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, ε_{1} = ε_{2} = –*v*ε, ε_{3} = ε, ε_{4} = ε_{5} = ε_{6} = 0 (no shear strain), and ε

being the axial strain in the optical fiber. The symbol *v* denotes the Poisson’s ratio

for the fiber.

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

where P_{ij} 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 ε_{0} is the constant strain.

- Linear

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

at z =*L*

- Gaussian

where ε_{0} 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 ξ is the thermo-optic coefficient of the fiber and Δ*T* is the temperature

change.

The temperature-induced grating period change is:

where η is the thermo-optic expansion coefficient.

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

- Uniform

where ΔT_{0} is the constant temperature.

- Linear

where L is the grating length, ΔT(0) is the temperature at Z = 0, and ΔT(L) is

the temperature at z = L.

- Gaussian

where Δ*T*_{0} is the peak temperature value and w is the normalized value of FWHM.

Other temperature distributions can be defined by user functions.