# Fiber Grating Sensor

Compatibility:

Temperature and strain change the grating period as well as the grating refractive
index. Consequently, the response of the grating device is changed when
temperature and strain distributions change.

## Strain-optic effect of fiber Bragg grating

The changes of optical indicatrix caused by strain are:

where, Îµ1 = Îµ2 = –vÎµ, Îµ3 = Îµ, Îµ4 = Îµ5 = Îµ6 = 0 (no shear strain), andÂ Îµ
being the axial strain in the optical fiber. The symbol v denotes the Poissonâ€™s ratio
for the fiber.

The strain-optical tensor for a homogeneous isotropic material is:

where Pij are the strain-optic constants,

The refractive index change is:

where the strain-optic coefficient y is defined as:

The grating period changes is:

The default strain distributions that can be applied to a fiber grating are listed below:

• Uniform

where Îµ0 is the constant strain.

• Linear

where L is the grating length, Îµ(0) is the strain at z = 0, and Îµ(L) is the strain
at z =L

• Gaussian

where Îµ0 is the peak strain value and w is the normalized value of FWHM.
Other strain distributions can be defined by user functions.

## Thermal-optic effect of fiber Bragg grating

The temperature-induced refractive index change is:

where Î¾Â is the thermo-optic coefficient of the fiber and Î”T is the temperature
change.

The temperature-induced grating period change is:

where Î·Â is the thermo-optic expansion coefficient.

The default temperature distributions that can be applied to a fiber are listed below:

• Uniform

where Î”T0 is the constant temperature.

• Linear

where L is the grating length, Î”T(0) is the temperature at Z = 0, and Î”T(L) is
the temperature at z = L.

• Gaussian

where Î”T0 is the peak temperature value and w is the normalized value of FWHM.
Other temperature distributions can be defined by user functions.