Question

For a fiber Bragg grating-based sensor, the shift in the Bragg wavelength gives information about the value of the measurand. For a Bragg wavelength of \(1550\) nm and effective index of \(1.44\), the grating period is nm (rounded off to two decimal places).

Hint:

Use the Bragg condition \(\lambda_B = 2 n_{eff} \Lambda\) and solve for the grating period \(\Lambda\).

Answer 1

Correct Answer: 538

Step 1: Find the wavelength of the light once it is inside the fiber.
Light slows down inside the fiber core, so its wavelength inside the medium shrinks by a factor of the effective index:
\[ \lambda_{fiber} = \frac{\lambda_B}{n_{eff}} = \frac{1550}{1.44} \approx 1076.39\ \text{nm} \]

Step 2: Relate the grating period to this in-fiber wavelength.
A Bragg grating reflects strongly when one grating period corresponds to half a wavelength inside the fiber, so that reflections from consecutive grating lines reinforce each other:
\[ \Lambda = \frac{\lambda_{fiber}}{2} \]

Step 3: Compute the grating period.
\[ \Lambda = \frac{1076.39}{2} \approx 538.19\ \text{nm} \]

Final Answer:
Rounded off to two decimal places, the grating period is $538.19$ nm. \[ \boxed{\Lambda = 538.19 \text{ nm}} \]