Global overview of the sensitivity of long period gratings to strain

doi:10.1016/j.optlastec.2015.11.019

Optics & Laser Technology

Volume 79, May 2016, Pages 62-73

https://doi.org/10.1016/j.optlastec.2015.11.019 Get rights and content

Highlights

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Statistical study on the influence of strain on the cladding modes of a LPG.
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The cross sensitivity to axial and radial strain can generally be neglected.
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It exists a linear correlation between the sensitivities to axial and radial strain.
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Highest sensitivities are obtained with smallest claddings and periods.
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Highest coupling coefficients are obtain with smallest claddings and periods.

Abstract

This paper presents the results of a statistical study of the influence of radial and axial strain on the cladding modes of long period gratings (LPG). Ten thousand gratings were randomly chosen in a parameter space and their sensitivities to strain in the range [−1000 μϵ; +1000 μϵ] were calculated. Cross-sensitivity to axial and radial strain was found to be generally very weak and can be neglected. However, a linear correlation between the sensitivities to axial and radial strain was found. The greatest sensitivities to axial strain were found in the range −0.55 pm/μϵ to −2 pm/μϵ and to radial strain between −0.3 pm/μϵ and 0.5 pm/μϵ. The absolute values of the sensitivities to axial and radial strain were found to decrease with the cladding radius and the grating period. The coupling coefficient is slightly affected by the strain. The LPGs with the smallest claddings and smallest periods exhibited the highest coupling coefficient and the highest sensitivities to strain.

Introduction

In 1978, Hill et al. [1] demonstrated that it was possible to induce a periodic modulation of the refractive index of the core of an optical fiber with light. This gave rise to intense research on optical fiber gratings, from which two principal structures emerged. The most commonly known is the fiber Bragg grating (FBG) [2]. The second is the long period grating (LPG) [3], [4], [5]. The period of modulation of FBGs is of the order of a few hundred nanometers, while the period of LPGs is of the order of a hundred microns.

This difference in modulation period leads to significant differences in their behavior. An FBG inscribed in a single mode fiber couples the incident core mode to the contra-propagative core mode. This means that the light is transferred by the grating from the mode propagating in the forward direction to the mode propagating in the backward direction. The degree of coupling depends on the wavelength. It is maximal for the resonant wavelength, called the “Bragg wavelength”. In consequence, the reflection spectrum of the grating exhibits a peak centered on the Bragg wavelength, while its transmission spectrum exhibits a hole around this wavelength.

An LPG couples the core mode to several co-propagative cladding modes. Again, each coupling is maximum for a resonant wavelength, which differs from one mode to another. Because of the coupling, light is injected in the cladding and finally flows out of the fiber due to inhomogeneities. The transmission spectrum then exhibits holes around all resonant wavelengths.

This property of an LPG makes it useful in sensors: any external influence which modifies the period of modulation or the refractive index of the fiber shifts the resonant wavelengths. The measurement of these shifts allows the strength of the influence to be retrieved. The influence of temperature, strain and the refractive index of the surrounding medium on the LPG has been widely studied (see for example [6], [7], [8]). However, the sensitivity of LPGs to strain remains an open question for two reasons. Firstly, LPGs are complex systems which contain several independent parameters. Most published studies consider a basic configuration and then vary each parameter individually. Results obtained in this way are valid for the original configuration but lack generality. Secondly, in all the studies the radial strain is assumed to be linked to the axial strain via Poisson's ratio. This is true if the fiber is fixed at two points on a monitored structure and free to deform in the transverse plane. But it can be completely wrong if the fiber is embedded in a host material [9], [10], where it is necessary to study the sensitivity of LPGs to axial and radial strain simultaneously. The aim of this paper is to remedy this gap, and produce results useful for the design of real-world strain sensors based on LPGs.

Using a statistical approach, we explored a parameter space using ten thousand random samples. Our methodology is explained in Section 2. Section 3 is devoted to the study of the cross-sensitivities, and presents new findings on the relationship between axial strain sensitivity and radial strain sensitivity. The influence of the various parameters is presented in Section 4. Section 5 presents the influence of the parameters on the coupling coefficient. We conclude with a presentation of some rules to optimize the sensitivity of LPGs to strain.

Section snippets

Parameter space

Each LPG has a characteristic periodic modulation of the effective index of the mode propagating in the core. This modulation can be obtained either by modifying the geometry of the fiber or by inducing a variation of the refractive index of the core with UV illumination. In the following, we will consider the latter case.

The fiber is made of two concentric cylinders: the core and the cladding (see Fig. 1). The radius of the core is a₁ and the radius of the cladding is a₂. The refractive index

Cross sensitivities

The aim of this section is to determine the influence of the axial strain on the sensitivity of the LPG to radial strain, and reciprocally. As explained above, for each configuration, the sensitivity of the resonant wavelength to radial strain, $α_{r}^{λ} (ϵ_{z})$ was calculated for different axial strains. We can then define the minimal sensitivity to radial strain: $α_{r, \min}^{λ} = \min_{ϵ_{z}} [α_{r}^{λ} (ϵ_{z})]$ the maximal sensitivity to radial strain: $α_{r, \max}^{λ} = \max_{ϵ_{z}} [α_{r}^{λ} (ϵ_{z})]$ the mean sensitivity to radial strain: $α_{r, mean}^{λ} = {〈 α_{r}^{λ} (ϵ_{z}) 〉}_{ϵ_{z}}$

Influence of the parameters

We will now neglect the cross-sensitivities for the reasons explained in the previous section, and consider the sensitivity of $λ_{LPG}$ to radial strain to be $α_{r, mean}^{λ}$ , and the sensitivity of $λ_{LPG}$ to axial strain to be $α_{z, mean}^{λ}$ .

In the range of parameters used, $α_{r}^{λ} \in$ [−20.6 pm/μϵ; −0.55 pm/μϵ] and $α_{z}^{λ} \in$ [−0.3 pm/μϵ; 10.4 pm/μϵ]. Most of the values of $α_{r}^{λ}$ are in the range −0.55 pm/μϵ to −2 pm/μϵ (see Fig. 9). The standard deviation of the series is 1 pm/μϵ. Most of the values of $α_{z}^{λ}$ fall between −0.3 pm/μϵ

Coupling coefficient

The coupling coefficient κ is a critical parameter. For any given length of an LPG, the depth of the hole in the spectrum directly depends on the coupling coefficient, and hence determines the precision of measurement that is possible. In order to maintain uniform precision during the measurement process, the depth must remain constant, as must the coupling coefficient. It is then necessary to accurately know the influence of strain on the coupling coefficient.

Let us briefly examine the

Conclusion

In this paper we have presented the results of a statistical study on the influence of radial and axial strain on the cladding modes of an LPG. Physical considerations have allowed us to reduce the number of free parameters to four: the order of the cladding mode, the cladding radius, the grating period, and the refractive index of the surrounding medium. The characteristics of ten thousand gratings were randomly chosen in this parameter space. The gratings were submitted to axial and radial

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Citation Excerpt :
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View full text

Full length articleGlobal overview of the sensitivity of long period gratings to strain

Highlights

Abstract

Introduction

Section snippets

Parameter space

Cross sensitivities

Influence of the parameters

Coupling coefficient

Conclusion

Photosensitivity in optical waveguidesapplication to reflection filter fabrication

Appl. Phys. Lett.

Fiber Bragg grating technology. Fundamentals and overview

J. Lightw. Technol.

Long-period fiber gratings as band-rejection filters

J. Lightw. Technol.

Characterization of refractive index change and fabrication of long period gratings in pure silica fiber by femtosecond laser radiation

Opt. Laser Technol.

Random period arc-induced long-period fiber gratings

Opt. Laser Technol.

Applications of long-period gratings to single and multi-parameter sensing

Opt. Express

Discriminated measures of strain and temperature in metallic specimen with embedded superimposed long and short fibre bragg gratings

Meas. Sci. Technol.

Architecture de capteurs à fibre optique pour la mesure simultanée des déformations axiales et radiales

Instrumentation Mesures et Métrologie

Full length article
Global overview of the sensitivity of long period gratings to strain