Waveguide lenses with multimode interference for low-loss slab propagation

It is shown that a nearly ideal two-dimensional focusing Gaussian beam can be synthesized by use of a linear combination of the two lowest-order even modes of an optical waveguide. This property can be used to couple laterally guided modes across slab waveguide regions with low loss. The technique is illustrated by use of a conventional multimode interference (MMI) geometry, in which the MMI coupler transforms the fundamental mode of an initial waveguide into a focusing Gaussian beam, which is then fed to a slab region. Two-dimensional beam propagation simulations show that the beam does not initially diverge in the slab region, but rather comes to a focus. A second MMI coupler then transforms the diverging beam back to the initial mode. A structure is designed that can couple the fundamental mode of a 9-microm-wide waveguide across an 88-microm-long slab region with only a 0.036-dB loss. This technique can be applied to improve the performance of small-angle waveguide crossings and integrated turning mirrors.     

Semi-vectorial analysis of a compact wavelength demultiplexer based on the tapered multimode interference coupler

Based on a parabolically tapered multimode interference (MMI) coupler with a deep-etched SiO₂/SiON rib waveguide, a compact wavelength demultiplexer operating at 1.30 and 1.55\mum wavelengths is proposed and analysed by using three-dimensional semi-vectorial finite-difference beam propagation method (3D-SV-FD-BPM). The results show that a MMI section of 330.0\mum in length, which is only 76% length of a straight MMI coupler, is achieved with the contrasts of 42.3 and 39.2dB in quasi-TE mode, and 38.4 and 37.8dB in quasi-TM mode at wavelengths 1.30 and 1.55\mum, respectively, and the insertion losses below 0.2dB at both wavelengths and in both polarization states. The alternating direction implicit algorithm with the Crank--Nicholson scheme is applied to the discretization of the 3D-SV-FD-BPM formulation along the longitudinal direction. Moreover, a modified FD scheme is constructed to approximate the resulting equations along the transverse directions, in which the discontinuities of the derivatives of magnetic field components H_y and H_x along the vertical and horizontal interfaces, respectively, are involved.     

Relaxed fabrication tolerance for self-imaging photonic crystal waveguide splitters using a tapered multimode interference region

The power imbalance between different waveguide outputs is compensated by manipulating the dispersion of the guided propagation in the multimode interference (MMI) region. This is attainable using a tapered region at the beginning of the MMI region that has been verified through simulation and experiment. From this, the fabrication tolerance for the diameters of holes in a tapered 1×3 photonic crystal waveguide (PhCW) splitter is relaxed up to a range of at least 27 nm. The output power is well-balanced to within 1 dB. The effective bandwidth of the splitters shifts only around 13 nm, for a reduction of 10 nm in the diameter of the PhCW holes. The optimized component is an outstanding ultracompact 1×3 splitter for the photonic integrated circuit (PIC).     

Mode selective directional couplers for overmoded waveguide systems

Two types of directional couplers for transverse electric (TE) modes are described: short and multihole couplers, respectively. They selectively pick one mode out of a mode mixture in an overmoded circular waveguide system. Unwanted modes are either statistically kept at low level or are suppressed by destructive interference in the coupling waveguide. Mode selectivity and directivity in multihole couplers oscillate up and down with an increasing number of holes, finally reaching a minimum of approximately 20 dB, unless there are competing modes with rational fractions of the beat wavelength. A multihole coupler for the TE₀₂ mode (28 GHz, 63.4 mm waveguide diameter, 41 holes) and a length of 1.6 m shows a calculated directivity of 68 dB and suppresses the unwanted modes TE₀₁ with 34 dB (24 dB), TE₂₂ with 37 dB (45 dB), and further modes TE_m (<5, m<6) with 17 dB to 34 dB in forward direction (figures in parentheses are for unwanted modes propagating in backward direction).A short directional coupler for the TE₀₁ mode (28 GHz, 63.4 mm waveguide diameter) with 16 holes and a length of 230 mm shows a directivity of 55 to 100 dB between 27.9 and 28.1 GHz, suppressing the TE₀₂ mode with 35 to 80 dB, the TE₀₃ mode with 30 to 65 dB, and the TE₂₂ mode with 30 to 70 dB.     

Four channel Mach–Zehnder demultiplexer using multimode interferometers in InP/InGaAsP

1 × 4 and 4 × 4 wavelength demultiplexers using multimode interferometer (MMI) were successfully demonstrated in InP/InGaAsP. Optical transmission characteristics were measured for each input to output for transverse electric (TE)/transverse magnetic (TM) modes. Reduced polarization sensitivity less than 0.3 nm was achieved in 1 × 4 MMI-MZ demultiplexer with –15 dB channel-to-channel cross talk. For 4 × 4 MMI-MZ demultiplexer, the optical crosstalk was well below –16 dB in TM mode for all input to output measurements.     

Modal interference of X-intersecting waveguide switches at large branching angles

The X-intersecting waveguide switch with large branching angles (=2–12°) is analysed using coupled mode theory. The results strongly highlight the importance of modal interference and are in good agreement with measured data.     

1x2 Multimode interference couplers based on semiconductor hollow waveguides formed from omnidirectional reflectors

A 1x2 hollow multimode interference (MMI) coupler based on semiconductor hollow waveguides formed from omnidirectional reflectors (SHOW-ODR) is demonstrated. The device has a shorter coupling length than a conventional silicon-on-insulator MMI coupler. A 2 dB uniformity was achieved at operating wavelengths between 1520 and 1562 nm. The device exhibited a weak polarization dependence in the TE and TM modes.     

Magnetic-Type Waves in a Tapered Waveguide of Subwavelength Cross Section

The characteristics of electromagnetic waves in a narrowing waveguide are investigated. A method for field analysis is developed based on the application of transverse modes parametrically dependent on the longitudinal coordinate. For a circular cross section waveguide, a system of equations for the wave amplitudes is obtained, the waves being coupled owing to a variable tilt of the walls. It is shown that in the adiabatic approximation, there exist independent eigenwaves whose structure reflects the field energy density variation due to the waveguide radius variation. A detailed analytical and numerical investigation of these fields has been carried out for a waveguide with a special profile of hypergeometric type. The applicability of the adiabatic approximation is studied and conversion of the fundamental mode into higher-order modes is assessed. The amplitudes of the higher-order modes are obtained using the Green function for ordinary differential equations. The region of the waveguide parameters is found where the higher-order mode amplitudes are not great and the adiabatic approximation is highly accurate. The dependence of the transmittance of a semi-infinite waveguide on the input radiation characteristics is obtained. It is established that the field amplitudes at the waveguide output strongly depend on the wavelength of the input radiation, on its transverse structure, and the waveguide profile steepness. The greatest output fields take place in the case of an abrupt dependence of the waveguide radius on the longitudinal coordinate.     

Numerical and experimental investigation of 2 × 2 multimode interference couplers in silica-on-silicon

In this paper we examine, theoretically as well as experimentally, the influence of a number of design parameters for a 2 × 2 multimode interference (MMI) coupler. We confirm that wide access waveguides are preferable but these should not exceed the width of the MMI. It is shown that the waveguide separation can be chosen in a reasonably wide range and that MMI's can be as short as directional couplers. That the imbalance is less than 0.2 dB if the length is within 5% of the optimum. Experimentally we observe the same variation, but at an imbalance of 0.6 dB. We show that this imbalance can be explained by a stress induced parabolic non-uniformity of the refractive index of the core across the MMI width with a peak variation of 5 × 10^–5.     

High-performance 90° hybrid based on a silicon-on-insulator multimode interference coupler

We propose a multimode interference coupler (MMI) design for high-index-contrast technologies based on a shallowly etched multimode region, which is, for the first time to our knowledge, directly coupled to deeply etched input and output waveguides. This reduces the phase errors associated with the high-index contrast, while still allowing for a very compact layout. Using this structure, we fabricate a 2 × 4 MMI operating as a 90° hybrid, with a footprint of only 0.65 mm × 0.53 mm, including all the structures necessary to couple light to a fiber array. We experimentally demonstrate a common mode rejection ratio better than -20 dBe and phase errors better than ±5° in a ~50 nm bandwidth.     

Compact multimode interference coupler with tapered waveguide geometry

In this paper, a novel MMI coupler, based on general interference, with tapered waveguide geometry has been proposed for reduction of coupling length. The coupling characteristics and power imbalance of the proposed structure are compared with conventional MMI structures by using a mathematical model based on sinusoidal modes. It is seen that the beat length for tapered MMI coupler with angle of taper ∼1.05° is reduced by ∼24% of that of conventional MMI coupler and the coupling characteristics obtained with the mathematical model, match well with those obtained by more sophisticated BPM computer aided design software. The power imbalance for tapered 3 dB MMI coupler is more sensitive to the wavelength than that for conventional 3 dB MMI coupler and variation of power imbalance with fabrication tolerance for both the MMI coupler is almost same.     

Design of a wavelength demultiplexer based on a parabolically tapered multimode interference coupler

A compact wavelength demultiplexer is designed for the operation at 1.30 and 1.55 μm wavelengths using the three-dimensional semi-vectorial beam propagation method. The parabolically tapered multimode interference (MMI) coupler based on the deep-etched SiO₂/SiON rib waveguide is introduced into the present demultiplexer for reducing the length. The numerical results show that a MMI section of 330.0 μm in length, which is only 76% length of a straight MMI coupler, is achieved with the contrasts of 42.3 and 39.2 dB in quasi-TE mode, and 38.4 and 37.8 dB in quasi-TM mode at wavelengths 1.30 and 1.55 μm, respectively and the insertion losses below 0.2 dB. The modified finite difference scheme is applied to approximate the resulting equations along the transverse directions, in which the discontinuities of the derivatives of magnetic field components H_y and H_x along the vertical and horizontal interfaces, respectively, are involved.     

一阶模的滤除及在Y分支和多模干涉结构中的应用

Y分支和多模干涉结构广泛应用于平面光波导器件中，在这些器件中，Y分支和多模干涉结构输出对称性具有重要意义。引入Y分支和多模干涉结构输出的不对称主要原因是这两种结构中产生了一阶导模，设计一种新的耦合器结构，在这个结构中．两根单模波导分别放置在一根多模波导两边，并且单模波导的传播常量与多模波导的一阶模的传播常量相同，这种结构可以将一阶导模滤除。在Y分支和多模干涉结构中使用了这种结构，模拟结果表明，采用这种耦合器的Y分支和多模干涉结构具有非常好的输出对称性。     

Analysis of multiple reflections in hybrid photonic crystal multimode interference coupler

In this paper the analysis of multiple reflections in photonic crystal (PhC) multimode interference (MMI) couplers using eigen-mode expansion method is presented. The analysis is conducted on a hybrid PhC structure which consisted of 1-D PhC multimode waveguide sandwiched between 2-D PhC input/output waveguides. In PhC multimode waveguide, where the mechanism of wave confinement is not due to total internal reflection but due to photonic bandgap properties, the reflectivity at 2-D PhC facet wall would be very large for all the guided modes in the waveguide when ever the image formed due to MMI effect does not coincides with the output access waveguide.     

Impact of waveguide sidewall roughness on the output uniformity and phase of MMI splitters

In this paper, we develop a model for the effects of waveguide sidewall roughness on the output uniformity and phase of a 3-dB MMI splitter. We achieve this by investigating analytically the effect of sidewall roughness on mode coupling in the MMI section of the splitter using the coupled mode and coupled power equations. Using these equations, the subsequent impact of mode coupling losses on the splitter output uniformity and phase is calculated and results for 1 × 2 and 2 × 2 splitters are presented and compared. Finally, to illustrate the impact of sidewall roughness on the operation of a waveguide device, the response of a Mach Zehnder interferometer comprising 2 × 2 splitters is investigated.     

新型1×N多模干涉分束器的三维设计与模拟

相比于传统的1×N对称型多模干涉（Mult-Mode Interference,MMI）分束器设计,提出了一种新型埋入式弱限制光波导分束器件.它的干涉区及输入输出波导采用倒锥形式,器件尺寸减小,且不均匀性与附加损耗也减小.以1×4的对称型MMI分束器为例,当只对干涉区采用倒锥形结构后,在TE偏振中心波长为1.55 μm时,器件长度减小了500 μm,均匀性增加了0.131 dB,而附加损耗仅增加了0.02 dB,波长响应较传统设计增加了40 nm.在此基础上,又在输入输出臂上也各增加倒锥形结构后,相比于传统设计附加损耗减小了0.02 dB,均匀性增加了0.139 dB,器件长度减小了500 μm.改进后的器件具有优越的容差性.器件采用掺氟型聚合物材料进行优化设计,通过在合理范围内偏离输出波导位置,使输出光强达到最大值.     

Multimode-interference-based crossing for metal-insulator-metal waveguides

We report a waveguide crossing based on a multimode-interference(MMI)structure for metal-insulator-metal(MIM)waveguides.The MMI-based crossing comprises two orthogonal intersecting MMI waveguides that are connected to the single-mode input/output waveguide symmetrically.Single self-images are formed at the crossing center and output plane of the MMI waveguide,thereby mitigating the crosstalk and improving the throughput.The characteristics of the proposed MMI-based crossing are investigated with the finite element method of Comsol Multiphysics.The results show that the throughput reaches -1.8 dB and the crosstalk is less than -46 dB at the wavelength of 1550 nm.     

Integrated optical cross strip polarizer concept

Passing across an abrupt junction from a thick vertically bimodal waveguide to a thinner single mode segment, guided light can undergo complete destructive interference, provided that the geometry and the phases of the modes in the initial segment are properly adjusted. We propose to employ this effect to realize a simple polarizer configuration, using a strip that is etched from a planar waveguide. A beam of light is made to pass the strip perpendicularly. The light enters from the single mode waveguide outside the strip into the strip segment, which is configured to support two modes. At the end of the strip, apart from reflections, the amount of power that is guided in the following lower segment depends on the local phases of the two modes. These phases are different for TE and TM light, hence we may expect a polarization dependent power transfer, resulting in polarizer performance for a properly selected geometry. The paper describes in detail the modeling of the device in terms of rigorous mode expansion. Design guidelines and tolerance requirements for geometric and material parameters are discussed. For typical Si₃N₄/SiO₂ materials, our calculations predict a peak performance of 34 dB polarization discrimination and 0.3 dB insertion loss for a device with a total length of about 12 m that selects TE polarization at a wavelength of 1.3 m.     

基于Si3N4/SiNx/Si3N4三明治结构的偏振无关1×2多模干涉型解复用器的设计

提出一种基于Si3N4/SiNx/Si3N4三明治结构多模干涉波导的偏振无关1×2解复用器,用于分离1310和1550 nm两个波长.通过合理选择三明治结构中间层SiNx的折射率,可以调节同一波长两个正交偏振态的拍长相等,实现偏振无关;根据多模干涉原理,通过合理选择多模干涉波导的长度与宽度,可以使两个波长的输出像点分别成正像和反像,实现解复用功能.运用三维有限时域差分法进行建模仿真,对结构参数进行优化,并对器件关键结构参数的制作容差进行了分析.结果表明:该器件多模干涉波导的尺寸为4.6μm×227.7μm,插入损耗低至0.18dB,输出波导间的串扰低至–25.7dB, 3dB带宽可达60 nm.另外,本文提出的器件采用Si3N4/SiO2平台,可有效减小波导尺寸,提高集成度,不仅实现了偏振无关,而且结构紧凑、损耗低,在未来的集成光路中具有潜在的应用价值.     

Design of Millimeter-Wave Power Divider with Coupled Line

A novel 35GHz 3dB power divider using coupled transmission line is presented. Unlike conventional Wilkinson divider circuit, only the 50 transmission lines are used in the design. The impedance matching can be achieved by coupled transmission line even mode characteristic impedance. The predicated and measured performances agree well.