A graded indexed optical fiber has a parabolic refractive index profile (α = 2). If the fiber has a numerical aperture = 0.22 the total number of guided modes at a wavelength of 1310 nm is given by:

Concept: 

The path followed by the light in a fiber is called the mode of the fiber. In a single-mode fiber, the light passes through one path only whereas in the case of multi-mode fiber, The number of modes propagating in a graded-index fiber can be estimated as:

Where α represents the refractive index profile and V is the mode volume given as

where a is the fiber core radius, λ is the wavelength of the optical source and N.A. is the numerical aperture.

Calculation:

Putting the values given in the question, we get (Assume fiber core radius, a = 25 μm)

Hence, the total number of guided modes are 174.

Additional Information

Numerical aperture is considered as a light-gathering capacity of an optical fiber given by

, 

where n1 is the refractive index of the core and n2 is the refractive index of the cladding.

Number of modes for step-index fiber, N =