Vector modes of rectangular-core dielectric waveguides: An improved perturbation approach

We present an improved analysis to obtain vector modes of a rectangular-core waveguide (RCW) structure whose dielectric constant profile is separable in x and y coordinates. Using this analysis, a perturbation method is then developed to obtain vector modes of a practical RCW. The propagation constants so obtained for a fully-buried and a ridge RCW structure using the present analysis are found to be in better agreement with reported numerical values than the ones obtained with an earlier reported perturbation approach [Kumar et al., Opt. Lett. 8 (1983) 63].     

Low-loss amorphous silicon-on-insulator technology for photonic integrated circuitry

We report the fabrication of low-loss amorphous silicon photonic wires deposited by plasma enhanced chemical vapor deposition. Single mode photonic wires were fabricated by 193 nm optical lithography and dry etching. Propagation loss measurements show a loss of 3.46 dB/cm for photonic wires and 1.34 dB/cm for ridge waveguides.     

A planar waveguide concave grating employing dielectric mirrors

Dielectric mirrors, which yield high-reflectances on grating facets, are proposed for the design of a planar waveguide concave grating. The transfer-matrix method is used to derive an expression for the reflectance of a series of air slots and high-index stacks. The FullWAVE software, a finite difference time-domain EM solver from R-Soft, is used to evaluate the loss of the resulting 2D waveguide grating. The simulation results show that the polarization-dependent loss (PDL) is below 0.25 dB when the proposed dielectric mirror is used. The influence of the width variation of the dielectric stack is also taken into account.     

Multichannel silicon WDM ring filters fabricated with DUV lithography

We have fabricated 9-channel silicon wavelength-division-multiplexing (WDM) ring filters using 193 nm deep-ultraviolet (DUV) lithography and investigated the spectral properties of the ring filters by comparing the transmission spectra with and without an upper cladding. The average channel-spacing of the 9-channel WDM ring filter with a polymeric upper cladding is measured about 1.86 nm with the standard deviation of the channel-spacing about 0.34 nm. The channel crosstalk is about −30 dB, and the minimal drop loss is about 2 dB.     

Impact of misfit dislocations on wavefront distortion in Si/SiGe/Si optical waveguides

Silicon-rich SiGe alloys represent a promising platform for the development of large-area single-mode optical waveguides to be integrated in silicon-based optical circuits. We find that SiGe layers epitaxially grown on Si successfully guide radiation with a 1.55 μm wavelength, but, beyond a critical core thickness, their optical properties are strongly affected by the clustering of misfit dislocations at the interface between Si and SiGe, leading to a significant perturbation of the local refractive index. Transmission electron microscopy and micro-Raman spectroscopy, together with finite-element simulations, provide a complete analysis of the impact of dislocations on optical propagation.     

Tunable discrete Talbot effect in inhomogeneous photonic lattices

We discuss the discrete Talbot effect in one- and two-dimensional waveguide lattices under the influence of an external potential. It is shown that the field recovery can be precisely tuned by changing the gradient of the potential. In a two-dimensional configuration, the diagonal coupling does not affect the period of recovery.     

Optimal design of multimode interference couplers using an improved self-imaging theory

Self-imaging theory is widely accepted as a good method in designing 1 × N multimode interference (MMI) couplers, but it is also true that self-imaging theory is not suitable for low-contrast structures. An improved self-imaging theory is proposed in this paper for the optimal design of low-contrast 1 × N MMI couplers. The average effective width of MMI waveguide and the average effective propagation constant of MMI waveguide are used as the basis to modify the conventional self-imaging theory. A direct calculation of the average effective width of low-contrast MMIs is presented. We use this approach in the optimal design of a 1 × 4 silica MMI coupler, and the results show that the improved self-imaging theory is more accurate than conventional self-imaging theory for low-contrast structures, the results also show that if the material parameters and the width of an MMI waveguide are fixed, the average effective width of the MMI waveguide will increase with the decrease of the height of the core layer.     

Analysis of symmetric and asymmetric nanoscale slab slot waveguides

Nanoscale slab slot waveguides provide for high optical confinement and have found abundant applications in silicon photonics. After developing an analytical mode solver for general asymmetric slot waveguides, the confinement performance of symmetric as well as asymmetric geometries was systematically analyzed and compared. For symmetric structures, 2D confinement optimization by varying both low-index slot and high-index slab width revealed a detailed saturation trend of the confinement factor with the increase of the studied width. Furthermore, simple design rules on how to choose the slot and slab width for achieving optimal confinement was obtained. For asymmetric structures, we demonstrated that the confinement performance was always lower than the 2D optimized confinement of the symmetric structures providing the two high-index slab layers and the two cladding layers have same refractive indices, respectively. In addition, the sensitivity of the confinement to the degree of asymmetry was studied, and we found that the fabrication tolerance on the material and structural parameters may be reasonably large for symmetric structures designed at optimal confinement.     

A Modified full-vectorial finite-difference beam propagation method based on H-fields for optical waveguides with step-index profiles

A modified full-vectorial finite-difference beam propagation method based on H-fields in solving the guided-modes for optical waveguides with step-index profiles is described. The propagation is split into two substeps. In the first substep, the field propagates in the absence of the cross-coupling terms, and then they are evaluated and double used in the second substep. An improved six-point finite-difference scheme is constructed to approximate the cross-coupling terms along the transverse directions. By using the imaginary-distance procedure, the field patterns and the normalized propagation constants of the fundamental modes for a buried rectangular waveguide and rib waveguide are presented, and the hybrid nature of the full-vectorial guided-modes is demonstrated. Solutions are in good agreement with the benchmark results from film mode matching method, which tests the validity and utility of the present method.     

Resonant coupling into hybrid 3D micro-resonator devices on organic/biomolecular film/glass photonic structures

We have designed and realized an integrated photonic family of micro-resonators (MR) on multilayer SU8/lipidic film/glass materials. Such a family involves hybrid 3D-MR structures composed of spherical glass-MR arranged upon organic pair-SU8-waveguides, an efficient coupling being ensured with a Langmuir-Blodgett Dipalmitoylphosphatidylcholine (DPPC-lipid from Avanti Polar^®) film whose thickness is ranging from 12 to 48 nm. We have characterized such add/drop filters, respectively, in intensity and spectral measurements, and experimentally achieved an evanescent resonant-photonic-coupling between the 3D-MR and the 4-ports structure through the DPPC-gap. Spectral resonances have been measured for 4-whispering gallery-modes (WGM) into such 3D-structures, respectively, characterized with a 0.97 nm free spectral range (FSR) and a high quality Q-factor up to 4.10⁴.     

Multimode interference wavelength multi/demultiplexer for 1310 and 1550 nm operation based on BCB 4024-40 photodefinable polymer

A 1310 and 1550 nm coarse wavelength multi/demultiplexer based on benzocyclobutene (BCB 4024-40) polymer is demonstrated for the first time. The device is designed based on a combination of general interference and paired interference mechanisms of multimode interference (MMI). It is fabricated on BK7 glass substrate with a thin layer of SiO₂ as cover. A cost effective chemical etching technique is used in the fabrication process to take advantage of the photosensitive nature of the polymer. The device length was significantly reduced by adopting the restricted multimode interference scheme, lower beat length ratio and cascaded MMI couplers. The measured crosstalk at 1310 nm was 14.4 dB and at 1550 nm was 20.6 dB. The measured insertion loss is around 3.2-3.5 dB for both ports.     

Full-vectorial analysis of bending waveguides using finite difference method based on H-fields in cylindrical coordinate systems

A full-vectorial (FV) analysis of optical dielectric waveguide bends by using finite difference (FD) method in terms of magnetic field components is developed in a local cylindrical coordinate system. The perfectly matched layer absorbing boundary conditions via the complex coordinate stretching technique are incorporated into the FV wave equations for effectively demonstrating the leaky nature of waveguide bends, and a six-point FD scheme is constructed to approximate the cross-coupling terms for improving the convergent behavior. The leaky modes of a typical rib waveguide bend are calculated and the complex propagation constants and the field patterns for TE- and TM-like modes are obtained. Solutions are good agreement with those from the film mode matching method, which shows the validity and utility of the established method.     

Solutions of the full- and quasi-vector wave equations based on H-field for optical waveguides by using mapped Galerkin method

The mapped Galerkin method in solving the full-vector and quasi-vector wave equations in terms of transverse magnetic fields (H-formulation) for optical waveguides with step-index profiles is described. By transforming the whole x-y space onto a unit square and using two-dimensional Fourier series expansion, the modal distributions and propagation constants for optical waveguides are obtained in the absence of boundary truncation. Results for step-index circular fiber, buried rectangular waveguide, and optical rib waveguide are presented. Solutions are good agreed with exact solutions and numerical results by using vector nonlinear iterative method, Fourier operator transform method, and vector beam propagation method.     

Characterization and applications of Ag nanoparticles in waveguides

This work reports the preparation, characterization and applications of silver nanoparticles synthesized through the chemical reduction of AgNO₃ and protected by surface modifier. In order to characterize the formation of nanoparticles and the role of synthesis parameters (time, temperature) several studies were made, such as UV-vis spectroscopy, TEM and AFM. We present the incorporation of Ag nanoparticles in sol-gel obtained matrix, because this technique allows the incorporation of larger concentrations of active optical agents and the obtainment of full-dense films at lower temperature than those possible by other methods. The final goal of this work is the preparation of 80SiO₂·20B₂O₃ films for active optical waveguides doped with Ag nanoparticles and Erbium. We are looking for the reinforcement of the fluorescence intensity due to the effect of the resonant coupling of both optical agents (Er and nanoparticles) to produce optical amplifiers.     

Tunable optical switch based on two orthogonal line defect waveguides

The transmission characteristics of a 2-dimensional (2D) square lattice photonic crystal waveguide (PCW) with an additional perpendicular line defect are investigated by the plane wave expansion method (PWM) and the finite difference time domain (FDTD) method. From simulation results and theoretical analysis, it is found that changing the refractive index of the dielectric columns in the additional line defect can effectively adjust the light transmission through the PCW. The working mechanism can be boiled down to either the excitation of a single defect mode or the contra-directional coupling of the two defect modes. And this mechanism can be used to design other tunable optical devices.     

The optical properties of planar waveguides in LiB3O5 crystals formed by Cu implantation

A planar optical waveguide has been formed in a LiB₃O₅ crystal using 6.0 MeV Cu⁺-ions with a dose of 1 × 10¹⁵ ions/cm² at room temperature. Possible propagating modes were measured at a wavelength of 633 nm using the prism-coupling method. The refractive index profiles of the waveguide were reconstructed by an effective refractive index method and the beam propagation method was used to investigate the properties of the propagation modes in the formed waveguide. The results suggest that the fundamental TE₀ and TM₀ modes may be well-confined and propagate a longer distance inside the waveguide. The implantation process was also simulated using the transport of ions in matter code (TRIM), which indicates that the nuclear energy deposition may be the main factor for the refractive index change.     

Reconstruction of extraordinary refractive index profiles of optical planar waveguides with single or double modes fabricated by O ion implantation into lithium niobate

A method named intensity calculation method (ICM), which is based on beam propagation method (BPM) and image processing, was carried out to reconstruct the extraordinary refractive index profile (RIP) of single-mode planar waveguide in lithium niobate (LiNbO₃), which was fabricated by multi-energy megaelectron-volt (MeV) O²⁺ ion implantation. In addition, it has been proved reasonable that the alternation of extraordinary refractive index induced by ion implantation into LiNbO₃ is mainly due to the degradation of polarization and reduction of material physical density. As a result, the possible extraordinary RIP of the double-mode planar waveguide could be reconstructed using BPM according to such a hypothesis and the calculated guiding mode values. The end-fire coupling and m-line arrangements were carried out to obtain the near-field modal patterns and dark-mode spectra of waveguides, respectively.     

Optimization of signal-to-noise ratio in integrated planar optical interconnects packages

The signal-to-noise ratio (SNR) of integrated planar optical (IPO) board-to-board interconnections system is analyzed. The SNR is derived as a function of separation between the boards, beam spot size, optical system efficiency, receiver thermal noise, thickness of the substrate, and the angle of propagation of the beam. Based on the analyses and the results obtained it is shown that the design of optical interconnects system can be optimized for maximum SNR using at least one parameter, namely, angle of propagation.     

Analysis and optimization of an InGaAsP/InP waveguide variable optical attenuator

An InGaAsP/InP waveguide variable optical attenuator (VOA) is proposed in this paper. The device consists of straight input and output waveguides and an S-bend waveguide. An electrode is deposited on a portion of the waveguide to form an active region so that its refractive index can be modified by a current injection, resulting in the variation of the transmitted optical power. The beam propagation method is employed in the numerical simulation and the device structure is optimized using a genetic algorithm. The optimized VOA has a low excess loss (<1 dB) and a large dynamic range of about 40 dB.