2 Ball Lens Fiber Coupler Calculator

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Fiber 1 Numerical Aperture, NA₁:

Fiber 2 Numerical Aperture, NA₂:

Ball Lens 1 Material:

Ball Lens 1 Index of Refraction:

Ball Lens 1 Diameter, D₁:

Ball Lens 2 Material:

Ball Lens 2 Index of Refraction:

Ball Lens 2 Diameter D₂:

d: --

EFL₁ (mm): --

BFL₁ (mm): --

EFL₂ (mm): --

BFL₂ (mm): --

Ball Lens Output NA: --

Equations and Corresponding Legend

$$ \text{NA} = \frac{2 \, d \left(n - 1 \right)}{n \, D} $$

$$ d = \frac{n \, D}{4 \left(n - 1 \right) \sqrt{ \frac{ \left( \frac{1}{\text{NA}} \right)^2 - 1 }{4} } } $$

$$ \text{EFL} = \frac{n \, D}{4 \left( n - 1 \right)} $$

$$ \text{BFL} = \text{EFL} - \frac{D}{2} $$

NA₁	Represents numerical aperture of the first fiber
NA₂	Represents numerical aperture of the second fiber
EFL₁	Represents the effective focal length of the first ball lens
EFL₂	Represents the effective focal length of the second ball lens
BFL₁	Represents the back focal length of the first ball lens
BFL₂	Represents the back focal length of the second ball lens

n₁	Represents the refractive index of the first ball lens
n₂	Represents the refractive index of the second ball lens
D₁	Represents the diameter of the first ball lens
D₂	Represents the diameter of the second ball lens
d	Diameter of the beam between the ball lenses

Notes:

Please use the American standard for number formatting rather than the European standard (i.e. for "two and a half," enter "2.5" rather than "2,5").
Ball Lens output NA must be <= Fiber 2 NA for complete coupling. shows complete coupling. shows incomplete coupling.

Description

Identify a compatible pair of ball lenses for coupling light from one optical fiber into another using the numerical aperture of each fiber, the ball lens material, and the ball lens diameter. Identical ball lenses are used when coupling light from one fiber optic to another fiber optic of similar NA, but different ball lenses may be needed when coupling light between fibers of different NA. The ball lens output NA must be less than or equal to the NA of the second fiber in order to maximize throughput.