes from

§8.9 Frequency Tuning in Parametric Oscillation Neglect second-order terms Extraordinary pump beam Ordinary signal and idler beams

§8.9 Frequency Tuning in Parametric Oscillation

§8.10 Power Output and Pump Saturation in Optical Parametric Oscillators Laser Oscillation: at steady state, the gain could not exceed the threshold value regardless of the intensity of the pump Parametric Oscillation: very similar to laser oscillation, the gain is “clamped” at its threshold value even if the pump field is increased beyond its threshold. Pump Saturation Experimental confirmation

§8.11 Frequency Up-Conversion Parametric interactions can be used to convert a signal from a “low” frequency to a “high” frequency by mixing it with a strong laser beam at , where + + Nonlinear Crystal Filter

§8.11 Frequency Up-Conversion Neglect depletion of pump wave A2 Solutions:

§8.11 Frequency Up-Conversion In case of small conversion efficiency: