Beat Length Research Articles

A Novel Photonic Crystal Fiber with Two Rings of Hybrid Elliptical Air-Holes for Single-Polarization Single-Mode Operation

A novel photonic crystal fiber (PCF) design with two rings of hybrid elliptical air-holes for single-polarization single-mode (SPSM) operation is presented. The proposed SPSM-PCF characteristics are investigated by using a full-vector finite element method (FEM) with perfect matched layer (PML) boundary conditions. The proposed SPSM-PCF can perform a single-polarization single-mode propagation. The modal birefringence of the proposed SPSM-PCF is as high as 0.00284 at the wavelength of 1.55 µm, the beat length is 0.546 mm. The confinement loss of the x-polarized mode is lower than 0.5 dB/km, whereas the loss of the y-polarized one is larger than 15 dB/km. Compared with the case of x-polarized mode, the y-polarized mode can be suppressed with a shorter fiber length. Variations of the mode field characteristics with input wavelength are given. For considering loss ratio and loss difference, the proposed PCF can perform SPSM operation with wide bandwidth of 600 nm. It indicates that this is a good solution to realize single-mode single-polarization operation.

Differential Rayleigh scattering method for measurement of polarization and intermodal beat length in optical waveguides and fibers

We propose a modification of the Rayleigh scattering method, which allows for measurement of polarization and intermodal beat length in single-mode and few-mode channel waveguides and optical fibers. A significant sensitivity increase is achieved by taking two high-resolution photographs in oblique scattered light of π-shifted intensity distributions produced by interference of polarization or spatial modes and applying Fourier analysis to the differential image. In the case of polarization beat length measurements, the π-phase shift is obtained by switching the polarization state at the fiber input, while in intermodal measurements, the π-phase shifting is realized by changing the excitation conditions. The usefulness of the method for characterization of channel waveguides and optical fibers is demonstrated in several examples. Moreover, we show that the combination of the spectral interferometry method with the proposed method allows for broadband measurements of differential phase and group effective indices.

Polarization maintaining highly birefringent small mode area photonic crystal fiber at telecommunication window

In this paper a highly polarization maintaining birefringent photonic crystal fiber at telecommunication window is reported via Full-Vectorial Finite Element Method (FV-FEM). By taking triangular lattice of three ring hexagonal structure PCF with suitable designing parameters such as symmetrical elliptical hole along radial axis of ellipticity a/b=5µm, air hole diameter d=1µm and pitch Λ=2.3µm, high birefringence (2.437×10-3) with small effective mode area(9.47µm2) and beat length (0.64cm) are found at wavelength 1.55µm.

Phase delay of polarisation modes in elastically twisted spun fibres

The evolution of the phase delay between linearly polarised orthogonal modes in a spun fibre elastically twisted around its axis has been studied experimentally and theoretically using a model for a helical structure of the built-in linear birefringence axes. The phase delay is a sinusoidal function of elastic twist angle, with an amplitude and period dependent on fibre parameters: spin pitch and built-in linear birefringence beat length. It is shown that, at a known spin pitch, phase delay versus elastic twist angle data can be used to determine the beat length of built-in linear birefringence in the range 0.01 to 100 mm. The theoretical analysis results are supported by experimental data for conventional and microstructured spun fibres.

Double S-bend structure for a compact two mode interference coupler

A double S-bend structure has been proposed for the reduction of coupling length of the 2 × 2 two mode interference (TMI) coupler. The coupling characteristics of the proposed structure are compared with those of conventional TMI structures using a simple mathematical model based on sinusoidal modes. The longitudinal beat length for the proposed TMI coupler is reduced by 15% of the beat length of a conventional TMI coupler. The effect of power imbalance on fabrication tolerance of the proposed TMI coupler is also studied and compared with other TMI couplers.

Refractive Index Sensor Using a Two-Hole Fiber

We propose to use a twin-hole fiber to measure refractive index of liquids The key idea is to have a single mode fiber (SMF) having two large air-holes running along the fiber length, the holes do not interact with the core. However, using wet chemical etching we can have access to the hole around the fiber, and further etching increases the holes diameter. The diameter is increased until the fiber exhibits a specific birefringence. Since the holes are open, by immersing the fiber in different liquids (n=1.33 to n=1.42) the value of the birefringence is modified and the refractive index of the liquid can be estimated from the change on the beat length. This process provides a very simple and highly sensitive mechanism for sensing refractive index in liquids, and can also be used for other applications.

矩形晶格微结构光纤偏振拍长稳定性的优化

矩形晶格微结构光纤偏振拍长稳定性的优化

Design of Nanoring Resonators Made of Metal-insulator-metal Nanostrip Waveguides

We report on the design of nanoring resonators made of metal-insulator-metal (MIM) nanostrip waveguides. The characteristics of the lightwave propagation through the silver-based MIM plasmonic waveguides with an air superstrate are examined. The effective refractive indices, the propagation losses, the bending losses, and the beat lengths are analyzed by using 2D and 3D finite element methods (FEMs). For the optimization of the nanoring resonators, we examined the resonant mode power and the Q factor with respect to the width of the MIM nanostrip and the separation between the ring resonator and the straight waveguide. We obtained an optimized nanoring resonator that had submicron diameters (R = 399 nm) and 3-order resonances at a 1550-nm wavelength. These nanoring resonators will play an important role as the basic building blocks for the realization of nanoscale photonic integrated circuits.

MODAL CHARACTERISTICS OF PLASMONIC NANOSTRIP WAVEGUIDES AND THEIR USE FOR FUNCTIONAL DEVICES

Modal characteristics of plasmonic nanostrip waveguides (PNWGs) have been analyzed for their use in the design of functional plasmonic devices. Also, the beat lengths of the plasmonic nanostrip directional coupler and the multimode interference (MMI) coupler, have been analyzed. We found a peculiar phenomenon in the direction coupler, which makes the coupling length zero and does not allow the optical coupling between two parallel PNWGs. We also found that there exists a minimal beat length in the gap between the two metal films in the MMI coupler. From these results a nano-ring resonator switch and a MMI wavelength splitter were designed.

Intermodal interferences in a multimode highly asymmetric two-core microstructured optical fiber

We investigate intermodal beatings in a multimode highly asymmetric two-core microstructured optical fiber. The modal interference theory plus finite-element calculations are used to define the expected spectral signature—beat length versus propagation length—of inter- and intra-core beating. The corresponding experimental data are in excellent agreement with these predictions over 2 orders of magnitude of the propagation length. The analysis of a similar single-core fiber confirms the identification of the beatings. Therefore, a simple framework can provide an adequate picture of propagation in complex multicore microstructured fibers.

Polarization dynamics in nonlinear anisotropic fibers

We give an extensive study of polarization dynamics in anisotropic fibers exhibiting a third-order index nonlinearity. The study is performed in the framework of the Stokes parameters with the help of the Poincar\'e sphere. Stationary states are determined, and their stability is investigated. The number of fixed points and their stability depend on the respective magnitude of the linear and nonlinear birefringence. A conservation relation analogous to the energy conservation in mechanics allows evidencing a close analogy between the movement of the polarization in the Poincar\'e sphere and the motion of a particle in a potential well. Two distinct potentials are found, leading to the existence of two families of solutions, according to the sign of the total energy of the equivalent mechanical system. The mechanical analogy allows us to fully characterize the solutions and also to determine analytically the associated beat lengths. General analytical solutions are given for the two families in terms of Jacobi's functions. The intensity-dependent transmission of a fiber placed between two crossed polarizers is calculated. Optimal conditions for efficient nonlinear switching compatible with mode-locking applications are determined. The general case of a nonlinear fiber ring with an intracavity polarizer placed between two polarization controllers is also considered.

Birefringence Analysis of Photonic-Bandgap Fibers Using the Hexagonal Yee's Cell

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> A full-vectorial finite-difference scheme utilizing the hexagonal Yee's cell is used in this paper to analyze the modes of photonic-bandgap fibers with <formula formulatype="inline"><tex Notation="TeX">${\rm C}_{6v}$</tex> </formula> symmetry. Because it respects the fiber's native symmetry, this method is free from any numerical birefringence. We also incorporate in it techniques for reducing the memory requirement (up to 3 to 4 times) and computational time, in particular by exploiting some of the symmetry properties of these fibers. Using sub-pixel averaging, we demonstrate quadratic convergence for the fundamental mode's effective index dependence on spatial resolution. We show that this method can be used to calculate the beat length of PBFs in which a birefringence is introduced by applying a small unidirectional stretch to the fiber cross section along one of its axes. Abrupt variations of the modeled fiber geometries with spatial resolution lead to oscillatory beat length convergence behavior. We can obtain a better estimate for beat length by averaging these oscillations. We apply a strong perturbation analysis to the fiber's unperturbed mode, calculated by our finite-difference method, to perform this averaging in a rigorous way. By fitting a polynomial to the predicted beat lengths as a function of grid spacing, we obtain an accurate estimate of the beat length at zero grid spacing. Reasonable convergence for the beat length is observed using a single processor with 8 GB of memory. </para>

Design and simulation of multimode interference based demultiplexers aided by computer-generated planar holograms

A 1.31/1.55 microm multimode interference based wavelength demultiplexer aided by computer-generated planar holograms is proposed. The device length is not limited to the common multiples of the beat lengths for the two wavelengths. The demultiplexer length is chosen as the first self-imaging length for 1.55 microm input, and a computer-generated holographic pattern is used to image the 1.31 microm input to the cross output port. The design and optimization of the holographic pattern is presented. The device performance is investigated using the beam propagation method.

Theoretical and experimental study of polarization characteristics of polarization maintaining fiber based on wavelength-sweeping modulation

We analyze theoretically the polarization characteristics of polarization maintaining fiber and study the basic measurement principles of beat length and polarization extinction ratio of this kind of optical fiber.According to the dependence of the phase difference between two orthogonally polarized modes (denoted as HE and HE) transmitted in the polarization maintaining fiber on the light wavelength, we propose the wavelength-sweeping modulation method to measure the beat length and the model birefringence. Based on this technique, the beat length and polarization extinction ratio of the PANDA polarization maintaining fibers (PMFs) (provided by Yangtze Optical Fiber and Cable Company, Wuhan, China) were investigated in detail. Experimental results show good consistent with the theoretical ones. We find that this method shows high measurement precision with the advantages of clear measurement principle and easy to operate. © 2010 Wiley Periodicals, Inc. Microwave Opt Technol Lett 52: 1466–1469, 2010; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.25244

A fourth-order Runge-Kutta in the interaction picture method for numerically solving the coupled nonlinear Schr¨odinger equation

A fourth-order Runge-Kutta in the interaction picture (RK4IP) method is presented for solving the coupled nonlinear Schrodinger equation (CNLSE) that governs the light propagation in optical fibers with randomly varying birefringence. The computational error of RK4IP is caused by the fourth-order Runge-Kutta algorithm, better than the split-step approximation limited by the step size. As a result, the step size of RK4IP can have the same order of magnitude as the dispersion length and/or the nonlinear length of the fiber, provided the birefringence effect is small. For communication fibers with random birefringence, the step size of RK4IP can be orders of magnitude larger than the correlation length and the beating length of the fibers, depending on the interaction between linear and nonlinear effects. Our approach can be applied to the fibers having the general form of local birefringence and treat the Kerr nonlinearity without approximation. For the systems with realistic parameters, the RK4IP results are consistent with those using Manakov-PMD approximation. However, increased interaction between the linear and nonlinear terms in CNLSE leads to increased discrepancy between RK4IP and Manakov-PMD approximation.

双折射拍长对波长不敏感的多孔光纤结构设计

双折射拍长对波长不敏感的多孔光纤结构设计

矩形晶格双折射多孔光纤宽带稳定拍长的优化设计

矩形晶格双折射多孔光纤宽带稳定拍长的优化设计

New beat length for writing periodic structures using Bessel beams

With the ultimate aim of exploiting the self-focusing behaviour to create periodic structures, we have investigated the behaviour of Bessel–Gauss beams in Kerr-like nonlinear media and have identified that a previously proposed nonlinear beat length is inaccurate with increasing power. By studying the behaviour of the beam we suggest a correction; providing a much better description of the beat length. This correction is tested against results from numerical simulations confirming the improved accuracy. Within the, scalar, nonparaxial limit we show that this modified beat length is valid for beam powers surpassing the paraxial self-focusing threshold. From this modified beat length equation, the appropriate experimental variables may be chosen to create accurate periodic structures by direct laser writing in a single exposure.

Distributed Temperature Sensor Interrogator Based on Polarization-Sensitive Reflectometry

In this paper, a polarization-sensitive reflectometry technique has been investigated in order to serve as an interrogating device in distributed sensing applications. As the sensing fiber has a beat length of about a few centimeters, a high-resolution reflectometer was required. A coherent optical frequency-domain reflectometer (OFDR) was used from this perspective. The principle is based on the linear dependence of fiber beat length on temperature. The reported experimental results detail the calibration method and discuss the features of the interrogating device in terms of temperature threshold and spatial resolution. The proposed system, exploiting the Rayleigh backscatter signal, offers an interesting alternative to existing systems, mainly based on nonlinear effects.

Modeling of the optical force between propagating lightwaves in parallel 3D waveguides

We present a rigorous analysis of the optical gradient force between coupled single-mode waveguides in three dimensions. Using eigenmode expansion we determine the optical mode patterns in the coupled system. In contrast to previous work, the sign and amplitude of the optical force is found to vary along the waveguide with a characteristic beating length. Our results establish design principles for optomechanically tunable directional couplers.