For an
optical fiber
An optical fiber, or optical fibre in Commonwealth English, is a flexible, transparency and translucency, transparent fiber made by Drawing (manufacturing), drawing glass (silica) or plastic to a diameter slightly thicker than that of a Hair ...
or
waveguide
A waveguide is a structure that guides waves, such as electromagnetic waves or sound, with minimal loss of energy by restricting the transmission of energy to one direction. Without the physical constraint of a waveguide, wave intensities de ...
, 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, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats.
It is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, tr ...
.
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 ci ...
, 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 a dimensionless number that gives the indication of the light bending ability of that medium.
The refractive index determines how much the path of light is bent, o ...
at radius ''r'', ''a'' is the
core
Core or cores may refer to:
Science and technology
* Core (anatomy), everything except the appendages
* Core (manufacturing), used in casting and molding
* Core (optical fiber), the signal-carrying portion of an optical fiber
* Core, the centra ...
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, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is ca ...
.
See also
*
Guided ray A guided ray (also bound ray or trapped ray) is a Ray (optics), ray of light in a multi-mode optical fiber, which is confined by the Fiber_optics#Principle_of_operation, core.
For Step-index profile, step index fiber, light entering the fiber will ...
*
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, NA has the propert ...
*
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 re ...
References
*
Fiber optics
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