Theoretical Modeling Of Refractive Index Change In Ion Implanted Nonlinera Otptical Crystal Waveguides

Integrated optics is a hot topic of the modern information technology. The optical waveguide is the foundation and core of the integrated optical system. At present, there are several conventional techniques for fabricating optical waveguides, including metal diffusion, ion exchange, epitaxial grouth and ion implantation. Among them, ion implantation is an available method to fabricate optical waveguide. The structure of waveguide can be modulated by varying implantation parameters due to accurate control of both the depth of barrier beneath the surface and the refractive indices of the materials. Implantation shows advantages in waveguide fabrication also because the crystal properties in waveguide can be retained. Different from the waveguides formed by other methods, refractive index profile in implant-waveguide is more complicated and shows intimate dependence on the implantation parameters, such as ion species, energy, dose of implanted ions and the crystallographic orientation of crystal. At present, experiment is the main method to determine the refractive index profile in implant-waveguide. This makes the ion implantation as a method of fabricating waveguides, be random and uncertain, thus seriously limits its application.The investigation of the mechanism is needed and valuable for both research and applications of ion-implanted waveguide.The main reseach contents and results in this paper are as follows:The dark mode properties of ion-implantated waveguide are studied using numerical method.According to the characteristics of light propagation in prism coupling system, the amplitude relationship of electromagnetic field is obtained from the Maxwell wave equation. The reflectivity expression is also obtained based on the the amplitude relationship expressed by transfer matrix.The dark mode spectrum from the different refractive index distribution in waveguide has been studied using numerical method when the parameters of prism coupling system and the refractive index profile are assumed according to the reflectivity expression in prism coupling system. The results show that the charactristic of dark modes can be described by the amplitude and the sharpness of peak in each mode, and the transmission properties of guide-mode can be determined accordingly. For example, a real and well confined guide-mode is always corresponding to a measured dip with large amplitude and good sharpness. The effective refractive index of the zeroth dark mode is correspongding to the surface refractive index of waveguide, the change of effective index can also represente the change of the surface refractive index in waveguide. The effective refractive index of the zeroth dark mode can be approximated to the surface refractive index of the waveguide when the dark mode characteristic is very good, but there will have a larger error between the effective refractive index of the zeroth dark mode and the surface refractive index of the waveguide when the dark mode characteristic is bad. The lateral spacing between the adjacent dark modes is related to the thickness of waveguide layer, the smaller the lateral spacing, the bigger the thickness of waveguide layer. Substrate change has a great effect on the characteristic of the leak dark mode. This result is instructive for the analysis of ion-implanted waveguide based on the measured dark model spectrum using prism coupling.The theoretical model of refractive index in ion implanted LiNbO3waveguides is established.According to the measurement results of train induced by ion implantation in LiNbO3crystal, it is assumed that there only has the normal strain along the ion implanted direction and has a linear relation between the strain and the lattice damage ration. A theoretical model is presented to understand the respective contributions of spontaneous polarization, molar polarization and molar volume, and photoelastic effect to the refractive index changes in ion implanted LiNbO3crystal. Compared to previous work, our model yields a better agreement with the measured refractive index profiles in ion implanted LiNbO3crystal. According to the model, the refractive index change during the damage ratio increasing from0tol is caculated and the contributions of the spontaneous polarization, the molar polarization and molar volume in modifying the refractive index in ion implanted LiNbO3crystal are also discussed. The results show that the relationship between lattice damage rate and dose is coincided well with the Avrami formula during ion implantated process. A linear relationship between damage ratio and dose during annealing process is obtained. The result ahows that the lattice damage dynamics during ion implantated process is different from the lattice repairing dynamics dur annealing process. The ordinary index continually decreases with the lattice damage ratio. As for the extraordinary index, it first increases and then decreases with the damage ratio. The change of refractive index is different even at a same lattice damage ratio for the crystal with different crystal orientations, it means that the refractive index varies depending on the direction.of ion implantion. When damage ratio varies from0to1, the refractive-index change related to molar polarization and molar volume increases and that caused by spontaneous polarization decreases. The index change from strain-induced photoelastic effect has a parabolic relation with damage ratio, thus it can be ignored when the damage ratio too low or too high. Around a medium damage level, the contribution of photoelastic effect is not negligible, especially for the extraordinary index change in the x-/y-cut LiNbO3and the ordinary index change in the z-cut LiNbO3, where the strain induced photoelastic effect could account for～15%of the total index change. The refractive index is direction-depending because the strain-induced photoelastic effect depends on the implantation direction.The characters of KTP crystal formed by He+-ions implantation with high dose and low energy are studied.The dark mode characteristics by prism coupling and back scattering/channel (RBS/C) spectral characteristics of z cut KTP crystal formed with300keV He ions at dose of4×1016,6×1016,8×1016and10×l016ions/cm2are studied. The dark-mode spectrum and RBS/C spectral characteristics from z cut KTP crystal formed with150keV He ions at dose of8×1016ions/cm2after annealed at different temperature are also studied. The results show that the dark mode characteristics become worse and the effective refractive index of the zeroth dark mode decreases as the implanted dose increasing. After implantation with same dose, the dark mode measurement from nx shows the poorest property, a better result is obtained in ny measurement and the best result is got in nz. According to the correspondence between the dark mode characteristic and the refractive index, it can be seen that the surface refractive index decreases with the dose increasing and the change of refractive index value is minimal for nx, moderate in ny, and maximal on nz. The amorphous layer can be found in KTP crystal suffering300keV He ions implantation, and lattice damage at sample surface accumulates with the ion dose increasing. In150keV He ions implanted KTP crystal, the saturated dose is8×1016ions/cm2, and the average index of completely damaged (i.e., amorphous) KTP is about1.74. In the annealing process in KTP crystal implanted with He ions at energy of150keV, the surface effective refractive index increases with the annealing temperature. After the annealing temperature of400℃, nx and nz approach to the refractive index of substrate KTP crystal, while nz still much deviates from the value of substrate KTP. But the extrapolated calculated value shows that along with the annealing temperature increase that the index trends to the value of virgin KTP after annealing at800℃. Different behavior of nx, ny and nz in ion implantation indicates that the refractive index change during ion implantated progress is different from that in annealling progress. The RBS/C spectrum shows that the damage lattice gets slightly recovery after annealing treatment, but the amorphous layer can not be removed. At the same time, the surface bubble agglomeration is studies after annealing. The results show that bubbles distributes sparsely on some area of KTP crystal surface implanted by He ions at300keV and8×1016ions/cm2, and the size of the largest bubble is about10μ m in diameter when the sample annealed at400℃for60mins. Extending annealing time to120mins at400℃, surface blister disappears and a uniform surface is observed. In the suface of KTP crystal implanted by He ions at300keV and8×1016ions/cm2, the bubbles agglomerate when the annealing temperature reaches400℃, but they only appear in a few places, and more bubbles can be observed in150keV sample than that of300keV sample. The maximum diameter of bubbles is about30μm.There has no bubble agglomeration in surface of KTP crystal implantanted at other doses and annealed at other temperatures. The KTP crystal appears some precipitates when the annealed temperature above800℃and is partial decomposited when the temperature more than900℃. Therefore, in the z-cut KTP, the He2bubble can not be agglomerated availably when dose less than8×1016ions/cm2. It has an important significance to the crystal ion cutting (CIS) technology in KTP crystal.The model of refractive index in ion implanted KTP waveguides is established.Based on the assumption of strain distrubtion in ion-implanted in LiNbO3crystal, a refractive index change model in ion-implanted KTP crystal is established duiring the lattice damage ratio, the model includes the molar polarizability and molar volume, the spontaneous polarization and the photoelastic effects. Using the first-order approximation of small quality, the effects of the molar polarizability and molar volume, the spontaneous polarization and the photoelastic effect on the refractive index change of is discussed, the results show that the contributatins of the three factors on the refractive index in implanted KTP crystal is the same as in implanted LiNbO3crystal. According the back scattering/channel (RBS/C) spectra of300keV He ions implanted KTP crystal, the lattice damage curve is extracted. Based on it, the damage ratio of sample surface is estimated. According to the prism coupling dark mode of300keV He ions implanted KTP crystal at different dose, the sample surface effective refractive index is obtained. The theoretical refractive index is obtained according to the model fumulation using the estimated surface damage ratio and the results show a consistent with the experimental refractive index in a certain range.The error between theoretical value and experimental data is also analyzed. The fact that refractive index change model of ion implantated KTP crystal has a same form of LiNbO3crystal, but only different model parameters, indicates that the model could be applied to all optical crystal when the model parameters are determined. It is important to further application of ion implantation waveguide. According to the model, the profile of refractive index versus the depth of waveguide is obtained using the extracted damage curve from backscattered/channel (RBS/C) spectra. The result is different from that of Reflectivity Calculation Method (RCM), which is a real distribution curve. The results indicate that the values of nx, ny and nz decrease during the implanted depthe increasing, until to the average index of completely damaged (i.e., amorphous) KTP which is1.74at the depthe of0.9μm, and then the optical barrer is formed. Among the optical waveguide formed in nx, ny and nz, the waveguide in nz easily becomes an effective waveguide than the others. During the dose increasing, the surface refractive index and the effective thickness of waveguide layer decreases gradually in a same kind of refractive index, such as in nx(or ny or nz). It is concordant with the results from the prism coupling dark mode of300keV He ions implanted KTP crystal. The refractive index distribution is also calculated with increasingthe damage ratio for different cut KTP crystal by He ions implanted. The results show that the value of refractive index is reduced with the damage ratio increasing. The value of ny, nz decreases monotonely, but that of nx decreases at first and then reachs a saturation region in x/y-cut KTP crystal. The change ratio of nx,ny is much more smaller then that of nz...