Theoretical modeling and characterization of annealedproton-exchanged planar waveguides in z-cut LiNbO3

Planar optical waveguides in z-cut LiNbO₃ fabricated by the annealed proton-exchange technique using pure pyrophosphoric acid as the initial proton source have been investigated. A generalized Gaussian function was used to accurately model the refractive-index profile, resulting in considerable improvements over previous work. The nonlinear dependence of the index on the proton concentration was verified by directly calculating the change in the area under the index versus depth curves. Annealing was found to allow for flexibility in the tailoring of the waveguide parameters. An empirical correlation of the changes in these parameters with the fabrication conditions was achieved through the use of a general power law     

Ti:LiNbO_3质子交换光波导

本文研究了在Ti扩散LiNbO_3衬底上用苯甲酸质子交换制备光波导的方法,以及单模条件、折射率分布、交换系数、表面状态和热稳定性等问题。     

Simplified Z-propagating DC bias stable TE-TM modeconvertor fabricated in Y-cut lithium niobate

A TE-TM mode converter, useful at either 0.632 or 0.840 μm, has been fabricated on y-cut LiNbO₃ by Ti indiffusion with the channel waveguide placed parallel to the z-axis. For TE polarized input, the maximum TM modulation depth is 97 percent at 0.632 μm with a 5-V (pp) drive and 99 percent at 0.840 μm with a 12-V (pp) drive. A similar device operating at 1.3 μm displays 98-percent TE-TM switching at 68 V. Operation involves only coplanar electrodes placed alongside the channel acting on the r₆₁ electrooptic coefficient. A separately deposited buffer layer is unnecessary. Testing indicates a substantially greater tolerance to electrode misalignment than afforded by similar structures formed in x-cut substrates. Data illustrating immunity to photorefractive drift in the presence of a DC bias voltage is presented for 0.840-μm wavelength operation     

Proton-exchanged LiNbO/sub 3/ optical waveguides using stearic acid

Proton-exchanged optical waveguides have been fabricated in z-cut LiNbO/sub 3/ using a new proton source: stearic acid. These waveguides were characterized optically and were found to exhibit a step index profile with Delta n=0.118 measured at 0.633 mu m. The propagation losses were typically around 1.5 dB/cm, and the diffusion constant and the activation energy for the proton-exchange process were measured to be 5*10/sup 6/ mu m/sup 2//h and 69 kJ/mol, respectively.<>     

Proton-exchanged optical waveguides in LiNbO/sub 3/ using octanoic acid

Low-loss proton-exchanged planar waveguides in z-cut LiNbO/sub 3/ were fabricated and characterized optically using octanoic acid as a proton source. The waveguide exhibited a step-index profile with an index change of 0.118 measured at 0.633 mu m. The lowest waveguide propagation loss measured was 1.2 dB/cm, and it was reduced further to 0.4 dB/cm after annealing. The diffusion rate and the activation energy using this acid were found to be lower than those reported using other acids.<>     

Integrated TE-TM mode converter on Y-cutZ-propagating LiNbO3 with an electrooptic phasematching for coherence multiplexing

The use of an integrated TE-TM mode converter as a coherence multiplexer is described. The component is based on a buried waveguide obtained by proton exchange and postannealing. The electrode structure consists of three electrodes. Two are used to achieve TE-TM conversion, and the third is used to perform phase matching to ensure a high conversion efficiency     

Analysis of Z-invariant and Z-variantsemiconductor rib waveguides by explicit finite difference beampropagation method with nonuniform mesh configuration

An efficient and simple explicit finite difference beam propagation method (EFD-BPM) incorporating nonuniform mesh is described. The criteria for stability are developed, and it is shown that this algorithm is power conserving when the stability criteria are met. EFD-BPM is applied to the analysis of single and coupled semiconductor rib waveguides and its accuracy is confirmed by comparing the results with the reported results. Nonuniform mesh is found to improve the efficiency of the method significantly for the analysis of weakly guiding waveguide structures. Several coupled rib waveguide structures with curved input and output branching sections are analyzed using both three-dimensional EFD-BPM and two-dimensional finite difference BPM combined with effective index approximation     

Frequency-dependent FDTD methods using Z transforms

The frequency-dependent finite-difference time-domain method (FD) ²TD method has been shown to be capable of correctly calculating electromagnetic propagation through media whose dielectric properties are frequency dependent. However, as researchers search for more elaborate applications, the formulation of the (FD)²TD methods becomes more complex. In this work, the mathematics of the (FD) ²TD method is developed using Z transform theory. This has the advantages of presenting a clearer formulation, and allowing researchers to draw on the literature of systems analysis and signal processing disciplines     

LiNbO3 optical waveguides formed in a new proton source

Proton-exchanged planar waveguides have been fabricated on Z-cut and X-cut lithium niobate crystals by using a new proton source formed by a mixture of benzoic and adipic acids. Waveguide index profiles and optical characteristics have been obtained at different values of the adipic-benzoic acid concentration ratio. The samples have been structurally characterized by Raman and infrared (IR) absorption spectroscopy and double-crystal X-ray diffraction. Good quality samples have been fabricated by using 30 mol% ratio dilution, showing very low scattering levels (<0.1 dB/cm), relatively high electrooptic coefficient (r₃₃=0.88 pm/V), and low relative percentage of interstitial protons (26%). The main factor limiting the waveguide optical properties is the substitutional-interstitial proton ratio, which can be easily controlled to produce good quality waveguides. A demonstration of the repeatability of the exchange process in the acid mixture is also provided     

Fabrication of LiNbO3 channel waveguides using water

A channel waveguide formed in LiNbO₃ was fabricated by using distilled water instead of acids for proton exchange and a self-aligned SiO₂ cap for diffusion. It was demonstrated that the water reaction is an important reaction to cause the index change in proton exchange     

Electro-optic effect in proton exchanged LiNbO3 andLiTaO3 waveguides

Electro-optic properties of proton-exchanged (PE) waveguide layers in LiTaO₃ and LiNbO₃ are studied and related to their optical characteristics. The proton-exchange process induces a degradation of the electro-optic activity in both types of waveguides, PE LiNbO₃ and PE LiTaO₃. The measured electro-optic effect is close to the detection sensitivity even when the exchange regime is performed at low temperatures for short periods of time. The PE samples have been annealed (APE waveguides) and the changes of their r₃₃ electro-optic coefficient has been followed at successively higher temperatures and periods of time. Subjected to annealing at temperatures between 265-420°C, the LiTaO₃ layers show a partially recovered r₃₃ coefficient, the recovering being different for quick and slow cooling of the samples. In thin APE LiNbO₃ waveguiding layers a restoration of r₃₃ up to 75% of the bulk value is observed due to the annealing at temperatures between 200-340°C     

Theoretical modeling of optical amplification in Er-doped Ti:LiNbO3 waveguides

An accurate theoretical analysis is presented describing optical amplification in Er-diffused Ti:LiNbO₃ channel waveguides. It follows as far as possible the theory already developed for Er-doped fibers. As optical pumping around λ_p≈1.48 μm is considered, a quasi-two-level model for the Er³⁺ ions is used with wavelength-dependent cross sections. The optical gain in the 1.53 μm<λ<1.64-μm wavelength range is evaluated. The characteristic parameters, as Er concentration profile, cross sections, pump, and signal mode distributions and waveguide (scattering) losses are taken from experiments. Examples of numerically calculated pump-, small-signal-gain-, and ASE-evolutions are presented. The model has been tested by comparing computed and experimentally observed gain characteristics for Xˆ- and Yˆ-cut LiNbO₃; an almost quantitative agreement has been obtained     

Binary images of cyclic codes over Z4

We determine all linear cyclic codes over Z₄ of odd length whose Gray images are linear codes (or, equivalently, whose Nechaev-Gray (1989) image are linear cyclic codes or are linear cyclic codes)     

Direct hardware solution to quadratic equation Z2⊕Z⊕β=0 in Galois fields based on normalbasis representation

Normal basis representation is considered to represent the elements of Galois fields. The quadratic equation, Z²⊕Z⊕β=0, is solved directly and a new, simple, regular and expandable hardware structure is introduced to solve this equation. The main advantage of this structure over the structures in non-normal basis representations is its independence from generating polynomial of the field     

Quasi-cyclic codes over Z4 and some new binarycodes

Previously, (linear) codes over Z₄ and quasi-cyclic (QC) codes (over fields) have been shown to yield useful results in coding theory. Combining these two ideas we study Z ₄-QC codes and obtain new binary codes using the usual Gray map. Among the new codes, the lift of the famous Golay code to Z₄ produces a new binary code, a (92, 2²⁴, 28)-code, which is the best among all binary codes (linear or nonlinear). Moreover, we characterize cyclic codes corresponding to free modules in terms of their generator polynomials     

Fabrication tolerance of Ti:LiNbO3 waveguides

A simulation program based on the three-dimensional beam propagation method (BPM) is used to study the fabrication conditions of single-mode Ti:LiNbO₃ waveguides. The calculated cutoff wavelengths are in good agreement with experimental data. The thickness of titanium needed to support the fundamental and first-order modes for three Ti strip widths (6, 7, and 8 μm) is calculated. The two-dimensional BPM is used to calculate the coupling length from the fabrication conditions. Results are consistent with measured data. The fabrication tolerances of the coupling length of directional couplers are also presented     

Second-harmonic generation efficiency in periodically poled LiNbO3 waveguides

Quasi-phase-matched second-harmonic generation efficiency in periodically poled LiNbO₃ using titanium indiffusion, has been theoretically investigated. This permits clarifying how the involved guided modes convert the triangle-shaped form of the ferroelectric polarization in the crystal, via the overlap integral between this form and these modes, into an effective periodic nonlinear coefficient. As a consequence, the periodic function that really permits the quasi-phase-matching operation is the modulation of this effective nonlinear coefficient, the shape of which can be far from a triangular shape, as shown using different cases of mode profiles     

Modeling of Ti:LiNbO3 waveguide devices. II.S-shaped channel waveguide bends

For pt.I see ibid., vol.7, no.3, p.533-9, 1989. Directly from design and fabrication parameters, the performances of S-shaped channel waveguide bends are calculated by using the same formalism described in Part I. The calculated insertion losses of S-shaped waveguide bends are in agreement with all experimental data found in the literature. Different S-curves for short-length low-loss waveguide bend design were also studied. Results show that the widely used sine-generated S-curve does not provide lower insertion loss than other S-curves     

Optical parametric oscillation in MgO:LiNbO3 driven by adiode pumped single frequency Q-switched laser

Optical parametric oscillation tunable over the 940-1220-nm spectral region has been obtained from a monolithic magnesium-oxide-doped lithium niobate ring resonator. The monolithic optical parametric oscillator (OPO) was pumped by the 532-nm second harmonic of a diode-laser-pumped single-frequency Q-switched Nd:YAG laser. The exceptional frequency and amplitude stability of the single-frequency pump source provided stable OPO output pulses     

Ti扩散LiNbO_3单模波导参数的测量

对Ti扩散LiNbO_3波导分别采用双曲正割和抛物线分布来近似其折射率的高斯分布,在两个波长下由相应的两种近似本征值方程分别推得了单模波导参数的计算公式,并在4880(?)和6328(?)激光波长下利用棱镜耦合器测量了单模波导参数,对测量结果给出必要的理论分析。