Emissions of Photonic Crystal Waveguides with Discretely Modulated Surfaces

Transmission properties of photonic crystal （PC） waveguides with discretely modulated exit surfaces are investigated numerically using the finite-difference time-domain （FDTD） method. Unlike the case of periodically modulated surfaces, where the transmission beam tends to be a single and directional beam, when the exit surfaces are modulated only at several discrete points, the emission power tends to split into multiple and directional beams. We explain this phenomenon using a multiple point source interference model. Based on these results, we propose a 1-to-N beam splitter, and numerically realized high efficiency coupling between a PC sub-wavelength waveguide and three traditional dielectric waveguides with a total efficiency larger than 92%. This simple, easy fabrication, and controllable mechanism may find more potential applications in integrated optical circuits.     

Design, Fabrication, and Measurement of Two-Dimensional Photonic Crystal Slab Waveguides

Two-dimensional photonic crystal slab waveguides on SOI wafer are designed and fabricated. Photonic band gap, band gap guided mode, and index guided mode are observed by measuring the transmission spectra. The experimental results are in good agreement with the theoretical ones.     

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.     

Transverse Writing of Multimode Interference Waveguides inside Silica Glass by Femtosecond Laser Pulses

Multi-mode interference waveguides are fabricated inside silica glass by transverse writing geometry with femtosecond laser pulses. The influences of several writing and reading factors on the output mode are systematically studied. The experimental results of straight waveguides are in good agreement with the simulations by the beam propagation method. By integrating a straight waveguide with a bent waveguide, a 1× 2 multi-mode splitter is formed and 2×3 lobes are observed in the output mode.     

Modelling and Analysis of Modal Behaviour in SOI Slot Waveguides

Mode behaviour for SOI slot waveguides is modelled and analysed using a numerical full vectorial method based on the film mode matching method （MMM）. Only the quasi-TE mode is investigated. Waveguide heights and slot widths, as well as silicon widths are properly chosen with respect to the single mode behaviour in the slot region. Comparison between the effective index method and our side loss method shows that our single mode condition is creditable. The optical power confinement in slot region for the quasi-TE mode is also studied and presented. We demonstrate that the maximum achievable optical power confinement Pslot and the maximum normalized average optical intensity Islot are 42% and 26um^-2, respectively.     

Bending Efficiency of Bent Multiple-Slot Waveguides

The bending efficiency of three-dimensional bent multiple-slot waveguides is studied by applying a combined method of effective-index and modified transfer-matrix methods. The effects of asymmetric structure, asymmetric slots, and asymmetric middle strips on the bending efficiency are investigated. We show that the bending efficiency can be improved by the use of asymmetric structures and asymmetric middle strips. The bending efficiency of different slot waveguides （up to quintuple-slot structure） is compared. It is revealed that although the single-slot waveguide in general provides the lowest bending loss for the same waveguide parameters, it is possible that the multiple-slot waveguide can present a lower bending loss than the single-slot one.     

Self-collimation and self-imaging effects in modulated waveguide arrays

Self-collimation and self-imaging are comparatively investigated for discretized light in engineered modulated arrays of optical waveguides. It is shown that self-imaging is a rather extraordinary effect related to a fortuitous band collapse and it is thus rather distinct from self-collimation.     

Geometry Parameter Optimization of Large Cross-Sectional S-Shaped Bent Rib Waveguides for Silicon Based Optical Switches

By using a genetic algorithm, geometry parameters of large cross-sectional S-bend rib waveguides are optimized aiming at the least total loss when the propagation loss is considered. Optimized results axe presented as an example of S-bend rib waveguides based on silicon-on-insulator （SOI） 4 × 4 optical switches. The value of 2 dB/cm is given to the propagation loss according to the experimental results. The simulation results indicate that the total loss drops from 1.0002rib down to 0.4375dB without considering a lateral offset. If the offset is adopted, the total loss reduces from 0.5463dB to 0.2365dB. In addition, the effect of the rib height ratio on the loss is analysed, and the optimal ratio is obtained to be 0.55.     

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.     

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.     

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.     

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.     

Femtosecond waveguide writing: a new avenue to three-dimensional integrated optics

Using tightly focussed femtosecond laser pulses, waveguides can be fabricated inside various glasses and crystals. This technique has the potential to generate not only planar but three-dimensional photonic devices. In this paper we present, to the best of our knowledge, the first true three-dimensional integrated optical device, a 1×3 splitter fabricated in pure fused silica. The optical properties of this device and possibilities for the fabrication of complex high-density integrated optical elements are discussed. Received: 23 December 2002 / Accepted: 6 January 2003 / Published online: 28 March 2003 RID="*" ID="*"Corresponding author. Fax: +49-3641/65-7680, E-mail: nolte@iap.uni-jena.de     

Multiple Wavelength-Channels in SPP Waveguides for Optical Communication

Surface plasmon polaritons （SPPs） can be excited, meanwhile some peculiar optical phenomena will appear when light irradiates metal structures under some conditions. Based on photonie band gap theory, in this Letter we present a kind of SPP waveguide with multiple wavelength-channels. By using the Bragg effect and introducing some geometric defect layers into a quasi-periodic metal heterowaveguide, the multiple SPP forbidden bands （SPFBs） in a given waveband can be generated, and the multiple SPP pass bands （SPPBs） with narrow bandwidth in each SPFB can be realized. The SPP propagation in metal heterowaveguide is calculated by FDTD and transfer matrix methods. By selecting appropriate thickness, position and the number of defect layers, two SPPBs can be achieved in the SPFBs around 1.31 and 1.55μm simultaneously.     

Display method with compensation of the spatial frequency response of a liquid crystal spatial light modulator for holographic femtosecond laser processing

Liquid crystal spatial light modulators, which are widely used as display devices for computer-generated holograms, have modulation characteristics that depend on spatial frequency. We describe a method for displaying a computer-generated hologram on a liquid crystal spatial light modulator with compensation of its spatial frequency response. Using this method, we demonstrate a binary phase grating with smaller dependence on the spatial frequency. We also demonstrate application of the display method to holographic femtosecond laser processing.     

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.     

Design and Fabrication of Polarization-Independent Micro-Ring Resonators

Origin of polarization sensitivity of photonic wire waveguides （PWWs） is analysed and the effective refractive indices of two different polarization states are calculated by the three-dimensional full-vector beam propagation method. We find that PWWs are polarization insensitive if the distribution of its refractive index is uniform and the cross section is square. An MRR based on such a polarization-insensitive PWW is fabricated on an 8-inch silicon-on-insulator wafer using 248-nm deep ultraviolet lithography and reactive ion etching. The quasi-TE mode is resonant at 1542.25nm and 1558.90nm, and the quasi-TM mode is resonant at 1542.12nm and 1558.94nm. The corresponding polarization shift is 0. 13 nm at the shorter wavelength and 0.04 nm at the longer wavelength. Thus the fabricated device is polarization independent. The extinction ratio is larger than 10dB. The 3dB bandwidth is about 2.Snm and the Qvalue is about 620 at 1558.90nm.     

Flexible Control of Light Propagation Using a Novel Photonic Crystal Hetero-Waveguide Based on Silicon-on-Insulator Slab

We demonstrate a photonic crystal hetero-waveguide based on silicon-on-insulator (SOI) slab, consisting of two serially connected width-reduced photonic crystal waveguides with different radii of the air holes adjacent to the waveguide. We show theoretically that the transmission window of the structure corresponds to the transmission range common to both waveguides and it is in inverse proportion to the discrepancy between the two waveguides. Also the group velocity of guided mode can be changed from low to high or high to low, depending on which port of the structure the signal is input from just in the same device, and the variation is proportional to the discrepancy between the two waveguides. Using this novel structure, we realize flexible control of transmission window and group velocity of guided mode simultaneously.     

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.