I currently calculate the numerical aperture of a 25/400 thulium-doped fiber produced by nufern. However, I do think there might be a mistake on the datasheet. Since I use the equation, NA=lamda/pie/w, (w is the radius of the beam spot). Then the NA I get is about 0.05, which is less than the NA (0.09) given in the following Nufern data sheet. So is there something wrong with my calculations? What about the NA parameter given by Nufern in the following datasheet? Is it right? How could the NA be used to calculate the size of a laser spot where at a distance away from the of the fiber output end?
Fibre numerical aperture is generally defined in terms of the core-cladding refractive index difference, NA = sqrt(n2core - n2clad), rather than the far field radiation angle which depends on wavelength and launch conditions.
The mode field radius depends not only on the core radius, but also on the fibre numerical aperture and on the operating wavelength. The modes of weakly guiding fibres are not entirely confined to the core, but include a decaying evanescent field which spreads out into the cladding.
A useful parameter is the normalised frequency: V = 2 pi a NA / lambda
where a is the core radius and lambda is fhe operating wavelength.
At 2 micron wavelength, 12.5 micron core radius and NA 0.09, V = 3.53, suggesting the fibre is not single mode. When V>2.405, the LP11 mode is supported in addition to the LP01 fundamental mode.
If only the fundamental LP01 mode is excited, 93% of the guided power is within the core. The mode field profile is described by a zero order Bessel function of the first kind within the core J0(U r/a), and the evanescent cladding field by a modifed bessel function of the second kind K0(W r/a)
A Gaussian approximation to the near field is: E(r) = E0 exp(-0.5 r2/w2)
For a step profile the RMS radius is approximately: w = a / sqrt(2 ln(V))
At V = 3.53, w = 7.9 micron (11 micron radius for 1/e2 intensity)
The far-field radiation distribution can be estimated assuming a Gaussian profile plane wave at the fibre exit facet. For large V-numbers, the mode field radius is rather weakly dependent on fibre numerical aperture.
For a more accurate analysis, solve for the near field Bessel profile, and use Fresnel-Kirchoff diffraction theory to calculate the field at an arbitrary distance from the exit face.
http://www.amazon.com/Optical-Waveguide-Theory-A-W-Snyder/dp/0412099500
Fibre numerical aperture is generally defined in terms of the core-cladding refractive index difference, NA = sqrt(n2core - n2clad), rather than the far field radiation angle which depends on wavelength and launch conditions.
The mode field radius depends not only on the core radius, but also on the fibre numerical aperture and on the operating wavelength. The modes of weakly guiding fibres are not entirely confined to the core, but include a decaying evanescent field which spreads out into the cladding.
A useful parameter is the normalised frequency: V = 2 pi a NA / lambda
where a is the core radius and lambda is fhe operating wavelength.
At 2 micron wavelength, 12.5 micron core radius and NA 0.09, V = 3.53, suggesting the fibre is not single mode. When V>2.405, the LP11 mode is supported in addition to the LP01 fundamental mode.
If only the fundamental LP01 mode is excited, 93% of the guided power is within the core. The mode field profile is described by a zero order Bessel function of the first kind within the core J0(U r/a), and the evanescent cladding field by a modifed bessel function of the second kind K0(W r/a)
A Gaussian approximation to the near field is: E(r) = E0 exp(-0.5 r2/w2)
For a step profile the RMS radius is approximately: w = a / sqrt(2 ln(V))
At V = 3.53, w = 7.9 micron (11 micron radius for 1/e2 intensity)
The far-field radiation distribution can be estimated assuming a Gaussian profile plane wave at the fibre exit facet. For large V-numbers, the mode field radius is rather weakly dependent on fibre numerical aperture.
For a more accurate analysis, solve for the near field Bessel profile, and use Fresnel-Kirchoff diffraction theory to calculate the field at an arbitrary distance from the exit face.
http://www.amazon.com/Optical-Waveguide-Theory-A-W-Snyder/dp/0412099500
Dear Xinyang SU,
I think maybe you confuse Gaussian Beam divergence and NA of optical fiber. the formula you use NA=lamda/pie/w is for Gaussian Beam divergence. If you calculate NA of optical fiber, you have to consider core-cladding refractive index difference, which confine light in the fiber.
I hope it will help.
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