Principle of operation

Applied on typical single mode fibers for telecommunication applications Core diameter ~10μ and Δn/n <0.4% (where Δn = n2-n1) Wavelength of application in the range of 1.55μ

The grating is the refractive index variation along the fiber’s core axis, with period Λ=λ Β /2n eff where n eff is the fiber’s effective index and λ Β is the free space Bragg wavelength The distribution of the refractive index variation inside the fiber’s core is as follows The grating has a specific length L and a small refractive index difference n3-n2

The grating acts as a dielectric mirror that reflects back the wavelength λ B whereas all the remaining wavelengths of the spectrum will be transmitted with small losses. The Bragg wavelength is determined by the grating’s periodicity and the effective index of the single mode fiber.

The wavelength reflection normalized bandwidth Δλ/λ Β is determined by the refractive index difference in the grating δn=n3-n2 The percentage of reflected power at λ Β is determined by δn and the length of the grating

Fabrication techniques The core of the fiber is doped with Ge (UV sensitive). The UV absorption by the Ge dopants, has a periodic occurrence due to the interference fringes in the core. The higher the duration of the UV absorption, the higher the refractive index variance.

Strain and Temperature sensing using FBGs The strain sensitivity of an FBG is the result of the variation ΔΛ, of the grating’s periodicity Λ, under the application of a longitudinal stress. This small variation results in a proportional variation Δλ B, of the maximum reflection wavelength λ B. An optoelectronic interrogation system records this chromatic shift and calculates the applied stress. Similar chromatic shift could be used for temperature measurement.

Reflectivity calculation (uniform gratings) The core’s refractive index variation inside the grating is as follows: where, Λ=λ Β /2n eff is the grating period and Δn ac, Δn dc are the amplitude of the index variation across the grating and the step index from the cladding to the core of the fiber, respectively.

Using the coupled mode theory, the reflectivity is calculated as follows: where L is the length of the grating and

The transmission coefficient is calculated as follows: Complicated numerical techniques are needed for the reflection and transmission calculation of non-uniform gratings as: