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     

Lithium–Niobate Channel Waveguide for the Realization of Long-Period Gratings

We propose a special lithium-niobate (LiNbO₃) single-mode waveguide for the realization of long-period gratings, which consists of a channel core embedded in a thin slab cladding. We fabricated the waveguide on a z-cut LiNbO₃ substrate with a two-step proton-exchange process and demonstrated its suitability for grating application with a number of removable photoresist long-period gratings deposited on the waveguide surface. The waveguide fabrication process and the LiNbO₃ waveguide structure could be further explored for the development of electrooptic gratings for high-speed applications.     

Proton-exchanged optical waveguides in Z-cut LiNbO3 using phosphoric acid

Proton-exchanged Z-cut LiNbO₃ planar waveguides formed using phosphoric acid were characterized optically. The refractive index profile and the diffusion parameters were studied systematically. These waveguides have propagation losses of less than 1 dB/cm and exhibit properties that are different from those obtained using benzoic acid. The index profile is not a simple step function and can be modeled accurately by a polynomial expression. A maximum surface index increase of 0.145 was measured at a 0.633-μm wavelength. The diffusion constant D₀ and the activation energy Q for the proton-exchange process using this acid were found to be 6.43×10⁸ μm²/h and 82.91 kJ/mol, respectively. The annealing properties of these waveguides were also established, and the effects of annealing on surface index change and waveguide depth increase were found to follow a power-law relationship     

TE-TM mode splitter with heterogeneously coupled Ti-diffused andNi-diffused waveguides on Z-cut lithium niobate

A coupling type mode splitter with an extraordinary polarisation and a random polarisation waveguide made by Ni and Ti indiffusion, respectively, on a Z-cut LiNbO₃ substrate is described for the first time. With optimised process parameters: a very small TM mode profile mismatch is obtained due to the similar characteristics of the Ti- and Ni-diffused waveguides. The measured extinction ratios of the TE and TM modes at 1.55 μm wavelength are >22 dB     

A TE-TM mode splitter in LiNbO3 by proton exchange andTi diffusion

A TE-TM mode splitter using branching waveguides made by proton exchange (PE) and Ti indiffusion (TI) in Z-cut LiNbO₃ is proposed and designed using the coupled mode theory. The TE-TM mode splitting was experimentally verified, and extinction ratios of 20 dB and more than 20 dB were successfully achieved for TM and TE modes, respectively. The effective index of the PE waveguide was controlled through the PE and postannealing time at fixed temperatures. An equivalent device for two-way communication is suggested and discussed theoretically     

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     

Fabrication of magnesium-oxide-induced lithium outdiffusionwaveguides

A short-time high-temperature diffusion process for the fabrication of the lithium niobate (LiNbO₃) optical waveguide with a magnesium-oxide (MgO) strip-loaded structure is presented. The deposited MgO layer causes the lithium to diffuse out of the LiNbO₃ substrate. The secondary ion mass spectroscopy (SIMS) data of the fabricated waveguide show that the lithium diffuses out of the substrate and gets into the MgO cover layer, which results in an increase in the extraordinary refractive index of the substrate. In particular, it is found that the diffused atoms are piled up near the LiNbO₃ and MgO interface. Also, the electrooptic effect of the fabricated waveguide is better than that of the conventional titanium-indiffused waveguide. Moreover, single-mode and single-polarization waveguides can be easily obtained without any significant surface guiding or surface damage on the crystalline substrate     

Singlemode channel waveguides and electrooptic modulators in KTiOPO4 for the short visible wavelength region

Single-mode channel waveguides at short visible wavelengths have been fabricated in KTiOPO₄ by Rb&rlhar2;K ion exchange in mixed melts of RbNO₃-KNO₃-Ba(NO₃)₂ . The technological parameters have been chosen by means of theoretical WKB- and “effective index” calculations concerning the singlemode region of the effective channel waveguide index N₀₀ at the given wavelength. Great diffusion anisotropy and small dispersion of the surface refractive index change guarantee singlemode operation of the very same channel waveguide from the blue up to the red. Typical attenuation of about 2.0 dB/cm for TM- and 1.5 dB/cm for TE polarization was obtained at λ=0.5145 μm. Light-induced refractive index changes (photorefractive effect) have been determined as a function of time, wavelength, guided optical mode intensity and temperature. The light-induced effects in Rb&rlhar2;K ion-exchanged channel waveguides in KTiOPO₄ are about two orders of magnitude smaller than those in annealed proton-exchanged channel waveguides in LiNbO₃. Electrooptic phase modulators have been successfully investigated concerning dynamic V_π measurements, the electric-optical field overlap and dc-drift phenomena. Design, fabrication and experimental results of integrated-optic Mach-Zehnder-interferometer modulators for short visible wavelengths are presented     

Finite element analysis of LiNbO3 waveguides with Si orSi/SiO2 overlay

LiNbO₃ waveguides with Si overlays are emerging as a basic building block for a variety of integrated-optic components, including modulators, high-efficiency gratings, and narrowband WDM filters. However, the development and optimization of these devices are, in large part, hindered by the lack of understanding of the specifics of the Si-on-LiNbO₃ structure which appear to differ dramatically from those of the Si and LiNbO₃ waveguides, considered separately. In this work, we provide a specific insight into the waveguiding properties of vertically stacked Si-on-LiNbO₃ waveguides. In particular, we present a detailed theoretical analysis of the effect of the Si film on the modal characteristics (propagation constant and field distribution) of the structure. The vectorial finite element method (VFEM) is used to numerically investigate a step-index and graded-index single-mode channel waveguide in LiNbO₃, with a Si or Si/SiO₂ multimode overlay. We show that for ~70% of all Si thicknesses, in the range from 0 to 1.6 μm, the highest order normal mode of the entire structure has more than 99.9% of the total energy confined in the LiNbO₃ region, i.e., beneath the Si overlay. This fact is quite intriguing given the fact a planar Si layer of submicron thickness on bulk LiNbO₃ is already multimoded. Furthermore, we show that the effective mode index of the structure is considerably modified compared to that of the LiNbO₃ waveguide while the propagation loss is, on the other hand, practically unaffected (~0.3 dB/cm) even in the presence of the lossy Si film, as confirmed by our previous experimental results. Evidently, large modulation of the effective index and low-loss propagation provide an ideal combination of properties suitable for the fabrication of high-reflectance corrugated waveguide gratings, essential for a number of practical devices, in particular, WDM filters     

An optical integrated circuit for time-division 2-D velocitymeasurement

An LiNbO₃ optical integrated circuit pigtailed with two single-mode fibres, which allows time-division two-dimensional velocity measurement, is discussed. To detect time-division multiplexed beat signals corresponding to velocity components v_X and v_γ of a moving object, a waveguide switch is integrated on a Z-propagating LiNbO₃ substrate of 28×7 mm² in addition to a waveguide interferometer with a frequency shifter. In the optical IC, either v_X or v_γ could be measured selectively with signal-to-noise ratio of 20 dB by driving an electronic gate placed after a photodiode in synchronization with the waveguide switch     

Mach-Zehnder modulators with lithium niobate ridge waveguidesfabricated by proton-exchange wet etch and nickel indiffusion

Mach-Zehnder ridge waveguide modulators on c⁺-LiNbO₃ by proton-exchange wet etch and nickel indiffusion are fabricated for the first time. Modulators operating at 0.633 μm and 1.31 μm are both produced, and the half-wave voltages are measured to be 4 V and 22.5 V, respectively, for an electrode length of 6 mm. The extinction ratios are 14 dB and 13.2 db, respectively, and can be improved by forming the ridge structure only at the electrode interaction region instead. These results make the wet-etched LiNbO₃ optical devices promising to take over the dry-etched ones in the near future     

An LiNbO3 integrated coherence modulator

The authors describe the principle of operation and the performance of a newly integrated LiNbO₃ modulator specially designed to generate optical delays of several millimeters. This is achieved by using the simultaneous propagation of the TE and TM modes in a waveguide and by taking benefit of the high natural birefringence of LiNbO₃. This modulator is well-suited to coherence modulation of light in fiber-optic transmissions. When powered by a short coherence source, the large optical delays induced by a cascade of such modulators can be used as information carriers to transmit several signals simultaneously. A demonstration is reported using a single source and two modulators in cascade to transmit signals simultaneously     

An improved procedure to calculate the refractive index profilefrom the measured near-field intensity

Refractive index profile of optical waveguides is reconstructed from the measured transmitted near-field intensity. A Butterworth low-pass digital filter is employed in the frequency domain to remove impulsive and high frequency fluctuations which have severe effects on the procedure to calculate the index profile from the measured power intensity. The proposed method has been applied to measure the index profile of monomode optical fiber, Ti:LiNbO₃ and buried MgTi:LiNbO₃ channel waveguides     

Photoinduced conversion of radiation polarization in integratedoptics components based on LiNbO3

Two photoinduced effects in LiNbO₃ optical waveguides (unidirectional waveguide mode conversion from ordinary to extraordinary polarization and radiation coupling out of waveguides with polarization plane rotation) are discussed. The circular photovoltaic tensor component in LiNbO₃ is determined experimentally, and a photovoltaic mechanism to explain photoinduced radiation coupling out of waveguides is proposed. The impact of the effects discovered on the performance of phase modulators is discussed     

Wavelength-tunable electrooptic polarization conversion inbirefringent waveguides

Wavelength-tunable, electrooptic polarization conversion in a birefringent waveguide accomplished with a multiple cascade of alternating TE←→TM mode converter and TE/TM phase shifter sections is analyzed. Such polarization converters have been demonstrated in LiNbO₃ and have been used as electrooptically tunable narrowband (Δλ⩽λ₀/1000) wavelength filters with tuning ranges of at least λ₀/200. It is shown that the polarization converter requires only two independent drive voltages and provides arbitrary polarization transformations from any general input polarization to any desired output polarization with simultaneous wavelength tunability. The device is characterized by its overall transfer matrix and the optical bandwidths and tuning ranges for various electrode geometries     

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     

Stress analysis method considering piezoelectric effects and itsapplication to static strain optic devices

A stress analysis method considering piezoelectric effects based on the finite-element method (FEM), which can be applied to arbitrarily anisotropic material-based optical waveguide devices, is newly formulated. To produce a two-step analysis of static strain optic (SSO) and electrooptic (EO) modulations of optical waveguide devices, this stress analysis is linked to the guided mode analysis and the beam propagation analysis taking into account the refractive index changes. Numerical examples are shown for strain-induced optical waveguides and strain-induced polarization mode converters on LiNbO₃ substrates     

Analysis of doped layer step waveguides using dark modes

Results for the analysis of index profiles in steplike waveguide layers formed by proton exchange in LiNbO₃ and epitaxially grown Ge-doped quartz are presented. Modeling of the profile with real modes is difficult unless many modes propagate. However, an analysis which includes the substrate modes recorded in dark mode measurements greatly increases the data and hence the confidence in the model of the index profile. Analysis using a reflectivity function provides the required precision. The data demonstrate that the epitaxial GeO₂ -doped layer has an index variation with depth     

Fabrication, characterization and index profile modeling ofhigh-damage resistance Zn-diffused waveguides in congruent andMgO:lithium niobate

A study of the fabrication and optical properties of planar waveguides fabricated in MgO:LiNbO₃ and LiNbO₃ substrates by diffusion of a ZnO film is presented. Transmission electron microscopy was used to show that using ZnO instead of metallic zinc as a source, and maintaining the ZnO film thickness below a prescribed value, greatly reduces second phase precipitation and produces usable waveguides. Dopant and refractive index profiles were characterized by electron microprobe analysis and interference microscopy, respectively. The dependence of the Zn diffusion coefficient on temperature and the dependence of the refractive-index change on Zn concentration are inferred from these measurements. A simple model is also reported which predicts the index profile of the waveguide given the film thickness, diffusion time and temperature. The validity of the model is demonstrated by comparison between calculated profiles and profiles measured by prism coupling and IWKB analysis     

Characterization of annealed proton exchanged LiNbO3waveguides for nonlinear frequency conversion

A thorough and detailed characterization of annealed proton-exchanged (APE) waveguides in Z-cut LiNbO₃ is described. The mode index measurements in planar waveguides as a function of wavelength and annealing time are reported, including useful analytical relations for the refractive index change, its dispersion, and the depth profile as a function of annealing parameters. Analytical expressions for the mode propagation characteristics are presented and experimentally verified with reasonable accuracy. It is shown that the planar waveguide characterization results can be used to model the channel waveguide characteristics accurately. The model provides closed-form expressions for the mode index and the mode field profile, and the theoretical results are in excellent agreement with the measured data. The technique is used to accurately predict the phase mismatch between the fundamental and second harmonic modes in frequency-doubling experiments using APE channel waveguides. An optimum waveguide geometry for which the phase mismatch is relatively insensitive to the waveguide nonuniformity was predicted and verified experimentally