The Influence Of Refractive Index Modulation On Frequency-doubling Of Ultrashort Pulses

The optical frequency conversion method is used to produce new frequencies of laser sources, which is one of the important means of modern laser technology. For mixed nonlinear crystals, by modulating refractive index(composition ratio), not only non-critical phase matching can be achieved, but also the phase-matching bandwidth can be widened, thereby it loosens requirements of monochromaticity and high power of incident light. Moreover, refractive index modulation can also improve the tuning characteristics of crystals.Firstly, this paper introduces the basis knowledge of nonlinear optical theory, which includes the nonlinear susceptibility, transient and steady-state second harmonic generation (SHG) coupled-wave equations, the influence of composition ratio on refractive index modulation, and introduction of the optical properties of KLN crystal and its advantage of wide-band SHG; and calculates the Selleimer equation of KLN crystal by using the average weight method. In order to clearly understand the influence of refractive index modulation on the process of SHG, we start from the the plane wave model, a set of steady-state coupled-wave equations of frequency doubling in the medium with the linearly modulated refractive index is derived from Maxwell equations. On this basis, a solution by the small signal approximation to the equations and the numerical solution by large-signal to the equations are given. Secondly, we take the KLN crystal with refractive index modulation as a SHG medium for ultrashort pulses. At the same time, a set of coupled-wave equations for ultrashort pulse SHG in the crystals with linearly and periodically (sinusoidally) modulated refractive indices is derived. For the linear modulation, a solution under the small signal approximation to the equations is given. Under the high conversion efficiency, the coupled-wave equations are numerically solved by a procedure. The dissertation includes an analysis of the influence of phase modulation parameter, group velocity mismatch and the wave-length of incident wave on the waveforms of frequency doubled pulses; shows the influence of the chirp of fundamental wave on SHG conversion. In the case of small signal, it is found that harmonic pulses have obviously been compressed and the beam quality have been improved, and the dependence of optimal chirp coefficient (narrowest width) on modulation parameter is given in theory. However, for the high conversion efficiency, the impact of chirp is lowered. Finally, for the sinusoidal modulation, we study the numerical solution under the small signal approximation to the equations, and provide a qualitative analysis of the influence of the period and the initial phase of sinusoidal modulation on SHG conversion. It is found that refractive index sinusoidal modulation can widen the phase-matching bandwidth and construct a multi-peak structure.