Analysis of the birefringence of a silicon-on-insulator rib waveguide

A detailed analysis of the polarization characteristics (birefringence) of a silicon-on-insulator (SOI) rib waveguide is given. The fundamental TE- and TM-polarized modes of the SOI rib waveguide are calculated by a semivectorial finite-difference method. The rib width and the slab height of the SOI rib waveguide are normalized with respect to the total height of the silicon layer. A general relation between the two normalized parameters for a nonbirefringent SOI rib waveguide is obtained. According to this relation a nonbirefringent SOI rib waveguide can easily be designed. The fabrication tolerance for a nonbirefringent SOI rib waveguide is also analyzed, revealing that the tolerance can be increased by use of a larger total height of the silicon layer.     

Performance of submillimeter square hollow waveguides

Propagation losses are determined for 100 microm x 100 microm square, hollow waveguides constructed from glass capillaries. The small size makes it possible to observe optical effects not easily seen with larger waveguides. The depletion of higher-order even modes creates a large, nonlinear loss. Over a distance of a meter the loss approaches the smaller, linear value expected for the fundamental mode. Additionally, the lowest two even modes beat to produce an oscillatory loss with a period of approximately 2 cm. Making the focal radius 0.35 the waveguide width minimizes these two effects. In a related study, 50-microm waveguides embossed in polydimethylsiloxane are shown to have losses similar to glass capillaries.     

Bending loss of elliptical-hole core circular-hole holey fibers bent in arbitrary bending directions

A holey fiber having a core with an elliptical-hole lattice structure, which is referred to as an elliptical-hole core circular-hole holey fiber (EC-CHF), can be easily designed as a single-polarization fiber by using the fundamental space-filling modes of the core and cladding lattices. However, because the guided mode in an EC-CHF has a polarization that arises from the large geometric anisotropy of the core lattice, the influence of the bending direction on the bending loss is a crucial issue for the practical implementation of EC-CHFs. Here, the bending losses of an EC-CHF bent in arbitrary angular orientations with respect to the core cross section are calculated numerically using the equivalent anisotropic step-index circular fiber model for a real EC-CHF, and the influence of the bending direction of the fiber on the bending loss is discussed.     

Laser direct writing polymeric single-mode waveguide devices with a rib structure

A focused argon-ion laser beam is used on a spin-coated polymeric thin-film deposited upon a SiO2/Si substrate to polymerize the core for fabrication of Gaussian profile optical channel waveguides. A rib structure that allows only the fundamental mode to propagate even with its higher dimension and high-index contrast between the core and the cladding was fabricated. When the thickness of the core-index region outside the rib section decreases, the waveguide produces higher-order modes at the output. The waveguide reported here has cross-sectional dimensions and numerical apertures that match the single-mode fibers for efficient coupling. I used a mixture of two intermiscible acrylate monomers for the cladding and the core of the waveguides. The polymerization process and its dependent dwell time or scan speed and the laser power intensity are shown. I present the operational characteristics of directional couplers using a rib waveguide structure with a core-cladding index difference.     

Single-mode operation in few-mode optical fibre based on resonant coupling

The design of a low-bending loss few-mode optical fibre is proposed. Low-bending loss for the fundamental mode is achieved by increasing the index contrast between the core and the cladding, and a microstructured mode filtering region is applied to filter out the higher-order modes in the fibre. Numerical results show that the fundamental mode loss is lower than 0.03 dB/turn and the high-order mode is higher than 4.4 dB/turn at the bending radius of 5 mm and 1300–1600 nm wavelength range.     

Lossy multilayer channel optical waveguides analyzed by the transmission line matrix method

We demonstrate that the three-dimensional vectorial transmission line matrix (TLM) method is applicable to the analysis of lossy multilayer optical waveguiding structures. Any lossy multilayer waveguide geometry, including sharp discontinuities in the transverse plane, can be treated taking into account the coupling between all optical field components. The complex propagation constants (propagation constants and the attenuation coefficients) for the fundamental TE-like and TM-like modes can be determined. These parameters of the fundamental TM-like mode of a typical lossy multilayer rib dielectric waveguide are obtained as functions of free-space wavelength. Calculation of the electric-field pattern is also included. Numerical comparisons with the argument principle method (for the case of lossy multilayer slab waveguides) and the spectral-index technique (for the case of lossy multilayer rib waveguides) are also included, and it is shown that the application of the TLM method to lossy multilayer optical waveguides is accurate.     

Improved silica-zirconia sol synthesis for fabrication of a single-mode embedded dielectric channel waveguide with low transmission losses

A novel inorganic-organic hybrid silica-zirconia solgel material, which can generate 10 microm thick film in a single spin-coating process, has been developed and employed in the fabrication of an embedded dielectric channel waveguide on a silica buffer layer of a silicon substrate. The fabricated channel waveguide core had steep ridge walls, good smoothness, and high robustness, and the novel sol synthesis enabled a precise control of the geometrical and optical parameters of the embedded dielectric channel waveguide. In the 1.55 microm telecommunication window, the fundamental modes TE(00) and TM(00) in the embedded channel waveguide had low transmission losses of 0.40 +/- 0.03 dB/cm and 0.59 +/- 0.03 dB/cm, respectively.     

Power losses in bent and elongated polymer optical fibers

This study performs experimental and numerical investigations into the power losses induced in bent, elongated polymer optical fibers (POFs). The theoretical analysis is based on a three-dimensional elastic-plastic finite-element model and makes the assumption of a planar waveguide. The finite-element model is used to calculate the deformation of the elongated POFs such that the power loss can be analytically derived. The effect of bending on the power loss is examined by considering seven different bend radii ranging from 10 to 50 mm. The results show that bending and elongation have a significant effect on the power loss in POFs. The contribution of skew rays to the overall power loss in bent, elongated POFs is not obvious at large radii of curvature but becomes more significant as the radius is reduced.     

Numerical analysis of bent waveguides: bending loss, transmission loss, mode coupling, and polarization coupling

A rigorous, full-vectorial and computationally efficient finite-element-based modal solution, together with junction analysis and beam propagation approaches have been used to study bending loss, transition loss, mode coupling, and polarization coupling in bent optical waveguides. The waveguide offset and their widths have been optimized to reduce the transition loss and the mode beating.     

Improved design of a polarization converter based on semiconductor optical waveguide bends

By using an efficient vector finite-element-based beam-propagation method, we present an improved design of a polarization converter. This design relies on the use of a single-section deeply etched bent semiconductor waveguide with slanted sidewalls. By careful adjustment of the bend radius, the waveguide width, and the sidewall angle we obtained a nearly 100% polarization conversion ratio with no appreciable radiation loss and a bending angle of less than 180 degrees .     

Evaluation of some GRIN fiber parameters and the associated fraction mode loss due to mechanically induced optical anisotropy

Some of the optical parameters of the bent multimode graded-index (GRIN) optical fiber in terms of indices of refraction, where the bending stresses broke the radial symmetry, are evaluated by use of multiple-beam Fizeau fringes. The variation of the index difference between the cladding index and core index in both the compression and tensile fiber regions is measured. The accuracy of measuring the index is +/- 1 x 10(-4). The spatial resolution of the method is 1.39 microm. Evaluation of the acceptance angle, the numerical aperture, and the V number profiles of the bent fiber from the interference pattern at both sides of the bent fiber are presented. The fraction of the mode number lost has been evaluated. The method was used to study the influence of compression on diminishing the index difference that leads to a dissipation of energy and a considerable mode loss. It is obvious from the experimental data that the change of the index difference due to bending strongly affects the fraction of propagating mode number, especially at the small radii of curvature. Ignoring the variation of the index difference we evaluating the number of propagated modes number leads to an insufficient determination of the mode loss. It subsequently leads to an incorrect determination of the mode dispersion and the interface loss in bent GRIN fibers. The study confirms that the deviation of the guide axis from straightness with the radius of curvature of less than 1 cm could lead to a significant fraction mode loss.     

High-index-contrast waveguides and devices

We present a theoretical and experimental study of high-index-contrast waveguides and basic (passive) devices built from them. Several new results are reported, but to be more comprehensive we also review some of our previous results. We focus on a ridge waveguide, whose strong lateral confinement gives it unique properties fundamentally different from the conventional weakly guiding rib waveguides. The ridge waveguides have distinct characteristics in the single-mode and the multimode regimes. The salient features of the single-mode waveguides are their subwavelength width, strong birefringence, relatively high propagation loss, and high sensitivity to wavelength as well as waveguide width, all of which may limit device performance yet provide new opportunities for novel device applications. On the other hand, wider multimode waveguides are low loss and robust. In addition, they have a critical width where the birefringence is minimal or zero, giving rise to the possibility of realizing intrinsically polarization-independent devices. They can be made effectively single mode by employing differential leakage loss (with an appropriate etch depth) or lateral mode filtering (with a taper waveguide). Together these waveguides provide the photonic wire for interconnections and the backbone to build a broad range of compact devices. We discuss basic single-mode devices (based on directional couplers) and multimode devices (multimode interferometers) and indicate their underlying relationship.     

具有PBL加劲的方钢管混凝土构件受弯性能

为研究具有PBL加劲的方钢管混凝土构件的受弯性能,该文进行了无加劲肋、钢板加劲肋和PBL加劲肋三种方钢管混凝土构件受弯性能的试验研究,同时考察PBL加劲肋孔径大小和间距的影响,试验结果表明,无加劲肋构件为单波鼓曲破坏,钢板加劲肋和PBL加劲肋构件均为双波鼓曲破坏;PBL加劲肋试件管内受拉混凝土裂缝分布更为均匀,裂缝宽度和间距更小,钢管与混凝土共同受力更好;PBL加劲肋对方钢管混凝土抗弯承载力提高不明显,抗弯刚度提高约20%;钢板加劲肋是否开孔对试件的刚度影响不大。该文还进行了PBL加劲肋构造参数的影响分析,结果表明:具有PBL加劲的方钢管混凝土构件抗弯承载力随着PBL加劲肋高度、宽度的增加而增加,随着开孔孔径d₀的增大而减小;开孔间距对承载力的影响很小。在试验研究和数值分析基础上,提出了具有PBL加劲的方钢管混凝土构件抗弯承载力的简化计算方法,建议在实际工程中,相对开孔孔径和间距分别取0.5和2.0为宜。     

Characteristic analysis of nanosilicon rectangular waveguides for planar light-wave circuits of high integration

When a full-vectorial finite-difference method is used, rectangular Si waveguides can be characterized for planar light-wave circuits of high integration. The single-mode condition for a rectangular Si waveguide is obtained first. The birefringence, which can be adjusted by modifying the thickness of the cladding layer, is also studied. For a nano-Si rectangular waveguide the pure bending loss is very small even for an ultrasmall bending radius (e.g., a few micrometers), and the transition loss becomes dominant. The width and height are optimized to minimize the bending radius for the requirement that the bending loss is smaller than 0.1 dB. Finally the coupling between two parallel straight waveguides is analyzed, and it is shown that there is an optimal width for the maximal coupling length.     

Multimode solution for the reflection properties of an open-endedrectangular waveguide radiating into a dielectric half-space: theforward and inverse problems

Open-ended rectangular waveguides are extensively used in nondestructive dielectric material evaluation. The dielectric properties of an infinite-half space of a material are calculated from the measured reflection properties referenced to the waveguide aperture. This calculation relies on a theoretical and numerical derivation of the reflection coefficient likewise referenced to the waveguide aperture. Most of these derivations assume the dominant mode field distribution across the waveguide aperture. However, when dealing with low permittivity and low loss dielectric materials, there may exist significant errors when calculating the dielectric properties from the measured reflection coefficient. These errors have also shown to be more significant in the upper frequency portion of a waveguide band. More accurate results are obtained when higher order modes are considered in addition to the dominant waveguide mode. However, most studies incorporating higher-order modes have used various approximations when calculating the reflection properties and have not provided a full discussion on the influences of dielectric properties of the infinite-half space and the frequency of operation. This paper gives a rigorous and exact formulation in which the dominant mode and the evanescent higher-order modes are used as basis functions to obtain the solution for the reflection coefficient at the waveguide aperture. The analytic formulation uses Fourier analysis in addition to the forcing of the necessary boundary conditions at the waveguide aperture. The solution also readily accounts for the complex contributions of both TE and TM higher-order modes. Finally, the influences of the dielectric properties of the infinite-half space and the frequency of operation are investigated     

Analysis of mode size transformation with a tapered directional coupler

A simple tapered directional coupler with a five-layered structure is employed for mode conversion between a single-order and higher-order modes. We investigate coupling from higher-order modes to a single-order field theoretically and experimentally. As a result, we confirm that the first two modes in the tapered waveguide are coupled with a single-order mode in another waveguide by computer simulation using the beam propagation method. Furthermore, we fabricated the actual device and observed the streak patterns of the first three modes.     

Modal properties of an external diode-laser-array cavity with diffractive mode-selecting mirrors

Coupled mode theory is used to describe the behavior of an external laser cavity consisting of a diode laser array and a diffractive mode-selecting mirror. The mirror is designed to establish a uniform-amplitude, uniform-phase fundamental mode. Coupled mode theory is then used to study the behavior of higher-order modes. We show that the maximum discrimination against higher-order modes occurs when the round-trip cavity length satisfies certain Talbot relations. In addition, this high modal discrimination can be maintained for arrays with large numbers of lasers without incurring significant loss in the fundamental mode.     

In-phase supermode selection in a multicore fiber laser array by means of a self-Fourier external cavity

A procedure is developed to determine the transverse-mode structure of a cavity consisting of a dense, evanescently coupled, waveguide laser array, which, in addition, is externally coupled by feedback from an external cavity. The formalism is used to determine the loss and phasing properties of a multicore fiber array coupled to an external self-Fourier cavity. Best performance is predicted for linear arrays of up to five cores, or two-dimensional arrays of up to 25 cores. A low-loss, in-phase, fundamental array mode is predicted, which achieves better than 30 dB discrimination against higher-order modes at periodically spaced values of the array length. However, we show that a shift in operating wavelength of typically a few nanometers can bring about near-perfect phasing and loss operation over a continuum of fiber lengths. With increased fill factor, significantly more of the output power can be concentrated in the central lobe of the far field but at the penalty of increased loss in the fundamental eigenmode.     

Beam homogenizer for hollow-fiber delivery system of excimer laser light

A beam homogenizer for a hollow-fiber-based, UV laser delivery system is proposed. A rectangular glass waveguide with an inner aluminum coating that has a 1-mm square cross section is attached at the output end of the circular-core hollow fiber with a 1-mm inner diameter. The rectangular waveguide generates a number of higher-order modes and results in a uniform top-hat profile. The configuration of the waveguide is designed by a ray-tracing technique so that both the low transmission loss and the high uniformity in the output beam are obtained. The fabricated waveguide shows a low loss of 0.4 dB, and the intensity variation coefficient is 7%. The output beam from the rectangular waveguide is expanded by a lens to the size larger than 10-mm square. It is also shown that the profile does not change with the bending condition.     

Nanoscale Guiding of Infrared Light with Hyperbolic Volume and Surface Polaritons in van der Waals Material Ribbons

Van der Waals (vdW) materials host a variety of polaritons, which make them an emerging material platform for manipulating light at the nanoscale. Due to the layered structure of vdW materials, the polaritons can exhibit a hyperbolic dispersion and propagate as nanoscale-confined volume modes in thin flakes. On the other hand, surface-confined modes can be found at the flake edges. Surprisingly, the guiding of these modes in ribbons—representing typical linear waveguide structures—is widely unexplored. Here, a detailed study of hyperbolic phonon polaritons propagating in hexagonal boron nitride ribbons is reported. Employing infrared nanoimaging, a variety of modes are observed. Particularly, the fundamental volume waveguide mode that exhibits a cutoff width is identified, which, interestingly, can be lowered by reducing the waveguide thickness. Further, hybridization of the surface modes and their evolution with varying frequency and waveguide width are observed. Most importantly, it is demonstrated that the symmetrically hybridized surface mode does not exhibit a cutoff width, and thus enables linear waveguiding of the polaritons in arbitrarily narrow ribbons. The experimental data, supported by simulations, establish a solid basis for the understanding of hyperbolic polaritons in linear waveguides, which is of critical importance for their application in future photonic devices.