core Estimated learning time: 9 h

PE1-2.1 Optical Fiber Waveguides

You can compute acceptance angle and numerical aperture, explain modes and the V-number, and distinguish step index, graded index and single mode fibres including cut-off wavelength and mode field diameter.

Numerical aperture is the fibre's light-gathering ability and follows straight from total internal reflection at the core-cladding boundary, so derive it once rather than memorising it. The V-number is the single parameter that decides how many modes a fibre supports, and single mode operation is simply V below 2.405 — a Bessel function zero showing up in a practical specification. Mode field diameter matters because in single mode fibre a real fraction of the power travels in the cladding, which is not what the ray picture suggests.

Work through these

  • The general optical fibre system; advantages of optical fibre communication

    The whole link in one diagram, and the reasons for using light at all: bandwidth, loss and immunity to interference. It is the frame for everything below.

  • Acceptance angle and numerical aperture

    Which rays get in and stay in, expressed as an angle and a number. The numerical aperture is the single figure quoted about a fibre's light gathering.

  • Skew rays

    Rays that do not pass through the axis, which the simple ray picture misses. They matter because they carry a significant part of the power in a real fibre.

  • Cylindrical fibres: modes and the V-number

    Moving from rays to modes, which is what the wave picture requires. The V-number decides how many modes a fibre supports, and it controls the whole classification below.

  • Mode coupling

    Power moving between modes as the fibre bends and varies. It is why the mode distribution settles down after some distance, which affects dispersion measurements.

  • Step index fibres and graded index fibres

    The two index profiles, and why the graded one exists: it equalises the travel time of different paths. That is the fix for the dispersion problem in the next topic.

  • Single mode fibres: cut-off wavelength

    Making the fibre carry only one mode, and the wavelength below which it stops doing so. Single mode is why long haul links work, so this item matters more than its length.

  • Mode field diameter and effective refractive index

    Two parameters describing how the light actually sits in a single mode fibre. They govern splice loss and bending loss, which are practical concerns in the next topic.

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