Complete leaky mode coupling in dual-core photonic crystal fibre based on the coupled-mode theory

This paper theoretically investigates the dependence of leaky mode coupling between inner core fundamental mode and outer core defect mode on phase and loss matching in pure silica dual-core photonic crystal fibres with the multi-pole method. The complete mode coupling can take place when both the phase and loss matching conditions are satisfied at the avoided anti-crossing wavelength. It shows the influences of cladding structure parameters including the diameters of cladding air holes d₁, diameters of outer core holes d₂ and hole to hole pitch Λ on the characteristics of leaky modes coupling. The coupled-mode theory is used to analyse the mode transition characteristics and the complete coupling can be clearly indicated by comparing the real and imaginary parts of propagation constant of the leaky modes.     

Simple high-order Galerkin finite element scheme for the investigation of both guided and leaky modes in anisotropic planar waveguides

A simple high-order Galerkin finite element scheme is formulated to compute both the guided and leaky modes of anisotropic planar waveguides with a diagonal permittivity tensor. Transparent boundary conditions derived from the Sommerfield radiation conditions are used to model the fields at the computational boundaries that allow the radiation into the high index cladding/substrate and decay into the low index cladding/substrate, hence work for both guided and leaky modes. Richardson's extrapolation is employed to achieve high-order accuracy by only using simple first-order-polynomial basis functions. Schemes up to sixth-order of accuracy in the effective index are demonstrated. The resulted non-linear sparse matrix eigenvalue equation is solved using an iterative procedure. The ability of the scheme to compute leaky and guided modes of various structures with isotropic and anisotropic materials, step and graded index profiles is demonstrated; including its applications to investigate the properties of ARROW structures.     

Perturbation theory of optical fibres with power-law core profile

The characteristics of graded-index optical fibres with power-law core profile and homogeneous cladding have been studied using perturbation theory. Analytical expressions are derived for the cut-off frequency, propagation constant and, in the case of leaky modes, the attenuation coefficient of an arbitrary mode on such a fibre. For the case of monomode fibres, excellent agreement is found with existing theoretical results for the propagation constant of the HE₁₁ mode and cut-off frequency of the TE₀₁ mode.On leave from Department of Physics, IIT, New Delhi, India.     

Large-core single-mode channel waveguide based on geometrically shaped leaky cladding

We propose a leaky channel waveguide structure for large-mode-area single-mode operation. The proposed structure is characterized by a uniform rectangular core and a specially designed cladding, through which all the confined modes are leaky. Single-mode operation is ensured by choosing the waveguide parameters properly so that the differential leakage loss between the first two modes is sufficiently high. A general power-law cladding geometry profile is considered, which is solved by the effective-index method in conjunction with the transfer-matrix-method to obtain the effective indices and leakage losses of the modes. We show that, with a suitable choice of cladding parameters, the waveguide can demonstrate extended single-mode operation in the wavelength range 750–1600 nm with a core area as large as 100 μm². Such a large confinement area for mode propagation can effectively suppress nonlinear optical effects. The waveguide is expected to find applications in the design of high-power lasers and amplifiers. PACS 42.82.-m; 42.82.Et; 42.79.Gn; 42.55.-f; 42.82.Bq     

A partially reflecting metal cladding: its effect on the modes of dielectric optical waveguides

If the metal cladding of a dielectric optical waveguide is sufficiently thin to be only partially reflecting, then the waveguide modes differ from those of the conventional metal-clad waveguide. The TE modes are little affected by a variation in the metal thickness but the TM modes change considerably due to a coupling between the waveguide modes and the surface plasma waves supported by both the metal: dielectric interfaces and the metal film. It is the refractive index of the dielectric cladding which is remote from the guiding core that determines whether the lowest order TM mode is the TM₀ or TM₁ mode. This dielectric cladding also strongly influences the attenuation of the TM modes and, if the guide supports a TM₀ mode, then the attenuation of the TM modes far from cut-off are an order of magnitude higher than that of the corresponding modes when the guide cannot support a TM₀ mode. If the guide can support a TM₀ mode then its dimensions can be chosen such that it will support the TE_N and TM_N modes with equal phase velocities. A lossless approximation is used to develop an expression which will specify the required guide dimensions directly and parametric plots of these dimensions are discussed.     

Leaky mode analysis of circular optical waveguides

A leaky mode is a bound mode below its cut-off frequency. It attenuates in the direction of propagation and approximates the portion of the radiation field within the optical waveguide that is significant far from the source. The characteristics, including attenuation coefficients, of leaky modes on the circular fibre are compared with those of the more familiar slab waveguide. Except for the HE_1m leaky modes, leaky modes attenuate much faster on the slab than on the circular fibre. The greater the /(azimuthal field variation) the smaller the attenuatioN. Thus, theI?1 leaky modes are important even at great distances from the source. An effective cut-off frequency is proposed. Above this frequency the mode is either weakly leaky or trapped. An expression for the number of weakly leaky and trapped modes is given. The power of leaky modes due to illuminating one end of the fibre is determined. The effect of material absorption is considered.     

Study of the behaviour of the fibre Bragg grating fabricated with cladding mode suppression fibre

One effective method for suppression of coupling from guided optical modes into cladding modes in an optical fibre Bragg grating is to use cladding mode suppression fibre. In this specially engineered fibre, the grating is written into the core and the inner cladding, both of which are photosensitive. A theory is presented in this paper to analyse the spectral characteristics of this kind of gratings. A fibre Bragg grating was experimentally fabricated with this kind of photosensitive fibre (PS-RMS-50 from StockerYale). It is shown both theoretically and experimentally that such gratings exhibit strong suppression of the coupling between core mode and cladding mode. The experimental result is in good agreement with the theoretical analysis.     

Cladding mode coupling in long-period gratings formed in photonic crystal fibers

We extend the improved effective index method (IEIM) to analyze the cladding mode of the photonic crystal fiber (PCF) and to predict cladding mode coupling in gratings. By introducing a new step-index fiber model for the PCF, the cladding mode coupling between a LP₀₁ core mode and HE₁₁ cladding mode in long-period gratings formed in PCF is accurately predicted by the IEIM. The fiber model works well for the PCF used here not only in predicting resonant mode coupling, but also in analyzing core and low-order cladding modes.     

Curvature effects on leaky modes in weakly guiding optical fibres

The effect of curvature on leaky modes with low losses in weakly guiding optical fibres is investigated, within a theoretical model where the cladding (outer cladding in case of multiclad fibres) is extended to infinity. Such modes already radiate rays in the cladding when the fibre is straight and two cases can be considered according to whether this ray pattern is modified near the core area in the bent fibre (strong curvature) or is not modified (weak curvature). A general loss formula is given for the case of weak curvature. The rays which are emitted in the curvature plane, towards the inner side of the bend are captured later on by the core and induce an oscillating modulation of the leakage loss, with an amplitude varying asR ^–1/2 but limited to a few per cent in practical cases (for weak curvatures). The case of strong curvatures is analysed in the special case of the LP 01 mode in fibres with a large depressed inner cladding, through a 2-D ray method. It is found that the loss oscillations are rapidly damped while the average loss is considerably increased.     

New method for calculating the spectra and radiation losses of leaky waves in multilayer optical waveguides

The efficiency of a new method for calculating the spectrum and attenuation coefficient of leaky electromagnetic modes is demonstrated with multilayer planar optical waveguides the guiding properties of which are determined by antiresonant reflection from the multilayer cladding (antiresonant reflecting optical waveguides) rather than by total internal reflection from the core-cladding interface as in standard optical waveguides. The new method applies to calculation of both electromagnetic modes in dielectric waveguides and electron quantum states in multibarrier semiconductor heterostructures. The characteristics of multilayer waveguides calculated by the new method are compared with published data obtained from a complex dispersion relation by the transfer matrix method. As an example, the wavelength dependence of the radiation losses for the first TE mode of a planar optical waveguide containing 52 pairs of layers is calculated.     

Dual-core leaky optical waveguide as an integrated-optic polarizer

We present a design of a dual-core leaky waveguide that can be used as an integrated-optic polarizer. The proposed polarizer works on the principle of mode filtering. The structure is characterized by two cores, namely core-1 and core-2 and a high index layer in the upper-most region, such a structure supports leaky modes. The leakage losses of the modes have been calculated by using the transfer matrix method (TMM). Single polarization operation is ensured by high differential leakage loss between fundamental TE and TM modes. We show TE-pass operation with 0.5 dB/mm loss in TE₀ mode and 13 dB/mm loss in TM₀ mode, and TM-pass operation with 0.36 dB/mm loss in TM₀ mode and 7.45 dB/mm loss in TE₀ mode. Besides single-polarization operation, single-mode operation of the structure is ensured by high leakage loss of all the other higher-order modes.     

Extension de la representation scalaire du champ aux fibres optiques à gaine finie

Résumé Le concept de mode LP introduit dans la théorie du guidage faible est étendu aux fibres optiques à gaine finie, pour les modes de gaine dont l'indice effectif reste voisin de l'indice de la gaine. Une étude plus précise montre ensuite comment les modes LP_mn dégénérés se scindent en modes HE_{m+1, n} et EH_{m–1, n} non dégénérés. On indique comment écrire la condition aux limites sur l'interface fibre/air pour la fonction scalaire qui décrit le champ; à l'ordre 0 (modes LP), il suffit d'annuler cette fonction.

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The LP mode concept, which was introduced in the weak guiding theory is extended to optical fibers with finite cladding, for cladding modes the effective index of which remains close to the cladding refractive index. A more accurate study shows how the degenerate LP_mn modes split into nondegenerate HE_{m+1, n} and EH_{m–1, n} modes. The boundary condition to be satisfied by the scalar field on the air/fibre interface is derived; for zeroth order (LP modes), this scalar field must be zero on this interface.

     

Investigation on characteristics of W-type fiber with an inner cladding made of negative refractive index materials

A doubly clad optical fiber with an inner cladding made of negative refractive index material was proposed and the modes distribution, dispersion and time delay were investigated by fully vectorial numerical method. The results indicate that HE₁₂ mode can be operated as a single mode, the cut-off frequency of modes shifts to low normalized frequency with increasing thickness of inner cladding made of negative index materials, large negative dispersion and time delay can be obtained and tailored by the inner cladding. These results provide theoretical basis for designing novel fibers or optical devices.     

长周期光纤光栅耦合常数的研究

长周期光纤光栅表现为前向传播的纤芯基模与同向传播的各阶次包层模式在特定波长时的模式耦合。由纤芯基模、一阶包层模式的场分布推得其功率分布 ,进一步得到两种模式的归一化常量。推导了纤芯基模与一阶各次包层模式 (HE1l/EH1l)的耦合常数。结果表明 ,纤芯基模与HE1l包层模式产生的耦合常数远大于与EH1l包层模式的耦合常数。次数低时 ,耦合常数随包层模式次数的升高而增大     

Field Solution and Characteristics of Cladding Modes of Optical Fibers

In this article, we give out the formulations of the fields in a three-layer fiber. For a typical step-index single-mode fiber, we calculate propagation constants and mode field profiles of the cladding modes in it. Results show that the hybrid cladding modes, whose azimuthal quantum number is not zero, can also be rigorously divided into HE and EH modes. Comparison with the results of the two-layer geometry approximation indicates that when solving the cladding modes in a fiber the simplified model is unsuitable.     

Modal redistribution and power loss in on-fibre devices

The mode coupling and optical power loss taking place in on-fibre devices are investigated. These devices are fabricated by removing the cladding of a multimode fibre and replacing it with a new material such as electro-optic or magneto-optic. Under an application of an external field the index of this modified cladding increases, leading to coupling among guided modes and coupling to radiation modes, resulting in optical power loss. The coupling among guided modes and the power loss are calculated as a function of the change in the index under the field and the length of the active region for the case when HE_1m modes are excited individually or in a group. Results indicate that on-fibre devices may be used as low-loss devices for applications involving sensors and delay lines.     

镀高折射率纳米膜的长周期光纤光栅特性研究

针对镀高折射率纳米膜的长周期光栅,建立了传感理论模型,研究了长周期光栅的谐振波长与纳米膜厚度及外界折射率的关系,给出不同纳米膜厚度下长周期光栅不同包层模式重组特性.研究发现,当长周期光栅外面镀上一层沿角向均匀分布的纳米膜时,随着膜厚变化会出现包层模分布的明显调制;适当选择镀膜参数和外界介质折射率,最低次包层模式HE1,2会成为镀膜层中的导模,其他的包层模式将会发生模式转换现象;对于较低次包层模式(如HE1.6),在模式转换的时候存在两步转换,而高次的包层模只有一步转换(如HE1.14).同时给出了包层模式转换对外界折射率响应的关系:当膜层厚度增加时,长周期光栅模式转换现象移至低折射率区域.     

长周期光纤光栅模式与耦合的研究

长周期光纤光栅是在光纤纤芯中沿轴向形成折射率周期性调制的带阻型光纤器件。与光纤布拉格光栅不同，它表现为前向传播的纤芯基模与同向传播的各阶次包层模式在特定波长的耦合。研究了纤芯基模、包层模式（HE1t/EH1t）及其有效折射率随波长的变化，研究了纤芯基模与包层模式（HE1t/EH1t）的耦合系数。研究表明，纤芯基模与一阶低次包层模式的有效折射率随波长增大而减小，纤芯基模与HE1t产生的耦合系数远大于与EH1t的耦合系数，并且包层模式次数较低时，耦合系数随次数的升高而增加。这与以前的研究结果有所不同。     

长周期光纤光栅中的包层模谐振

本文给出了光纤中包层模的电场形式,指出包层膜的电场形式与弱导光纤中导模的电场形式不同,对光纤中基模与包层模电场沿光纤横截面分布的重叠情况的分析表明,长周期光纤光栅除了能将HE₁₁导模耦合到HE_1p包层模外,也可以将其耦合到EH_1p包层模。基于耦合模理论的计算表明,耦合到EH_1p和EH_1,p-1包层模的耦合波长相近,对于典型的单模光纤,当p>4时耦合到这两个模式的耦合系数是可比的。     

Single mode optical fiber characterisation by the LP11 mode radiation pattern

We describe a method for determining the V-value from the far-field radiation pattern of dual mode optical fibers (this method is an extension of the work by Gambling et al. for the LP₁₁ modes). The method involves measurements of the maximum radiation angle and the angle of the first minimum. Curves are presented which can be used with dual mode fibers, determining the core diameter, the refractive index difference between core and cladding, as well as the V-value in the single mode regime for longer wavelength operation with the help of dispersion curves of the dopant materials.