Principle of operation

Principle of operationApplied on typical single mode fibers for

telecommunication applicationsCore 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=λΒ/2neff where neff is the fiber’s effective index and λΒ 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 λB 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/λΒ is determined by the refractive index difference in the grating δn=n3-n2

The percentage of reflected power at λΒ is determined by δn and the length of the grating

Fabrication techniquesThe 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 FBGsThe 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 ΔλB, of the maximum reflection wavelength λB.

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=λΒ/2neff is the grating period and

Δnac, Δndc are the amplitude of the index variation

across the grating and the step index from the cladding

to the core of the fiber, respectively.

dcac nznnn

2cos

cleff nnn

Using the coupled mode theory, the reflectivity is calculated as follows:

where L is the length of the grating and

LjL

Lqr

sinhcosh

sinh*

effn2

acnjq

222 q

The transmission coefficient is calculated as follows:

Complicated numerical techniques are needed for the reflection and transmission calculation of non-uniform gratings as:

LjLt

sinhcosh