Iron Doped Lithium Niobate Crystals In Modulation Instability

Modulation instability （MI） is a fundamental phenomenon that exists in manynonlinear wave systems in nature. The phenomena of MI has been identified andstudied in various physical systems, such as fluids, plasmas, molecular chains，nonlinear optics and so on，so now it is one of the important content of the study ofnonlinear physics. Modulation instability means that due to the combined effects ofdiffraction or dispersion and nonlinearity, Small perturbations in the amplitude or thephase of optical waves grow exponentially and can make a broad optical beam or aquasi-continuous wave（quasi-cw）pulse that propagate in the nonlinear media breaksup into filaments. These broken filaments are actually soliton column, so MI is oftenseen as a prelude to the formation of bright solitons. Soliton is one of effectivemethods that can achieve a beam to manipulate another beam or beam self-control,but the modulation instability often appears in the process of the formation of soliton.We can effectively avoid the MI if we find out the conditions that lead to the MI andthe factors that impact MI, and then we can achieve the beam self-control. Therefore,the study of MI is a very important and a far-meaning subject in the nonlinear optics.On this basis, we mainly study the modulation instability in the self-defocusingphotorefractive media LiNbO₃:Fecrystal in our paper. We find out the conditionsthat lead to the MI and the factors that impact MI in LiNbO₃:Fecrystal, the maincontent of our paper can be summarized as follows:1. We make a brief introduction to theoretical knowledge of the physical mechanismand the main features of photorefractive effect and the photorefractive effect ofLiNbO₃:Fecrystal, and we make a brief review of time solitons and spatial solitons,photorefractive spatial solitons and the research course of solitons. We introduce theconcept, classification and the research course of the MI briefly.2.We report on the experimental observation of the modulation instability inself-defocusing photorefractive LiNbO₃:Fecrystal. Experimental results show that the MI is related to the illumination time; and it is also related to the angle thatbetween the direction of c-axis and the direction of the threadlike beam that illuminatethe crystal, we find this condition is different to needed condition about the anglebetween the c-axis and the direction of the filament of the white-light MI appear. Andthe modulation instability pattern is also related to the shape of the incident light. Inaddition, we experimentally observe the O-light MI in LiNbO₃:Fecrystal withother conditions unchanged.3. We mainly compare the MI in LiNbO₃:Fecrystal by using the spatial filter anda pair of lens, we find the needed conditions for the appearance of the MI is same inthis both cases but the using of this pair of lens do accelerate the appearance of the MI.In addition, we also find when we use this pair of lens, the number of the interferencefringes generated by the interference of the front and rear surfaces of the lensincreases if the MI does not appear and the interference fringes become broken. Thisis the first time for the observation of the MI and the increasing of the interferencefringes in the same experimental setup.4. We observe the MI and frequency-doubling of interference fringes spatialfrequency in LiNbO₃:Fecrystal by the same experimental setup，and we find outthe needed conditions that they appear. We find that frequency-doubling appears if thenonlinearity of the c-axis can not offset the needed threshold that expand the noise,otherwise the modulation instability appears. They restrict each other and they can notappear at the same time.5. We observe the modulation instability that induced by both intrinsic noise and theamplitude mask with periodic photonic lattices in LiNbO₃:Fecrystal and comparetheir differences. The participating of amplitude mask speeds up the appearance of themodulation instability. We observe the modulation instability in two situations whenthe amplitude mask with periodic photonic lattices is used and with other conditionsunchanged. One is when the principle axis of the photonic lattices is parallel to the caxis of the crystal and another is when the principle axis of the photonic lattices is tilted 45°relative to the direction of c axis. And we find that the photonic lattices havea strong suppression to the further appearance of the MI when the principle axis of thephotonic lattices is tilted 45°relative to the direction of c axis.