Research On Ion-Implantation Optical Waveguide Using Numerical Method

Ion implantation, as an outstanding method to modify the surface property of materials, is confirmed to be an effective method for fabricating various waveguide structures. Up to now, many waveguide structures have been formed by ion implantation in most optical materials such as optical crystals, glass, semiconductors and polymers etc.Since the refractive index distribution plays a critical role in determine the natureof optical waveguides, the reconstruction of refractive index profile (RIP) is animportant goal of scientific research. For this reason, scientists have made a variety ofmethods to determine the refractive index distribution, such as reflectance calculationmethod (RCM), the parameterized index profile reconstruction (PIPR) andinverse-Kramer-Brillouin-Wentzel method (iWKB). RCM, which combined aGaussian function with a linear function, assumes the model of refractive indexdistribution in waveguide firstly and then the waveguide is divided layer by layeraccording to the refractive index distribution model. By adjusting function parameters,the reflection and refraction between the layers are calculated. For a given set of curveparameters, a numerical routine is used to calculate the corresponding waveguidemode indices. A numerical optimization technique is then used to adjust theparameters of the RIP such that the sum of the square of the errors between measured(usually measured using coupling prism-module) and calculated mode indices isminimized. The result corresponding to the minimum error is believed to describe thereal RIP in waveguide. PIPR assumed that the surface index change due to theimplantation is described by a straight line, and the index barrier is approximated bytwo half Gaussians. Then the free parameters are adjusted to best match the measuredmode indices. The PIPR and RCM have some similarity. Both assume that thewaveguide index profile can be described approximately by two half-Gaussian curves.RCM and PIPR are ideally suitable for the following cases, such as epitaxial growth,and ion implanted waveguides, in which the index profile has a steep index function, even an optical barrier. The iWKB method is typically used to determine RIP showing a monotic index change of optical waveguide from the measured mode indices and cannot be applied to characterize waveguides formed by ion implantation. The iWKB has been proved to be remarkably accurate in some cases, such as in-diffused or ion-exchanged waveguides in which the index is gradually changing with penetration depth. In order to achieve smaller error in employing these methods (RCM, PIPR and iWKB), the number of measured waveguide mode greater than or equal to three is generally required.Since the conventional methods of determining the refractive index distribution are usually applicable to the waveguides with the mode number more than two, to develop a new method which can describe the RIP of waveguide with guiding modes less than two, or even in the case of single-mode waveguides is of great significance. In this dissertation, numerical method has been used to solve this problem.Beam propagation method (BPM), with clear concept and easy to implement and master, is capable of simulating complex geometry of the optical device in the field of optoelectronic devices. It has been extensively applied in computer-aided design (CAD). Based on this technology many commercial simulation softwares are developed and promoted. The introduction of numerical analysis to the study of refractive index profile in ion implantation optical waveguide, as well as other waveguide-specific physical phenomena has important theoretical value and application prospects.The BPM can be used to simulate the light propagation process in ion implanted waveguide. However, in order to determine the refractive index profile of single-mode waveguides, the similarity comparison between the results of simulation and experimental measured results is required. It involves the relevant content of digital iImage processing. In this paper, both measured and simulated intensity image are converted into 256-level gray scale ones and every pixel of the image is corresponding to a value between 0 and 255. Two image's comparability is Euclidean distance defined as Where Ed(m, s) is the Euclidean distance, N is the color orders, for 256-level gray scale image, N is equal to 255, s_i and m_i are the gray scale histogram value of simulated and measured, respectively.In order to express comparability clearly, another equation in percentage described as Eq. (2) is adopted in intensity calculation.Where Sim(m, s) is the comparability value, P is the count of gray levels calculated in the simulation process, else parameters are the same meaning as those in Eq. (1). If measured and simulated intensity image are identical, the Sim(m, s) is equal to 100%.Based on the BPM and digital image processing technique, numerical method has been used to determine the RIP of single (or double) mode channel (or planar) ion-implantation optical waveguide. Besides those works, numerical method has been used to design the parameters of ion-implantation waveguide, and also applied to investigate some special physics phenomenon of ion-implantation waveguide, such as "strange mode" and "double-barrier" structure. The main results are as follows:Lithium niobate crystal has unique electro-optical, photoelastic, piezoelectric, non-linear properties, and exhibits excellent mechanical and chemical stability. It has been widely used in a variety of integrated optics and active acousto-optical devices, such as modulators, multiplexers, switches, and waveguide amplifiers. In the recent works, it has been reported that the fabrication of channel and planar waveguides in lithium niobate crystal by MeV heavy ion implantation (O²⁺), and the guiding modes of the formed waveguides are single- (1539 nm) or double-mode (633 ran). Positive changes of n_e refractive index happened in the waveguide region. As is known, the RIP dominates the properties of the waveguide, however the RIP of the single mode channel waveguides formed by ion implantation could not determined by the conventional methods directly. A method (which is named as Intensity Calculation Method (ICM)) is developed to decide the RIP in those waveguides. It can be used to determine the index profile in channel and planar waveguides formed by ion implantation without bringing any damage to the sample. In this dissertation, ICM has been applied to predict the refractive index profile in O² ion-implanted LiNbO₃ (LN) single- and double-mode waveguide successfully. In this method, BPM is applied to simulate the light wave propagates in the optical waveguide. The measured near-field intensity distributions of guiding mode by end-fire out-coupling and that from calculation by BPM are analyzed and compared, the refractive index profile in the channel (or planar) waveguide could be finally obtained based on these analyses.Double-mode planar waveguide was formed by O²⁺ ion implantation at three energies of (3.0, 3.6 and 4.5 MeV) and respective doses of (1.8, 2.2 and 4.8)×10¹⁴ ions/cm2 in vacuum at room temperature. ICM shows some difficulties in dealing with the multimode ion-implanted waveguide simply because the total output intensity cannot be clearly distinguished into each guided modes by our present experimental devices. The extraordinary RIP of a double-mode waveguide will be reconstructed by using BPM combining with Hu's theoretical model. Through BPM calculation of RIP from Hu's model, the calculated mode indices of different modes can be obtained. The calculated modes corresponding to the minimum variance of the experimental values of the modes is considered to be the actual distribution of the refractive index in optical waveguides.The damage profile in the ion-implantation optical waveguide can be usually simulated out by SRIM (The Stopping and Range of Ions in Matter) software, while the RIP of ion-implantation single-mode optical waveguide can be determined by the ICM. Once those parameters are well defined, numerical simulation is carried out to simulate lateral mode profiles from channel waveguides with different strip widths. The final results of the simulation and the measured results are compared. The result that the calculated and the actual measured data agree well suggests that the analysis method can be used in the design of the waveguide structure.Some special physical phenomena, such as strange mode and double-barrier have been observed in the waveguides formed by ion implantation. For these phenomena, researchers have made a number of models to explain. Some analyses attribute the "strange mode" to the existence of a subsidiary optical well next to the main nuclear damage optical barrier. They can be observed when measured using varying wavelengths or suffering surface polishing. In this dissertation, numerical calculation method is employed to testify the reasonableness of the existence of "strange modes". The waveguide with double index barriers can be formed by mutli-enregy ion implantation. The RIP in the waveguide is unknown and difficult to reconstruct using the conventional methods mentioned before. In the dissertation a successful analysis is introduced to deal with this problem. A hypothetical index profile based on the lattice damage is firstly assumed, following the RCM is used to calculate the effective modes of waveguide. Meanwhile, the results of BPM numerical calculation for double-barrier-mode optical waveguides can also be obtained. Then the comparison between the calculated values and the measured results by coupling prism is carried out, the parameters corresponding to the smallest variance is believed to describe the actual index distribution in the waveguide. By comparison of RCM and BPM calculation, it is found that the accuracy of the results can be enhanced by additional BPM amendment.