Optical Fibers

imageAn optical wave guide is a structure that "guides" a light wave by constraining it to travel along a certain desired path.  If the transverse dimensions of the guide are much larger than the wavelength of the guided light, then we can explain how the optical waveguide works using geometrical optics and total internal reflection.

A wave guide traps light by surrounding a guiding region, called the core, made from a material with index of refraction ncore, with a material called the cladding, made from a material with index of refraction ncladding < ncore.
Light entering is trapped as long as sinθ > ncladding/nncore.

imageLight can be guided by planar or rectangular wave guides, or by optical fibers.

An optical fiber consists of three concentric elements, the core, the cladding and the outer coating, often called the buffer.  The core is usually made of glass or plastic.  The core is the light-carrying portion of the fiber.  The cladding surrounds the core.  The cladding is made of a material with a slightly lower index of refraction than the core.  This difference in the indices causes total internal reflection to occur at the core-cladding boundary along the length of the fiber.  Light is transmitted down the fiber and does not escape through the sides of the fiber.

imageLight injected into the fiber optic core and striking the core-to-cladding interface at an angle greater than the critical angle is reflected back into the core.  Since the angles of incidence and reflection are equal, the light ray continues to zigzag down the length of the fiber.  The light is trapped within the core.  Light striking the interface at less than the critical angle passes into the cladding and is lost.

imageFibers for which the refractive index of the core is a constant and the index changes abruptly at the core-cladding interface are called step-index fibers.

Step-index fibers are available with core diameters of 100 mm to 1000 mm.  They are well suited to applications requiring high-power densities, such as delivering laser power for medical and industrial applications.

Multimode step-index fibers trap light with many different entrance angles, each mode in a step-index multimode fiber is associated with a different entrance angle.  Each mode therefore travels along a different path through the fiber.  Different propagating modes have different velocities.  As an optical pulse travels down a multimode fiber, the pulse begins to spread.  Pulses that enter well separated from each other will eventually overlap each other.  This limits the distance over which the fiber can transport data.  Multimode step-index fibers are not well suited for data transport and communications.

image

imageIn a multimode graded-index fiber the core has an index of refraction that decreases as the radial distance from the center of the core increases.  As a result, the light travels faster near the edge of the core than near the center.  Different modes therefore travel in curved paths with nearly equal travel times.  This greatly reduces the spreading of optical pulses.

imageA single mode fiber only allows light to propagate down its center and there are no longer different velocities for different modes.  A single mode fiber is much thinner than a multimode fiber and can no longer be analyzed using geometrical optics.  Typical core diameters are between 5 mm and 10 mm.


When laser light is coupled into a fiber, the distribution of the light emerging from the other end reveals if the fiber is a multimode or single mode fiber.

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Optical fibers are used widely in the medical field for diagnoses and treatment.  Optical fibers can be bundled into flexible strands, which can be inserted into blood vessels, lungs and other parts of the body.  An Endoscope is a medical tool carrying two bundles of optic fibers inside one long tube.  One bundle directs light at the tissue being tested, while the other bundle carries light reflected from the tissue, producing a detailed image.  Endoscopes can be designed to look at regions of the human body, such as the  knees, or other joints in the body.

Link:  The endoscope

Problem:

In a step-index fiber in the ray approximation, the ray propagating along the axis of the fiber has the shortest route, while the ray incident at the critical angle has the longest route.  Determine the difference in travel time (in ns/km) for the modes defined by those two rays for a fiber with ncore = 1.5 and ncladding = 1.485.

imageSolution:
If a ray propagating along the axis of the fiber travels a distance d, then a ray incident at the critical angle θc travels a distance L = d/sinθc.
The respective travel times are td = dncore/c and tL = dncore/(sinθc c).
sinθc = ncladding/ncore. θc = 81.9 deg.
For d = 1000 m we have td = 5000 ns and tL =5050.51 ns.
The difference in travel time is therefore 50.51 ns/km.