In an
optical fiber
An optical fiber, or optical fibre in Commonwealth English, is a flexible, transparent fiber made by drawing glass (silica) or plastic to a diameter slightly thicker than that of a human hair. Optical fibers are used most often as a means to ...
, the normalized frequency, ''V'' (also called the V number), is given by
:
where ''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, λ is the
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, tro ...
in vacuum, ''n''
1 is the maximum
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, or ...
of the core, ''n''
2 is the refractive index of the homogeneous cladding, and applying the usual definition of the
numerical aperture ''NA''.
In multimode operation of an optical fiber having a
power-law refractive index profile
For optical fibers, a power-law index profile is an index of refraction profile characterized by
: n(r) =
\begin
n_1 \sqrt & r \le \alpha\\
n_1 \sqrt & r \ge \alpha
\end
where
\Delta = ,
and n(r) is the nominal refractive index as ...
, the approximate number of bound modes (the
mode volume
In fiber optics, mode volume is the number of bound modes that an optical fiber is capable of supporting.
The mode volume ''M'' is approximately given by V^2 \over 2 and \left(\right), respectively for step-index and power-law index profile f ...
), is given by
:
where ''g'' is the profile parameter, and ''V'' is the normalized frequency, which must be greater than 5 for the approximation to be valid.
For a
step-index fiber, the mode volume is given by ''V''
2/2. For single-mode operation, it is required that ''V'' < 2.4048, the first root of the
Bessel function
Bessel functions, first defined by the mathematician Daniel Bernoulli and then generalized by Friedrich Bessel, are canonical solutions of Bessel's differential equation
x^2 \frac + x \frac + \left(x^2 - \alpha^2 \right)y = 0
for an arbitrar ...
''J''
0.
See also
*
Abbe number
In optics and lens design, the Abbe number, also known as the V-number or constringence of a transparent material, is an approximate measure of the material's dispersion (change of refractive index versus wavelength), with high values of ''V'' in ...
References
*{{FS1037C MS188
Fiber optics