Guided ray

Last updated

A guided ray (also bound ray or trapped ray) is a ray of light in a multi-mode optical fiber, which is confined by the core.

For step index fiber, light entering the fiber will be guided if it falls within the acceptance cone of the fiber, that is if it makes an angle with the fiber axis that is less than the acceptance angle, [1]

,

where

θ is the angle the ray makes with the fiber axis, before entering the fiber,
n0 is the refractive index along the central axis (core) of the fiber, and
nc is the refractive index of the cladding.

The quantity is the numerical aperture of the fiber. The quantity is sometimes called the total acceptance angle of the fiber.

This result can be derived from Snell's law by considering the critical angle. Light that enters the core with an angle below the acceptance angle strikes the core-cladding boundary at an angle above the critical angle, and experiences total internal reflection. This repeats on every bounce within the fiber core, and so the light is confined to the core. The confinement of light by the fiber can also be described in terms of bound modes or guided modes. This treatment is necessary when considering single-mode fiber, since the ray model does not accurately describe the propagation of light in this type of fiber.

See also

Related Research Articles

<span class="mw-page-title-main">Diffraction</span> Phenomenon of the motion of waves

Diffraction is the interference or bending of waves around the corners of an obstacle or through an aperture into the region of geometrical shadow of the obstacle/aperture. The diffracting object or aperture effectively becomes a secondary source of the propagating wave. Italian scientist Francesco Maria Grimaldi coined the word diffraction and was the first to record accurate observations of the phenomenon in 1660.

<span class="mw-page-title-main">Refractive index</span> Ratio of the speed of light in vacuum to that in the medium

In optics, the refractive index of an optical medium is a dimensionless number that gives the indication of the light bending ability of that medium.

<span class="mw-page-title-main">Total internal reflection</span> Reflection of a wave from a boundary between two media (rather than refraction)

In physics, total internal reflection (TIR) is the phenomenon in which waves arriving at the interface (boundary) from one medium to another are not refracted into the second ("external") medium, but completely reflected back into the first ("internal") medium. It occurs when the second medium has a higher wave speed than the first, and the waves are incident at a sufficiently oblique angle on the interface. For example, the water-to-air surface in a typical fish tank, when viewed obliquely from below, reflects the underwater scene like a mirror with no loss of brightness (Fig. 1).

A graded-index or gradient-index fiber is an optical fiber whose core has a refractive index that decreases with increasing radial distance from the optical axis of the fiber.

<span class="mw-page-title-main">Numerical aperture</span> Characteristic of an optical system

In optics, the numerical aperture (NA) of an optical system is a dimensionless number that characterizes the range of angles over which the system can accept or emit light. By incorporating index of refraction in its definition, NA has the property that it is constant for a beam as it goes from one material to another, provided there is no refractive power at the interface. The exact definition of the term varies slightly between different areas of optics. Numerical aperture is commonly used in microscopy to describe the acceptance cone of an objective, and in fiber optics, in which it describes the range of angles within which light that is incident on the fiber will be transmitted along it.

For an optical fiber or waveguide, a radiation mode or unbound mode is a mode which is not confined by the fiber core. Such a mode has fields that are transversely oscillatory everywhere external to the waveguide, and exists even at the limit of zero wavelength.

<span class="mw-page-title-main">Step-index profile</span> Refractive index profile in optical fibre

For an optical fiber, a step-index profile is a refractive index profile characterized by a uniform refractive index within the core and a sharp decrease in refractive index at the core-cladding interface so that the cladding is of a lower refractive index. The step-index profile corresponds to a power-law index profile with the profile parameter approaching infinity. The step-index profile is used in most single-mode fibers and some multimode fibers.

<span class="mw-page-title-main">Snell's law</span> Formula for refraction angles

Snell's law is a formula used to describe the relationship between the angles of incidence and refraction, when referring to light or other waves passing through a boundary between two different isotropic media, such as water, glass, or air. In optics, the law is used in ray tracing to compute the angles of incidence or refraction, and in experimental optics to find the refractive index of a material. The law is also satisfied in meta-materials, which allow light to be bent "backward" at a negative angle of refraction with a negative refractive index.

In optics, the Fraunhofer diffraction equation is used to model the diffraction of waves when plane waves are incident on a diffracting object, and the diffraction pattern is viewed at a sufficiently long distance from the object, and also when it is viewed at the focal plane of an imaging lens. In contrast, the diffraction pattern created near the diffracting object and is given by the Fresnel diffraction equation.

Etendue or étendue is a property of light in an optical system, which characterizes how "spread out" the light is in area and angle. It corresponds to the beam parameter product (BPP) in Gaussian beam optics. Other names for etendue include acceptance, throughput, light grasp, light-gathering power, optical extent, and the AΩ product. Throughput and AΩ product are especially used in radiometry and radiative transfer where it is related to the view factor. It is a central concept in nonimaging optics.

A prism coupler is a prism designed to couple a substantial fraction of the power contained in a beam of light into a thin film to be used as a waveguide without the need for precision polishing of the edge of the film, without the need for sub-micrometer alignment precision of the beam and the edge of the film, and without the need for matching the numerical aperture of the beam to the film. Using a prism coupler, a beam coupled into a thin film can have a diameter hundreds of times the thickness of the film. Invention of the coupler contributed to the initiation of a field of study known as integrated optics.

<span class="mw-page-title-main">Ray (optics)</span> Idealized model of light

In optics, a ray is an idealized geometrical model of light or other electromagnetic radiation, obtained by choosing a curve that is perpendicular to the wavefronts of the actual light, and that points in the direction of energy flow. Rays are used to model the propagation of light through an optical system, by dividing the real light field up into discrete rays that can be computationally propagated through the system by the techniques of ray tracing. This allows even very complex optical systems to be analyzed mathematically or simulated by computer. Ray tracing uses approximate solutions to Maxwell's equations that are valid as long as the light waves propagate through and around objects whose dimensions are much greater than the light's wavelength. Ray optics or geometrical optics does not describe phenomena such as diffraction, which require wave optics theory. Some wave phenomena such as interference can be modeled in limited circumstances by adding phase to the ray model.

<span class="mw-page-title-main">Optical fiber</span> Light-conducting fiber

An optical fiber, or optical fibre in Commonwealth English, is a flexible, transparent fiber made by drawing glass (silica) or plastic to a diameter slightly thicker than that of a human hair. Optical fibers are used most often as a means to transmit light between the two ends of the fiber and find wide usage in fiber-optic communications, where they permit transmission over longer distances and at higher bandwidths than electrical cables. Fibers are used instead of metal wires because signals travel along them with less loss; in addition, fibers are immune to electromagnetic interference, a problem from which metal wires suffer. Fibers are also used for illumination and imaging, and are often wrapped in bundles so they may be used to carry light into, or images out of confined spaces, as in the case of a fiberscope. Specially designed fibers are also used for a variety of other applications, some of them being fiber optic sensors and fiber lasers.

<span class="mw-page-title-main">Dispersive prism</span> Device used to disperse light

In optics, a dispersive prism is an optical prism that is used to disperse light, that is, to separate light into its spectral components. Different wavelengths (colors) of light will be deflected by the prism at different angles. This is a result of the prism material's index of refraction varying with wavelength (dispersion). Generally, longer wavelengths (red) undergo a smaller deviation than shorter wavelengths (blue). The dispersion of white light into colors by a prism led Sir Isaac Newton to conclude that white light consisted of a mixture of different colors.

A Liljequist parhelion is a rare halo, an optical phenomenon in the form of a brightened spot on the parhelic circle approximately 150–160° from the sun; i.e., between the position of the 120° parhelion and the anthelion.

<span class="mw-page-title-main">Core (optical fiber)</span> Part of an optical fiber that carries light

The core of a conventional optical fiber is the part of the fiber that guides the light. It is a cylinder of glass or plastic that runs along the fiber's length. The core is surrounded by a medium with a lower index of refraction, typically a cladding of a different glass, or plastic. Light travelling in the core reflects from the core-cladding boundary due to total internal reflection, as long as the angle between the light and the boundary is greater than the critical angle. As a result, the fiber transmits all rays that enter the fiber with a sufficiently small angle to the fiber's axis. The limiting angle is called the acceptance angle, and the rays that are confined by the core/cladding boundary are called guided rays.

In an optical fiber, the normalized frequency, V, is given by

Cladding in optical fibers is one or more layers of materials of lower refractive index in intimate contact with a core material of higher refractive index.

Acceptance angle is the maximum angle at which incoming sunlight can be captured by a solar concentrator. Its value depends on the concentration of the optic and the refractive index in which the receiver is immersed. Maximizing the acceptance angle of a concentrator is desirable in practical systems and it may be achieved by using nonimaging optics.

A compound prism is a set of multiple triangular prism elements placed in contact, and often cemented together to form a solid assembly. The use of multiple elements gives several advantages to an optical designer:

References

  1. DeVeau, Russell L. (2000). Fiber Optic Lighting: A Guide for Specifiers. The Fairmont Press, Inc. ISBN   0-88173-325-3 . Retrieved 14 October 2016.

PD-icon.svg This article incorporates public domain material from Federal Standard 1037C. General Services Administration. Archived from the original on 2022-01-22.