Hybrid single-mode and multimode optical fiber

An optical system, comprising:

• a hybrid optical fiber connected to a single-mode optical fiber, wherein, during transmissions at a wavelength of 1550 nanometers, at least 98 percent of the power of the single-mode optical fiber's fundamental mode is coupled into the hybrid optical fiber's fundamental mode;
• wherein the hybrid optical fiber comprises:
• an optical core including (i) a first core region having a radius as of between 1.5 microns and 9 microns, and (ii) a second core region surrounding the first core region;
• an optical cladding surrounding the optical core;
• wherein the optical core's first and second core regions are such that the optical core has a refractive index profile n(r) defined by the following equation:
• n
• ⁡
• (
• r
• )
• =
• {
• n
• 0
• +
• Δ
• s
• r
• <
• a
• s
• n
• 0
• ·
• 1
• -
• 2
• ·
• Δ
• ·
• (
• r
• a
• )
• α
• a
• s
• ≤
• r
• <
• a
• where,
• as is the radius of the first core region;
• a is the radius of the second core region;
• Δs is a positive step refractive index difference between the first core region and the second core region;
• n0 is the maximum refractive index of the second core region;
• α is a non-dimensional parameter that defines the index profile shape of the second core region, and α≧1;
• Δ is the normalized refractive index difference defined by the relationship
• Δ
• =
• n
• 0
• 2
• -
• n
• 1
• 2
• 2
• ⁢
• n
• 0
• 2
• ,
• where n1 is the minimum refractive index of the second core region.