GRATINGS
A grating is an important element in WDM systems for combining and separating individual wavelengths. Basically a grating is a periodic structure or perturbation in a material. This variation in the material has the property of reflecting or transmitting light in a certain direction depending on the wavelength.
Thus gratings can be categorized as either transmitting or reflecting. Here we will concentrate on reflection gratings, since these are widely used in optical fiber communications.
Grating principle
Figure 4.1 defines key parameters for a reflection grating. Here $θ_i$ is the incident angle of the light, $θ_d$ is the diffracted angle, and ˄ (lambda) is the period of the grating (the periodicity of the structural variation in the material).
In a transmission grating consisting of a series of equally spaced slits, the spacing between two adjacent slits is called the pitch of the grating.
- Constructive interference at a wavelength λ occurs in the imaging plane when the rays diffracted at the angle $θ_d$ satisfy the grating equation, given by
$$A(sin\theta_i-sin\theta_d)=m\lambda$$
Here m is called the order of the grating. In general, only the first-order diffraction condition m=1 is considered.
A grating can separate individual wavelengths since the grating equation is satisfied at different points in the imaging plane for different wavelengths.
Fiber Bragg gratings
One embodiment is to create a fib-siner Bragg grating (FBG) in an optical fiber. This can be done by using two ultraviolet light beams to set up a periodic interference pattern in a section of the core of a germania-doped silica fiber.
Since this material is sensitive to ultraviolet light, the interference pattern induces a permanent periodic variation in the core refractive index along the direction of light propagation. This index variation is illustrated in Fig. 4.2, where n1 is the refractive index of the core of the fiber, n2 is the index of the cladding, and Λ is the period of the grating.
If an incident optical wave at λ0 encounters a periodic variation in refractive index along the direction of propagation, λ0 will be reflected if the following condition is met: $λ_0=2_{neff}$ Λ, where n effective ($n_{eff}$ ) is the average weighting of the two indices of refraction $n_1$ and $n_2$.
When a specific wavelength $λ_0$ meets this condition, that wavelength will get reflected and all others will pass through.
In the FBG illustrated in Fig. 4.2, the grating spacing is uniform along its length. It is also possible to have the spacing vary along the length of the fiber which means that a range of different wavelengths will be reflected by the FBG. This is the basis of what is known as a chirped grating.
Application of Fiber Gratings
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