How this calculation works
A step-index optical fiber uses an index difference between core and cladding to guide light. Numerical aperture describes a geometric acceptance cone, while normalized frequency combines that index contrast with core size and wavelength. This page reports both quantities and compares V with the ideal first higher-mode cutoff. The external launch medium changes the acceptance angle but does not change V for the same core, cladding and vacuum wavelength.
NA = √(ncore²−nclad²); V = 2πa NA/λ; sinθaccept = NA/nexternalA worked example
With core index 1.45, cladding 1.444, radius 4 µm and wavelength 1550 nm, NA is about 0.131773. V is about 2.1366, below the ideal first higher-mode cutoff. The air acceptance half angle is about 7.572 degrees. Doubling core radius doubles V but leaves the geometric numerical aperture and acceptance angle unchanged.
Good to know
Only a straight circular step-index fiber is represented. Graded-index and photonic-crystal structures have different mode behavior and cannot use this cutoff as a general classification rule. Bending, coupling alignment, mode-field diameter, attenuation and chromatic bandwidth are absent. The page does not replace a manufacturer’s measured fiber specification.
Reference: Thorlabs — fiber numerical aperture tutorial (opens in a new tab) ↗
What this calculation answers
A step-index optical fiber uses an index difference between core and cladding to guide light. Numerical aperture describes a geometric acceptance cone, while normalized frequency combines that index contrast with core size and wavelength.
This page reports both quantities and compares V with the ideal first higher-mode cutoff. The external launch medium changes the acceptance angle but does not change V for the same core, cladding and vacuum wavelength.
The Snell refraction critical angle and Brewster angle calculator supplies the interface refraction law behind geometric guidance, but the fiber mode cutoff additionally depends on wavelength and core radius.
Use the right input conventions
Core radius is entered in micrometres, not diameter. Wavelength is in nanometres and converted into matching units. Core index must exceed cladding index for the supported guiding model.
The acceptance angle is a half angle relative to the fiber axis. If the geometric NA divided by external index reaches or exceeds one, the cone is limited to a hemisphere and that condition is stated explicitly.
Interpret the result
V below approximately 2.4048 is the familiar weak-guidance step-index criterion for excluding the first higher mode. It should not be interpreted as a measured bandwidth or a guarantee that a particular installed cable behaves ideally.
Increasing wavelength reduces V when geometry and indices are held fixed. Increasing core radius raises V. These dependencies explain why a fiber can be single mode over one wavelength range and support more modes elsewhere.
Work through the example
With core index 1.45, cladding 1.444, radius 4 µm and wavelength 1550 nm, NA is about 0.131773. V is about 2.1366, below the ideal first higher-mode cutoff.
The air acceptance half angle is about 7.572 degrees. Doubling core radius doubles V but leaves the geometric numerical aperture and acceptance angle unchanged.
Where the model stops
Only a straight circular step-index fiber is represented. Graded-index and photonic-crystal structures have different mode behavior and cannot use this cutoff as a general classification rule.
Bending, coupling alignment, mode-field diameter, attenuation and chromatic bandwidth are absent. The page does not replace a manufacturer’s measured fiber specification.
A few questions, answered
Does external immersion change V?
Not if the core, cladding and vacuum wavelength stay unchanged; it changes the launch acceptance angle.
What changes in the comparison?
Double core radius to cross the ideal higher-mode cutoff.