J. C. Biswas

Modal profiles in Ti:LiNbO3 two-waveguide and three-waveguide couplers by effective-index-based matrix method

Abstract Graded-index optical channel waveguides like Ti-indiffused LiNbO 3 waveguides have been modelled by effective refractive index profile along the lateral direction, discretising the profile and then using the matrix method. This effective-index-based matrix method, which was earlier used to compute the modal propagation constants of Ti:LiNbO 3 channel waveguides and directional couplers [Fib. Integrat. Opt. 17 (1998) 139] and the bending loss [J. Opt. Commun. 155 (1998) 125], has been established in this paper as a computationally fast, analytical method to compute electric field and modal intensity profiles in single and coupled waveguides. In order to handle coupled waveguides consisting of three waveguides, the concept of overlap integral has been used to analyse power coupling to the middle waveguide for applications in power splitting. Some of the computed intensity profiles have been compared with experimental data obtained by the authors. Although computation has been performed only for TE and TM polarisations, the method has the inherent capability of handling arbitrary polarisation.

Analysis of directional coupler electro-optic switches using effective-index-based matrix method

Abstract The effective-index-based matrix method (EIMM) has been used to simulate the characteristics of integrated-optic directional coupler switch (both the uniform-Δ β and reversed-Δ β types) based on electro-optic (EO) effect. The characteristics are derived from the distributions of optical power and electrical modulating field within the device. The analysis was focused on directional coupler switching devices made by the diffusion of titanium in lithium niobate (Ti:LiNbO 3 ) substrates and incorporation of suitable electrodes. The simulated results are found to match well with available experimental results and other numerical simulation results obtained from the literatures. Although the computations are performed for Ti:LiNbO 3 waveguides, the model is applicable to arbitrary graded-index waveguides with the known refractive index profile and electro-optic coefficient. EIMM is found computationally well efficient and considerably faster than beam propagation method (BPM).

Modelling of titanium indiffused lithium niobate channel waveguide bends: a matrix approach

Abstract An analytical model for computation of bending loss of Ti:LiNbO 3 channel waveguide bends has been presented. The analytical steps involved are as follows. The 2D refractive index profile over the cross-section of Ti:LiNbO 3 waveguide is first transformed to 1D effective-index profile along the lateral direction. A conformal mapping technique is then used to transform the effective-index profile of the waveguide bend to that of an equivalent straight waveguide. A stair-case type step-index profile is generated from the equivalent effective-index profile in lateral direction by partitioning the latter into a large number of thin sections of varying refractive indices. The overall transfer matrix of the step-index layered structure so obtained may be computed by the progressive multiplication of individual 2×2 transfer matrices relating the field components in adjacent layers. The excitation efficiency of the wave in the guiding layer shows a resonance peak around the mode propagation constant. The full-width-half-maximum (FWHM) of this peak determines the power attenuation coefficient of the bent waveguide. The losses due to the discontinuity of the curvature are also computed. The computed results for different bends including S-bends are in good agreement with the published experimental data. The computation using the model is quite fast and versatile to consider arbitrary waveguide dimensions, Ti-film thickness, diffusion parameters and wavelength of light for both TE and TM polarizations. The model, in principle, is not limited to Ti:LiNbO 3 channel waveguides only but is valid for any arbitrary graded-index channel waveguide bends provided that the refractive index profile and the wavelength dependence of the refractive index are known.

Simulation of refractive index profiles for titanium indiffused lithium niobate channel waveguides

Abstract A generally applicable method to simulate the two-dimensional profiles of Ti-concentration and refractive index of Ti:LiNbO3, waveguides is presented. The influence of the fabricational parameters on the refractive index profiles has been studied in detail. The model parameters are extracted from the available experimental data. The computed values of surface refractive index change agree closely with the experimental results. The model is also extended for coupled waveguides.

Integrated optical waveguides in LiNbO3: modeling and experimental analysis

Graded-index optical channel waveguides rare fabricated by diffusion of Ti in LiNbO3. A model has been developed for calculating the mode profiles of the same, by first finding the effective refractive index profile along the lateral direction, and then discretizing the profile and applying the matrix method. This effective-index-based matrix method has been presented in this paper and established as a computationally fast, analytical method to computer modal electric field and intensity profiles in single and coupled graded-index channel waveguides. The method can be used in coupled systems consisting of three or more waveguides where the input power may be launched to any of the waveguides. Some of the computed intensity profiles have been compared with experimental data. Although computation and measurements have been performed only for TE and TM polarizations, the method has the inherent capability of handling arbitrary polarization.

A three-waveguide polarization independent power splitter on lithium niobate substrate

Abstract A three-waveguide polarization independent power splitter on LiNbO 3 substrate is proposed and demonstrated. Splitting ratio between the output ports and the excess loss of the device are found independent of the polarization states of the input light. The measured imbalance of the output power levels and the average excess loss of a 1×2 polarization independent power splitter are 0.2 dB and 0.58 dB, respectively. The device can be cascaded in tree-structure to fabricate 1×2 N power splitters which are important in optical communication networks.

Semi-Analytical Simulation of Titanium-Indiffused Lithium Niobate–Integrated Optic Directional Couplers Consisting of Curved Waveguides

Integrated optic directional couplers consisting of curved waveguides are simulated analytically by solving the Riccati equation. The coupling coefficient between the curved waveguides with a parabolically varying gap and the condition of total power transfer between the waveguides are derived. In order to compute the overall coupling coefficient and hence the power distribution along the waveguides for Ti:LiNbO 3 curved waveguide directional couplers, the coupling coefficient for straight waveguide couplers is computed for different gaps using the effective-index-based matrix method (EIMM). Finally, the power distribution in the curved waveguides along the length is computed. The method is mostly analytical except the effective-index method and is computationally simple.

Simultaneous compensation of dispersion and losses using Er-doped double-core optical fiber

The Er-doped double-core dispersion compensating fiber (EDDCF) has been fabricated using modified chemical vapor deposition (MCVD) technique. We have obtained 14 dB gain at 1550 nm (using a diode laser of 980 nm wavelength which provides 100 mW of pump power) with dispersion of about −165 ps/km nm. It is useful for the optical fiber network where amplification as well as negative dispersion is necessary. We are the first to report the experimental realization and characterization of the EDDCF.

Analytical model for computing propagation constant of Ti:LiNbO3 periodically segmented waveguides by effective-index-based matrix method

The effective-index-based matrix method (EIMM), which was earlier used to analyze single-mode continuous waveguides, has been also extended to the analysis of periodically segmented waveguides (PSWs) formed by Ti indiffusion in LiNbO 3 . The Ti-concentration profiles and the induced refractive index changes of Ti:LiNbO 3 PSWs have been computed for different waveguide dimensions and fabrication parameters at the design wavelength by using approximate analytical models. The effective index profile of the PSW is obtained by averaging the contributions from different regions along the segments, and EIMM is then applied for computing propagation constants of the PSWs. The cut-off wavelength of PSW has been computed as a function of duty cycle, keeping the period constant. This PSW, when used as one arm of an asymmetric directional coupler (ADC) along with the other arm formed by a continuous waveguide, can be used as a tunable filter.

Fabrication and characterization of erbium-doped titanium-indiffused lithium niobate waveguides for an integrated-optic amplifier

Erbium is doped into z-cut Lithium Niobate (LiNbO3) substrate by thermal diffusion from thin Er film. XPS, PL and reflection studies have been carried out in order to characterize the doped sample and to test the suitability for amplifying signal at the wavelength 1530 nm. Straight waveguides of different widths (10, 15 and 100 micrometer) have been fabricated on the Er-doped sample by Ti diffusion. Loss measurements for the Er:Ti:LiNbO3 waveguides have been done by using lasers of wavelengths 633 and 1300 nm.