A wide-band polymeric electro-optic modulator array based on unidirectional coupling between multi-mode waveguide array and a vertical configured dumping planar waveguide

A polymeric wide-band electro-optic (EO) modulator array based on unidirectional mode-coupling between the guiding multi-mode waveguide array and a vertical configured planar dumping waveguide was developed. A low insertion loss of <1.7 dB was obtained due to asymmetrically designed guiding waveguide and the dumping waveguide. A modulation depth of 91% was achieved with the device length of 3.5 cm at a low driving voltage of 3.2 V. The employment of the dumping planar waveguide not only provides an efficient way to achieve the unidirectional coupling mechanism, but also effectively confines the light coupled from the guiding waveguides within the planar dumping waveguide. The combination of unidirectional coupling and light confinement effects ensures low cross talk of <22 dB between adjacent guiding waveguides. Since the proposed modulator is based on the unidirectional coupling mechanism, it is intrinsically wide-band. A wide-band operation from 1308 to 1324 nm was experimentally obtained. The unidirectional mode-coupling-based wide-band modulation principle can be readily applied to other wavelengths, such as 1330 and 1550 nm ranges.     

Mode-selective coupler for wavelength multiplexing using LiNbO<Subscript>3</Subscript>:Ti optical waveguides

A mode-selective directional coupler based on titanium in-diffused channel waveguides in lithium niobate is investigated. This coupler may be utilized as a key part of an add-drop multiplexer for dense wavelength division multiplexing in optical network nodes. The proposed coupler is based on evanescent coupling of the fundamental mode of a single-mode channel to the first higher mode of a parallel bi-modal waveguide. Our experimental results show that a compact directional coupler with coupling efficiencies larger than 90%, large bandwidth around 1550 nm, and with negligible polarization dependence can be realized using electro-optic lithium niobate substrates. Presented at 9-th International Workshop on Nonlinear Optics Applications, NOA 2007, May 17–20, 2007, Świnoujście, Poland     

Coupled mode analysis of light modulation in dielectric waveguides

A detailed analysis of electrooptic light modulation in optical waveguides is presented. Several important problems of a waveguide modulator, such as the difference of waveguide axes from crystalline electrooptic ones, the distribution of transverse and longitudinal field components of light modes, and the traveling-wave property of the modulating field, are discussed. The analysis is based on the coupled mode theory, regarding the modulation as the coupling among sidebands of unperturbed waveguide modes. The coupled mode equation is derived for the modulation in optical waveguides. It can be solved if the normal modes of the waveguide are given. Actually the equation is solved for the modulation in dielectric slab waveguides and the mechanism of modulation is discussed. The results of the analysis are applied to designing two types of waveguide modulators. In an example (10.6 μm modulator with a GaAs slab waveguide) a new efficient crystal orientation is found. The calculated phase retardation with this orientation is 0.13 rad/(V·cm) with a 1 μm thick slab. Another example of a 0.633 μm modulator using a LiTaO₃ crystal as a substrate is also described.     

Hybrid vertical directional coupling between a long range surface plasmon polariton waveguide and a dielectric waveguide

To investigate light coupling between a long range surface plasmon polariton (LRSPP) waveguide and a conventional integrated optical component, a hybrid vertical directional coupler consisting of a LRSPP waveguides and a dielectric waveguide is investigated and fabricated. In the proposed coupler the dielectric waveguide and LRSPP waveguide are vertically configured for dense integration and strong coupling. The characteristics of the even and odd super-modes of the coupler are also analyzed to design the device. The fabricated device exhibits damped sinusoidal behavior along the coupling length due to propagation loss of the LRSPP waveguide. The maximum power transfer of 86% from the LRSPP waveguide to the dielectric waveguide is achieved at the coupling length of 600 μm. The measured characteristics of the device are in relatively good agreement with a theoretical analysis.     

Negative index and indefinite media waveguide couplers

We study the coupling interaction between dielectric waveguides and coupling elements made from negative-refracting media. The coupling configuration consists of a length of dielectric waveguide, which terminates either directly into or near a planar layer composed of the negative-refracting medium, and is followed by a second waveguide. Radiation output from the first waveguide is refocused at the position of the second waveguide, so that the negative-refracting layer serves as a coupler between the waveguides. Because both isotropic negative-index layers and bilayers of indefinite media can recover the near-field, evanescent components of a source field distribution, the coupling between the input and output waveguides can be highly efficient – in principle providing perfect, lossless coupling. We present simulations and some initial experimental results illustrating the coupling effect, and speculate on the potential for optical fiber couplers and integrated modulators. PACS 42.79.Gn; 41.20.-q; 42.70.-a     

Asymmetric plasmonic-dielectric coupler with short coupling length, high extinction ratio, and low insertion loss

Asymmetric directional coupling between a hybrid plasmonic waveguide with subwavelength field confinement and a conventional dielectric waveguide is investigated. The proposed hybrid coupler features short coupling length, high coupling efficiency, high extinction ratio, and low insertion loss; it can also be integrated into a silicon-based platform. This coupler can be potentially adopted for signal routing between plasmonic waveguides and dielectric waveguides in photonic integrated circuits. Furthermore, it can be exploited to efficiently excite hybrid plasmonic modes with conventional dielectric modes.     

星形光波导耦合器的耦合特性分析

根据TE0模光波导的本征场分布、瑞利索末菲标量衍射积分公式和激励源与光波导耦合的匹配效率公式,给出光波导端面衍射和耦合的归一化发射系数和接收系数计算公式,推导出光波导端面非接触耦合的耦合效率计算公式。光波导模场分布采用高斯函数近似表达,给出简洁的计算光波导端面非接触耦合的耦合效率函数表达式。最后,基于星形光波导耦合器结构参量的特点,将累加运算采用积分运算近似表达,给出星形光波导耦合器接收光波导总的接收效率与耦合器基本参量的关系,阐明了星形光波导耦合器的耦合特性。     

Vertical coupling characteristics between hybrid plasmonic slot waveguide and Si waveguide

For development of complementary metal–oxide–semiconductor (CMOS)-compatible integrated optical circuits, vertical directional coupling between a hybrid plasmonic slot waveguide and a Si waveguide is theoretically investigated in detail. To determine the vertical separation gap and efficient coupling length, we investigate the characteristics of the even and odd supermodes at a wavelength of 1.55 μm. The vertical coupler transfers 90% of the power carried by the Si waveguide to the hybrid plasmonic slot waveguide after normalizing to reference waveguides when the gap is 60 nm and the coupling length is 2.6 μm. Because of the lossy hybrid guided mode in the plasmonic waveguide, the transmitted power exhibits damped sinusoidal behavior depending on the overlapping length. The proposed vertical coupler shows more efficient light coupling between a dielectric and plasmonic waveguide in comparison to the other types of hybrid coupler, and can be exploited further for on-chip integrated opto-electronic circuits.     

Grating-assisted coupling of optical fibers and photonic crystal waveguides

We propose and analyze a highly efficient method of coupling light from optical fibers to two-dimensional photonic crystal waveguides. Efficient coupling is achieved by positioning of a tapered fiber parallel to the linear defect, where the photonic crystal's cladding functions as a grating coupler and provides field confinement as well. Numerical simulations indicate that better than 90% transmission is possible with a full width at half-magnitude bandwidth of 12nm. It is shown that one can increase the bandwidth by increasing the field overlap between the two waveguides.     

Total internal reflection-evanescent coupler for fiber-to-waveguide integration of planar optoelectric devices

We present a method for parallel coupling from a single-mode fiber, or fiber ribbon, into a silicon-on-insulator waveguide for integration with silicon optoelectronic circuits. The coupler incorporates the advantages of the vertically tapered waveguides and prism couplers, yet offers the flexibility of planar integration. The coupler can be fabricated by use of either wafer polishing technology or gray-scale photolithography. When optimal coupling is achieved in our experimental setup, the coupler can be packaged by epoxy bonding to form a fiber-waveguide parallel coupler or connector. Two-dimensional electromagnetic calculation predicts a coupling efficiency of 77% (- 1.14-dB insertion loss) for a silicon-to-silicon coupler with a uniform tunnel layer. The coupling efficiency is experimentally achieved to be 46% (-3.4-dB insertion loss), excluding the loss in silicon and the reflections from the input surface and the output facet.     

Perpendicular coupler for whispering-gallery resonators

In this Letter, we report on a perpendicular coupler (PC) for whispering-gallery resonators; it is a near field waveguide optimized for high coupling efficiency. The PC provides highly efficient tunneling coupling between the waveguide and microresonator without the need of a phase matching condition, and saves space for integration components. Compared to the Lorentz-shape in the transmission spectrum of the parallel coupler, the reflection spectrum of the PC shows an asymmetric Fano-shape near resonance. Furthermore, we demonstrate that the collection efficiency can be enhanced by near field scatterers, with a maximal efficiency of about 75%. Our simulations show that the PC is not sensitive to most parameters (including the refractive index of the waveguide), which makes the PC optimal for the application of whispering-gallery modes.     

High efficiency,small size,and large bandwidth vertical interlayer waveguide coupler

Since the advent of three-dimensional photonic integrated circuits,the realization of efficient and compact optical interconnection between layers has become an important development direction.A vertical interlayer coupler between two silicon layers is presented in this paper.The coupling principle of the directional coupler is analyzed,and the traditional method of using a pair of vertically overlapping inverse taper structures is improved.For the coupling of two rectangular waveguide layers,a pair of nonlinear tapers with offset along the transmission direction is demonstrated.For the coupling of two ridge waveguide layers,a nonlinear taper in each layer is used to achieve high coupling efficiency.The simulation results show that the coupling efficiency of the two structures can reach more than 90%in a wavelength range from 1500 nm to 1650 nm.Moreover,the crosstalk is reduced to less than-50 d B by using multimode waveguides at intersections.The vertical interlayer coupler with a nonlinear taper is expected to realize the miniaturization and dense integration of photonic integrated chips.     

Design of tunable asymmetric directional coupler filter using periodically segmented Ti:LiNbO3 waveguides

A tunable wavelength filter is designed using Ti:LiNbO₃ asymmetric directional coupler. One arm of the directional coupler is made of continuous waveguide while the other arm is periodic segmented. This segmentation reduces the lithographic steps and hence the fabrication cost required for such asymmetric coupler based filter. The propagation constant of periodical segmented and continuous waveguides are analysed using Effective-Index-based Matrix Method. The tunability is achieved using electro-optic property of LiNbO₃.     

统一非对称光波导横向耦合模理论分析

光波导横向耦合模理论包含正交耦合模理论和非正交耦合模理论两大类, 为了追求形式上的完美, 两类理论没有统一的解析解, 并且都没有对非匹配耦合系统中耦合功率的非对称性进行深入研究. 本文一方面由Helmholtz方程出发推导出了一种新型的非正交耦合模方程, 并对两类理论中的耦合模方程进行了统一处理和求解, 得到了一种统一的解析解; 另一方面根据所得到的统一的解析解对非匹配耦合系统中耦合功率的非对称性进行了详细研究, 计算结果表明非匹配耦合系统中的最大互耦合功率和最小自耦合功率均可用统一的解析解进行近似计算. 关键词： 光波导 耦合模理论 耦合器 最大耦合功率     

Analysis and design of efficient coupling in photonic crystal circuits

A rigorous analysis and design of efficient coupling from photonic crystal (PhC) waveguides into conventional dielectric waveguides is reported. Closed-form expressions for the reflection and transmission matrices that completely characterize the scattering that occurs at the interface are derived based on an eigenmode expansion technique and a Bloch basis. Analytic expressions are used to analyze the reflection into PhC waveguides. We obtain that negligible reflection can be achieved by choosing a certain interface within a PhC unit cell. Furthermore, analytic expressions are used to design a novel and compact coupler structure in order to achieve high coupling efficiency when broad dielectric waveguides are considered. Thereby, transmission efficiencies near 100 from the fundamental guided Bloch mode into the fundamental waveguide mode are achieved.     

多波导定向耦合器耦合特性

利用拉普拉斯变换,将多波导定向耦合器的耦合模方程组变换为三对角线性方程组,并采用追赶法求出了该方程组的通解;进一步,给定初始条件,进行拉普拉斯变换反演,即可严格地求出该耦合模方程组的解。采用该方法研究了5波导定向耦合器光从一个波导入射和等光强从5个波导入射时的耦合特性,求出了耦合模方程组解的解析表达式,给出了每个波导中光功率变化规律曲线。利用该方法,可很方便地求出任意有限数目波导组成的定向耦合器在任意入射条件下耦合模方程组的解,因此对于多波导定向耦合器结构的合理设计,具有非常重要的意义。     

Nanoplasmonic directional couplers and Mach–Zehnder interferometers

We present a novel design and analysis of two nano-scale plasmonic devices: a directional coupler and a Mach–Zehnder interferometer. The designs of the two devices are based on our recent work on the air-gap coupler that resulted in high coupling efficiency between a dielectric waveguide and a plasmonic waveguide. The two devices are embedded between two dielectric waveguides and operate at optical telecom wavelengths. The overall efficiency was 37% for a 2×2 directional coupler switch and above 50% for the proposed designs for a Mach–Zehnder Interferometer. The efficiency in the proposed devices can be increased using broader plasmonic waveguides.     

Nonclassical properties of a contradirectional nonlinear optical coupler

We investigate the nonclassical properties of output fields propagated through a contradirectional asymmetric nonlinear optical coupler consisting of a linear waveguide and a nonlinear (quadratic) waveguide operated by second harmonic generation. In contrast to the earlier results, all the initial fields are considered weak and a completely quantum-mechanical model is used here to describe the system. Perturbative solutions of Heisenberg's equations of motion for various field modes are obtained using Sen–Mandal technique. Obtained solutions are subsequently used to show the existence of single-mode and intermodal squeezing, single-mode and intermodal antibunching, two-mode and multi-mode entanglement in the output of contradirectional asymmetric nonlinear optical coupler. Further, existence of higher order nonclassicality is also established by showing the existence of higher order antibunching, higher order squeezing and higher order entanglement. Variation of observed nonclassical characters with different coupling constants and phase mismatch is discussed.     

Directional coupler with soliton-induced waveguides

We demonstrate a directional coupler that employs two waveguides induced by two mutually incoherent photorefractive solitons propagating in parallel at close proximity. Efficient coupling from one waveguide to the other is achieved for probe beams at wavelengths much longer than that of the solitons. We study the mutual coupling as a function of distance between solitons.