Speed of light in Fibers

Speed of light

The speed of light in a vacuum (denoted as \(c\)) is: \(299,792,458\) metres per second.

Refractive index

The speed of which light propagates through transparent materials will be is less than \(c\), by a coefficient called refractive index.

The formula to calculate the speed given a refractive index (called \(n\)) is: \(v = c/n\).

Air (at standard temperature and pressure) has a refractive index of \(1.000273\), meaning that light can only travel at \(\approx 299,710,637m/s\) which is \(\approx 82km/s\) slower than \(c\).

See list of refractive indexes per materials.

Optical fibers

Fibers are made from the following materials: Silica, Fluoride glass, Phosphate glass and Chalcogenide glass. Their respective refractive index are 1.458, 1.51, 1.701 and unknown. Note that I can’t guarantee that these measurements were done in the same conditions.

These materials range from \(\approx 94,173km/s\) to \(\approx 123,548km/s\) slower than \(c\), or approximately \(\approx 2/3\) of \(c\).

Repeater

Optical fibers over a long distance need to be repeated every few 100km to combat light attenuation. Near-infrared wavelengths are generally used because this wavelength has the lowest attenuation rate.

Note that each repeaters require power which is routed through the cable.

Apollo example

Apollo transatlantic submarine cable system (now owned by Vodafone).

Based on submarinenetworks.com the Apollo cable network uses Alcatel-Lucent’s 1620 Light Manager (LM).

It supports WDM but for the sake of example let’s only consider the band 2:

I have no idea what type of fiber Apollo uses but let’s use Corning® SMF-28® as an example. Which with a wavelength of \(1550 nm\) has a refractive index of \(1.4682\).

One particular path called Apollo South has a length of \(\approx 5,582km\).

The maximum theoretical speed is \(\approx 204,190,477m/s\) (again, approximately \(\approx 2/3\) of \(c\)), it takes \(~27ms\) for the light to cross the ocean. This is excluding any light repeaters or network equipment on the way.

Radio

As a side note, it’s possible to communicate between similiar distances closer to \(c\) using various radio frequencies, as the radio waves travel through air instead of fibers.

This technology is mostly used for trading and comes with its own problem, see kc1ght.com’s article for more information.

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Sven Sauleau

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