Reconstruction of extraordinary refractive index profile of O ion-implanted LiNbO3 single-mode channel waveguide based on beam propagation method and image processing

A method bases on beam propagation method and image processing is brought forward to reconstruct the extraordinary refractive index profile of the ion-implanted single-mode channel waveguide in lithium niobate. Channel waveguide is formed by O²⁺ ion implantation at three energies of (3.0, 3.6 and 4.5 MeV) and respective doses of (1.8, 2.2 and 4.8) × 10¹⁴ ions/cm² in vacuum at room temperature. Only one enhanced-index mode is observed for extraordinary light at 1539 nm by prism-coupling method. TRIM’98 code is used to simulate the damage profile in channel waveguide. The modes pattern of TE and TM are measured by use of end-face coupling method.     

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.     

Talbot Effect in Three Waveguide Arrays

By taking the coupling between the non-neighbourhood waveguides into account, the coupling characteristic of three waveguide arrays is analysed. The strong coupling equation of three waveguides is dealt with Laplace transform and LU decomposition. The general field evolution equation is obtained by inversion of the Laplace transform. The results show that the self-imaging conditions （Talbot effect） do not satisfy in general. The theoretical predictions are in good agreement with the BPM simulations.     

Families of spatial solitons in a two-channel waveguide with the cubic-quintic nonlinearity

We present eight types of spatial optical solitons which are possible in a model of a planar waveguide that includes a dual-channel trapping structure and competing (cubic-quintic) nonlinearity. The families of trapped beams include “broad” and “narrow” symmetric and antisymmetric solitons, composite states, built as combinations of broad and narrow beams with identical or opposite signs (“unipolar” and “bipolar” states, respectively), and “single-sided” broad and narrow beams trapped, essentially, in a single channel. The stability of the families is investigated via the computation of eigenvalues of small perturbations, and is verified in direct simulations. Three species-narrow symmetric, broad antisymmetric, and unipolar composite states-are unstable to perturbations with real eigenvalues, while the other five families are stable. The unstable states do not decay, but, instead, spontaneously transform themselves into persistent breathers, which, in some cases, demonstrate dynamical symmetry breaking and chaotic internal oscillations. A noteworthy feature is a stability exchange between the broad and narrow antisymmetric states: in the limit when the two channels merge into one, the former species becomes stable, while the latter one loses its stability. Different branches of the stationary states are linked by four bifurcations, which take different forms in the model with the strong and weak coupling between the channels.     

Anomalous behaviour in a Bragg reflection waveguide

A novel asymmetric Bragg reflection waveguide (BRW) showing anomalous dispersion characteristic is presented. The abnormal behaviour of increase of modal effective index with wavelength is primarily caused by the changes taking place in the imaginary part of the Bloch wavevector, in the periodic stratified cladding. The phase velocity and the group velocity dispersion characteristics for the waveguide have also been analyzed. Such an anomalous behaviour can find applications in the design of integrated optical devices.     

Flat-topped beam output from a double-clad rectangular dielectric waveguide laser with a high-index inner cladding

A novel method to produce a flat-topped laser beam by using a double-clad rectangular waveguide laser with high-index inner cladding is presented. The waveguide dispersion equation for cosine mode was deduced, the condition for the flattened mode was given out, relative gains for guided modes were calculated numerically and analyzed. Results indicate that a gain advantage for the flattened mode is clear, a flat-topped laser beam can be achieved when the optical confinement factor, the gain intensity and the output coupler are chosen suitably.     

Multimode-Waveguide-Based Optical Power Splitters in Glass

Low-loss glass-based buried multimode waveguides are fabricated by using the field-assisted Ag＋-Na＋ ionexchange technique, and multimode optical power splitters are investigated. The measured loss of the multimode waveguides is lower than 0.1 dB/cm, and the additional loss of the multimode optical power splitters is lower than 1.3 dB under the uniform splitting condition.     

Optimal design for a flat-top AWG demultiplexer by using a fast calculation method based on a Gaussian beam approximation

Passband broadening of an AWG (array waveguide grating) demultiplexer with an MMI (multimode interference) coupler connected at the end of a tapered input waveguide is considered. An explicit formula based on the field propagation of an approximate Hermit-Gaussian beam is used to calculate quickly and reliably the spectral response of the AWG demultiplexer. The widths of the input waveguide, the output waveguides and the MMI coupler are optimized. The optimal design is verified with the experimental measurement.     

Adiabatic three-waveguide directional coupler

We propose a three-waveguide directional coupler based on adiabatic evolution of a single normal mode of the system and analyze its switching properties using coupled mode theory. In our scheme the propagation coefficients of the waveguides are constant and the coupling coefficients are variable. This device works in the case that the propagation coefficients of the two outer waveguides are identical and that the coupling coefficients are designed to act in a counterintuitive order.     

The peculiarities of discrete diffraction in two-dimensional optical waveguide arrays

The fundamental peculiarities of discrete diffraction in the two-dimensional waveguide arrays were studied. The discrete diffraction properties of such arrays can be effectively altered, depending upon the input conditions. By slightly changing the input conditions, light can experience normal diffraction in one-direction and experience anomalous diffraction in the other.     

Analytical and numerical study on grating depth effects in grating coupled waveguide sensors

The in-coupling process for grating-coupled planar optical waveguide sensors is investigated in the case of TE waves. A simple analytical model based on the Rayleigh–Fourier–Kiselev method is applied to take into account the depth of the grating coupler, which is usually neglected in the modeling. Analytical expressions are derived both for the position and width of the in-coupling peaks to illustrate the effects of grating depth on the guided mode resonances in grating coupled waveguide sensors. Numerical computations verify the model for shallow gratings both in terms of peak shape and position and provide the limitations for the analytical formulas.     

Comparison of the electro-optic coefficient r33 in well-defined phases of proton exchanged LiNbO3 waveguides

The electro-optic coefficient, r₃₃, of proton exchanged LiNbO₃ waveguides has been measured in well-defined phases of the exchanged layer. Namely, in two low index-jump α-phases, i.e. unannealed soft-exchanged (SPE) and annealed (APE) guides, and in two high index-jump phases, i.e. β₁ guides and, for comparison, ordinary proton exchanged (PE) guides (having a mixture of phases). The following values have been obtained (in pm/V): 22.1±0.6 for SPE; 20.9±0.7 for APE; 0.33±0.01 for β₁; and 0.76±0.04 for PE. Differences between these values are discussed in terms of the structure of the phase involved. Received: 18 May 2001 / Revised version: 22 August 2001 / Published online: 30 October 2001     

Integrated waveguide splitter fabricated by Cs-Na ion-exchange

This paper reports a optical power splitter fabricated by Cs⁺-Na⁺ ion-exchange in KF3 glass. The propagation loss of the waveguide is about 0.25 dB/cm derived from measured contrast ratio and 3 dB bandwidth.     

Cascade arrangement of irregular optical phased arrays

We present the principle of cascade arrangement of irregular optical phased arrays. The optical phased-array beam deflector comprises arrayed optical waveguides that are spaced irregularly and arranged in a two-stage cascade. Relations between optical path differences and corresponding center-to-center spacings among elements in each stage are found, and phase matches between the two stages are achieved. Simulation shows a wide scanning angle with dramatically suppressed sidelobes.     

Self-collimation and beam splitting in low-index photonic crystals

We study self-collimation and beam splitting in low-refractive-index photonic crystals created within chalcogenide glass. We propose a beam splitter structure that allows direct experimental verification of photonic-crystal effects at optical wavelengths in a straightforward and definitive manner. The beam splitter provides angular separation of 90° using a highly compact spatial footprint, thus delivering direct application in highly integrated photonic devices.     

Multi-layer cladding leaky planar waveguide for high-power applications

We design a multi-layer cladding large-core planar waveguide that supports a single guided mode. The waveguide works on the principle of higher-order mode discrimination. The cladding of the waveguide is formed by alternate low- and high- index regions, which helps leaking out of higher-order modes while retaining the fundamental mode over the entire length of the waveguide. The structure is analyzed by the transfer-matrix method and the leakage losses of the modes have been calculated. We show that a waveguide formed in silica with numerical aperture 0.24 and core width 10 μm can be designed to exhibit single-mode operation at 1550-nm wavelength. Such a structure should find applications in high-power planar waveguide lasers and amplifiers.     

Photonic Crystal Waveguide Intersection Based on Self-Imaging of Multi-Mode Interference

A new mechanism of intersection formed by two line defect photonic crystal （PC） waveguides are numerically investigated using the finite-diFference time-domain method. The results show that the normalized crosstalk is smaller than 10^-4; the reflection is smaller than 10^-3, and the transmission is larger than 0.999. The authors analyse the physical origins and find that a modified self-imaging process in the intersected multi-mode region is the main reason of the excellent performance. This kind of multi-mode interference based intersection may find potential applications in PC optical circuits.     

Simple low-loss waveguide bends using ARROW effect

A new concept for reducing bend loss in dielectric planar waveguides is presented. It is based on the introduction of a set of antiresonant reflecting optical waveguides (ARROWs) on the outside of the bent core and defined in the same fabrication step as the main bend. It has been ascertained by simulation that the bending loss can be significantly reduced. The method is compatible with other bend-lossreduction strategies, as well as with different waveguiding structures, such as rib and buried waveguides and fibers.This revised version was published online in August 2005 with a corrected cover date.     

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.     

Design of optical polarization splitters in a single-section deeply etched MMI waveguide

The design of a single-section polarization splitter in a deeply etched semiconductor MMI waveguide is presented. Numerically simulated results indicate that the semiconductor MMI exhibits considerable polarization dependence and, utilizing this effect, a compact 1.6-mm-long polarization splitter may be fabricated to yield more than 8-dB polarization separation and only 0.11-dB optical loss, using a very simple design-approach. Received: 16 May 2001 / Revised version: 14 August 2001 / Published online: 2 November 2001