Explain the following terms in optical fiber: a) Total internal reflection b) Critical angle c) Acceptance angle d) Attenuation e) Numerical aperture.

a) Total internal reflection (TIR): When light travels from a denser medium (core, \(n_1\)) to a rarer one (cladding, \(n_2<n_1\)) at an angle of incidence greater than the critical angle, it is completely reflected back into the denser medium. Light is guided along the fibre by repeated TIR at the core–cladding boundary.

b) Critical angle (\(\theta_c\)): The angle of incidence in the core at which the refracted ray grazes the interface (angle of refraction = 90°). \(\sin\theta_c=n_2/n_1\).

c) Acceptance angle (\(\theta_a\)): The maximum angle to the fibre axis at which light can be launched into the fibre and still be guided by TIR. \(\sin\theta_a=\sqrt{n_1^2-n_2^2}/n_0\). Rays within the acceptance cone (half-angle \(\theta_a\)) are transmitted.

d) Attenuation: The reduction in optical power along the fibre, caused by absorption, Rayleigh scattering, bending losses and so on. \(\alpha=\dfrac{10}{L}\log_{10}\dfrac{P_{in}}{P_{out}}\) dB/km. It is minimum near 1.55 µm (about 0.2 dB/km).

e) Numerical aperture (NA): The sine of the acceptance angle (fibre in air), which measures the light-gathering ability of the fibre. \(NA=n_0\sin\theta_a=\sqrt{n_1^2-n_2^2}\approx n_1\sqrt{2\Delta}\).

  acceptance cone
     \  θa          cladding n2
  ----\------------------------------
       \  /\  /\  /\   core n1 (TIR at φ > θc)
  ------\/--\/--\/--------------------
                     cladding n2