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In an ], the '''normalized frequency''', ''V'' (also called the '''V number'''), is given by {{short description|Property of an optical fiber}}
In an ], the '''normalized frequency''', {{mvar|V}} (also called the '''V number'''), is given by
<math display=block>
:<math>V = {2 \pi a \over \lambda} \sqrt{{n_1}^2 - {n_2}^2}\quad = {2 \pi a \over \lambda} \mathrm{NA},</math> V = {2 \pi a \over \lambda} \sqrt{{n_1}^2 - {n_2}^2} = {2 \pi a \over \lambda} \times NA,
⚫ where ''a'' is the ] radius, &lambda; is the ] in vacuum, ''n''<sub>1</sub> is the maximum ] of the core, ''n''<sub>2</sub> is the refractive index of the homogeneous cladding, and applying the usual definition of the ] ''NA''.
</math>
⚫ where {{mvar|a}} is the ] radius, {{mvar|&lambda;}} is the ] in vacuum, {{math|''n''<sub>1</sub>}} is the maximum ] of the core, {{math|''n''<sub>2</sub>}} is the refractive index of the homogeneous cladding, and applying the usual definition of the ] {{mvar|NA}}.


In multimode operation of an optical fiber having a ], the approximate number of bound modes (the ]), is given by In multimode operation of an optical fiber having a ], the approximate number of bound modes (the ]), is given by
:<math>{V^2 \over 2} \left( {g \over g + 2} \right)\quad,</math> <math display=block>
{V^2 \over 2} \left( {g \over g + 2} \right)\ ,
</math>
where ''g'' is the profile parameter, and ''V'' is the normalized frequency, which must be greater than 5 for the approximation to be valid. where {{mvar|g}} is the profile parameter, and {{mvar|V}} is the normalized frequency, which must be greater than 5 for the approximation to be valid.

⚫ For a ], the mode volume is given by {{math|''V''<sup>2</sup>/2}}. For single-mode operation, it is required that {{math|''V'' < 2.4048}}, the first root of the ] {{math|''J''<sub>0</sub>}}.


== See also ==
⚫ For a ], the mode volume is given by ''V''<sup>2</sup>/2. For single-mode operation is required that ''V'' < 2.405, which is the first root of the ] ''J''<sub>0</sub>.
⚫ * ]


==References== == References ==
*{{FS1037C MS188}} *{{FS1037C MS188}}


] ]
]
⚫ ]

Latest revision as of 03:56, 12 September 2024

Property of an optical fiber

In an optical fiber, the normalized frequency, V (also called the V number), is given by V = 2 π a λ n 1 2 − n 2 2 = 2 π a λ × N A , {\displaystyle V={2\pi a \over \lambda }{\sqrt {{n_{1}}^{2}-{n_{2}}^{2}}}={2\pi a \over \lambda }\times NA,} where a is the core radius, λ is the wavelength in vacuum, n1 is the maximum refractive index of the core, n2 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, the approximate number of bound modes (the mode volume), is given by V 2 2 ( g g + 2 )   , {\displaystyle {V^{2} \over 2}\left({g \over g+2}\right)\ ,} 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. For single-mode operation, it is required that V < 2.4048, the first root of the Bessel function J0.

See also

References

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