For an
optical fiber
An optical fiber, or optical fibre, is a flexible glass or plastic fiber that can transmit light from one end to the other. Such fibers find wide usage in fiber-optic communications, where they permit transmission over longer distances and at ...
or
waveguide
A waveguide is a structure that guides waves by restricting the transmission of energy to one direction. Common types of waveguides include acoustic waveguides which direct sound, optical waveguides which direct light, and radio-frequency w ...
, a radiation mode or unbound mode is a mode which is not confined by the fiber core. Such a mode has fields that are transversely oscillatory everywhere external to the waveguide, and exists even at the limit of zero
wavelength
In physics and mathematics, wavelength or spatial period of a wave or periodic function is the distance over which the wave's shape repeats.
In other words, it is the distance between consecutive corresponding points of the same ''phase (waves ...
.
Specifically, a radiation mode is one for which
:
where ''β'' is the imaginary part of the axial
propagation constant
The propagation constant of a sinusoidal electromagnetic wave is a measure of the change undergone by the amplitude and phase of the wave as it propagates in a given direction. The quantity being measured can be the voltage, the current in a ...
, integer ''l'' is the azimuthal index of the mode, ''n''(''r'') is the
refractive index
In optics, the refractive index (or refraction index) of an optical medium is the ratio of the apparent speed of light in the air or vacuum to the speed in the medium. The refractive index determines how much the path of light is bent, or refrac ...
at radius ''r'', ''a'' is the
core
Core or cores may refer to:
Science and technology
* Core (anatomy), everything except the appendages
* Core (laboratory), a highly specialized shared research resource
* Core (manufacturing), used in casting and molding
* Core (optical fiber ...
radius, and ''k'' is the free-space wave number, ''k'' = 2π/''λ'', where ''λ'' is the wavelength. Radiation modes correspond to
refracted rays in the terminology of
geometric optics
Geometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician ...
.
See also
*
Guided ray A guided ray (also bound ray or trapped ray) is a ray of light in a multi-mode optical fiber, which is confined by the core.
For step index fiber, light entering the fiber will be guided if it falls within the acceptance cone of the fiber, that ...
*
Numerical aperture
In optics, the numerical aperture (NA) of an optical system is a dimensionless number that characterizes the range of angles over which the system can accept or emit light. By incorporating index of refraction in its definition, has the property ...
*
Cladding (fiber optics)
Cladding in optical fibers is one or more layers of materials of lower refractive index in intimate contact with a core material of higher refractive index.
The cladding causes light to be confined to the core of the fiber by total internal ...
References
*
Fiber optics
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