In an optical wave guide light is guided by total internal reflection (TIR).  The guide traps light by surrounding a guiding region, called the core, made from a material with index of refraction n_core, with a material called the cladding, made from a material with index of refraction n_cladding < n_core.  Light entering is trapped as long as sinq > n_cladding/n_ncore.

Optical fibers are either step-index fibers or graded-index fibers.  For step-index fibers the refractive index of the core is a constant and the index changes abruptly at the core-cladding interface.  The core in a graded-index fiber has an index of refraction that decreases as the radial distance from the center of the core increases.

These allowed distributions of the electromagnetic field across the fiber are referred to as the modes of the fiber.  When the diameter of the core is large compared to the wavelength of the light propagating through the fiber, then the number of allowed modes becomes large and the fiber is called a multimode fiber.  In ray optics the modes are associated with a different entrance angles.  Only the fundamental zero-order mode is transmitted in a single mode fiber.

The numerical aperture (NA) of a fiber is defined as n_i times the sine of the maximum angle at which light rays can enter the fiber and be conducted down the fiber.

Bandwidth measures the data-carrying capacity of an optical fiber.  It is expressed as the product of the data frequency and the distance over which data can be transmitted at that frequency.

Attenuation is measured in decibels (dB).
A(dB) = 10 log₁₀(P_in/P_out)  or 10^(A/10) = P_in/P_out.  P_out = 10^-(A/10) P_in
P_in and P_out refer to the optical power going in and coming out of the fiber.

Step index multimode and single mode fibers:

Mode-field diameter is a measure of the spot size or beam width of light propagating in a single-mode fiber. Mode-field diameter is a function of source wavelength, fiber core radius, and fiber refractive index profile.