Detailed investigation of self-imaging in multimode photonic crystal waveguides for applications in power and polarization beam splitters

Properties of the self-imaging effect based on multimode interference (MMI) in multimode photonic crystal waveguides (PCWs) are investigated and analyzed in detail. By combining photonic band gap (PBG) and total internal reflection (TIR) effects in PCWs, self-imaging phenomena are achieved for both TE and TM polarizations. To observe the images reproduced by this self-imaging phenomenon, finite-difference time-domain (FDTD) simulations are performed on a multi-mode PCW. From these numerical simulations the reproduced images are identified and their positions along the propagation axis are described. We also, present the design and simulation of novel polarization-insensitive power splitter and polarization splitter. The simulation results show that the optimized devices have excellent transmission efficiencies as well as wide operating frequency bandwidths and small structure size. So, the proposed devices are promising and may play an important role in high-density photonic integrated circuits in the future.     

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.     

Splitting-on-demand optical power splitters using multimode interference (MMI) waveguide with programmed modulations

Reconfigurable multi-channel optical power splitter is proposed and its optical properties are calculated. The device can dynamically reconfigure the number of splitting channels by providing programmed refractive index modulations on a multimode interference (MMI) waveguide. A reconfigurable 3-channel optical power splitter is designed to work as 1 × 1, 1 × 2 or 1 × 3 optical power splitter depending on the state of the heat electrodes using thermo-optic modulation, and the input light can be distributed to three output channels with sequential orders. The device can work in the whole C-band (1530-1565 nm) with extinction ratio better than −29.0 dB, excess loss better than −0.45 dB, imbalance better than 0.08 dB and polarization dependent loss (PDL) better than 0.14 dB. The design conception is scalable to a multi-channel splitting-on-demand optical power splitter which can divide input light to 1, 2, …, N output channels equally by using the 3-channel reconfigurable optical power splitter as a building block.     

基于自映像的光子晶体波导分束器的设计

通过研究2维正方晶格光子晶体波导多模干涉的自映像效应,优化设计了一种新型1×2光子晶体波导分束器,采用时域有限差分法对其传输特性进行模拟分析。设计过程中,根据多模干涉耦合区中周期出现的双重像的位置确定两个单模输出波导的位置,通过在分束器输入和输出耦合区的连结处设置介质柱,改变输入和输出耦合区中的模场分布,实现模式匹配,从而明显减小分束器的反射损耗。计算结果表明:设置的介质柱归一化半径分别为0.08和0.177时,对于波长为1.55 μm的入射光,该分束器的透射率可高达93%。     

基于自映像的光子晶体波导分束器的设计

通过研究2维正方晶格光子晶体波导多模干涉的自映像效应,优化设计了一种新型1×2光子晶体波导分束器,采用时域有限差分法对其传输特性进行模拟分析。设计过程中,根据多模干涉耦合区中周期出现的双重像的位置确定两个单模输出波导的位置,通过在分束器输入和输出耦合区的连结处设置介质柱,改变输入和输出耦合区中的模场分布,实现模式匹配,从而明显减小分束器的反射损耗。计算结果表明:设置的介质柱归一化半径分别为0.08和0.177时,对于波长为1.55μm的入射光,该分束器的透射率可高达93%。     

Design and fabrication of high-efficiency photonic crystal power beam splitters

Efficient beam splitters in a planar photonic crystal waveguide with corrugated terminators were designed, fabricated, and characterized. Experimental results showed that these beam splitters have high splitting efficiency and power intensity in the propagation direction, an achievement made possible through a design method employing a genetic algorithm-based optimization method. High-efficiency power beam splitters are useful components in integrated optics, and the design implemented here is particularly suited for integration with other optical components.     

Investigation of self-imaging based on the field distribution in multimode photonic crystal waveguides

We have investigated the self-imaging phenomena based on the field distribution in two-dimensional multimode photonic crystal waveguides (PCWs) by the finite-difference time-domain (FDTD) method. The new self-imaging conditions are given for the mirrored images and the direct images. The self-imaging distributions in multimode PCWs can be explained by the new self-imaging conditions and the superposition of “sub-images”. The results of numerical simulation show a good agreement with the theoretical predictions.     

Study on self-imaging properties for line-tapered multimode interference couplers

The line-tapered multimode interference (MMI) couplers have advantage of compact dimension compared with conventional straight MMI couplers and then are more suitable for integrated optical components. In this paper, the self-imaging properties including general self-image and overlapping-image properties for the line-tapered MMI couplers are discussed thoroughly. Based on the width equation we defined, compact equations for the positions, amplitudes, phases of general images and overlapping images are deduced. Three disciplines for general self-imaging and four disciplines for overlapping-imaging are summarized and discussed. In addition, the overlapping-image properties are further studied by matrix analytic method and an inductive reasoning method of constructing phase and intensity matrix is developed based on it. Finally, all the theoretical results are compared with simulations results obtained by the finite-difference beam propagation method (FD-BPM). Both theoretical and simulation results are shown in this paper and demonstrated to be coincided with each other to a great extent.     

Analysis of optical rib self-imaging multimode interference (MMI) waveguide devices using the discrete spectral index method

We have developed a semianalytical approach to study the propagation characteristics of multimode interference (MMI) waveguide structures. The effect of transverse crosssection geometry on self-imaging length and optical power throughput are investigated. We present results confirming that the nonquadratic modal dispersion encountered in stripe-loaded waveguides impairs self-imaging performance. Results indicate that the image degradation is more predominant for asymmetrically fed MMI waveguides.     

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 and fabrication of a compact multimode interference splitter with silicon photonic nanowires

A compact multimode interference （MMI） splitter with silicon photonic nanowires on silicon-on-insulator （SOI） substrate is designed and fabricated. The footprint of the MMI section is only approximately 3×10 （μm）. The simulation results show that the device may have a low excess loss of 0.04 dB. The transmission loss of the silicon photonics wire is measured to be 0.73±0.3 dB/mm. The compact size and low transmission loss allow the device to be used in ultra-compact photonic integrated circuits. The device exhibits a good light splitting function. In a spectral range of 1549-1560 nm, the excess loss is 1.5 dB and the average imbalance between the two channels is 0.51 dB.     

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.     

硅光子晶体TE模式光下路分束器设计

设计了基于自准直效应的硅光子晶体TE模式13和12光下路分束器。13光下路分束器由4个分束镜组成,而12下路分束器由3个分束镜和1个反射镜组成。利用多光束干涉原理推导出光下路分束器各个出口的透射谱理论公式。通过选择合适的分束镜,可以得到不同分束比例的光下路分束器。对于13光下路分束器,设计了1∶1∶1和1∶2∶3两种分束比例;对于12光下路分束器,设计了1∶1和1∶2两种分束比例。再利用时域有限差分软件数值模拟了透射谱,其结果与理论设计一致。当下路波长为1550 nm时,13和12两种光下路分束器的大小均约为10 m 10 m,自由光谱区为36 nm,覆盖了整个光通信C波段。     

硅光子晶体TE模式光下路分束器设计

设计了基于自准直效应的硅光子晶体TE模式13和12光下路分束器。13光下路分束器由4个分束镜组成,而12下路分束器由3个分束镜和1个反射镜组成。利用多光束干涉原理推导出光下路分束器各个出口的透射谱理论公式。通过选择合适的分束镜,可以得到不同分束比例的光下路分束器。对于13光下路分束器,设计了1∶1∶1和1∶2∶3两种分束比例;对于12光下路分束器,设计了1∶1和1∶2两种分束比例。再利用时域有限差分软件数值模拟了透射谱,其结果与理论设计一致。当下路波长为1550 nm时,13和12两种光下路分束器的大小均约为10 m 10 m,自由光谱区为36 nm,覆盖了整个光通信C波段。     

All-optical controllable trapping and transport of subwavelength particles on a tapered photonic crystal waveguide

We propose that a tapered photonic crystal waveguide design can unify optical trapping and transport functionalities to advance the controllability of optical manipulation. Subwavelength particles can be trapped by a resonance-enhanced field and transported to a specified position along the waveguide on demand by varying the input wavelength. A simulated transport ability as high as 148 (transport distance/wavelength variation) is obtained by the waveguide with 0.1° tilted angle. Stable trapping of a 50 nm polystyrene particle can be achieved with input power of 7 mW. We anticipate that this design would be beneficial for future life science research and optomechanical applications.     

Modulation of focus using photonic crystal waveguide

We study theoretically that a photonic crystal waveguide with modulated output surface can focus electromagnetic wave just like a lens. The characters of the focus are sensitive to the surface morphology and can be modulated by adjusting the parameters. Two methods are proposed to modify the focus, and an interesting off-axis focus is found in an asymmetrical structure.     

Large-area metallic photonic crystal fabrication with interference lithography and dry etching

Large-area one-dimensional periodic metallic structures were fabricated on a waveguide layer with interference lithography and dry etching. As narrow as 115-nm gold nanowires were obtained with a period of 395 nm, covering a homogeneous area as large as 5 × 5 mm². Extinction measurements demonstrate the strong coupling between waveguide mode and gold-particle plasmon resonance. We demonstrate good agreement with a scattering-matrix theory. The dispersion of the metallic photonic crystals was obtained by angle-resolved measurements. This method represents a simple and low-cost way to fabricate large-area metallic photonic crystals.     

Beaming effect in multimode photonic crystal by using coupled waveguides

Beaming effect of a multimode photonic crystal (PC) covered by a waveguide array on the exit plane is investigated theoretically. The simulation results show that the multimode PC can make the incident light split into two beams, which can be regarded as secondary sources radiating light into the waveguide array. As a result, many light beams can be generated in the array by the coupling among the waveguides, and the interference of these light beams after passing the system leads to directional emission. Additionally, the directional emission is greatly affected by the beam distribution on the exit plane of the system. Once the main light beams are formed on the exit plane of the system by modulating the system size, steady beaming effect can be obtained in the horizontal direction.     

Direct imaging of multimode interference in a channel waveguide

By use of a near-field scanning optical microscope in collection mode, multimode interference was directly measured in an annealed proton-exchanged LiNbO3 waveguide. Periodic transitions from a single-peaked Gaussianlike intensity distribution to a double-peaked intensity distribution were observed. The intensity distribution along the waveguide was calculated, and the results agree well with the experimental observation.