It is customary in the theory of optical fibers to make the weakly guiding approximation n. A set of coupledmode equations is derived to describe mode propagation in uniform and slightly nonuniform cylindrical opticalfiber systems. Koch, lowloss hollowcore silicaair photonic bandgap fibre, nature 424, 657 2003. Coupledmode theory of nonlinear propagation in multimode. Coupled mode theory of round optical fibers wiley online library. Institute of electro optical engineering and department of photonics national sun yatsen university kaohsiung 80424, taiwan abstractin this paper, the coupled mode theory is used to analyze apodized. The chapter illustrates the derivation of coupled mode equations based on perturbation theory, which is first presented and then concrete methods calculating the. Ankiewicz, fibre couplers composed of unequal cores, electon. This approach describes in a natural way the influence of the waveguide, and in principle allows of the possibility of investigating soliton propagation when more.
This paper presents a comprehensive theory of mode coupling in optical fibers with imperfections. Coupledmode and coupledpower theories are described for multicore fiber design and analysis. In such nonhermitian waveguides, the standard coupled mode theory fails. Use is made of the statistical ensemble of similar fibers introduced by marcuse for studying mode coupling in optical. Coupledmode theory of raman amplification in lossless.
Coupled mode theory for long period grating written in 980nm pumped erbium doped fiber rashmi singh and enakshi k. Rp photonics encyclopedia mode coupling, coupledmode. It is found that these two methods predict markedly different characteristics for the optical power of plss and its dependence on the separation distance between adjacent nanowires. Rongqing hui, in introduction to fiber optic communications, 2020. Keywords fiber bragg grating coupling coefficient optical waveguide waveguide structure couple mode theory. Here we propose a t wodimensional finite element model for computing crosstalk using supermodes calculated from direct eigenmode analysi s of a dualcore fiber structure.
Raman amplification in weakly guiding optical fibers is investigated for the two cases of weak and strong mode coupling. The fiber grating bending sensing technology is based on its axial strain sensing characteristics. Optical fibers and optical waveguides comprise a core, in which light is confined, and a cladding, or substrate is surrounded by the core. Coupled mode theory based modeling and analysis of. Optical fibers based communication networks are part and parcel of todays knowledge based society.
A coupledmode theory is derived from the scalar wave equation for the interaction between forward and. Coupled mode theory of round optical fibers marcuse 1973. Maxwells equations, boundary conditions, and the complex poynting vector are mentioned in the chapter. Complex coupledmode theory for optical waveguides weiping huang and jianwei mu department of electrical and computer engineering, mcmaster university. Derivation of coupled mode equations, coupling coefficients, reflectivity equation, fwhm, grating profile, phase mask fabrication method. First, in order to satisfy the law of power conservation, modecoupling coefficients are redefined and then, closedform powercoupling coefficients are derived based on exponential, gaussian, and triangular autocorrelation functions. Osa complex coupledmode theory for optical waveguides. Sharma department of electronic science university of delhi south campus newdelhi110021, india abstract we describe the behavior of long period gratings lpg in 980nm pumped erbium doped optical fibers. Weakly guiding optical fibers are discussed along with coupled mode theory and coupled power theory. As a result of recent technological advances in fabrication, light can be guided through 1 km of glass fiber with a loss as low as 0. A systematic approach for designing zerodgd coupled multi. Application of the complex coupledmode theory to optical. Pdf application of the complex coupledmode theory to. A set of equations describing pulse propagation in multimode optical fibers in the presence of an intensitydependent refractive index is derived by taking advantage of the coupledmode theory usually employed for describing the influence of fiber imperfections on linear propagation.
The paper begins with the derivation of a general coupled. Coupled mode theory for the leaky modes of a bent fiber. Katsunari okamoto, in fundamentals of optical waveguides second edition, 2006. We show, in particular, that different methods employed in the literature lead to physically distinct results. Pdf coupled mode theory for optical waveguides jianwei. The analysis using the above model shows that only a few most relevant basis. Osa general coupled mode theory in nonhermitian waveguides. Coupledmode theory for allfiber acoustooptic modulator. Improved coupledmode theory for codirectionally and contradirectionally coupled waveguide arrays r. Ray optics and optical systems optical resonators integrated optics. The paper begins with the derivation of a general coupled wave theory based on the modes of the ideal fiber. If the bragg condition is satisfied, the contributions of reflected light from each grating plane add constructively in the backward direction to form a back reflected peak with center wavelength defined by the grating period. Spectral characteristic of uniform fiber bragg grating using couple mode theory 42 solutions for the oscillating and propagating waves 6.
In the preceding two chapters, the transmission characteristics of independent planar optical waveguides and optical fibers have been investigated. Coupled mode theory describes this energy exchange, and serves as the primary tool for designing optical couplers, switches, and filters. The complex coupledmode theory cmt is applied to optical fiber grating structures of circular cross section. Fiber bragg grating coupling coefficient optical waveguide waveguide structure couple mode theory. Applications of the coupled mode theory are also considered, taking into account a slab. We apply our theory to the nonhermitian paritytime symmetric waveguides, and obtain excellent agreement with results obtained by finite element fullwave simulations. The authors give a brief historic perspective of the coupled mode theory. It is for the first time that we can treat guided and radiation field in a unified and straightforward fashion without having to resort to cumbersome radiation modes. We generalize the coupled mode theory with a properly defined inner product based on reaction conservation. A brief account of the recent development of the cmt for coupled optical waveguides is given. The development and applications of the theory in microwaves in early years and in optoelectronics and fiber optics in recent years are described.
Improved coupledmode theory for codirectionally and. The perturbed coupledmode theory is used to discuss the solutions of coupledmode equations for optical fiber when there are multiple parts being perturbed, and the multiplechannel modulation is. A systematic approach for designing zerodgd coupled multicore optical fibers midya parto, mohammad amin eftekhar, mohammadali miri, rodrigo amezcuacorrea, guifang li, demetrios n. Coupledmode theory of optical waveguides ieee journals. The formalism of coupledmode theory is adopted for describing nonlinear pulse propagation in optical fibers, the coupling being induced by the nonlinear part of the refractive index. Under this assumption, each mode can provide an independent communication channel for information transmission through the fiber.
The radiative fields are treated in terms of discrete complex modes similarly to the. Coupled mode theory for long period grating written in. Marcuse, coupled mode theory of round optical fibers, j bell syst tech 52, 817843 1973. Dynamic coupledmode theory of nonlinear propagation in. Coupled mode theory is particularly useful when a slight perturbation has a large effect on the distribution of modal power, e.
Joan manuel gene bernaus abstract we start by describing what sdm is, the problem at hand for its been considered and the different solutions it can provide. Propagation modes in a mmf are mutually orthogonal, and ideally there is no energy exchange between different modes during propagation. Mode coupling on a lossy fiber is investigated and a simple. Yamashita, a simple coupledmode analysis method for multiplecore optical fiber and coupled dielectric waveguide structures, ieee trans. Pdf coupled mode theory for optical waveguides jianwei mu. Ieee photonics journal coupledmode theory of mpi in qsm fibers denote quantities referring to the fundamental mode and the subscript 1 to denote quantities refer ring to the higher order mode. Pdf coupledmode theory approach to nonlinear pulse. Coupled mode theory for surface plasmon polariton waveguides. The coupling between fibers of an array made up of n identical fibers each at the vertex of a polygon and one at the center, which is not necessarily the same as its n neighbors, is determined. Coupled mode theory optical fibers anisotropic media. Pdf complex coupledmode theory for optical waveguides. Application of the complex coupledmode theory to optical fiber grating structures. Investigation on crosstalk in multicore optical fibers a. We remove some ambiguities associated with the coupled mode description of light propagation in fiber bragg gratings fbgs.
Pdf coupled mode theory for surface plasmon polariton. The coupledmode theory of parallel waveguides is derived from a variational principle for the propagation constant of the waveguidewave solution using a superposition of the uncoupled modes as a trial field. Propagation modes an overview sciencedirect topics. Coupledmode theory of multipath interference in quasi. Pier online coupledmode theory for optical waveguides. The significant distinctions are discussed both for interferometric systems and intensityonly spectral measurements. They then consider lossless coupling of two modes in time. The superposition principle says that eigenmodes of linear systems are independent of each other. Christodoulides creol, college of optics and photonics, university of central florida, orlando, florida 328162700, usa. The complex coupledmode theory is applied to bragg grating in slab waveguides and validated by rigorous modematching method. Coupledmode theory of raman amplification in lossless optical fibers capasso, f di porto, p. Fiber bragg gratings fbgs can be understood is fibers which are equipped with additional means for mode coupling for example, for reflecting light with short period gratings or for coupling to modes guided modes or cladding modes propagating in the same direction with long period gratings. The general theory is applied to a simplified description of guided and radiation modes of the fiber that is valid for small core.
The general theory is applied to a simplified description of guided and radia tion modes of. In the term mode coupling, as used in physics and electrical engineering, the word mode refers to eigenmodes of an idealized, unperturbed, linear system. Coupled mode theory of round optical fibers marcuse. Syms optical devices section, department of electrical engineering, imperial college, exhibition road, london sw7, uk. Light, guided along the core of an optical fiber, is scattered by each grating plane. Fullvectorial coupled mode theory for the evaluation of macro. The method of analysis is known as coupled mode theory, or zdependent perturbation theory. This chapter illustrates the coupled mode theory, which describes the mutual light wave interactions between two propagation modes.
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