|MadSci Network: Physics|
Reference: John E. Midwinter, “Optical Fibers for Transmission”
John Wiley & Sons, NY, 1979.
The optical refractive index of fused silica (SiO2) glass is modified with dopants to
produce a core light guiding region with an optical refractive index that is 1.0 to 1.5
percent greater than the cladding glass. For multimode and single mode step index fibers
operating at wavelengths near 850 nm a typical cladding would have a refractive index of
1.518 and the core would have a refractive index of 1.538 which is 1.3% greater. The
velocity of propagation in the multimode step index fiber would be near the speed of light
(c) divided by 1.538. Single mode step index fibers would have a slightly lower velocity of
propagation because a good portion of the optical mode travels in the cladding layer. To
confine the single mode more tightly to the core fibers with a W refractive index profile
have been developed; however, the major reason that the W profile was develops was to
reduce wavelength dispersion (velocity differences) in the system which limits the product
of the fiber length and operating bandwidth.
Graded index fibers have a complex refractive index profile with an index well and a
parabolic index core. An index profile for a graded index fiber taken
from Midwinter’s book is shown below.
The diameter of the parabolic core is 40 micrometers with a change of index at the center
of the core (relative to the cladding) of +0.01.
The depressed well has a diameter between 40 and 60 micrometers with a change of index
(relative to the cladding) of -0.003 at the minimum. It is very difficult to calculate the
composite velocity of propagation in graded index fibers because of the complex path
through which each ray travels.
In my radar related work we have constructed precision programmable fiber optic delay
lines with one picosecond steps in delay over 100 km (60 mile) lengths. In all cases we
could not rely on calculating the velocity within the fibers and we had to make precise
time delay measurements while trimming the length of the fibers. At this point thermal
changes in the length of the fibers also becomes an important factor and the temperature
of the long of the fibers must be also be stabilized.
The Jet Propulsion Laboratory's Deep Space Network antennas at Goldstone, CA use
optical fiber links to transmit atomic clock signals between antennas to phase them for
microwave frequency inteferometric measurements. They also have to stabilize the
temperature of their several kilometer long distribution links.
Best regards, Your Mad Scientist
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