Power-law index profile

For optical fibers, a power-law index profile is an index of refraction profile characterized by

$n(r)={\begin{cases}n_{1}{\sqrt {1-2\Delta \left({r \over \alpha }\right)^{g}}}&r\leq \alpha \\n_{1}{\sqrt {1-2\Delta }}&r\geq \alpha \end{cases}}$

where $\Delta ={n_{1}^{2}-n_{2}^{2} \over 2n_{1}^{2}},$

and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle n(r)} is the nominal refractive index as a function of distance from the fiber axis, Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle n_1} is the nominal refractive index on axis, Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle n_2} is the refractive index of the cladding, which is taken to be homogeneous (Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle n(r)=n_2 \mathrm{\ for\ } r \ge \alpha} ), Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \alpha} is the core radius, and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle g} is a parameter that defines the shape of the profile. Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \alpha} is often used in place of Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle g} . Hence, this is sometimes called an alpha profile.

For this class of profiles, multimode distortion is smallest when Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle g} takes a particular value depending on the material used. For most materials, this optimum value is approximately 2. In the limit of infinite Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle g} , the profile becomes a step-index profile.

See also

• Graded-index fiber

References

•  This article incorporates public domain material from the General Services Administration document: "Federal Standard 1037C".

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