Fiber Bragg grating

Fiber Bragg gratings are optical interference filters inscribed in optical fibers . Wavelengths that are within the filter bandwidth around λ _B are reflected.

Optical fiber with Bragg grating = grating period, n = refractive index, P _I = input power, P _B = reflected power, P _T = continuous power, = wavelength of the light
${\displaystyle \Lambda }$ ${\displaystyle \lambda }$

construction

The individual layers are written into the glass fiber using UV light (e.g. an excimer laser with λ = 248 nm). In the fiber core there is a periodic modulation of the refractive index , with high and low refractive index ranges, which reflects the light of a certain wavelength ( band stop ). The center wavelength of the filter bandwidth in single-mode fibers results from the Bragg condition:

${\displaystyle \lambda _{B}=n_{\text{eff}}\cdot 2\Lambda =n_{\text{eff}}\cdot \lambda }$

Here n _{eff is} the effective refractive index and Λ the grating period. The effective refractive index n _eff depends on the geometry (core and cladding diameter) of the waveguide, the refractive indices n ₁ , n ₂ , n ₃ and on the wave modes. Here, λ _{B is} the wavelength in a vacuum and λ the (effective) wavelength in the waveguide. The spectral width of the band depends on the length of the fiber Bragg grating and the strength of the refractive index change between the adjacent refractive index ranges.

function

The wave propagates both in the core and in the cladding of the waveguide, analogous to an electromagnetic wave ( photons ) in the finite potential well . Therefore the effective refractive index depends on all three refractive indices. In the mantle, the intensity distribution of the wave decreases with the exponential function .

The core of the fiber is composed of successive sections of length λ / 2 = Λ (in the medium). The length Λ is made up of two λ / 4 pieces that differ in the refractive index . At each interface, part of the amplitude fed in is reflected by the Fresnel reflection ( Fresnel formula (perpendicular incidence) ). The periodic change in the refractive index or the wave impedance causes the reflected wave to experience either a phase jump of 0 ° or 180 ° at the end of each λ / 4 segment. Multiple reflections lead to constructive interference in the reflected wave . This sequence of λ / 2 layers roughly corresponds to the counterpart of an anti-reflective coating , in which the two times crossing a λ / 4 layer (with the path difference λ / 2) leads to destructive interference.

For manufacturing reasons, the difference between the refractive indices n ₂ and n ₃ is not very great, which is why complete amplitude cancellation is not possible with too few successive layers.

The electrical analog of a fiber Bragg grating at considerably longer wavelengths would be a sequence of λ / 2 line pieces with different wave impedances. Due to the mismatch at each connection point, some of the energy is reflected.

Applications

• In optical communication technology as a filter to separate different channels in the wavelength division multiplex method ( WDM )
• wavelength-selective fiber reflector for fiber-coupled diode lasers
• optical element in the resonator of a fiber laser
• Sensors for temperature and strain based on the changing reflected wavelength:

The wavelength shifts with the temperature T and the relative elongation of the glass fiber: ${\displaystyle \lambda _{\text{B}}}$ ${\displaystyle \delta _{\lambda }}$ ${\displaystyle \epsilon }$

${\displaystyle {\frac {\delta _{\lambda }}{\lambda _{\text{B}}}}=k\cdot \epsilon +\alpha _{\text{n}}\cdot \delta _{\text{T}}}$

With:

${\displaystyle \alpha _{\text{n}}}$: Change in the refractive index, typ 5… 8 × 10 ⁻⁶ K ⁻¹

${\displaystyle k}$: Constant, typ. 0.78

The expansion of the fiber is made up of the proportion of the expansion applied from the outside and the thermal expansion : and the temperature dependence of : ${\displaystyle \epsilon _{\text{m}}}$ ${\displaystyle \epsilon _{\text{T}}}$ ${\displaystyle \epsilon =\epsilon _{\text{m}}+\epsilon _{\text{T}}}$ ${\displaystyle \delta _{\text{T}}}$ ${\displaystyle {\frac {\delta _{\lambda }}{\lambda _{\text{B}}}}}$

${\displaystyle \delta _{\text{T}}={\frac {1}{k\cdot \alpha _{\text{T}}+\alpha _{\text{n}}}}\cdot {\frac {\delta _{\lambda }}{\lambda _{\text{B}}}}}$

With:

${\displaystyle \alpha _{\text{T}}}$: thermal expansion of the glass fiber, typically 0.6 × 10 ⁻⁶ K ⁻¹

and for the strain dependence : ${\displaystyle \epsilon }$

${\displaystyle \epsilon ={\frac {1}{k}}\cdot {\frac {\delta _{\lambda }}{\lambda _{\text{B}}}}}$

and with a simultaneous change in temperature and mechanical load:

${\displaystyle \epsilon ={\frac {1}{k}}\cdot {\frac {\delta _{\lambda }}{\lambda _{\text{B}}}}-\left(\alpha _{\text{struktur}}+{\frac {\alpha _{\text{n}}}{k}}\right)\cdot \delta _{T}}$

Fiber Bragg gratings resolve pressure forces of several bar and temperature changes of 100 K quite well. A typical grating tuned to 1500 nm shifts by 0.1 nm for a temperature change of 10 K, as well as a change in length of 10 ⁻⁴ .

literature

• Frank Pfeiffer: Influence of ionizing radiation on the functionality of fiber optic Bragg sensors . 2000 ( online - dissertation, University of Duisburg-Essen, Faculty of Engineering).

Web links

• Strain measurement with fiber Bragg grating sensors , 2007
• Strain measurement with fiber Bragg grating (PDF file; 3.63 MB)