Glass optical waveguide with variable cross section

A drawn glass element for producing glass optical waveguides, comprising:

• two first length portions with a first cross-sectional area and which define the two ends of the glass element;
• an intermediate length portion between the two first length portions, which has a second cross-sectional area smaller than the first cross-sectional area;
• a first transition portion between the intermediate length portion and one of the first length portions;
• and
• a second transition portion between the intermediate length portion and another of the first length portions, wherein the first and second transition portions have a cross-sectional area that steadily changes and merges from the first cross-sectional area into the second cross-sectional area,
• wherein the first and second transition portions have a central third, wherein the central third has a cross section (A) that increases more slowly than a function
• A
• ⁡
• (
• l
• )
• =
• 0
• .
• 9
• ⁢
• 5
• *
• (
• A
• 1
• -
• A
• 2
• )
• *
• [
• 1
• 2
• +
• 1
• 2
• ⁢
• tanh
• ⁡
• (
• 6
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• l
• -
• l
• 0
• l
• u
• )
• ]
• ,
• wherein l is a length coordinate in mm, A1 is a first second cross-sectional area in mm2, A2 is a second cross-sectional area mm2, lu is a length of the first and second transition portions in mm, and l0 is a length coordinate of a midpoint of the first and second transition portion in mm.