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Why Modes? 

Transmission patterns are named after so-called modes not only because of plain amount of incident ray angles. The reason is that when light enters the optical fiber, energy oscillations are trapped between walls of the cladding, and light becomes a standing wave. Similar thing happens in all waveguides (electromagnetic, sound).

Two components of the standing wave: electric and magnetic, are oscillating perpendicularly to each other. Wavefront of standing waves propagates to crosswise direction (perpendicular to both EM oscillations) along the fiber core with speed near to speed of light. This means that light in the fiber consists from transverse standing waves. Modes are distinguished by number of peaks and nodes present in a standing wave pattern:

• Fundamental mode has no nodes and oscillation pattern is half-wavelength. This mode is main mode for single-mode optical fibers. It corresponds
  to the direct perpendicular angle of light incidence into the cable, so that single ray of light propagates in the center of the core, as most of the energy is concentrated in the center (where is the biggest standing wave amplitude).
• Higher order modes describe behavior of light, when it enters core at an angle (acceptance cone). Standing waves with bigger amount of peaks are considered to be of higher order.