A mode is a path that a light wave can follow as it travels down the core of an optical Fiber. The characteristics of an optical Fiber is determined by the three parameters ;

1. Composition of the material; that include the information of refractive indices of the material,

2. The nature of light, it means the wavelength of light which is used.

3. The diameter of the core and the length of the optical fiber

The possible number of modes that can be travel through the core are related by the above mentioned three parameters via V-number or Normalized Frequency.

The V-Number is a dimensional quantity, that combines all the 3-parameters , like the core radius ‘a’ the index difference, and the operating wavelength.  For a single mode fibers, The V-number is always less than and or equal to 2.405 which corresponds to the cut-off wavelength lambda c that separates the single mode region from multi mode region.