Elasto–optical behavior model of a step-index fiber under localized pressure

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Abstract

The intensity attenuation of a step-index optical fiber under localized pressure is investigated using the elasto–optical theory and the principles of geometrical optics. A model with a Gaussian variation of the refractive index in the axial direction is used to evaluate the effect of applied pressure on the external coating of the fiber. The results are compared with experimental measurements obtained using a prototype of an optical fiber pressure sensor.

Highlights

► The intensity attenuation of a step-index fiber under localized pressure is evaluated. ► The model is based in the elasto–optical theory and the geometrical optics. ► The refractive index is modeled as a Gaussian function of the position and stress. ► Numerical solution and experimental data of a pressure sensor prototype are compared. ► The model describes some effects of external agent on the light transmission loss.

Introduction

The extensive research on optical fibers (OF) is associated with their wide ranging technological applications in different areas, such as medicine, telecommunications and a substantial variety of sensors for measuring physical variables such as temperature [1], pressure [2], force [3] and levels of liquids [4], [5]. Therefore, the study of the structural, optical and elastic properties of optical materials [6], [7] and the investigation of new materials [8] for optical fibers and their response to external agents is an actual research field [9], [10].

The effects on the transmission of light in an OF in response to an external agent are problematic for optical telecommunications, but these effects can be useful in sensing technologies [7]. In optical fiber sensing, the changes in the properties of light, such as its intensity, phase, frequency or polarization can be used as a measure of an external agent, and the usefulness of the sensor depends on the magnitude of this change.

There are many mechanisms that can cause a change in intensity of light when it passes through an OF [11]. When an optical fiber is bent or subjected to thermal loading or an applied force, the intensity of the light is attenuated; this loss of intensity depends on the characteristics of the fiber, and its sensitivity can be used to detect variations in the surrounding medium.

The intensity-based fiber sensors require only simple signal processing, in which the values of the physical properties measurement are directly associated with the changes in the light intensity. There are factors, such as fluctuations of the light source and others not related to the environmental effect to be measured [11], [12], [13], which affect the measurement accuracy. However, several techniques have been developed to ensure that this type of sensor achieves good performance [14], [15], [16].

The optical transmission loss in an optical fiber under external stress has been extensively researched due to its applications in telecommunications and sensors [17], [18]. Numerous studies have been conducted to determine the power loss in single-mode and in multimode fibers. The light intensity modulating sensors are primarily multimode fibers. In the case of multimode fibers, the modal theory can be replaced by geometrical optics, which provides a good approximation to the exact results [5].

When an external force is applied to a transparent elastic medium, the medium becomes birefringent. This phenomenon is well-known as the photo-elastic (opto–elastic) effect in which optical anisotropy is produced in an optically isotropic medium, such as an optical fiber, when an external force is applied. The study of the elasto–optical behavior of materials under stress has received considerable interest [19], [20], [21], [22].

In this work, we evaluate the intensity loss of a step-index optical fiber under a localized pressure within the elasto–optical theory and the framework of geometrical optics. A model with a Gaussian variation of the refractive index in the axial direction is used to evaluate the intensity loss. The results are compared with experimental measurements obtained from an optical fiber pressure sensor prototype.

Section snippets

Theory

A multimode step-index OF of polymethyl methacrylate (PMMA) is considered to be ideally undisturbed. In the geometrical optics (GO) framework, we assume that a light ray is traveling in the direction of the fiber axis. The intensity of this ray will be the sum of intensities of all the rays traveling in the fiber of diameter d by full reflection and also by the partial reflection of the light. Then, we consider that the ray travels in a homogeneous and isotropic medium and that this ray is not

Results and discussion

To compare the numerical and experimental results, a prototype of a pressure sensor was used. The electronic components of this device consist of an emitter circuit with a 650 nm LED and a receiver circuit with a PT333C phototransistor, which converts the light into an electric current. The mechanical component is essentially a screw press, which applies a controlled and quantified pressure over the PMMA multimode step-index optical fiber. The light intensity, I0, in a stress free fiber and the

Conclusions

A theoretical model based on the geometrical optics, the elasticity and the elasto–optical theories was proposed to investigate the variation in light intensity in a step-index plastic optical fiber under pressure. In the model, an isotropic, homogeneous and elastic fiber core was assumed, and a plane-wave front of monochromatic light traveling along the fiber axis with constant intensity was considered. A Gaussian-type behavior for the variation in the refractive index was proposed. The

Acknowledgments

This study is supported by Consejo Nacional de Ciencia y Tecnología (CONACYT), México. We appreciate the support from Posgrado en Ciencias Físicas, Universidad Nacional Autónoma de México.

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