Effective-index Based Matrix Method Research Articles

Passive polarization splitter using zero-gap directional coupler in LiNbO3

Low-crosstalk zero-gap directional coupler (ZDC) based TE-TM polarization splitter/combiner was designed at 1.55 µm transmitting wavelength using titanium indiffused LiNbO3 technology and effective-index based matrix method (EIMM). Single mode waveguides and ZDC were designed from its fabrication parameters. The coupling length of ZDC was optimized to 1826 µm to achieve a splitter crosstalk around −60 dB for both polarizations. At input and output ends of ZDC low-loss cosine-generated S-bent waveguides were used. For proof-of-concept, the device was fabricated and tested. Details of fabrication technology of the device are discussed. DC sputtering process was adopted for titanium film deposition, and wet-oxygen ambient was used during high-temperature diffusion of titanium into LiNbO3 to suppress lithium out-diffusion. Our first experiment with the splitter yields crosstalk values −10.79 dB for TE and −10.21 dB for TM mode. The measured fiber-device total insertion losses were 3.13 dB and 5.15 dB for TE and TM polarizations. The higher crosstalk values of the fabricated polarization-splitter can be significantly lowered by using optical detector of higher efficiency, and coupling length compensation during mask-data generation.

A 1 × 2 polarization-independent power splitter using three-coupled silicon rib waveguides

This work presents the development of a three-waveguide polarization-independent 1 × 2 power splitter using the silicon-on-insulator platform. Design of the device was accomplished by the effective index based matrix method and coupled mode theory. The component was fabricated using a readily available silicon-on-insulator substrate of a 5 μm thick device layer and characterized at 1.55 μm wavelength of light. The fabricated device has an insertion loss of 11.43 dB for transverse electric (TE) polarization and 11.80 dB for transverse magnetic (TM) mode, which indicates its polarization-independent behavior. The power splitting shows an imbalance of 0.23 dB for the TE mode and 0.82 dB for TM mode, which is due to the fabrication error of the separation of outer arms from the central input waveguide. The design can be extended for any 1 × 2N 3-dB power splitter, which will be very useful for optical interconnects and fiber-optic communication networks.

Multilayered photonic integration on SOI platform using waveguide-based bridge structure

A waveguide based structure on silicon on insulator platform is proposed for vertical integration in photonic integrated circuits. The structure consists of two multimode interference couplers connected by a single mode (SM) section which can act as a bridge over any other underlying device. Two more SM sections acts as input and output of the first and second multimode couplers respectively. Potential application of this structure is in multilayered photonic links. It is shown that the efficiency of the structure can be improved by making some design modifications. The entire simulation is done using effective-index based matrix method. The feature size chosen are comparable to waveguides fabricated previously so as to fabricate the proposed structure easily.

Design of a Directional Coupler based on UV-Induced LiNbO3 Waveguides

AbstractA semi-analytical technique, effective index-based matrix method (EIMM), has been applied to determine the coupling length of continuous wave UV-written directional coupler for different gaps between the waveguides as well as the pure bending loss and transition loss of S-curved waveguides estimated to optimize the transition length (

Comparative study between the results of effective index based matrix method and characterization of fabricated SU-8 waveguide

A study regarding the validity of effective-index based matrix method (EIMM) for the fabricated SU-8 channel waveguides is reported. The design method is extremely fast compared to other existing numerical techniques, such as, BPM and FDTD. In EIMM, the effective index method was applied in depth direction of the waveguide and the resulted lateral index profile was analyzed by a transfer matrix method. By EIMM one can compute the guided mode propagation constants and mode profiles for each mode for any dimensions of the waveguides. The technique may also be used to design single mode waveguide. SU-8 waveguide fabrication was carried out by continuous-wave direct laser writing process at 375nm wavelength. The measured propagation losses of these wire waveguides having air and PDMS as superstrates were 0.51dB/mm and 0.3dB/mm respectively. The number of guided modes, obtained theoretically as well as experimentally, for air-cladded waveguide was much more than that of PDMS-cladded waveguide. We were able to excite the isolated fundamental mode for the later by precise fiber positioning, and mode image was recorded. The mode profiles, mode indices, and refractive index profiles were extracted from this mode image of the fundamental mode which matched remarkably well with the theoretical predictions.

Effective index-based matrix method for silicon waveguides in SOI platform

The work makes an attempt to design and analyze silicon waveguides in silicon on insulator (SOI) platform with the aid of effective index-based matrix method (EIMM). Effective index method is used for wave confinement in depth direction of the waveguides, thus effective indices of the guided modes are computed. A transfer matrix method is applied on the resulted one-dimensional lateral index profile to compute the guided mode propagation constants. Both wire and rib waveguides are designed from its fabrication parameters for single-mode wave propagation at a transmitting wavelength of 1.55μm. Bending losses of bent wires are estimated by a suitable conformal transformation along with EIMM. From our computed results, it is seen that the bending radii exceeding 1μm have negligibly small bending losses. The mode profiles of the silicon wires within the waveguides are also computed for both transverse electric (TE) and transverse magnetic (TM) polarizations. Analysis of some special structures, such as wire waveguide with slanted etched walls, and directional coupler made up of straight and/or curved coupled waveguides are also presented. Some of the computed results of this semi-analytical EIMM are validated with commercially available 2D-FDTD method.

Comparison of calculated and measured refractive index profiles of continuous wave ultravoilet written waveguides in LiNbO3 and its analysis by effective index based matrix method

The refractive index profiles of the continuous wave (CW) UV-written waveguides in congruent LiNbO3 crystal are theoretically computed and compared with the evaluated profiles from the measured mode intensity distributions. It has been observed that change in activation energy of Li-indiffusion affects the computed refractive index profiles to a large extent, and the computed and measured profiles match fairly well for 305 nm and 275 nm written waveguides with an activation energy equal to ∼1.3 eV. The calculated refractive index profiles are used in effective index based matrix method (EIMM) to compute the guided mode propagation constants of these waveguides at 632.8 nm transmitting wavelength. For both the writing wavelengths, the waveguides are single mode in nature, which tally with experimental results. The bending losses of the bent waveguides for different bending radii are also computed using a conformal mapping technique along with EIMM. Finally, the behavior of CW UV-written waveguides under an applied electric field is physically analyzed. Accumulated space charge for 305 nm written waveguides is identified for its comparatively low electro-optic coefficient than the waveguide written with 275 nm UV laser.

Semianalytical method to study silicon slot waveguides for optical sensing application

High-index contrast slab and slot optical waveguides have a high index variation both along the lateral and vertical interfaces and are usually analyzed numerically, requiring large computer memory and time. In this article, their analysis is done semianalytically using an effective-index based matrix method. This method, which is computationally very fast, was earlier used successfully for low-index profile waveguide structures only and is now suitably modified for use in high-index contrast structures. The electric field profile of the waveguide structures is plotted and the effective refractive index at different wavelengths is calculated. The results are compared with results obtained from numerical techniques like finite element method, finite-difference time-domain, and beam propagation method and they match very well. The dependence of their different optical characteristics with the waveguide parameters is also studied. These studies will help in obtaining improved sensitivity of slot waveguides for sensing applications.

Analysis of Ti:LiNbO 3 zero-gap directional coupler for wavelength division multiplexer/demultiplexer

For the purpose of multichannel integrated-optical wavelength division MUX/DEMUX design, the wavelength tuning method of Ti:LiNbO 3 zero-gap directional coupler is analysed by effective-index based matrix method (EIMM). In this method, first, the 2D refractive index profile of the Ti:LiNbO 3 zero-gap directional coupler is transformed into lateral 1D effective-index profile by WKB method. Finally, matrix method is applied to this effective-index profile and the propagation constants are computed from the resonance peaks of the excitation efficiency versus propagation constant characteristics. It has been shown that the channel wavelength tuning can be achieved by varying the Y-branching angle at the input and output of the device or by a slight variation of two-mode-section length. The method of electro-optic fine tuning of the channel wavelength and channel separation of the device has also been investigated. A cascaded structure with proper parameters for four-channel application is also simulated and the results are presented.

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.

Analytical model for computing propagation constant of <inline-formula><math display="inline" overflow="scroll"><msub><mi>Ti:LiNbO</mi><mrow><mn>3</mn></mrow></msub></math></inline-formula> 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.

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

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).