Question

What is Numerical aperture? Explain the use of optical fibre in temperature sensor. The core diameter of a multimode step index fibre is 50 μm. The numerical aperture is 0.25. Calculate the number of guided modes at an operating wavelength of 0.75 μm. 

Answer 1

1. Numerical aperture is the parameter which provides information about the acceptance angle i.e. the angle at which if the light ray enters the fibre it is sure to have total internal reflection experienced, that too in terms of parameters associated with fibre i.e. refractive index of core and cladding
`NA = sqrt( 2μ_1^2. (μ_1 - μ_2)/ μ_1`

`mu_1 = sqrt(2 ∇)`
2. In optical fibre sensor particular applications the inherent physical property of the fibre material is utilised. The variations in refractive index of the fibre under the influences of external forces lead to the possibility of an optical fibre used as an transducer
3. Types of optical fibre:
1. Extrinsic or hybrid or passive sensors.
2. Intrinsic or active sensor
Given:
d= 50μm, NA = 0.25, λ₀ = 0.75μm 
To find: N= number of modes
`N =( V^2) / 2`
`V = ( ᴨd )/ (λ_0) (NA)`
V = 52.36 
∴ Number of modes =` ((52.36)^2) / 2 = 1371`