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Design of Uniform Fiber Bragg grating using Transfer matrix method
For entire grating T=
The reflection coefficient is calculated by the relation
R =
Solution of the Couple Mode Equations:
If the grating is uniform along z, then the coupled mode equations are coupled first-order ordinary
differential equations with constant coefficients, for which closed-form solutions can be found when appropriate
boundary conditions are specified. The reflectivity of a uniform fiber grating of length L can be found by
assuming a forward-going wave incident from z = − , passing through the grating and requiring that no
backward-going wave exists for z ≥ L , i.e., u(L) = 1, and v(L) = 0 . The amplitude and power reflection
coefficients ρ = v (0)/ u (0) and r =
2 , respectively, can then be shown to be
ρ = =
R=
2 = sinh 2 (ΩL)/ (cosh 2 (ΩL) - /k 2 )
Where Ω =
III. RESULTS AND DISCUSSION:
The parameters used for the simulation of the fiber Bragg grating are as given in the table.1
Table1: simulation parameters
core refractive index 1.64
λ B (center wavelength)
1550 nm
λ 1 (lower limit of wavelength)
1546.9 nm
λ 2 (upper limit of wavelength)
1553.1 nm
Δ neff
0.5e-4 to 3.5e-4
ν (fringe visibility) 1
Length (L)
2 mm to 35 mm
N (number of grating) 100
Λ (grating period)
L/N
For different values of grating length (table2), Reflected spectra was obtained and analyzed. From the
spectra, it was confirmed that the spectral properties of uniform gratings comes out to be similar to sinc
function. The reflection spectra for different grating lengths are shown in the figure 2,3,4.
Table2: Reflectivity for different grating length and for different deln
Grating Length in
mm
Reflectivity (%)
For deln(δ n)=1e-4
Reflectivity (%)
For deln(δ n)=2e-4
2 14.77 44.83 58.85
3 29.43 70.21 82.57
4 44.83 85.52 93.22
5 58.77 93.2 97.51
8 85.44 99.39 99.99
10 93.22 99.99 99.99
12 96.92 99.99 99.99
14 98.61 99.99 99.99
15 99.09 99.99 99.99
17 99.99 99.99 99.99
20 99.99 99.99 99.99
22 99.99 99.99 99.99
25 99.99 99.99 99.99
27 99.99 99.99 99.99
30 99.99 99.99 99.99
32 99.99 99.99 99.99
35 99.99 99.99 99.99
Reflectivity (%)
For deln(δ n)=2.5e-4
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