GATE 2026 IN Q.64: solution and answer

GATE 2026 · INQ.64 · 2 marks · NAT

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)

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Answer and solution

ANSWER

The grating period is about 538.19 nm.

Official answer: 537.00 to 539.00Source: Official answer key, GATE 2026 IN (IIT Guwahati)

For a first-order fibre Bragg grating, the Bragg condition is $λ_{B} = 2 n_{eff} Λ$ .
Rearrange for the grating period: $Λ = \frac{λ _{B}}{2 n _{eff}}$ .
Substitute $λ_{B} = 1550 nm$ and $n_{eff} = 1.44$ : $Λ = \frac{1550}{2 \times 1.44} = \frac{1550}{2.88}$ .
Divide: $Λ \approx 538.19 nm$ .

KEY IDEA

A fibre Bragg grating reflects the wavelength that satisfies $λ_{B} = 2 n_{eff} Λ$ (first order). Given the Bragg wavelength and effective index, the period is $λ_{B} / (2 n_{eff})$ .

WATCH OUT FOR

Leaving out the factor 2 and using $Λ = λ_{B} / n_{eff}$ , which gives about 1076.39 nm, twice the correct value.

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GATE 2026 IN Q.64: solution and answer

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