Simplified coupling power model for fibers fusion

Fiber coupler fabrication used for an optical waveguide requires lossless power for an optimal application. The previous research coupled fibers were successfully fabricated by injecting hydrogen flow at 1 bar and fused slightly by unstable torch flame in the range of 800–1350°C. Optical parameters may vary significantly over wide range physical properties. Coupling coefficient and refractive index are estimated from the experimental result of the coupling ratio distribution from 1% to 75%. The change of geometrical fiber affects the normalized frequency V even for single mode fibers. V is derived and some parametric variations are performed on the left and right hand side of the coupling region. A partial power is modelled and derived using V, normalized lateral phase constant u, and normalized lateral attenuation constant, w through the second kind of modified Bessel function of the l order, which obeys the normal mode and normalized propagation constant b. Total power is maintained constant in order to comply with the energy conservation law. The power is integrated through V, u, and w over the pulling length of 7500 μm for 1-D. The core radius of a fiber significantly affects V and power partially at coupling region rather than wavelength and refractive index of core and cladding. This model has power phenomena in transmission and reflection for an optical switch and tunable filter.     

Study and investigation of long period grating as refractive index sensor

In this paper, we have investigated the response of long period grating (LPG) as refractive index sensor. The response has been studied for refractive index variation ranging from 1 to 1.45. In this work, we found that the sensing mechanism is based on two different aspects. First is the change of coupling power from the guided core mode to other co-propagating cladding modes and second is the wavelength shift of the peak resonant wavelengths from their original positions due the change of refractive index of the environmental (external) medium surrounding the cladding of the grating.     

Efficient coupling and relaxed alignment tolerances in pigtailing of a laser diode using dual ball lenses

In this paper, we report an efficient coupling scheme with relaxed misalignment tolerances. The proposed coupling scheme consists of two ball lenses of same diameter (1 mm) and different refractive indices. The second ball lens which is facing the fiber tip has a higher refractive index (1.833), whereas the first one which faces the laser diode has a refractive index of 1.5. Employing Gaussian and ABCD ray tracing optics, the theoretically obtained coupling efficiency can reach a unity with relaxed working distance (separation of the coupling system from the fiber tip) in the range between 1 and 4 mm at some optimum positions of the coupling lenses with regard to each other and to the facet of the laser diode. It has been found that if the distance between the first ball lens and the laser diode (d₁) is fixed at 1.1 mm, which is twice its focal length, the coupling efficiency and the working distance as well as the misalignment tolerances are greatly affected by variation of the separation between the two ball lenses (s), and for this proposed coupling scheme the highest coupling efficiency and largest working distance are obtained when s is in the range of 0.3-0.35 mm. Above and below this range there is a significant reduction in the values of the above-mentioned parameters. Experimentally, the Nd:YAG laser welding system has been used for the alignment and welding of the coupling components in a butterfly configuration; the experimentally obtained coupling efficiency of the proposed coupling system was around 75% with relaxed working distance. From the effect of lateral and angular offsets on coupling efficiency, it is clearly noticed that the mode field of laser diode is transformed from elliptical into circular and hence effectively matched with that of the single-mode fiber.     

Development of single mode fiber coupling coefficient using kinetic model

We propose a simple kinetic model that can be used to improve the coupling coefficient value of a single mode fiber coupler in the fabrication process. The proposed model is time independent, where the internal and external parametric functions are included. The simulation is integrated over the coupling ratio range for the various fiber separations. The coupling coefficient value of the device is examined by using the coupling ratio range from 1% to 75%. The result obtained is compared with the experimental results, where it is noted that the separation of fiber cores significantly affects the coupling coefficient, exhibiting exponential behavior. We also found that the coupling coefficient gradient is significantly changed with respect to the coupling ratio. This model can be used to determine power losses of the fiber coupler at the coupled region, while the fabrication of the fiber coupler is operated.     

Variational analysis of propagation characteristics in thermally diffused expanded core fibers

We present a scalar variational method for the analysis of light-propagation characteristics in thermally diffused expanded core (TEC) fibers. The method leads to simple closed-form expressions regarding the mode field diameter, numerical aperture, waveguide dispersion as well as coupling losses produced by radial, longitudinal and angular misalignments. The dependence of coupling losses on the ‘taper ratio’ and normalized frequency is investigated and previous predictions that TEC fibers transmit light more effectively in free space over the order of millimeters, is confirmed. The coupling losses between small core diameter step-index fibers typically used in most erbium-doped fiber amplifiers and TEC-fibers is also considered.     

光子晶体光纤模式特征的研究

从基空间填充模出发，将光子晶体光纤的包层等效成均匀介质，从而将光子晶体光纤等效为阶跃折射率光纤。利用等效折射率模型，对光子晶体光纤的模式特征进行了详尽的研究，主要包括模式特性、传输常量、模场分布、功率限制特性、瑞利散射损牦特性、色散特性，等等。并通过功率限制因子这一参量将它与单模光纤进行比较。结果表明，光子晶体光纤单模工作波长范围比较宽，功率限制因子比较高，可用于制作更高抽运效率的光纤放大器。     

Nonlinear Refractive Index of Er3+-Doped Fiber and Its Application to Nonlinear Fiber Coupler

A large change in the refractive index originating in the transition absorption of erbium ions is induced in an Er³⁺-doped fiber. It is shown that the Er³⁺-doped fiber exhibits the nonlinear refractive index of n₂=7.4 × 10⁻¹⁵ m²/W, which is 10⁵−10⁶ times larger than that caused by the optical Kerr effect in a usual silica fiber at the pumping, wavelength of 514.5 nm. The large nonlinear refractive index occurred in a fiber directional coupler fabricated with the Er³⁺-doped fiber optically changes the coupling condition. The coupling ratio changes up to 0.16 by increasing the pumping power up to 0.7 mW.     

An estimation of the baseband transfer function of multimode optical fibers

This paper discusses an alternative criterion for estimating the baseband transfer function of multimode optical fibers. The optical fibers having little mode conversions show that the baseband frequency characteristics are affected strongly by the launching condition of an input optical pulse. In the criterion presented here, the baseband transfer function in such fibers is estimated by considering the launching condition that excites all fiber modes uniformly in amplitudes. In order to obtain such a transfer function, the actual responses affected by the launching conditions are measured together with the modal power distributions for different kinds of launching conditions. A numerical procedure is then presented that enables us to derive the baseband transfer function independently of modal power distributions. Experimental results at λ x= 633 nm and 856 nm are presented for step index fibers (0.1 and 0.2 km long) having a core radius of 30 pm (its refractive index is 1.452) and a refractive index difference of 0.7%.     

An estimation of the baseband transfer function of multimode optical fibers

This paper discusses an alternative criterion for estimating the baseband transfer function of multimode optical fibers. The optical fibers having little mode conversions show that the baseband frequency characteristics are affected strongly by the launching condition of an input optical pulse. In the criterion presented here, the baseband transfer function in such fibers is estimated by considering the launching condition that excites all fiber modes uniformly in amplitudes. In order to obtain such a transfer function, the actual responses affected by the launching conditions are measured together with the modal power distributions for different kinds of launching conditions. A numerical procedure is then presented that enables us to derive the baseband transfer function independently of modal power distributions. Experimental results at λ x= 633 nm and 856 nm are presented for step index fibers (0.1 and 0.2 km long) having a core radius of 30 pm (its refractive index is 1.452) and a refractive index difference of 0.7%.     

Optically controllable variable fiber optical attenuator integrated in conventional optical fiber

New type of optically controllable variable fiber optical attenuator based on thermo-optical effect in liquid cladding of optical fiber is described. The thermo-optical effect in liquid cladding optical fiber causes refractive index contrast changes in core–cladding interface, what enables to change the propagating optical signal power with temperature. The temperature change is achieved by fiber based heating element using laser radiation. Attenuation up to −12 dB was achieved in static dependence and dynamic response confirmed rise time up to 24 ms.     

保偏光纤熔锥区的传输特性分析

建立了保偏光纤熔锥区截面的有限元模型,基于热-结构-电磁多物理场耦合有限元方法,分析了保偏光纤熔锥区的传输特性.给出了热应力导致的保偏光纤应力双折射及折射率变化曲线;分析了随着拉伸长度的增加,传输模式的转换以及传播常量的变化;分析了随着芯径的减小,应力区对电磁场分布的影响.     

Automatic determination of refractive index profile of fibers having regular and/or irregular transverse sections considering the refraction of light rays by the fiber

A new model, using non-destructive two- and/or multiple-beam interferometric techniques, is suggested for measuring the refractive index profile of fibers having regular and/or irregular cross-sectional shape taking into consideration the refraction of the light rays by the fiber. The proposed model is applied for three different fibers having different cross-sectional shapes and different refractive index profiles. These fibers are PPT, homogeneous fiber, with circular cross-section, graded index optical fiber of circular cross-sectional shape and Dralon fiber of irregular cross-section. To validate the proposed model it is used, firstly, to calculate the index profile for a standard PPT fiber. Secondly, the calculated results for the irregular Dralon fiber and GR-IN optical fiber are compared with that calculated using other conventional method. From this comparison, we recommend that the refraction must be taken into account to obtain accurate results especially for birefringent fibers and graded index optical fibers.     

Propagation characteristics of nonlinear optical fibers with complex refractive index. A transmission line model approach

The transmission line model has been modified in order to evaluate nonlinear waves guided by optical fibers with complex refractive index. It is proven that the proposed model is able to tackle fibers with losses or gain, under the presence of arbitrary nonlinearity. The method is applied for the calculation of weakly guided lossy nonlinear optical fibers considering various configurations and Kerr nonlinearity. Power depended propagation characteristics have been calculated and plotted for the fundamental mode and the potential use of the method in optical fiber amplifiers with index nonlinearity is also discussed.     

重构多信道光纤光栅的改进离散层析算法

对重构多信道光纤光栅的离散层析算法进行了优化.在各信道加入相移的基础上,运用非线性最小二乘法对耦合系数进行高斯曲线拟合,降低了折射率调制深度的最大值且可以将剧烈变化的折射率调制深度平滑化.仿真表明,较之改进前的折射率调制最大值（0.001 3）,利用新算法在折射率调制最大值为0.000 5时成功设计了一个8信道光纤光栅,极大地降低了对光纤光敏性的要求.同时,折射率调制曲线的平滑化降低了光栅的实际刻写难度.     

Dependence of output power in modulated optical fiber ring resonator on nonlinear refractive index

Nonlinear dynamics in optical fiber ring resonators (OFRRs) can be applied to the estimation of the nonlinear refractive index of optical fibers. The output power of the OFRR becomes convergent, periodic, and chaotic with an increase in the input power. In this study, the dependence of the output power on the nonlinear refractive index is analyzed numerically. The critical input power at which the convergent state changes to the periodic state decreases smaller as the nonlinear refractive index increases. In addition, the maximum oscillation width of the output power decreases monotonically with the nonlinear refractive index. These dependences are sensitive to the parameters of the OFRR. The estimation of the nonlinear refractive index can be realized effectively using the maximum or minimum critical input power, and the maximum oscillation width of the output power even under a subtle fluctuation in the optical fiber ring length.     

The measurement of sucrose concentration by two-tapered all-fiber Mach–Zehnder interferometer employing different coupling structures and manufacture processes

The sucrose concentration measurement and characteristics of light coupling taper structure on sensitivity with various fabrication processes of taper structure for all-fiber Mach–Zehnder interferometer (AFMZI) are presented. Using fusion splicer with electrical discharge, the standard single-mode fiber is employed to be fabricated as conical coupling/decoupling taper structure. The basic two fabrication processes are designed as single fusion-stretching (SFS), multiple fusions without stretching (MF). The third advanced process is composed of SFS and multiple fusions without stretching processes, and called multiple fusions with single stretching (MFSS). Various types of coupling/decoupling taper structures were fabricated based on the three kinds of fabrication processes. The effects of geometry shape including taper waist, taper angle, and sensing length on sensing sensitivity of AFMZIs are estimated. The modifications of fiber core and cladding induced by thermal effect affect the refractive index distributions and shapes of taper structure. The effects of refractive index changes of fiber core and cladding on sensing sensitivity are also discussed. The AFMZI was tested by measuring aqueous sucrose solution of refractive index unit (RIU) from 1.333 to 1.420 RIU. The optical spectrums are measured by a spectrometer. The spectrum dip shifts and sensing sensitivity was measured and calculated, respectively. As shown in results, sensing sensitivities of AFMZIs of taper structure fabricated by MFSS and multiple fusions without stretching processing are generally higher than SFS. The reasons could be aimed on materials modification through thermal effect on blurring fiber core-cladding interface and proper taper angle of taper structure. The more homogeneous refractive index distribution on fiber core-cladding interface, the more detecting light power decoupled through core-cladding interface to interact with exterior environment and enhance the sensing sensitivity. Similarly, an appropriate taper angle also provides a better coupling/decoupling performance. The optimal sensitivities relative to low refractive index, high refractive index, and full refractive index range are 87.62, 133.55, and 104.20 nm/RIU, respectively, and the corresponding sensing length are 30, 50, and 30 mm, respectively, with taper angle of 25° and taper waist of 40 μm.     

Fiber core mode leakage induced by refractive index variation in high-power fiber laser

This paper presents an investigation of specific optical fiber core mode leakage behavior that occurs in high-power double-clad fiber lasers as a result of thermally-induced refractive index variations. A model of the power transfer between the core modes and the cladding modes during thermally-induced refractive index variations is established based on the mode coupling theory. The results of numerical simulations based on actual laser parameters are presented. Experimental measurements were also carried out, the results showed good agreement with the corresponding simulation results.     

Mismatch considerations in laser diode to monomode fiber excitation via a hemispherical lens on the elliptical core fiber tip

We present what, as per our knowledge, is the first theoretical investigation of the coupling efficiency of a laser diode to a single-mode fiber via a hemispherical microlens on the elliptical core fiber tip in presence of possible transverse and angular misalignments. Using the ABCD matrix for refraction by a hemispherical lens on the tip of an elliptical core single-mode fiber, we present analytical expressions of such coupling efficiencies and investigate the corresponding losses due to possible transverse and angular misalignments. The concerned calculations involve little computations. Our analysis takes into consideration the limited aperture provided by the hemispherical lens. The results should be useful in optimum launch optics for designing suitable hemispherical microlenses on the tip of elliptical core fibers or circular core fibers which suffer from noncircularity.     

微米光纤耦合型环境折射率传感器

本文展示一种由两根微米光纤构成的耦合型环境折射率传感器。微米光纤表面存在倏逝波,芯外介质折射率微小的改变将引起倏逝场分布变化,从而导致能量在耦合器两臂中的重新分配。本文通过测量耦合器两端出射光功率的比值来对葡萄糖溶液的浓度进行传感,实验结果表明该微米光纤耦合型传感器的浓度传感灵敏度可达1.58 mol·L~(-1)。本文用耦合模理论详细分析了两根相邻微米光纤的耦合效率与芯外介质折射率之间的关系,发现减小耦合区的光纤的直径,增大入射光波长或增大耦合长度,都可以进一步提高这种传感器的灵敏度。     

Inner cladding influence on mode interaction in symmetry-free photonic crystal fibers under heat load

A further output power scaling of Yb-doped double-cladding photonic crystal fiber lasers, required for practical applications in many industrial fields, is currently prevented by thermal effects, which significantly worsen the beam quality. In this work the mode interaction and, consequently, the single-mode regime of Yb-doped air-silica symmetry-free photonic crystal fibers have been numerically investigated in different heat load conditions using simulation tools based on the finite element method. The effect of the main inner cladding geometric parameters, in particular of the inner cladding dimension, on the guided-mode delocalization has been analyzed, with the aim to identify a design of the large mode area active fiber providing single-mode operation despite the presence of thermal effects. Simulation results have demonstrated that the inner cladding enlargement causes a stronger coupling between core-guided and cladding modes, as well as an increase of the differential overlap between fundamental and first higher-order mode for moderate heat load values. However, the inner cladding influence becomes less important under severe heat load, being the fiber behaviour mainly affected by the thermally-induced refractive index change in the doped core.