Beam Expansion

An optical taper can be used on the output-end of an optical fiber using its angle changing property to alter the angular distribution of the output intensity. For example, if a lower output divergence than the fiber normally exhibits is desired, a magnifying taper can be used. Alternately, if a larger divergence is required, a minifying taper can be used.

The well-known concept of conservation of brightness states that if light losses are negligible, the spatial and angular content of the light anywhere within or at either end of a taper are described by:

Where subscript i refers to input, o to output parameters.

A = cross sectional area of the light distribution normal to the taper axis.

θ = maximum angular extent of the light distribution.

n = refractive index of the medium where θ is measured.

d_o = output diameter.

Since n sin θ = NA and A_i/A_o = d_i²/d_o², it follows that:

As an example, choose a 3:1 input taper and the output NA is 0.22:

Light is confined to the core if it strikes the interface between the core and the cladding at
an angle to the surface, θ_c, of equal to or less than:

To obtain the best possible coupling efficiency, the launch NA must be 0.073 or less, and
the focal point of the beam should be in the neck down region of the taper.

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