Field transformation in a multimode optical waveguide with random irregularities of the film surface

A self-consistent mathematical model for the transformation of the average intensity of the mode spectrum I(z) of a waveguide field in a multimode planar optical waveguide with a step profile and rough surface is developed. This model is based on the matrix model for multiple scattering of modes in an optical waveguide. The elements of the intermode scattering matrix are found, which describe the process of mutual transfer of the energy of modes along a waveguide and their transformation into radiation modes. The transformation of the I(z) modes in waveguides with large-and small-scale inhomogeneities is investigated. It is shown that the largest qualitative differences in the noted dependences manifest themselves only in the initial portions of the optical waveguide. The length z of these portions is much smaller than the characteristic scale length L _k at which the fundamental energy of the kth mode excited in the optical waveguide is renewed. The effect of self-filtration of the mode spectrum I(z) is described, as a result of which a stable (normalized), independent of distance z, distribution I* is formed. It is established that irregularities of the optical waveguide boundaries exert a depolarizing effect on a guided light beam. The specific features of the normalization of the radiative dissipation of a group of modes I_i(z) in an optical waveguide are investigated. It is ascertained that, in the case of small-scale irregularities, the attenuation coefficient is described by a nonlinear monotonic dependence α(z), which asymptotically converges to the value α*, characteristic of the normalized field I*. When the optical-waveguide film has large irregularities, the dependence α(z) is characterized by a pronounced maximum due to the formation of alternative channels of radiative dissipation of the energy of waveguide modes.     

Study of the Effect of Pulsed-Periodic Electric Field and Linearly Polarized Laser Radiation on the Properties of Liquid-Crystal Waveguide

Integrated-optical waveguides with a nematic liquid-crystal 4-cyano-4’-pentylbiphenyl (5CB) waveguiding layer have been investigated for different polarizations of incident laser radiation and under a pulsed-periodic electric field. A dependence of the damping coefficient of waveguide modes and the sizes of quasi-steady-state irregularities of nematic liquid-crystal layer on the linear polarization of laser radiation and the strength of pulsed-periodic field has been found experimentally. The correlation length is estimated for waveguiding layer irregularities. The waveguide scattering method has provided a resolution in correlation length exceeding the classical resolution limit by approximately an order of magnitude. The observed decrease in the damping coefficient of waveguide modes and irregularity sizes under external field is explained by the decrease in the correlation length of director fluctuations.     

Mode-amplitude transformation in multimode waveguide with quasisinusoidal boundary

Amplitude variations of modes (excited by a point source in a multimode waveguide) due to scattering by an uneven boundary are calculated in a Born approximation. The boundary is a sine curve with a smoothly varying (in space) amplitude. It is shown that amplitude distortions of a given mode are chiefly caused by inhomogeneities located on certain (particular to each mode) regions of the surface. The concept of Fresnel zones for the modes is introduced to simplify analysis of the corresponding effects.Institute of Applied Physics, Russian Academy of Sciences. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 35, No. 5, pp. 440–450, May, 1992.     

Bandwidth enhancement by differential mode attenuation in multimode photonic crystal Bragg fibers

In multimode bandgap guiding fibers higher-order modes have high radiation losses. Once excited, after a short propagation distance such modes are leaked out of the fiber core. Reduction of the number of excited modes in the fiber core leads to a decrease of intermodal dispersion and a dramatic enhancement of fiber bandwidth. Due to the increase in the propagation loss, bandwidth enhancement by differential mode attenuation also leads to the reduction of the maximal length of a usable fiber span. We demonstrate that by proper design of a photonic crystal reflector long fiber spans of high bandwidth are possible.     

Numerical investigation of characteristics of laser radiation scattered in an integrated optical waveguide with three-dimensional inhomogeneities

Specifics of theoretical analysis of wave phenomena in irregular integrated optical waveguides are investigated. The object of the investigation and the main types of irregularities (smooth, statistical, and sharp) are described. The goals of the numerical modeling are formulated. The structure of the program and the general structure of the algorithm allowing numerical investigation of guided modes’ scattering from 3D-irregularities of an integrated optical waveguide are described. The dispersion relations of the TE and TM modes of the integrated optical waveguide under investigation, as well as field patterns of the radiating TE modes of the substrate and the laser radiation scattered from the three-dimensional guiding-layer inhomogeneities of an integrated optical waveguide, are presented. The results are analyzed in detail. The methods developed can be used for numerical investigation of the characteristics of laser radiation scattered in various optical waveguides with three-dimensional irregularities.     

Modal dispersion due to photon–plasmon coupling in a SNOM tip

The mesoscopic effect of spectral modulation is used to experimentally investigate the possible effect of a metal-coated SNOM tip on the intermodal dispersion of an optical fiber. Highly regular modulation registered in a fixed spectral region of the broadband light transmitted by a 200 nm SNOM tip yields the value of optical path difference (OPD) in the two-mode model. To investigate the origin of this OPD a series of spectral measurements accompanied with a gradual reduction of the multimode fiber tail length has been performed. The results indicate that the observed OPD consists of two clearly distinguishable contributions: the OPD in the non-coated multimode fiber and the OPD in the metal-coated SNOM tip. The first one is a result of the inherent modal dispersion of an optical fiber. A numerical consideration shows that the second one can be attributed to a mode-dependent contribution of surface plasmon polaritons: one of the two modes couples to plasmons stronger than the other one, resulting in a remarkably slower propagation. This leads to a completely different value of intermodal dispersion, which actually changes its sign in the SNOM tip. Proposed is a logical explanation for such kind of a sign-switching behavior.     

Analytic approach to dielectric optical bent slab waveguides

A rigorous classical analytic frequency domain model of confined optical wave propagation along 2D bent slab waveguides and curved dielectric interfaces is investigated, based on a piecewise ansatz for bend mode profiles in terms of Bessel and Hankel functions. This approach provides a clear picture of the behaviour of bend modes, concerning their decay for large radial arguments or effects of varying bend radius. Fast and accurate routines are required to evaluate Bessel functions with large complex orders and large arguments. Our implementation enabled detailed studies of bent waveguide properties, including higher order bend modes and whispering gallery modes, their interference patterns, and issues related to bend mode normalization and orthogonality properties.     

Fiber-modes and fiber-anisotropy characterization using low-coherence interferometry

An optical low-coherence interferometry technique has been used to simultaneously resolve the mode profile and to measure the intermodal dispersion of guided modes of a few-mode fiber. Measurements are performed using short samples of fiber (about 50 cm). There is no need for a complex mode-conversion technique to reach a high interference visibility. Four LP mode groups of the few-mode fiber are resolved. Experimental results and numerical simulations show that the ellipticity of the fiber core leads to a distinct splitting of the degenerate high-order modes in group index. For the first time, to the best of our knowledge, it has been demonstrated that degenerate LP11 modes are much more sensitive to core shape variations than the fundamental modes and that intermodal dispersion of high-order degenerate modes can be used for characterizing the anisotropy of an optical waveguide.     

基于少模光纤的SBS光谱阈值特性分析

受激布里渊散射会影响少模光纤传输系统中的信噪比、传输距离与传输容量,是影响传输系统入纤功率提高的重要因素。对阶跃型少模光纤的受激布里渊散射谱的阈值进行了研究,运用了布里渊散射谱、模式联运谱的数学模型对少模光纤散射特性进行了分析,探讨了少模光纤布里渊散射增益谱、阈值增益系数,以及光纤各参量对少模光纤阈值的影响。分析结果表明：SI-10阶跃型少模光纤中存在五种不同的传播模式,不同模式有各自的传输常数以及有效折射率,各模式相互作用导致模式展宽、增益降低,且布里渊散射谱峰值增益系数为3.9×10-11 m·W-1。阈值增益系数受到光纤传感距离的影响,在相对较短距离传输中阈值急速下降,且其趋势随长度增加渐趋平缓,当光纤长度达到22 km时阈值增益系数趋于常数18.1。少模光纤的阈值因光纤长度的递增而递减,且递减趋势渐缓趋于常数20.5 dBm;少模光纤不同模式受激布里渊散射的阈值也因光纤长度的递增而递减最终趋于常数,且不同模式的阈值因模式阶数的递增而递增;少模光纤的阈值随着光纤衰减系数和纤芯半径的递增而递增,且增加趋势缓慢增大。不同衰减系数的光纤其阈值在不同长度趋于常数,衰减系数越大受激布里渊散射阈值越大越容易趋于一常数。     

Attenuation of a Stoneley wave and higher Lamb modes due to the scattering by two-dimensional irregularities of the walls of a fluid-filled borehole

Attenuation of Stoneley waves and higher Lamb modes propagating along an irregular surface of a fluid-filled borehole is investigated. This problem generalizes the problem on the attenuation of Rayleigh waves by an irregular surface of an empty borehole [10]. The technique used to evaluate the attenuation coefficient is based on the perturbation method (surface irregularity heights are considered to be small in comparison with the wavelength) and the mean field method. As a result, an expression is obtained for the partial coefficients of the eigenmode attenuation due to the scattering of eigenmodes by the irregularities of the borehole walls into the same or other eigenmodes, as well as into the bulk longitudinal and transverse waves. The frequency-dependent behavior of the partial attenuation coefficients of both Stoneley waves and higher modes is analyzed against the ratio between the irregularity correlation length and the borehole radius for different correlation functions of irregularities.     

Theory of waveguide light scattering in an integrated optical waveguide in the presence of noise

We develop a vector theory of waveguide monochromatic light scattering in an integrated optical waveguide with arbitrary three-dimensional irregularities in the presence of noise. The electrodynamical problem of laser radiation scattering in an irregular waveguide is solved by the method of coupled modes with the help of the theory of perturbations. The approximate solution of the inhomogeneous three-dimensional wave equation is derived by the method of modes and the method of Greens functions. The obtained Greens function is analyzed for the cases of propagating and evanescent modes of an irregular asymmetric optical waveguide. Analytical formulas for the near- and far-zone radiation fields are presented. A preliminary analysis of these formulas is given.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 48, No. 1, pp. 63–75, January 2005.     

S弯曲聚合物热光型可变衰减器的特性

提出一种热光聚合物可变光衰减器(VOA)的设计分析,利用S弯曲的波导提高衰减效率,BPM法模拟中验证其衰减动态范围可达60 dB,实现60 dB的衰减计算功耗为60 mW,附加弯曲损耗小于0.3 dB.并且具有很好的极化独立性,串扰低,尺寸小,易于集成.     

Enhancing capacity of coherent optical information storage and transfer in a Bose-Einstein condensate

The coherent optical information storage capacity of an atomic Bose-Einstein condensate is examined. The theory of slow light propagation in atomic clouds is generalized to the short-pulse regime by taking into account group velocity dispersion. It is shown that the number of stored pulses in the condensate can be optimized for a particular coupling laser power, temperature, and interatomic interaction strength. Analytical results are derived for a semi-ideal model of the condensate using the effective uniform density zone approximation. Detailed numerical simulations are also performed. It is found that the axial density profile of the condensate protects the pulse against group velocity dispersion. Furthermore, taking into account the finite radial size of the condensate, multimode light propagation in an atomic Bose-Einstein condensate is investigated. The number of modes that can be supported by a condensate is found. The single-mode condition is determined as a function of experimentally accessible parameters including trap size, temperature, condensate number density, and scattering length. Quantum coherent atom-light interaction schemes are proposed for enhancing multimode light propagation effects.     

从薄膜波导传播衰减的角度研究光学薄膜的损耗:(Ⅰ)理论分析

本文从理论上分析了光学薄膜中的三种基本缺陷:折射率消光系数、表面粗糙度以及折射率不均匀性对薄膜内导波传播衰减的影响.基于这些缺陷对光学薄膜内不同导模传播衰减作用的不同,提出了一种区分薄膜中的吸收与散射损耗的方法.     

Attenuation and scattering of axisymmetrical modes in a fluid-filled round pipe with internally rough walls

The attenuation of axisymmetric eigenmodes in a cylindrical, elastic, fluid-filled waveguide with a statistically rough elastic wall is studied. It is shown that small perturbation theory can be used to relate explicitly the statistical characteristics of the internal wall surface roughness of an elastic pipe to the attenuation and scattering coefficients of the acoustic modes in the filling fluid. Analytical expressions for modal attenuation coefficients are obtained. The analysis of the frequency dependent attenuation coefficients and the ratio between the roughness correlation length and the inner radius of the pipe is made for different correlation functions of the roughness. It is shown that two scale parameters control the overall behavior of the modal attenuation coefficients. These are the ratios of the roughness correlation length and the inner pipe radius to the acoustic wavelength. The numerical results for sound propagation in a pipe and in a borehole with statistically rough, elastic walls are obtained and discussed.     

Bright and dark 40 GHz parabolic pulse generation using a picosecond optical pulse train and an arrayed waveguide grating

We demonstrate parabolic optical pulse generation by manipulating the intensity and phase of individual longitudinal modes of a 40 GHz picosecond optical pulse train in the spectral domain. Bright and dark parabolic pulses were generated from a 40 GHz mode-locked fiber laser using a 64-channel arrayed waveguide grating pulse shaper. The obtained parabolic pulse, which can easily generate a linear chirping, is useful for a number of applications to optical signal processing applications, including pulse compression and time-domain optical Fourier transformation.     

Intermodal interference of LP0j modes in optical fiber with liquid core

We present intermodal interference of modes LP_0j in silica optical fiber with liquid core. An appropriate detection method is proposed for observation of intermodal interference of LP_0j modes. Measured spectral dependencies reveal a clear local minimum, where position is a function of optical fiber parameters. We focused on investigation of dependence of that minimum position on length of optical fiber with liquid core. From measured spectral dependencies the evident blue shift of local minimum is observed as length of optical fiber increases. Character of spectral characteristics correspond with intermodal interference of modes LP_0j and is demonstrated by numerical calculations. Presented intermodal interference in combination with liquid-filled core of optical fiber can be attractive for sensing applications.     

Loss calculations in bent multimode optical waveguides

We present a straightforward geometric optics method to calculate the power attenuation induced by a circular bend in the axis of a multimode optical waveguide. The method involves tracing of rays and use of generalized power transmission coefficients. Both slab and fibre waveguides (with either step-index or parabolic core profiles) have been considered; the source has been assumed to be Lambertian.     

A multimode model of a waveguide laser cavity with mirrors of arbitrary radius of curvature

A multimode model is developed to determine optical losses in a waveguide laser cavity of cylindrical symmetry with mirrors of arbitrary radius of curvature. Within the framework of the model, it is possible to vary the parameters of the resonator: waveguide length, distance between the waveguide and mirrors, radius of curvature of the mirrors in a wide range taking account of mutual conversion of up to 10 waveguide modes and 20 modes of free space. The model was applied successfully to determine the optimal geometry of a semiconfocal cavity. A. N. Sevchenko Scientific-Research Institute of Physical Problems, 7 Kurchatov Str., Minsk, 220064, Belarus; e-mail: v.saetchnikov@rfe.bsu.unibel.by. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 66, No. 6, pp. 779–783, November–December, 1999.